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Natural dynamics and matrix models of a fucus distichus (phaeophyceae, fucales) population in Vancouver,… Ang, Put Ong 1991

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NATURAL DYNAMICS AND MATRIX MODELS OF A FUCUS DISTICHUS (PHAEOPHYCEAE, FUCALES) POPULATION IN VANCOUVER, BRITISH COLUMBIA, CANADA by PUT ONG ANG JR. B.Sc, University of the Philippines, 1976 M.Sc, University of the Philippines, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Botany) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1991 © PutOng Ang Jr., 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the. University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. . it is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of BOTANY  The University of British Columbia Vancouver, Canada Date OCTOBER 4. 1991 DE-6 (2/88) Abstract Abstract p. ii Patterns of reproduction, micro-recruitment, macro-recruitment, age- and size-dependent reproduction, growth and mortality in a population of the brown alga Fucus distichus in Vancouver, British Columbia, Canada, were examined from May 1985 to November 1987. Using log linear and association analyses, age and size are both found to be significant, but size more so than age, as descriptors of the demographic parameters. Reproductive plants were found throughout the sampling period, but peaked in fall and winter of each year. Estimated monthly egg production, calculated by the observed number of eggs in clusters extruded from the receptacle, is independent of plant size. Two types of recruits were monitored. Microrecruits (< 1 month-old of microscopic size) are germlings developed from fertilized eggs. Their numbers were assessed using settling blocks. Macrorecruits are detectable by the unaided eye and are plants appearing in the permanent quadrats for the first time. The recruitment pattern of microrecruits is significantly correlated with reproductive phenology and patterns of potential and estimated monthly egg production. However, peaks in micro-recruitment are not always followed by peaks in macro-recruitment. This apparent discrepancy is probably due to a differential survivorship of microrecruits over time or to the possible existence of a "germling bank". Patterns of survival and emergence of macrorecruits may be independent of those of microrecruits or may be unrelated to the prevailing reproductive phenology. This population of Fucus distichus showed seasonal variations in plant mean length and growth rates. Mean length was greater in winter (4.2-5.3 cm) and lower in summers of 1986 and 1987 (2.7 - 4.3 cm). Absolute growth rates showed a Abstract p. iii significantly opposite trend, being higher in spring and summer (0.24 - 1.17 cm/month) and lower in fall to winter (-0.5 - 0.4 cm/month). The relationship between reproduction, growth and mortality was also evaluated in terms of the cost of reproduction. There is no clear indication of cost of reproduction with respect to the longevity or mortality of fertile vs. non-fertile plants. Fertile plants, especially those > 17 cm in length, tend to exhibit negative or zero growth much more often than non-fertile plants, suggesting the cost of reproduction may be manifested in the form of reduced growth rather than in greater mortality or shorter longevity of the fertile plants. The failure to detect cost of reproduction may be due to the modular character of the plants, where cost occurs at the level of the modules (branches) rather than at the level of the whole plant. The effect of density on mortality and growth among recruits in this population was also monitored. In the first 2 months of development, germlings growing at high density experienced a lower mortality than those growing at lower densities. At later stages (> 2 months), the effect of density on mortality was reversed. Plant growth rate was generally not related to density but was related to plant length. The dynamics of the population was further evaluated with a 9 x 9 matrix model based on recruit stages and plant size. From the elasticity analysis, the survival and transition of the plants among size classes was found to be the most important parameter and contributed at least 50% to the population growth rate (lambda). Fucus does not grow by vegetative propagation, the population can only experience positive growth in the presence of recruitment. The current population size structure is unstable and is very different from the projected stable distribution. Overall, the population is on the decline. However, it is likely that the population may recover by occasional pulses of a large number of recruits, an example of which was observed in 1986. p. iv TABLE OF CONTENTS Page Abstract ii Table of Contents iv List of Tables viii List of Figures xii Foreword xviii Acknowledgements xix Dedications xx GENERAL INTRODUCTION 1 The Population of Fucus distichus L. emend. Powell 4 The Study Site 5 Organization of the Thesis 6 CHAPTER 1: Natural Dynamics of a Fucus distichus Population: Reproduction and Recruitment INTRODUCTION 7 MATERIALS AND METHODS 10 Quadrat Size and Number of Replicates 10 Age vs. Size as the Descriptor of Reproductive Events 10 Reproductive Phenology 12 Egg (Zygote) Production 12 Recruitment .... 13 Statistical Analysis 14 RESULTS 15 Age vs. Size as the Descriptor of Reproductive Events 15 Reproductive Phenology 17 Egg Production 18 Table of Contents p. v Recruitment 21 DISCUSSION 23 CHAPTER 2: Age- and Size-Dependent Growth and Mortality in a Population of Fucus distichus L. emend. Powell INTRODUCTION 51 MATERIALS AND METHODS 54 Age, Size (Length), and Absolute Growth Rates 54 Mortality and Survivorship 55 Age vs. Size as the Descriptor (Predictor) of Growth and Mortality 56 Statistical Analyses 57 RESULTS 57 Overall Seasonal Trend 57 Age Distribution, Length and Growth 58 Size Class Distribution, Age and Growth 59 Mortality and Survivorship 60 Log Linear and Association Analyses on Age vs. Size as the Descriptor of Growth and Mortality 62 DISCUSSION 63 CHAPTER 3: Cost of Reproduction in Fucus distichus L. emend. Powell INTRODUCTION 90 MATERIALS AND METHODS 92 RESULTS 94 DISCUSSION 97 CHAPTER 4: Experimental Evaluation of Density-Dependence in a Population of Fucus distichus L. emend. Powell INTRODUCTION ., 119 MATERIALS AND METHODS 120 Seeded Density Blocks 120 Natural Density Squares 121 Table of Contents p. vi Statistical Analyses... 122 RESULTS 123 Seeded Density Blocks 123 Natural Density Squares 126 DISCUSSION 127 CHAPTER 5: Matrix Models for Algal Life History Stages INTRODUCTION 156 THE MODELS 158 Monophasic Model 160 Diphasic Model 160 Triphasic Model 161 Sensitivity and Elasticity Analyses 162 EXAMPLES 163 Example 1 163 Example 2 166 DISCUSSION 170 CHAPTER 6: Simulation and Analysis of the Dynamics of a Population of Fucus distichus L. emend. Powell INTRODUCTION 179 THE MODEL 181 PARAMETER ESTIMATION 183 Transition Among the Size Classes (P) ... 183 Fecundity (F) 184 Transition Among Microrecruits (R\ and R2) 185 Transition from Microrecruits to Macrorecruits 185 Germling Bank (G) 186 METHODS OF ANALYSES AND SIMULATION 186 Analysis of the Model 187 Table of Contents p. vii Monthly Matrix 187 Yearly Matrix 188 Simulation and Projection , 189 Randomized Monthly Matrices 189 Randomized Seasonal Matrices 190 Randomized Yearly Matrices 190 RESULTS 191 Analysis of the Model 191 Monthly Matrix 191 Yearly Matrix 193 Simulation and Projection.. 195 DISCUSSION 196 SUMMARY DISCUSSION 234 LITERATURE CITED 239 APPENDIX A: Age vs. Size as the Descriptor of Growth and Mortality in Fucus distichus L. emend. Powell 253 Log Linear Analysis 254 Association Analyses 254 APPENDIX B: Transition Matrices from Permanent Quadrats and Elasticity Analysis on Monthly and Yearly Matrices 261 p. viii LIST OF TABLES Page Table 1.1 Fucus distichus. Log linear analysis on the effect of age vs. size on the probability of reproduction 31 Table 1.2 Fucus distichus. Simple, multiple and partial associations among age and size vs. reproduction 32 Table 1.3 Fucus distichus. Results of ANCOVA on the effect of plant size on fertile area with sampling time as the covariate 33 Table 1.4 Fucus distichus. A.) Mean number of eggs (+ S.E.) discharged from 5 conceptacles per receptacle at different time periods. B.) Results of two-level nested ANOVA and C.) Tukey Multiple Comparison Test on the difference in the number of eggs produced per conceptacle over time 34 Table 1.5 Fucus distichus. Results of ANCOVA on the effect of fertile area on number of conceptacles with sampling time as the covariate 35 Table 1.6 Fucus distichus. Results of ANCOVA on the effect of fertile area on total number of eggs from all clusters with sampling time as the covariate 36 Table 1.7 Fucus distichus. Correlation matrices showing Pearson Correlation Coefficient ( r ) (in italics) or Spearman Rank-order Correlation Coefficient ( rs ) between variables 37 Table 2.1 Fucus distichus. Matrix of Spearman rank-order correlation coefficients between age and growth rate (AGR), and age and length in different cohorts in each quadrat (Q) 71 Table 2.2 Fucus distichus. Matrix of Spearman rank-order correlation coefficients between plant length and growth rate (AGR) per quadrat (Q) over different time periods 72 Table 2.3 Fucus distichus. Matrix of Spearman rank-order correlation coefficients between plant length and growth rate (AGR) in different cohorts in each quadrat (0) • • • 73 Table 2.4 Fucus distichus. Results of ANCOVA on the effect of time on the survivorship of plants of each cohort. The covariates are the cohorts listed in the table... 74 List of Tables p. ix Table 2.5 Fucus distichus. Results of log linear analysis on the effect of age vs. size on growth, with or without the effect of mortality, and on mortality alone.... 75 Table 3.1 Fucus distichus. Results of ANCOVA on the effect of plant size on plant dry weight with sampling time as the covariate. Data represent monthly samples from October 1985 to November 1987 105 Table 3.2 Fucus distichus. Results of ANCOVA on the effect of A. plant size, B. and C. plant dry weight, on dry weight of receptacles with sampling time as the covariate. Monthly samples included in each analysis are indicated 106 Table 3.3 Fucus distichus. Results of ANCOVA on the effect of A. plant size, and B. plant dry weight on proportion of dry weight allocated to receptacles (reproductive effort), with sampling time as the covariate. Monthly samples included in each analysis are indicated 107 Table 3.4 Fucus distichus. Contingency table on the relationship between reproduction and mortality based on pooled data from October 1985, January, May 1986, January, April 1987 108 Table 3.5 Fucus distichus. Contingency table on the relationship between reproduction and longevity based on pooled data from October 1985, January, May, August 1986, January, and April 1987 109 Table 3.6 Fucus distichus. Contingency table on the relationship between reproduction and longevity based on pooled data from different time periods as given in Table 3.5 110 Table 3.7 Fucus distichus. Contingency table on the relationship between reproduction and growth rate (cm/month) based on pooled data from different time periods as given in Table 3.5 Ill Table 3.8 Fucus distichus. Contingency tables and results of Log linear analyses on the relationship among reproduction, size and A. mortality, B. longevity, and C. growth rate 112 Table 3.9 Fucus distichus. Results of ANCOVA on the effect of A. longevity and B. plant size on the ratio between number of months a plant remained reproductive and number of months a plant survived after becoming reproductive (fertility/longevity ratio), with sampling time as the covariate 115 Table 4.1 Fucus distichus. Results of ANCOVA on the effect of density on mortality of plants over time in the settling blocks seeded initially with different densities of germlings and with sampling time as the covariate. Sampling periods included in each analysis are indicated 137 List of Tables p. x Table 4.2 Fucus distichus. Results of two-level nested ANOVA on the difference in the mean length of plants among blocks seeded in November 1986 with different initial densities of germlings. Sampling periods included in each analysis are indicated 138 Table 4.3 Fucus distichus. Results of ANCOVA on the effect of plant density on mean plant length over time in the settling blocks with the initial seeding density as the covariate. Data included in each analysis are indicated. Sampling period is from November 1986 to November 1987. 139 Table 4.4 Fucus distichus. Results of ANCOVA on the effect of plant density on mean plant growth rate over time in the settling blocks with sampling time as the covariate. Sampling periods included in each analysis are indicated 141 Table 4.5 Fucus distichus. Results of Multiple Regression on the effect of mean density and mean length on mean absolute growth over time among plants on the settling blocks 142 Table 4.6 Fucus distichus. Results of ANCOVA on the effect of density on mortality of plants over time in the cleared plots. The covariate in each analysis is indicated. Sampling period is from July 1986 to May 1987 143 Table 4.7 Fucus distichus. A.) Mean length (cm ± S.E.) of plants among the density squares at different times. B.) and C.) Results of two-level nested ANOVA on the difference in the mean length of plants among density squares with different initial densities of recruits. Sampling periods included in each analysis are indicated 144 Table 4.8 Fucus distichus. Results of ANCOVA on the effect of plant density on mean plant length over time in the cleared plots. The covariate in each analysis is indicated. Sampling period is from July 1986 to May 1987 145 Table 4.9 Fucus distichus. Results of ANCOVA on the effect of plant density on mean plant growth rate over time in the cleared plots with sampling time as the covariate. Sampling period is from July 1986 to May 1987 146 Table 5.1. Matrix models of algae with A. monophasic, B. diphasic, and C. triphasic life history, and their corresponding column vector. Symbols follow those used in Fig. 5.2 and correspond to the transition elements in the respective life cycle graph 173 Table 5.2. Projection matrix S for the population of Sargassum siliquosum with a monophasic life history, and its corresponding sensitivity matrix S s and elasticity matrix E s . The Column vector S^  shows the arrangement of the size classes 174 List of Tables p. xi Table 5.3. Projection matrix L for a population of Laminaria longicruris with a diphasic life history, and its corresponding sensitivity matrix SL and elasticity matrix E L . The column vector L N shows the arrangement of the stage and size classes 175 Table 6.1 Fucus distichus. Monthly transition matrices for the Fucus population. Transition elements are mean values from the transition matrices of the 3 permanent quadrats. Mean monthly density (per 0.25 m2) of the population is given as a column vector with the respective categories defined in the matrix N. 204 Table 6.2 Fucus distichus. Transition matrices of one-year cycles derived from the multiplication of monthly transition matrices. The inclusive time period represented by each matrix is indicated 212 Table 6.3 Fucus distichus. Results of the simulation showing the mean + S.D., and highest and lowest growth rates (lambda) recorded from using different combinations of transition matrices projected over different fixed periods of time. The mean value is based on 100 replicates 217 Table 6.4 Fucus distichus. Dominant eigenvalues of the seasonal matrices 218 Table A.l Fucus distichus. Results of the log linear analyses on the effect of age vs. size on growth, with or without the effect of mortality, in different seasons. Values given as G statistic 256 Table A.2 Fucus distichus. Results of the log linear analyses on the effect of age vs. size on mortality at different seasons in each quadrat. Values given as G statistic 258 Table B.l Fucus distichus. Monthly transition matrix for each permanent quadrat. 263 Table B.2 Fucus distichus. Results of elasticity analyses on monthly transition matrices showing the proportional contribution of each transition element to population growth 282 Table B.3 Fucus distichus. Results of elasticity analyses on yearly transition matrices showing the proportional contribution of each transition element to population growth 289 p. xii LIST OF FIGURES Page Figure 1.1 Fucus distichus. A . Density-area curve used to determine the appropriate quadrat size for use in sampling the Fucus population. Density recorded in each of the 6 replicates and the mean density (± S.E.) for each quadrat size are indicated. B. Density-sample size curve used to determine the number of replicates to be used in sampling the population. For sample size > 1, each data point is a mean value with S.E. not shown 38 Figure 1.2 Fucus distichus. A . Mean probability (% + S.E.) of becoming reproductive for the first time among plants in each size class and B. mean probability (% + S.E.) of being reproductive in each size class. Both measures were based on plants from all cohorts 39 Figure 1.3 Fucus distichus. A . Mean probability (% + S.E.) of becoming reproductive for the first time at each age and B. mean probability (% + S.E.) of being reproductive at each age. Both measures were based on plants from all cohorts 40 Figure 1.4 Fucus distichus. Percentage (% + S.E.) frequency distribution of individuals divided among 6 size classes. The individuals were sampled monthly from Jul 85 to Nov 87, except Aug 85 and Nov 86 41 Figure 1.5 Fucus distichus. Percentage (% + S.E.) of plants with receptacles from Sep 85 to Nov 87. Percentage calculated as number of fertile plants divided by total number of all plants, or by number of plants > 4.5 cm long (plants in size class 3 and above) 42 Figure 1.6 Fucus distichus. Frequency (% + S.E.) distribution of fertile plants in size classes 3 to 6. The individuals were sampled monthly from Sep 85 to Nov 87, except Nov 86. No fertile plant was found in size classes 1 and 2 43 Figure 1.7 Fucus distichus. Probability (% + S.E.) of being reproductive among plants within each size class. Sampling frequency as in Fig. 1.6 44 Figure 1.8 Fucus distichus. Relationship between log fertile area and plant size for each season 45 Figure 1.9 Fucus distichus. Relationship between log fertile area and plant size for pooled data from all seasons except summers, 1986, 1987, and spring, 1987 , 46 List of Figures p. xiii Figure 1.10 Fucus distichus. Relationship between log number of conceptacles and area of receptacles for pooled data from Nov 85, Mar 86, Oct 86, and Jan 87 . 47 Figure 1.11 Fucus distichus. Relationship between mean number of eggs (± S.E.) and area of receptacle for pooled data from Nov 85, Mar 86, Oct 86, and Jan 87. Each data point represents mean number of eggs from 5 conceptacles multiplied by the number of conceptacles in each receptacle 48 Figure 1.12 Fucus distichus. Potential and estimated number of eggs produced per 25 cm2 of Fucus zone every month, with maximum and minimum 95% confidence limits of the estimates. See text for more details on how the calculations were made 49 Figure 1.13 Fucus distichus. Monthly mean number of microrecruits (+ S.E.) counted on 25 cm2 settling blocks and monthly mean number of macrorecruits (± S.E.) recorded per 25 cm2 of permanent quadrats 50 Figure 2.1 Fucus distichus. Seasonal patterns of change in mean (+ S.E.) plant length and absolute growth rates of the population from False Creek. Error bars < 0.4 cm (for length) or cm/month (for growth rate) not shown 76 Figure 2.2 Fucus distichus. Monthly mean (+ S.E.) age structure of the population. Data are from means of three quadrats 77 Figure 2.3 Fucus distichus. Patterns of change in mean (+ S.E.) length and growth rates of cohorts from the 3 permanent quadrats over time. Date in each graph indicates the time when the cohort was first detected in the population. Error bars < 2.0 cm or cm/month not shown 78 Figure 2.4 Fucus distichus. Mean (± S.E.) length and growth rates of plants of the same age at different times during the monitoring period from September 1985 to November 1987. Error bars < 2.0 cm or cm/month not shown. Due to differences in the longevity of monthly cohorts, plants of all ages are not always present at all times 79 Figure 2.5 Fucus distichus. Mean frequency (% ± S.E.) size class distribution of the plants of known age. Data are from mean values of the 3 permanent quadrats. Error bars < 2.5% not shown 80 Figure 2.6 Fucus distichus. Seasonal patterns of change in mean (+ S.E.) age and length of plants in different size classes. Data are from mean values of the 3 permanent quadrats. Error bars < 2.5 months or 0.04 cm not shown 81 List of Figures p. xiv Figure 2.7 Fucus distichus. Seasonal patterns of change in mean (± S.E.) growth rate of plants in different size classes. Data are from mean values of the 3 permanent quadrats. Error bars < 0.25 cm/month not shown 82 Figure 2.8 Fucus distichus. Mean survivorship curves (logjo) of different cohorts in the 3 permanent quadrats. Data for July 1985 included all plants < 1 cm which were present in July 1985. Error bars not shown 83 Figure 2.9 Fucus distichus. A. Mean age of plants that survived and died during the monitoring period. Data are mean values for each permanent quadrat. Mean age of plants that survived ( ) or died (....) from the 3 quadrats are also given. Error bars not shown. B. Mean (± S.E.) length of plants that survived and died during the same period. Data are from mean values of the 3 permanent quadrats. Error bars < 0.16 cm not shown 84 Figure 2.10 Fucus distichus. Mean probability of mortality (% + S.E.) of plants of the same age over time. Data are from mean values of the permanent quadrats. Error bars < 8.5% not shown. Due to differences in the longevity of monthly cohorts, plants of all ages are not always present at all times 85 Figure 2.11 Fucus distichus. Monthly mean probability of mortality (% + S.E.) of plants of different ages. Data are from mean values of the permanent quadrats. Error bars < 3.0% not shown 86 Figure 2.12 Fucus distichus. Mean probability of mortality (% + S.E.) of plants from the same size class over time. Data are from mean values of the permanent quadrats. Error bars < 2.5% not shown 87 Figure 2.13 Fucus distichus. Monthly mean probability of mortality (% + S.E.) of plants from different size classes. Data are from mean values of the permanent quadrats. Error bars < 3.0% not shown 88 Figure 2.14 Fucus distichus. Mean (+ S.E.) ratio of log partial association coefficient (T) of size vs. age as a state variable in describing growth rates with or without the effect of mortality, and in describing mortality. Data are based on mean values for the permanent quadrats. A ratio > 0 indicates that size is more important than age as a predictor of the demographic parameter 89 Figure 3.1 Fucus distichus. Linear regression of plant dry weight vs. plant size. Only reproductive plants (plants > 4.5 cm) were included 116 Figure 3.2 Fucus distichus. Linear regression of dry weight of receptacle vs. A. plant size, and B. Plant dry weight 117 List of Figures p. xv Figure 3.3 Fucus distichus. Linear regression of reproductive effort (proportion of receptacle dry weight over total plant dry weight) vs. A. plant size, and B. plant dry weight.. 118 Figure 4.1 Fucus distichus. Density of the plants in each density block over time. Dotted lines are curves fitted by second order polynomial for high density blocks and third order polynomial for mid and low density blocks to indicate the general pattern of decline in density among the 3 groups of density blocks. 147 Figure 4.2 Fucus distichus. Linear regression of plant mortality vs. plant density in the density blocks at different time periods. A.) November 1986 to January 1987, B.) January 1987 to November 1987 148 Figure 4.3 Fucus distichus. Pattern of change in plant length with the decline in plant density in each group of density blocks over time 149 Figure 4.4 Fucus distichus. Changes in the size distribution of the plants among the density blocks measured as zero-centered skewness. Each symbol represents the same block over different times. The dotted line connects the mean values for each sampling period 150 Figure 4.5 Fucus distichus. Changes in the absolute growth rate of the plants in each density block over time. Curve lines are fitted by second order polynomial for high density blocks and third order polynomial for mid and low density blocks to indicate the general pattern of change in mean growth rates among respective density blocks 151 Figure 4.6 Fucus distichus. Linear regression of plant mortality vs. plant density in the density squares. Only data from July 1986 to January 1987 were pooled .. 152 Figure 4.7 Fucus distichus. Changes in the size distribution of plants in the density squares over time measured as zero centered skewness. Each symbol represents the same block over different times. The dotted line connects the mean values for each sampling period 153 Figure 4.8 Fucus distichus. Changes in plant length with the decline in plant density over time in each group of density squares 154 Figure 4.9 Fucus distichus. Changes in the mean absolute growth rate of the plants in each density square over time. The regression lines relating the mean growth rate to density for each period are indicated 155 Figure 5.1. Flow diagram of a diphasic algal life history showing most of the possible transitions from stage to stage, or within the different size classes. Numbers List of Figures p. xvi denote size class number, as: asexual, d: diploid, f: female, m: male, p: parthenogenetic, z: zoosporic 176 Figure 5.2. Simplified flow diagram of (A) monophasic life history with sporophyte as the only dominant stage, (B) diphasic life history and (C) triphasic life history. In (B) and (C), only the female gametophytes are shown. D: degeneration, R: recruitment, G: growth, P: probability of staying in same stage or size class, V: vegetative regeneration, c: cystocarpic, g: gametophytic, j: juvenile, r: recruit, s: sporophytic, numbers: size class number 177 Figure 5.3. Stable size distribution and reproductive values as a function of the stage/size classes for (A) Sargassum siliquosum and (B) Laminaria longicruris. G: gametophyte, R: recruits, J: juvenile (size class 1), S number: size class number 178 Figure 6.1. Mean number of plants in each size class and total number of plants recorded from field observations over time, compared with the number simulated from the matrix models. Dotted outlines indicate the upper and lower boundaries of + S.E. respectively, of the field estimates 219 Figure 6.2. Survivorship of recruits and plants in different size classes over time as estimated from the matrix models 220 Figure 6.3. Dominant eigenvalue (population growth rate) calculated for each monthly matrix M (with recruitment) and monthly submatrix D (without recruitment). Dotted horizontal line indicates eigenvalue = 1 221 Figure 6.4. Relative contribution (%) of different matrix parameters in each monthly matrix M to population growth rate, as estimated from elasticity analysis. 222 Figure 6.5. Relative contribution (%) of survivorship and fecundity of each size class to population growth rate, as estimated from elasticity analysis on each monthly matrix M 223 Figure 6.6. Proportion (%) of all recruits vs. other plants in the size classes at stable distribution calculated for each monthly matrix M. Recruits included all intermediate stages of microrecruits and other plants included all plants from size classes 1 (with macrorecruits) to 6 224 Figure 6.7A. Proportion (%) of plants in different size classes at stable distribution calculated for each monthly matrix M from Jul-Sep 85 to Apr-May 86, compared with the corresponding observed monthly distribution of the plants in the field 225 List of Figures p. xvii Figure 6.7B. Proportion (%) of plants in different size classes at stable distribution calculated for each monthly matrix M from May-Jun 86 to Feb-Mar 87, compared with the corresponding observed monthly distribution of the plants in the field 226 Figure 6.7C. Proportion (%) of plants in different size classes at stable distribution calculated for each monthly matrix M from Mar-Apr 87 to Oct-Nov 87, compared with the corresponding observed monthly distribution of the plants in the field 227 Figure 6.8. Reproductive values (log) of all recruits and plants in each size class calculated for each monthly matrix M 228 Figure 6.9. Dominant eigenvalue (population growth rate) calculated for each yearly matrix S (with recruitment), yearly sub matrix D Y (without recruitment), and yearly matrix S with transition from microrecruit to germling bank set to 0 (without germling bank). Only the starting month of each yearly matrix is indicated in the x axis. Dotted horizontal line indicates eigenvalue = 1. .. 229 Figure 6.10. Relative contribution (%) of different matrix parameters in each yearly matrix Y to population growth rate, as estimated from elasticity analysis. X axis legend as in Fig.6.9 230 Figure 6.11. Relative contribution (%) of survivorship, fecundity and transition from plant to microrecruits of each size class to population growth rate, as estimated from elasticity analysis on each yearly matrix Y. X axis legend as in Fig. 6.9. 231 Figure 6.12. Proportion (%) of all recruits vs. other plants in the size classes at stable distribution calculated for each yearly matrix Y. X axis legend as in Fig. 6.9. Recruits included all intermediate stages of microrecruits and other plants included all plants from size classes 1 (with macrorecruits) to 6 232 Figure 6.13. Reproductive values (log) of all recruits and plants in each size class calculated for each yearly matrix Y. X axis legend as in Fig. 6.9. 233 Figure A.l. The relative importance of size vs. age in describing plant growth rate with or without considering the effect of mortality in the analysis. The results are based on pooled data for each quadrat representing different times of the year. Relative importance is given as a ratio of log association coefficients. Ratio > 0 indicates that size is more important than age and vice versa... 259 Figure A.2. The relative importance of size vs. age in determining the probability of plant mortality in each quadrat at different times of the year 260 p.xviii Foreword The major part of this thesis has been published, accepted for publication, or has been submitted for publication as: Ang, P. Jr. O. 1991 Natural dynamics of a Fucus distichus L. emend. Powell, population: Reproduction and recruitment. Mar. Ecol. Prog. Ser. (Accepted) Ang, P. Jr. O. 1991 Age- and size- dependent growth and mortality in a population of Fucus distichus L. emend. Powell. Mar. Ecol. Prog. Ser. (Accepted) Ang, P. Jr. O. 1991 Cost of reproduction in Fucus distichus L. emend. Powell. Mar. Ecol. Prog. Ser. (Submitted) Ang, P. Jr. O. and De Wreede, R.E. 1991 Density-dependence in a population of Fucus distichus L. emend. Powell. Mar. Ecol. Prog. Ser. (Submitted) Ang, P. Jr. O. and De Wreede, R.E. 1990 Matrix models of algal life history stages. Mar. Ecol. Prog. Ser. 59: 171-181. Ang, P. Jr. O. and De Wreede, R.E. 1991 Simulation and analysis of the dynamics of a population of Fucus distichus L. emend. Powell. Mar. Ecol. Prog. Ser. (Submitted) p. xix Acknowledgements This study was partially funded by Natural Science and Engineering Research Council of Canada grant no. 5-89872 to R. De Wreede, and by a Sigma Xi grant-in-aid. I held a UBC graduate fellowship, an International Centre for Oceans Developement (ICOD) fellowship, an Edith Asthon Memorial Scholarship, and a Kit Malkin Scholarship during the duration of this study. I thank my supervisor, Robert De Wreede, and members of my supervisory committee, Paul G. Harrison and Roy A. Turkington, for their advice, insight, and very thorough and critical review of every stage of my thesis development. I also appreciate their friendship and moral support throughout the duration of my study. Critical comments from and/or discussion with G. Bradfield, H. Caswell, M. Dring, R. Foreman, T. Klinger, J. Myers, T. Norton, J. Pearse, R. Santos, G. Sharp, S. Williams and anonymous reviewers on all or some chapters (manuscripts) of this thesis were most helpful. Technical assistance from M. Weis on the Kontron Image Analyzer was invaluable. I thank C. Lai for advice on statistical analyses, S. De Wreede, M. Mercedez-Pascual and M. Weis for help with the computer programming and/or graphics. I am grateful for the support and trust of K. Cole, P.J. Harrison and C. Borden particularly during difficult times. The former and present staff of the Department of Botany and the Biology Program, especially B. Chan, T. Chappell, M. Crosson, P. Harrison, J. Heyes, W. Hunter, J. Oliveira, S. Wielesko, and E. Wilkie deserve a special thank for making my stay at UBC just that much easier. I thank fellow graduate students, especially A. Arsenault, B. Benedict, B. Compton, M. Da Silva, A. Deroschers, L. Dyck, M. Fernando, K. Gratto, L. Green, J.H. Kim, G. Kendrick, K. Marr, R. Mason, D. Renfrew, L. Samuel, F. Shaughnessy, G. Subramaniam, R. and K. Thomson, L. Yip and many others for the friendship, company, helps, and encouragement. I also appreciate many friends from the Philippines, as well as from all over the world for their thought fulness, concerns and care. Finally, I am most indebted to my family, especially to my mother, for her patience, understanding and support and to whom this thesis is wholeheartedly dedicated. p. XX In Memory of My Father... To My Mother GENERAL INTRODUCTION Marine algae are dominant features of coastal rocky intertidal and subtidal communities. These algae are not only important as the primary producers, they also provide the physical structures upon which other plants and animals live. An understanding of the dynamics of algal populations is important to the understanding of the processes involved in the organization of these marine communities. Compared to higher plants and animals, there are relatively few demographic studies on algae (see reviews by Chapman 1986a, Santelices 1990). This is partly because of physical inaccessibility of many algal populations, and partly because of the complex life histories exhibited by many of them. Thus, it may not be possible to follow every stage in the growth and development of an algal population. However, because of such complex life histories, studies on algal population dynamics are also essential in furthering our understanding of life history theory and evolutionary biology in general. To understand the biology of a population, questions commonly asked are: how many individuals are there? How long do they live? How large do they become? and how fast? When do they reproduce? How many offspring do they produce? How many of these offspring survive to become reproductive? Based on answers to these questions, population biologists were able to construct mathematical models to describe and predict the dynamics of the population (e.g. Nisbet and Gurney, 1982). Computer simulations further our understanding of population dynamics, both theoretically and applied (e.g. Getz and Haight 1989). Mathematical models may be useful in providing a theoretical framework on which the relative importance of the different stages of the population may be assessed. Specifically, assumptions may first be made about certain parameters of the population, parameters which may not be readily available. The validity of the model can then be tested in the field based on the simulation results. General Introduction p. 2 Gaps in information can be identified and the model may be modified subsequently based on additional information to make it more realistic. Many natural experiments (e.g. mass mortality of sea urchins) or man-made interferences (e.g. harvesting of a population) provide opportunities for testing projections and forecasts from population models. The matrix model, first developed by Lewis (1942) and Leslie (1945, 1948) for age-structured animal population, is one of the more common models used in demographic studies. In its basic form, the model is given by the equation: AN, = N , + i Where A = 0 F/ . Po 0 0 • 0 0 • 0 • • Pn-1 0 i = 1, 2, 3...n F,- is the fecundity value for each age class i, P; is the probability of surviving from age class i to age class /+1. N, is the column vector describing the age structure of the population at time t, and N, + j is the age structure at time t+l. Various extensions of this model have made it applicable to organisms grouped in growth stages (e.g. Lefkovitch 1965) or in sizes (e.g. Usher 1966). Plant population biologists have found models based on size more appropriate for their use since, in many cases, plant size is more closely correlated to demographic events than is plant age (Harper 1977, Caswell 1986). Hughes (1984) also proposed that colonial organisms General Introduction p. 3 such as corals are better grouped by size than by age. Several models have now been proposed for trees grouped in growth sizes (Hartshorn 1975, Enright and Ogden 1979), annuals grouped by age and size (Law, 1983), biennials grouped by age or size (Werner and Caswell 1977), or grouped by size and sex (Meagher 1982). Among the utilities of matrix analysis are easy calculation of population growth rate, stable structure, and reproductive value. Sensitivity and elasticity analyses allow measurement of the relative importance of each element of the matrix to overall population growth (Caswell 1989). It is not clear what state variable, e.g. age, size, or stage, can best describe demographic events in algae. There is uncertainty associated with aging the individuals (e.g. Hymanson et al. 1990). If size could be shown to be a better state variable than age, then the problems associated with aging the individuals are no longer important. Matrix models belong to the family of discrete deterministic models and share their many limitations, e.g. an inherent assumption of the time-invariant transition probability. However, many algal demographic events, like growth, reproduction, and die back, follow discrete phases. Hence, matrix models, given their other utilities, have the potential to be a useful tool for the study of algal population dynamics. Although several algal populations have been studied in some detail (Chapman 1986a), none of these studies provide sufficient data on the structure of the population, either based on age or size or other state variable, reproduction, recruitment, and survivorship of the adults and recruits, to lend itself to matrix analysis. Indeed, to test the utility of matrix models, or any other model in general, there is a need for a more complete study of an algal population than what is now available in the literature. General Introduction p. 4 The general objectives of this thesis are: 1. To conduct a detailed study on a population of the brown alga Fucus distichus L. emend. Powell in order to understand changes in its reproduction, recruitment, growth and survivorship. 2. To construct a matrix model that will describe the dynamics of this population and to test the utility of this model in providing a better understanding of algal population dynamics. THE POPULATION OF FUCUS DISTICHUS L. EMEND. POWELL The population of Fucus distichus was chosen for this undertaking for two main reasons. It is found in the high intertidal zone and is therefore easily accessible for any intensive monitoring. It is also one of the few algae whose biology is relatively well understood. Fucus distichus (Fucaceae, Fucales, Phaeophyta) is common on northern north Pacific and northern Atlantic coasts (Powell 1957, Liming 1985, p.30). There is uncertainty about the nomenclature of the common Fucus found along the coast of Pacific North America. Scagel et al. (1989) considered this entity to be F. gardneri Silva. Earlier, Rice and Chapman (1985) grouped one sample from Central Puget Sound area in Washington state with F. evanescens C. Ag. In this thesis, I follow the opinion of Powell (1957) to consider the monoecious Fucus with caecostomata as F. distichus and make no distinction among the subspecies. Voucher specimens were collected and deposited at the University of British Columbia Phycological Herbarium (UBC). Typical for Fucus, growth of F. distichus is characterized by division of an apical meristematic cell resulting in dichotomous branching. When the plant becomes fertile, the distal end of the branch becomes enlarged and swollen to form a receptacle with General Introduction p. 5 numerous conceptacles. Fucus distichus is monoecious, since both antheridia and oogonia are found in the same conceptacle. The probability of successful fertilization is extremely high. Pollock (1970) describes fertilization in this species. A more detailed description of the morphology and reproduction of this and related species is given in Bold and Wynne (1985 and the literature Cited therein). The life history of Fucus distichus is diplontic, monophasic (i.e., with only one dominant phase). Although the dominant thallus is sometimes considered to be a sporophyte, and the oogonium a megasporangium containing the female gametophyte, and the antheridium a microsporangium containing the male gametophyte (Jensen 1974), such distinction is not necessary from a population ecological point of view because both "gametophytes" are not separate from the sporophyte. Throughout this thesis, I use the terms "individual(s)" or "plant(s)" to refer to the sporophytic (diploid) plant which produces gametes by meiosis. THE STUDY SITE The study area is located along the southern seawall of False Creek, Vancouver, British Columbia, Canada (49°17'N, 123°7'W). The wall is approximately 1.5 km long and is made of slabs of granite. It supports an almost pure stand of Fucus distichus. Water in the creek is brackish, with salinity usually around 15 °/ 0 0 . Fucus plants form a distinct zone 1.5 to 2 m in width along the seawall 2.5 m above the Lowest Normal Tides (LNT). There is a good tidal flush in the creek and the tidal cycle is semi-diurnal. Plants are exposed to air in daytime during the summer and at night during the winter. General Introduction p.. 6 ORGANIZATION OF THE THESIS Field manipulations, laboratory experiments and computer simulations were conducted to address the stated objectives. The results of these are organized into 6 chapters briefly described below: Chapter 1 addresses questions on reproductive phenology, recruitment, and the importance of age vs. size as descriptors of reproductive events. Chapter 2 deals with growth and mortality as a function of age and/or size. Chapter 3 assesses the cost of reproduction in terms of the survival of reproductive vs. non-reproductive plants and the relationship between growth and reproduction. Chapter 4 examines the density-dependent survivorship and growth of recruits using settling blocks with known density of recruits and clearing plots in the field. Chapter 5 proposes matrix models that correspond to the 3 basic types of algal life histories and gives examples to show the utility of these models. Chapter 6 describes matrix models that correspond to monthly and yearly transitions within the population of Fucus and analyzes the relative importance of each demographic parameter to the population growth rate. CHAPTER 1 Natural Dynamics of a Fucus distichus Population: Reproduction and Recruitment INTRODUCTION Reproduction and recruitment of benthic macroalgae have been the subjects of considerable interest for several decades. Reproductive phenology and/or recruitment patterns have been examined in many intertidal (e.g. David 1943, Knight and Parke 1950, Burrows and Lodge 1951, Edelstein and McLachlan 1975, Niemeck and Mathieson 1976, Gunnill 1980a, 1980b, 1986, Ang 1985a, 1985b) and subtidal populations (e.g. Kain 1964, 1975, Rosenthal et al. 1974, Chapman 1984a, 1986b, Schiel 1985a, 1985b, De Wreede 1986, Reed 1990a). Various factors, such as light, photoperiod, salinity and temperature, have been shown to affect the initiation and development of reproductive structures (McLachlan et al. 1971, Bird and McLachlan 1976), the discharge of propagules (Jaffe 1954, Norton 1981, Pringle 1986), as well as the germination and growth of recruits (Moss and Sheader 1973, Shannon et al. 1988). Recruitment is defined as the addition of new individuals to a population (Doherty and Williams 1988 in Santelices 1990). Algal species produce spores or other propagules by the hundreds of thousands (Umezaki 1984, Bhattacharya 1985, Amsler and Neushul 1989, Pacheco-Ruiz et al. 1989). Many of these spores or propagules are capable of surviving long distance dispersal (Reed et al. 1988, see also reviews by Hoffmann 1987 and Santelices 1990). However, there is currently no consensus on what constitutes a recruit in an algal population. Observations have been made either at the microscopic stage during settlement of propagules or at the macroscopic stage, when the propagules have become large enough to be visible to unaided eye. Rarely have the observations been made at both stages (Santelices 1990). These stages, i.e. the dispersal, Chapter 1 Reproduction and Recruitment p. 8 microscopic and macroscopic stages, are analogous respectively to the planktonic larval stage, settlement and post-settlement stages of marine sessile animal populations. The variable rate of recruitment among marine animals and how this could affect the adult population structure has long been recognized by fisheries biologists (Sale 1990). Until recently, most animal recruitment studies assume that there is a steady stream of larvae coming into the population. The failure of any recruits to establish in the population is largely due to events related either to settlement, like absence of suitable habitat, or to post-settlement, like competition or predation (Underwood and Fairweather 1989). It has now been shown that reproductive phenology may be decoupled from recruitment, especially in an open population (Roughgarden et al. 1988). Oceanographic currents may carry eggs or larvae away from the spawning ground to a different habitat such that the number of recruits that become available to a population are unrelated to the reproductive state of that population. Eggs and larvae experience a very high rate of mortality during dispersal. The number that eventually survives to be recruited into a population is therefore highly variable in time and space. Underwood and Fairweather (1989) pointed out that the failure to observe any recruitment in a population may simply be due to the absence of any recruits, and not due to any physical or biological constraints on them. Seasonal or yearly variations in recruitment have been documented in only a few algal studies (e.g. Edelstein and McLachlan 1975, Gunnill 1980a, 1980b, Reed and Foster 1984). Most of these studies are based on recruits at the macroscopic stage. Given that any intermediate stage, from propagules to the final appearance in the population as small plants, is likely to experience variable mortality, it is reasonable to expect that variability in the rate of recruitment can be significant in time and space. However, much less is known about the dynamics of the microscopic stage. There is a need to Chapter 1 Reproduction and Recruitment p.9 relate the dynamics at this stage with those of other stages in order to better understand the process of recruitment. Many field studies have used clearing or provision of substrata to follow growth of recruited plants to maturity and/or senescence. Tagging or mapping has been used to follow the fate of individuals. In many cases, results from these studies were used in a life table analysis, with age as a state variable, to evaluate survivorship and life expectancy (e.g. Gunnill 1980a, 1980b, 1986, Chapman and Goudey 1983, Chapman 1986b, Dayton et al. 1984). However, the relationship between age and reproduction has not been considered in these studies. Because of their morphological plasticity, size is a better state variable as a descriptor of population dynamics than age in many higher plants and colonial animals (Harper 1977, Caswell 1989). Many algae also exhibit plasticity in morphology (Norton et al. 1981). It is therefore likely that size is also a better state variable than age as a descriptor of algal population dynamics. The reproductive potential of algae is usually expressed in terms of per unit biomass or per unit fertile area, both of which could be a function of size (length). A minimum length requirement before reproductive structures are formed has been suggested by Knight and Parke (1950) and Edelstein and McLachlan (1975) for species of Fucus. More recently, reproduction in the brown alga Laminaria longicruris Pyle. has been found to be size-specific (Chapman 1986b). Lazo and McLachlan (1990) also found good correlation between size (biomass) and reproductive pattern in the red alga Chondrus crispus Stackhouse. This chapter evaluates various events related to reproduction and recruitment in Fucus distichus L. emend Powell. The relative importance of age versus size as a descriptor of reproductive events was evaluated using log linear and association analyses. Reproductive phenology was monitored and reproductive potential, i.e., egg (zygote) Chapter 1 Reproduction and Recruitment p. 10 production, was assessed based on plant size. Also, the temporal pattern of recruitment was monitored using settling blocks and counts of new plants appearing within permanent quadrats every month. Recruitment pattern was then correlated with reproductive phenology and pattern of egg production. MATERIALS AND METHODS Quadrat Size and Number of Replicates Individual Fucus plants are defined by the erect branch arising from the holdfast. To follow and monitor specific individuals in the population, permanent quadrats were set up at random locations within the Fucus zone. Chapman (1984b) suggested that a quadrat size of 1/4 m2 (50 x 50 cm) is appropriate for a population with a density in the range of 500 plants/ m2. I tested this in May 1985. Quadrats of 10 x 10 cm, 20 x 20 cm ...up to 50 x 50 cm were used to count all visible Fucus plants (minimum size = 1 mm) within the quadrat. Quadrats larger than 50 x 50 cm were not used as it was obvious that such larger sizes would be unwieldy and impractical at this site. The density-area curve (Fig. 1.1A) leveled off at quadrat sizes between 40 x 40 cm to 50 x 50 cm, suggesting that a quadrat of this size range is appropriate for this study. To find the appropriate number of replicates that would represent the population, quadrats of different sizes were used. The density-sample size curve (Fig. 1. IB) leveled off at sample size of 3 replicates for quadrat size of 40 x 40 cm or 50 x 50 cm, indicating that when using a quadrat of this size, 3 replicates are sufficient to represent the population. Age vs. Size as the Descriptor of Reproductive Events Three permanent quadrats of 50 x 50 cm each were set up in the Fucus zone in July 1985. The quadrats were placed randomly at more or less the same height above sea level within a 200 m section of the seawall. Each quadrat was divided into 25 smaller Chapter 1 Reproduction and Recruitment p. 11 squares and individuals within each square were mapped monthly from July 1985 to November 1987 (except August 1985 and November 1986). New plants in the quadrats were recorded. These plants were usually less than 5 mm in length when they were first detected. Size was measured from the holdfast to the tip of the longest branch. By monitoring the fate of these new plants (recruits), it was possible to evaluate the age and size at first reproduction as well as the probability of being reproductive as a function of age and size class among different cohorts. Age 1 is defined as the first month when the plant appeared in the permanent quadrat. Receptacle initiation starts at the tip of a branch. It was easy to differentiate an incipient receptacle from a more mature one, but there was no easy way to ascertain if a more mature one was fecund, i.e. was producing gametes. Sideman and Mathieson (1983) used four criteria to designate a reproductive Fucus plant, namely: (1) most apices have fertile receptacles, (2) both antheridia and oogonia have clear and visible septa, (3) conceptacles are raised above the receptacular surface, and (4) presence of mucilage extruded from the conceptacles. Here, first reproduction for a plant is indicated by the first appearance of receptacle(s) showing conspicuous, slightly elevated conceptacles. Because these plants were also being monitored for longevity and changes in plant length, they could not be collected, nor could the receptacles be excised to examine the conceptacles under a microscope. At times, therefore, a subjective decision was made to designate the stage of first reproduction. Ten cohorts, from September 1985 to July 1986, were included in the analyses. Cohorts initiated after July 1986 did not develop mature receptacles at the end of the observation period in November 1987. To test whether age or size is a better descriptor of reproductive events, two statistical analyses were used (Caswell 1989). Log linear analysis is a qualitative test that allows an evaluation of the relative contribution of age, or size, to predicting the occurrence of a reproductive event. It also allows an evaluation of the contribution of age to this Chapter 1 Reproduction and Recruitment p. 12 prediction when the contribution of size is known and vice versa for size and age. The second analysis is based on the Goodman-Kruskal Tau coefficient, a measure of association (Goodman and Kruskal 1954) and partial association developed by Gray and Williams (1975). This evaluates quantitatively the relative contribution of either age or size to predicting the reproductive event when the other state variable is taken into account. Partial association of size and reproduction with age and that of age and reproduction with size can then be expressed as a ratio. Size is more important than age as a descriptor of a reproductive event if the ratio is > 1, or age is more important if the ratio is < 1. Caswell (1989) gives a more detailed account of these analyses with applications in many plant and animal examples. Reproductive Phenology All plants 1 cm or longer within the 3 permanent quadrats were measured to the closest mm from the holdfast to the tip of the longest branch. Their reproductive status was also recorded. In addition, 4 to 7 quadrats of 10 x 10 cm were placed randomly in the Fucus zone monthly over the same period. All visible plants within the quadrats were collected and brought to the laboratory. The size of each plant was similarly measured to the nearest mm. Receptacles from each reproductive plant were cut, placed in petri dishes and photocopied. An image of the surface area was then measured using a Kontron Image Processing System and areas of all receptacles from each fertile plant were totaled. A total of 38,843 Fucus plants were censused for their reproductive status over the 29 months of sampling. Egg (Zygote) Production Additional collections of 10 plants were made haphazardly, at low tide, from the site in November 1985, March, August and October 1986, and January 1987 to represent fall-winter, spring, summer, fall and winter plants respectively. Each time, in the Chapter 1 Reproduction and Recruitment p. 13 laboratory, one receptacle from each plant was placed in a petri dish with enough filtered seawater to float the receptacle approximately 1 cm above the bottom of the dish. This allowed eggs discharged from individual conceptacles to stay in identifiable clusters. Receptacles were kept at 16h light: 8h dark, at 15 °C (or 10 °C for winter collection), under low light (40 uE m"2 s"1). Discharge usually took place within 72 hours. After discharge, the receptacle was removed and the number of conceptacles in the receptacle was counted. Surface area of the receptacle was also measured using the Kontron Image Processing System. The number of eggs in a cluster was counted under a stereo-microscope. It was very rare (< 1 %) to find eggs which did not undergo cleavage, so it can be assumed that most discharged eggs were fertilized. Each cluster corresponded to the position of a conceptacle, so the number of eggs per cluster corresponded to the number of eggs discharged from individual conceptacles. However, boundaries between clusters were not always very distinct. In case of overlap, the mid line between clusters was used to partition the two clusters during counting. Three to five clusters were counted per receptacle, and the total number of clusters from each receptacle was also recorded. Recruitment The seawall is made of granite. Small chips of granite (2 - 3 cm in length) were collected from the site and were cemented (Poly Cement, Le Page's Limited, Bramalea, Ontario, Canada) into 5 x 5 cm blocks exposing as much of the granite surface as possible. These blocks were left for 48 hours to cure. After curing, they were placed in an aquarium with flowing freshwater for a week, then in seawater for at least a month to leach out any possible toxic chemicals from the cement. Finally, they were cleaned with a wire brush and rinsed in freshwater. In a preliminary seeding experiment conducted in October 1985, no difference was observed between germlings Chapter 1 Reproduction and Recruitment p. 14 growing on the granite or on the cement part of the block. There was no significant difference in the number of germlings settled on either surface (Mann Whitney 17 test, P=0.106, n = 12). This was also true for the recruits settled on the first set of blocks laid out in the field (Mann Whitney U test, P=0.129, n=14). Starting in October 1985, 24 settling blocks were placed in cement holding pockets constructed 2 months earlier and located randomly in the field site. Every month thereafter, up to October 1987, these blocks were retrieved and replaced with a new set. The number of blocks retrieved varied depending on the loss rate. Loss rate ranged from 0 to 50%. From June 1986 on, only 11 blocks were set out each month because some of the holding pockets were destroyed. Since settling blocks were put in place during the later part of each month, they were exposed to colonization by algal propagules in the subsequent month before being retrieved. Settling blocks retrieved from the field were brought back and placed in aquaria with filtered seawater and kept in the growth chamber at environmental conditions described earlier for the egg production experiment. All these recruits were no older than one month when the blocks were retrieved. They were easy to recognize because of their size (around 300 ^ m), and so could be counted easily under a stereo-microscope. In addition, new plants that first appeared monthly in the 3 permanent quadrats were recorded as new recruits from July 1985 to November 1987. Statistical Analyses Data were tested for normality (Lilliefor's test) and homogeneity of variance (Bartlett's test), except for data used in distribution-free log linear and association analyses. When appropriate, data were log (x + 1) transformed to meet the assumptions of parametric statistics. Other methods of transformation were also attempted. Chapter 1 Reproduction and Recruitment p. 15 Covariation between time and size of plant was compared using ANCOVA, with fertile area (i.e. area of the receptacle) as the dependent variable. Mean number of eggs discharged per conceptacle among receptacles over time was evaluated using two-level nested ANOVA. The effect of fertile area on the number of conceptacles was analyzed using ANCOVA, with sampling time as the covariate. Relationships between the number of conceptacles and fertile area, and between the number of eggs and fertile area were evaluated in a regression analysis. Pearson correlation or Spearman rank-order correlation was used to relate the pattern of recruitment against reproductive phenology and pattern of egg production. All statistical analyses were performed using SYSTAT (Wilkinson 1988). RESULTS Age vs. Size as the Descriptor of Reproductive Events Cohorts with members becoming reproductive were divided into 5 size classes. Size class 1 included all plants < 1 cm in length, size class 2, 1 - < 4.5 cm, size class 3, 4.5 - < 9.5 cm, size class 4, 9.5 - < 14.5 cm, and size class 5, > 14.5 cm. Plants were also grouped into 6 age classes: age class 1 for plants in ages 1 to 3 months; age class 2, ages 4 to 6; age class 3, ages 7 to 9; age class 4, ages 10 to 12; age class 5, ages 13 to 15; and age class 6, ages > 15 months. There were only 20 plants older than 19 months (0.4% of total) so they were lumped together with plants in age class 6. Two distinctions may be made with respect to the probability of the plant becoming reproductive at any size or age. One is the size or age of first reproduction, i.e. when the receptacle was first formed, and second, the probability of being reproductive at any size or age. Several receptacles may be formed at the same time, or one after the other, at different terminal branches such that a Fucus plant could remain reproductive for prolonged periods. Or there may be time gaps between the formation of receptacles, Chapter 1 Reproduction and Recruitment p. 16 giving the plant a semblance of iteroparity (see Chapter 3). A measure of the probability of being reproductive is therefore different from a measure of size or age of first reproduction. Both measures were based on the actual percentage of plants that were reproductive. There was no consistent pattern in the probability of becoming reproductive for the first time in each size class. On average, plants were most likely to be 9.5 to 14.5 cm in size when the first receptacle was formed (Fig. 1.2A). Some plants were reproductive at sizes between 4.5 to 9.4 cm. Plant smaller than 4.5 cm (size classes 1 and 2) never formed receptacles. In general, the larger the plant, the more likely for it to become reproductive (Fig. 1.2B). Some plants as young as 7 months old became reproductive, but reproduction could also be much delayed. No plants younger than 7 months old ever formed receptacles. There was no discernible pattern in the probability of age at first reproduction among older plants (Fig. 1.3A). One plant from the September 1985 cohort, lost 22 months later, never became reproductive. In contrast, the probability of being reproductive at any age generally increased with age (Fig. 1.3B). Only plants in size classes 4 to 5 and age classes 3 to 6 were used in the log linear analysis and the test for partial association. Plants in size and age classes 1 to 2 never became reproductive. Only a few members of size class 3 became reproductive. Inclusion of size class 3 in the analyses resulted in more than 20% of cells in the contingency table having a frequency value less than five, thus making results of the analyses doubtful. Exclusion of size class 3 did not affect the conclusions of the analyses. As the likelihood of becoming reproductive increased with size.as well as with age, it was possible that both age and size could be significant predictors of the reproductive Chapter 1 Reproduction and Recruitment p. 17 fate of a plant. This is confirmed by the log linear analyses (Table 1.1). The results are given in terms of the G statistic, which is 2 times the value of the log likelihood ratio and which approximates a chi square distribution better than the log likelihood ratio (Sokal and Rohlf 1981). Predictions of a reproductive event from age and size taken together (Age x Size x Repro), from age (Age x Repro) or size (Size x Repro) alone, or from age given the known contribution from size (Age x Repro/ Size) or vice versa (Size x Repro/ Age) are all highly significant. However, the index coefficients of association are small (Table 1.2). Analyses of associations measure the extent to which reproduction (formation of receptacle) is predicted by knowledge of age (Age x Repro) or size (Size x Repro) alone, or taken together (Age/Size x Repro), or of age when size is taken into account (Age x Repro : Size) or vice versa (Size x Repro : Age). A perfect association has an index coefficient of 1. Small index coefficients suggest that only a small proportion of the variances associated with reproduction can be accounted for by the knowledge about age and/or size. The ratio of partial association (Table 1.2) indicates that size is 57% better as a predictor of reproduction than age. Reproductive Phenology When the whole population is considered, an additional 6th size class for plants longer than 19.4 cm can be designated (Fig. 1.4). The other 5 size classes are the same as those designated earlier. In most cases, size class 1 contained the most individuals. Size class 1 included most of the new recruits (see section on recruitment below) and was usually more sparse during fall. The pattern of frequency distribution in the other size classes was less consistent over time. Reproductive plants were present throughout the sampling period from September 1985 to November 1987 (Fig. 1.5). In general, a larger proportion of plants was fertile in fall to early spring than in late spring and summer. Most fertile plants belonged to Chapter 1 Reproduction and Recruitment p. 18 size classes 4 and 5 (Fig. 1.6). The probability of being fertile in size classes 3 to 6 followed a general seasonal trend, being least likely in early summer, and most likely in fall and winter (Fig. 1.7), Plants in size class 6 were almost always fertile in fall and winter. The slopes of the regression between ferule area and plant size are not significantly different over time (Table 1.3), so all the data can be pooled. However, regressions for summers (June to August 1986 and 1987) and for spring (March to May 1987) are not significant (Fig. 1.8), so only data from other seasons which show significant regressions were pooled. The resulting linear regression line (Fig. 1.9) is significant and accounts for 37% of the variation of the pooled data. If all the data had been pooled, i.e. including those from summers 1986, 1987 and spring 1987, the regression line would still be significant but would have accounted for only 28% of the variation within the data (log Y = 0.044 + 0.069X, 1^ =0.28, P<0.001, n=302). Egg Production The number of eggs discharged from the conceptacles was variable (Table 1.4A). Results from a two-level nested ANOVA suggest that the number discharged per conceptacle is significantly different among receptacles and over time (Table 1.4B). The Tukey Multiple Comparison test indicates that the difference among times is mainly due to the low number of eggs discharged from receptacles in August 1986 (Table 1.4C). On average, 188 eggs (+ 15.63 S.E.) were discharged per conceptacle in August 1986 and about double that number (366 + 12.91) was discharged in each of the other months. To test the difference between number of eggs discharged and the number of eggs that are potentially available within a conceptacle, in January 1987, 5 conceptacles each from 5 receptacles were smeared and the number of oogonia within each conceptacle Chapter 1 Reproduction and Recruitment p. 19 was counted. Typically, 8 eggs are produced per oogonium in Fucus (Bold and Wynne 1985), so the number of oogonia multiplied by 8 should give the potential number of eggs that could become available. Some of the oogonia were very small (< 200 fim) and the eggs they contained were about half, or less than half, the size of those in the bigger oogonia. It is very likely that these were immature oogonia and would presumably continue to develop and discharge eggs at a later time. An examination of the receptacles used in the egg production experiment revealed the presence of a number of immature oogonia in an otherwise empty conceptacle. The actual number of eggs discharged per conceptacle (353 ± 23.7 S.E.) is significantly different from the number of eggs present inside a conceptacle (979 + 89.4) (Two-level nested ANOVA, F 1 ) 4 0 = 102,357, P<0.001). Results from an ANCOVA indicate that the relationship between fertile area and the number of conceptacles is not significantly different among seasons, except for August 1986 (Table 1.5). This relationship is curvilinear for pooled data representing all other seasons except August 1986 (Fig. 1.10), and accounts for 63% of the variation. The mean number of eggs produced by a receptacle with a given surface area can therefore be obtained by multiplying the mean number of eggs produced per conceptacle by the number of conceptacles per receptacle and regressed against the area of the receptacle (Fig. 1.11). The regression line is linear and significant. Regression lines from Figures 1.9 and 1.11 can be used to estimate the number of eggs produced from any size of plant > 4.5 cm and for times other than the summers of 1986 and 1987, and the spring of 1987, using the following equations: log Y logX = 4.121 + 0.117X = -0.014 + 0.076Z Chapter 1 Reproduction and Recruitment p.20 where Y is the number of eggs, X is the area of the receptacle (fertile area), and Z is the size of plant. Because of the lack of a significant relationship between fertile area and the size of plants in summer, mean area was used to predict the number of conceptacles and then multiplied by mean number of eggs per conceptacle for August to give the number of eggs produced per plant. This was also done for plants in spring of 1987. Not all conceptacles from the same receptacle produced eggs at the same time. Receptacles also persisted through a period longer than one month. Hence, calculations made above give the potential number of eggs that can be produced during the life span of the receptacles as measured at a particular point in time. The number of new plants recruited into a population may be more closely related to the actual number of eggs discharged at a particular time, than to the potential number. Actual number of eggs discharged can be calculated by multiplying the number of eggs in a cluster by the number of clusters produced by the receptacle at one time. Results of ANCOVA indicate that the relationship between the area of a receptacle and the number of egg clusters is not significantly different over time (Table 1.6). This relationship is always non-significant (Linear Regression, 1^ =0.049, P=0.269, n=27). The number of clusters produced, and hence the actual number of eggs, is independent of the size of the receptacle, hence also of plant size. The mean number of eggs in each cluster multiplied by the mean number of clusters produced by each receptacle at any one time was therefore used in the calculation for the estimated number of eggs produced monthly by each plant. Density of Fucus plants and the percentage of fertile plants in different size classes varied over time. Assuming no significant immigration of eggs from other Fucus populations, the potential and estimated number of eggs available in the population at Chapter 1 Reproduction and Recruitment p.21 any one time would not only depend on the number of eggs produced by each plant, but would also depend on plant density and the probability of these plants being fertile. The potential and estimated number of eggs available in the population at any one time is therefore better projected on a per area rather than on a per plant basis. In either case, however, the production pattern exhibited should be comparable. The potential and estimated number of eggs per 25 cm2 of ground surface in the Fucus zone produced by the population from 1985 to 1987, with maximum and minimum 95% confidence limit, differs by about 5 orders of magnitude (Fig. 1.12). In both cases, production of eggs is highly correlated with the reproductive phenology of the plants (Table 1.7). Recruitment Two types of recruits were considered. Microrecruits collected on settling blocks presumably developed from eggs recently (i.e. within one month) discharged. They were small and could not be seen with the unaided eye. It usually took at least 3 to 4 months before these recruits became visible, i.e. became 1 mm or bigger (Chapter 4). Visible plants appearing for the first time in the permanent quadrats and recorded as macrorecruits were therefore older, and must have developed from eggs discharged at least 3 or 4 months earlier. Monthly mapping of individuals in each permanent quadrat allowed the detection of any new plants that appeared in the quadrat. Although there was always a possibility of counting the same individual as a new recruit over successive months, this was a potential problem only during April to July 1986 when the number of recruits was very high (Fig. 1.13). In case of doubt, an individual was assumed to be an older plant. A decision like this had to be made in < 10% of the cases. Hence, while there could be an under-estimation of the number of macrorecruits that actually appeared in the permanent quadrats, the extent of this under-estimation Chapter 1 Reproduction and Recruitment p. 22 was probably minimal. A total of 25,508 microrecruits and 29,537 macrorecruits were censused throughout the 2-year sampling period. Three big pulses of microrecruits were recorded within this period (Fig. 1.13). These pulses ranged from 266 plants (+ 52.5 S.E.) per 5 x 5 cm settling block in January 1986, to 509.5 plants (± 115.5 S.E) per block in March 1987. These pulses, however, were not always associated with peaks in fertility. Nevertheless, since the blocks were exposed to colonization for only a month, and presumably microrecruits developed only from eggs released recently, the recruitment pattern recorded on these blocks should be related to the reproductive pattern at the time when these blocks were retrieved (i.e. after having been exposed for a month for colonization), or that of the preceding month (i.e. one month antecedent), at the time when blocks were laid. This is confirmed by a highly significant positive correlation between the reproductive phenology and the overall recruitment pattern (Table 1.7). Although there were no microrecruits collected in the summer months of both years, the possible presence of eggs during those periods is suggested by the estimated monthly egg production. There is a significant positive correlation between both the estimated and potential egg production and the recruitment patterns over the 2-year period (Table 1.7). The pattern of macro-recruitment in permanent quadrats is very different from that of micro-recruitment. Macrorecruits were present throughout the sampling period and peaked only once - during spring to summer of 1986. Given that it took at least 3 to 4 months to become a macrorecruit, the peak in spring to summer of 1986 appeared to follow the first big pulse of microrecruits and a high fertility period in the preceding few months. However, such a pattern was not repeated in the following year although the population experienced another peak of fertility in fall to winter of 1986 and 2 more pulses of microrecruits. Unlike the micro-recruitment pattern, macro-recruitment did not peak and fall abruptly. Interestingly, there is a significant negative correlation Chapter 1 Reproduction and Recruitment p.23 between the pattern of macro-recruitment and reproductive phenology (Table 1.7), as well as with the estimated monthly egg production pattern. No significant correlation can be detected between macro-recruitment pattern of up to 3 months antecedent and reproductive phenology, nor with estimated and potential egg production patterns (Table 1.7). DISCUSSION A minimum size requirement before commencement of reproduction has been reported for many higher plants (see Harper 1977 for examples). This phenomenon has received considerably less attention among algae. Size-specific first reproduction was mentioned mainly as a part of studies on reproductive phenology. Among intertidal fucoids, Knight and Parke (1950) observed that young plants of Fucus vesiculosus L. usually attained a length of 15-20 cm, and for F. serratus L., a little longer at 18-25 cm, before forming receptacles. Niemeck and Mathieson (1976) noted that all reproductive plants of F. spiralis L. were longer than 9.5 cm during July to September, the period of maximum reproduction. This latter size range is similar to what I found for F. distichus. There is more information on age-specific reproduction. Except for short-lived algae which reproduce and die within the same year or season, most long-lived (> 1 year) algae tend to reproduce in their second year and/or thereafter (see review by De Wreede and Klinger 1988). However, there are some exceptions. Similar to my observations, Knight and Parke (1950) and Edelstein and McLachlan (1975) noted that a small number of Fucus individuals became reproductive in their first year. In most studies on age-specific reproduction, age is based, on the time when the young plant was first detected in the field or in clearings. But the time lapse between actual recruitment as a spore or zygote and when the recruit becomes visible may vary, so the actual age Chapter 1 Reproduction and Recruitment p. 24 at first reproduction may vary accordingly. Work by Chapman (1986b) on Laminaria longicruris has probably the closest estimate of true age of reproduction. In this population of Fucus I studied, both age and size should ideally be taken into consideration when describing reproduction. Low association indices of age and/or size (Table 1.2) suggest that knowledge about other state variables, like biomass, number of bifurcations etc., may also contribute significantly to the prediction of reproduction. However, it is not possible to measure all state variables in a population study. Considering age versus size, the use of size offers some logistic advantages over the use of age. As mentioned earlier, most studies on age involved tagging or mapping and monitoring of plants over a period of time. The actual age of plants could only be estimated reliably if monitoring starts from the time when plants first enter the population. Other aging techniques may be available, such as counting of growth rings in kelps (Novaczek 1981, De Wreede 1984, 1986) or air bladders in Ascophyllum nodosum (L.) Le Jol. (Cousens 1984); their applicability is, however, rather specific. These techniques also have other limitations. Counting growth rings necessitates the destruction of the plant. Although some morphological characters like stipe length may be related to age, hence may be used to estimate age (De Wreede 1984), this relationship is site-dependent (De Wreede 1984, Hymenson et al. 1990). The time between initial recruitment and formation of the first air bladder in Ascophyllum varies among plants (Baardseth 1970a, Cousen 1985, Vadas and Wright 1986). Also, absolute age can not be determined for this species because of vegetative regeneration (Keser et al. 1981). Size measurement is more straight forward. While ways to monitor changes in sizes of individuals may be equally tedious, the history of individuals under study need not be known. Although my study, as well as studies by Chapman (1986b) and Lazo and McLachlan (1990), all indicated that size is the better predictor of reproductive events, Chapter 1 Reproduction and Recruitment p. 25 the examples are too few to justify making a generalization about all algae. The use of size in population studies also needs to be further evaluated with respect to other demographic parameters such as growth and mortality (see Chapter 2). A general trend of reproductive phenology for temperate intertidal algae seems to be that, with some exceptions, peaks of reproduction occur either in winter (fall to winter or winter to spring) or in summer (spring to summer or summer to fall) (Hoffman 1987). The pattern varies from place to place and from species to species. Ascophyllum nodosum (David 1943), Fucus vesiculosus (Knight and Parke 1950), F. spiralis (Niemeck and Mathieson 1976) and Postelsia palmaeformis Ruprecht (Dayton 1973) had reproductive peaks in summer, while F. serratus (Knight and Parke 1950), F. distichus ssp. distichus (Edelstein and McLachlan 1975) and Pelvetia fastigiata (J. Ag.) De Toni (Gunnill 1980a) peaked in winter. Fucus serratus showed different peaks in reproduction in different places, e.g. September in Wembury, Devon, November in Port Erin, Isle of Man (Knight and Parke 1950). Similarly, for F. distichus, my study indicated its peak of reproduction to be in fall to winter, but another study on the same species in Puget Sound, Washington, USA, indicated that the peak of reproduction was in June (Thorn 1983). Reproductive phenology could vary by a few months even among nearby populations due to different topographical aspects (Gunnill 1980a). In both my studies and the Washington example, reproductive plants were recorded throughout the year. The number of propagules produced by algae, whether in the form of eggs, spores, zygotes or germlings, is usually assessed either by counting the undischarged propagules within reproductive structures (Kain 1975, De Wreede 1986) or by counting propagules released into a known volume of sea water over a certain period of time (Anderson and North 1966, Bhattacharya 1985, Amsler and Neushul 1989). The former method calculates the reproductive potential of the plant and assumes that all Chapter 1 Reproduction and Recruitment p.26 propagules in the reproductive structure will eventually become available for recruitment. The latter method estimates the actual number available over a particular sampling period and does not consider possible further development of new propagules in the reproductive structure. This may not be a problem with some kelps as sori normally become necrotic and disintegrate after discharge of zoospores (Klinger 1984) or are abscised from the blade at the beginning of spore release (Amsler and Neushul 1989). However, fucoids have been shown to discharge eggs over prolonged periods of time. From my study, oogonia within conceptacles were found to be in different stages of development and conceptacles of the same receptacle did not release eggs all at the same time. The latter observation was also reported by Edelstein and McLachlan (1975). Subrahmanya (1957) noted that gametes could still be found in deteriorating receptacles of Pelvetiafastigiata. Similarly, I observed that some receptacles collected from the field, although showing signs of necrosis, still contained oogonia. It is not certain if eggs which were not released at one time would eventually mature and be released later. It is possible that some oogonia never develop to maturity. The potential number of eggs calculated in my study (Le. number of eggs per conceptacle x number of conceptacles in the receptacle) included eggs that are yet to develop and be discharged in immature conceptacles. However, this may still be an under-estimate of the maximum reproductive potential of the plant as this does not include conceptacles that have yet to develop. It is also not certain if new oogonia, hence new eggs, could develop within an "old" conceptacle. A complete account of this potential may be impossible to obtain unless techniques can be developed to follow the complete series of events occurring within the conceptacle. In contrast, what is critical to the dynamics of a population may not be the potential number of propagules available throughout its reproductive season, but what is available at any particular time. In my study, the number of eggs discharged at one Chapter 1 Reproduction and Recruitment p.27 time was independent of plant size and was presumably only a function of the number of reproductive plants per unit area. Discharge may be localized depending on the dispersion of reproductive plants and may not occur at the same time for all plants. The actual number of eggs available per unit time per unit area may therefore be far less than what is given as estimated production in Figure 1.12. Significant correlations among reproductive phenology, potential and estimated egg production, and micro-recruitment patterns (Table 1.7) support the idea that as more plants become reproductive, more eggs are formed to become recruits, hence more microrecruits are detected on the settling blocks. However, the absence of corresponding peaks in macrorecruits following pulses of microrecruits in November 1986 and March 1987 suggests that a greater abundance of eggs does not always translate into more individual plants entering the population. There may be a differential survivorship of microrecruits at different times. The number of microrecruits during these peak recruitment periods was in the range of 100 to 1000 recruits per settling block, whereas the estimated number of eggs available during the same periods was 3.5 x 103 per 25 cm2. So at least 3 to 30% of the eggs were recruited as microrecruits during these periods. Assuming a 3-month growth period, only 0.4 to 12% of these microrecruits survived to become macrorecruits. Most recruitment studies have been based on macrorecruits, i.e. recruits at first detectable size, and have assumed that recruits developed from propagules recently released (Knight and Parke 1950, Edelstein and McLachlan 1975, Gunnill 1980a, 1980b, 1986, Dayton et al. 1984, Reed and Foster 1984, Ang 1985b). This assumption is reasonable if reproduction is seasonal and hence significant recruitment tends to follow peak reproduction. In my study, it may seem reasonable to attribute the presence of macrorecruits throughout the year to the continuous presence of reproductive plants. However, the absence of microrecruits in spring and summer of 1986, and summer of Chapter 1 Reproduction and Recruitment p. 28 1987, clearly makes this assumption less tenable. It has been speculated that propagules from the tail end of the reproductive season probably do not contribute to the population (Edelstein and McLachlan 1975, Gunnill 1980a). It is possible that a low percentage of reproductive plants in the early summer of 1986 and 1987 may have contributed some microrecruits, but the contribution could be very small and localized and hence insignificant for the whole population. From the estimated minimum monthly egg production (Fig. 1.12), it is possible that no eggs were available during these periods. On the other hand, some of the microrecruits from the peak reproductive period may have persisted and become detectable in size very much later. In a preliminary experiment, I was able to maintain microrecruits in culture chambers for up to at least a year under 8h light: 16h dark, 10 °C and low light (20 fiE m"2 s"1), minimal nutrients (seawater changed only once every 2-3 months). When outplanted in the field, these recruits grew to detectable size (around 5 mm). Moss and Sheader (1973) reported that the fucoid Halidrys siliquosa (L.) Lyngb. can germinate in darkness, germlings can survive for 120 days in darkness and resume normal growth when transferred to light. Edelstein and McLachlan (1975) noted that growth of sporelings of Fucus distichus ssp distichus could last over a prolonged period and many remained in an embryonic stage for 5 to 6 months. The continuous presence of macrorecruits in the population I studied may therefore be due to the existence of a "germling bank" of microrecruits, which survive for a prolonged period and grow to detectable size only when conditions become favourable. The pattern of their survival and emergence as macrorecruits is therefore independent of the prevailing reproductive or micro-recruitment patterns. Kain (1964) pointed out the possibility of a perennating gametophyte in Laminariales that could continue to supply sporophytic recruits into the population. This is supported by Novaczek (1984a) who observed that gametophytes of Ecklonia radiata (C. Ag.) J. Chapter 1 Reproduction and Recruitment p. 29 Ag. survived seven months, and young sporophytes 80 days, in darkness at 10°C and resumed growth and reproduction when illuminated. Small fronds (Cousens 1985) or suppressed shoots (Vadas and Wright 1986) under the canopy in Ascophyllum nodosum were suggested to serve as a "meristem bank" that could persist in the presence of the canopy but which could fill the place of the canopy once this canopy has been removed or damaged. The existence of a "germling bank" in this Fucus population remains to be experimentally verified. This may involve the placement of settling blocks with known number of microrecruits under different environmental conditions, e.g. under or without Fucus canopy, and monitoring of the growth and survival of individuals over time. In a related experiment on density-dependent growth and mortality of Fucus recruits (Chapter 4), I have observed that recruits exhibited different growth rates resulting in skewed distribution of plant sizes. What proportion of macrorecruits could have developed from the "germling bank" was not evaluated. The existence of a "germling bank" would be particularly significant if it contributes to a large number of macrorecruits. In that case, while micro-recruitment may be very patchy and episodic (see Reed et al. 1988), the existence of a "germling bank" would tend to stabilize fluctuations in the size of the population overtime. Given the time lapse for microrecruits to develop into macrorecruits, positive correlations between macro-recruitment pattern and reproductive phenology and the egg production pattern are not expected. It is interesting, however, to note the negative correlation between them (Table 1.7.). The peak reproductive period was also the time when Fucus plants were longest (Chapter 2). While the number of eggs discharged during the peak reproductive period may be independent of plant size, a canopy provided by larger plants may maintain a more favourable environment for the survival of microrecruits. Hruby and Norton (1979) observed a greater abundance of individual Chapter 1 Reproduction and Recruitment p.30 species colonizing slides placed underneath a canopy of Ascophyllum nodosum than in open sites. Sites beneath a canopy remain moist during low tide. This may be particularly critical for the False Creek Fucus population beginning in the spring when the period of low tide occurs during day time. When larger plants died back because of disintegration of receptacular branches or because of increased mortality, increased light penetration would likely enhance growth of microrecruits (McLachlan 1974), making them more visible within a shorter time. Since plant length is also positively correlated with reproductive phenology (Pearson's linear correlation coefficient r=0.60, P=0.001, n=26), the negative correlation between macro-recruitment pattern and reproductive phenology (as well as between estimated egg production pattern which is related to reproductive phenology) is more likely to be due to a negative correlation with plant length than with reproductive phenology per se. Much remains to be done to illustrate the relationship between patterns of micro- and macro-recruitment. This is one area that has received little attention mainly because of logistic problems associated with its study. The dynamics of micro-recruitment may prove to be important in the overall understanding of changes in algal population structure. Problems associated with aging of algae may be less critical if size can be shown to be a substitute for age as a predictor of algal population dynamics. This in turn may allow more work to be carried out on algal population dynamics based on size. Chapter 1 Reproduction and Recruitment p. 31 Table 1.1 Fucus distichus. Log linear analysis on the effect of age vs. size on the probability of reproduction. See Text for explanation of the models. Model df G P Age x Size x Repro 3 15.00 0.0002 AgexRepro 3 20.48 0.0001 Size x Repro 1 40.94 < 0.0001 Age x Repro/Size 3 21.88 < 0.0001 Size x Repro/ Age 1 42.34 < 0.0001 Chapter 1 Reproduction and Recruitment p.32 Table 1.2 Fucus distichus. Simple, multiple and partial associations among age and size vs. reproduction. See text for explanation of the associations. Association Index coefficient 0.034115 0.064782 0.114043 0.052672 0.082750 Ratio of Partial Association Size/Age = 1.571034 Age x Repro Size x Repro Age/Size x Repro Age x Repro : Size Size x Repro : Age Chapter 1 Reproduction and Recruitment p.33 Table 1.3 Fucus distichus. Results of ANCOVA on the effect of plant size on fertile area with sampling time as the covariate. Source of Variation df MS F P Size 1 9.799 45.743 < 0.001 Time 25 0.274 1.280 0.174 Size x Time 25 0.231 1.079 0.367 Error 250 0.214 Chapter 1 Reproduction and Recruitment p.34 Table 1.4 Fucus distichus. A.) Mean number of eggs (+ S.E.) discharged from 5 conceptacles per receptacle at different time periods. B.) Results of two-level nested ANOVA and C.) Tukey Multiple Comparison Test on the difference in the number of eggs produced per conceptacle over time. A. Receptacle Nov 85 Mar 86 Date Aug 86 Oct 86 Jan 87 1 285.0 ±25.7 388.0 ±36.6 225.8 ±14.3 238.8 ±25.1 351.0 ±33.5 2 261.2 ±60.4 508.6 ±43.2 97.0 ± 7.2 309.4 ±53.9 333.2 ±67.3 3 443.6 ±36.5 407.8 ±26.6 201.4 ±18.7 400.6 ±42.6 209.6 ±22.9 4 399.4 ±70.5 315.0 ±76.8 153.0 ±22.4 447.4 ±54.9 307.0 ±60.9 5 370.6 ±37.8 298.4 ±65.6 182.6 ±29.8 373.8 ±51.2 351.6 ±35.8 B. Source of Variation df MS F P Among Times 4 0.509 22.380 < 0.001 Among Receptacles 20 0.168 2.789 < 0.001 Error 100 0.023 C. Matrix of Tukey Pairwise Comparison Probabilities Nov 85 Mar 86 Aug 86 Oct 86 Jan 87 Nov 85 1.000 Mar 86 0.645 1.000 Aug 86 0.018 < 0.001 1.000 Oct 86 0.999 0.443 < 0.001 1.000 Jan 87 0.994 0.465 < 0.001 1.000 1.000 Chapter 1 Reproduction and Recruitment p. 35 Table 1.5 Fucus distichus. Results of ANCOVA on the effect of fertile area on number of conceptacles with sampling time as the covariate. Data included in the analysis are indicated. Source of Variation df MS F P A. Al l seasons: November 1985; March, August, October 1986; and January 1987 Area 1 0.057 6.023 0.017 Time 4 0.097 10.247 < 0.001 Area x Time 4 0.060 6.319 < 0.001 Error 72 0.009 Ml seasons except August 1986 Area 1 0.539 61.159 < 0.001 Time 3 0.076 8.577 < 0.001 Area x Time 3 0.022 2.456 0.071 Error 62 0.009 Chapter 1 Reproduction and Recruitment p.36 Table 1.6 Fucus distichus. Results of ANCOVA on the effect of fertile area on total number of eggs from all clusters with sampling time as the covariate. Source of Variation df MS F P Area 1 1.88xl07 0.813 0.379 Time 3 2.44xl07 1.054 0.392 Area x Time 3 2.41xl07 1.040 0.397 Error 19 2.32xl07 Chapter 1 Reproduction and Recruitment p. 37 Table 1.7 Fucus distichus. Correlation matrices showing Pearson Correlation Coefficient ( r) (in italics) or Spearman Rank-order Correlation Coefficient ( rs) between variables. Log in transformed number of microrecruits was used in Pearson correlation analysis. Number of cases in parentheses. Variables Reproductive Phenology Estimated Egg Production Potential Egg Production Microrecruits Microrecruits (1 month antecedent) Macrorecruits Macrorecruits (1 month antecedent) Macrorecruits (2 month antecedent) Macrorecruits (3 month antecedent) Reproductive phenology 0.567** (24) 0.525** (24) -0.407* (27) -0.277 (24) -0.257 (25) -0.309 (23) 0.473* (23) 0.372 (24) -0.354* (26) -0.211 (24) -0.098 (24) -0.010 (23) 0.759 ***(26) 0.396* (23) 0.279 (24) -0.080 (26) 0.031 (24) 0.082 (24) 0.219 (23) 0.531 ** (26) * 0.01 < P <> 0.05 ** 0.001 < P <. 0;01 *** P < 0.001 Chapter 1 Reproduction and Recruitment p.38 C\l E o 0.3 0.2 0.1 0.0* CO I— z 5 Q_ CO Lul Q A • MEAN ± S .E . I. o o o 0 . T * o ? T 1 4 9 16 25 36 QUADRAT SIZE ( x 100 c m 2 ) QUADRAT SIZE ( x100 c m 2 ) o o 4 * — A 16 • • 9 • 25 0 1 SAMPLE SIZE (Number of Replicates) Figure 1.1 Fucus distichus. A. Density-area curve used to determine the appropriate quadrat size for use in sampling the Fucus population. Density recorded in each of the 6 replicates and the mean density (+ S.E.) for each quadrat size are indicated. B. Density-sample size curve used to determine the number of replicates to be used in sampling the population. For sample size > 1, each data point is a mean value with S.E. not shown. Chapter 1 Reproduction and Recruitment p.39 60 ^ 4 0 LU CO 20 + ^ 0 —. 60 CD < § 4 0 Q_ 20 0 A SIZE CLASS 3 ( 4.5 - < 9.5 cm ) SIZE CLASS 4 ( 9.5 - < 14.5 cm ) SIZE CLASS 5 ( > 14.5 cm ) B SIZE CLASS Figure 1.2 Fucus distichus. A. Mean probability (% + S.E.) of becoming reproductive for the first time among plants in each size class and B. mean probability (% + S.E.) of being reproductive in each size class. Both measures were based on plants from all cohorts. Chapter 1 Reproduction and Recruitment p.40 80 60 LU CO + 40-20 0 00 OQ 80-< O 6 01 at CL 40 20 o A 1 B 1 i . I n 8 10 12 14 16 18 20 22 A G E ( MONTH ) Figure 1.3 Fucus distichus. A. Mean probability (% + S.E.) of becoming reproductive for the first time at each age and B. mean probability (% + S.E.) of being reproductive at each age. Both measures were based on plants from all cohorts. Chapter 1 Reproduction and Recruitment p.41 80i 60 40 20 0 30i >" 20 O z LJJ 10 O 0 U J C£ 20i 10 0 SIZE CLASS 1 ( < 1 cm ) il SIZE CLASS 3 ( 4.5 - < 9.5 cm ) Hlllililii SIZE CLASS 5 ( 14.5 - < 19.5 cm ) lil JliiUii.il illilliU SIZE CLASS 2 ( 1 - < 4.5 cm ) SIZE CLASS 4 ( 9.5 - < 14.5 cm ) JU lllllt.il Ulillllm, SIZE CLASS 6 (> 19.5 cm ) J A O D F A J A O D F A J A O D J A O D F A J A 0 D F A J A 0 D 1985 1986 1987 1985 1986 1987 TIME Figure 1.4 Fucus distichus. Percentage (% + S.E.) frequency distribution of individuals divided among 6 size classes. The individuals were sampled monthly from Jul 85 to Nov 87, except Aug .85 and Nov 86. Chapter 1 Reproduction and Recruitment p.42 O z o t— or: o Q_ O CL 70-I 60-Ld _ J • 50-1— CU 40-Ld Li-Cn \— 30-Z s 20-CL 10-0-T It • -< > - ALL PLANTS • PLANTS 1 4.5 cm T." I v. . . / i i i ml l.i i r •A O-.D F A J A 0 D F A J A 0 D 1985 1986 1987 TIME Figure 1.5 Fucus distichus. Percentage (% ± S.E.) of plants with receptacles from Sep 85 to Nov 87. Percentage calculated as number of fertile plants divided by total number of all plants, or by number of plants > 4.5 cm long (plants in size class 3 and above). Chapter 1 Reproduction and Recruitment p.43 SIZE CLASS 4 A O D F A J A O D F A J A O D A O D F A J A O D F A J A O D 1985 1986 1987 1985 1986 1987 TIME Figure 1.6 Fucus distichus. Frequency (% + S.E.) distribution of fertile plants in size classes 3 to 6. The individuals were sampled monthly from Sep 85 to Nov 87, except Nov 86. No fertile plant was found in size classes 1 and 2. Chapter 1 Reproduction and Recruitment p.44 8O-1 SIZE CLASS 3 60 40^ 20 0 SIZE CLASS 4 I _ SIZE CLASS 5 Tl SIZE CLASS 6 A J A O D F A J A O D F A J A O D A J A O D F A J A O D F A J A O D 1985 1986 1987 1985 1986 1987 TIME Figure 1.7 Fucus distichus. Probability (% + S.E.) of being reproductive among plants within each size class. Sampling frequency as in Fig. 1.6. Chapter 1 Reproduction and Recruitment p.45 Oct - Nov 85 Y = 0.177 + 0.069X Jun - Aug 86 Y = -0.251 + o.osox Mar - May 87 Y - 0.668 + 0.034X n = 24 r 2 = 0.104 P - 0.124 Dec 85 - Feb 86 Y = -0.569 + 0.093 n - 41 r 2 = 0.40 P < 0.O01 Sep - Oct 86 Y = 0.389 + 0.074X n - 25 r 2 - 0.38 P - 0.001 Jun - Aug 87 Y = -0.390 + 0.073X n = 23 r 2 - 0.15 P = 0.068 Mar — May 86 Y - 0.061 + 0.082X n - 84 r 2 - 0.40 P < 0.001 10 15 20 25 30 35 0 Dec 86 - Feb 87 Y 0.445 + 0.085X 5 10 15 20 25 30 35 0 PLANT SIZE ( c m ) Sep - Nov 87 , Oct 88 Y = 0.174 + 0.070X n . 17 r 2 - 0.43 P - O.004 o 10 15 20 25 30 35 Figure 1.8 Fucus distichus. Relationship between log fertile area and plant size for each season. Chapter 1 Reproduction and Recruitment p. 46 CNI E o < LU < Ld on Ld Li_ O O 3.5 n 2.5 1.5-0.5-- 0 . 5 -- 1 . 5 0 o Oct-Nov 85 A Dec 85-Feb 86 • Mar-May 86 v Sep-Oct 86 o Dec 86-Feb 87 • Sep-Nov 87, Oct 88 Y = -0.014 + 0.076X 2 = 0.37 n = 236 P < 0.001 10 15 20 25 30 35 SIZE ( c m ) Figure 1.9 Fucus distichus. Relationship between log fertile area and plant size for pooled data from all seasons except summers, 1986, 1987, and spring, 1987. Chapter 1 Reproduction and Recruitment p.47 CO LU < 3.51 • L 2.5^ LU^ o o §3i .5H O o o NOV 85 • OCT 86 * MAR 86 o JAN 87 Y = 1.07 + 0.36X - 0.03X-r 2 = 0.63 n = 70 P < 0.001 2 3 4 5 6 7 8 FERTILE AREA ( c m 2 ) Figure 1.10 Fucus distichus. Relationship between log number of conceptacles and area of receptacles for pooled data from Nov 85, Mar 86, Oct 86, and Jan 87. Chapter 1 Reproduction and Recruitment p.48 o NOV 85 * OCT 86 FERTILE AREA ( c m 2 ) Figure 1.11 Fucus distichus. Relationship between mean number of eggs (+ S.E.) and area of receptacle for pooled data from Nov 85, Mar 86, Oct 86, and Jan 87. Each data point represents mean number of eggs from 5 conceptacles multiplied by the number of conceptacles in each receptacle. Chapter 1 Reproduction and Recruitment p.49 CO o o LU LL_ ^ OCM 2 6 i 22 18 14 10 6-j 2 LU m ID § m CM - 2 O O 5n 4 3 2 1 0-I -1 B POTENTIAL PRODUCTION ~i 1 r ESTIMATED PRODUCTION J A O D F A J A O D F A J A O D 1985 1986 1987 T I M E Figure 1.12 Fucus distichus. Potential and estimated number of eggs produced per 25 cm2 of Fucus zone every month, With maximum and minimum 95% confidence limits of the estimates. See text for more details on how the calculations were made. Chapter 1 Reproduction and Recruitment p.50 CM m (j CM o m w t: ZD O UJ or o m o CO o 600-n — ° Microrecruits • — • Macrorecruits • p a r 1 2 CM E HO o in CM I-8 A 0 D F A J A O D F A J A O 1985 1986 1987 TIME 6 = -4 CO hz ZD 01 CJ LU a : o cr: o < CO !< on Q < ZD a LU z < cr: LU CL Figure 1.13 Fucus distichus. Monthly mean number of microrecruits (+ S.E.) counted on 25 cm2 settling blocks and monthly mean number of macrorecruits (+ S.E.) recorded per 25 cm2 of permanent quadrats. CHAPTER 2 V p. 51 Age- and Size-Dependent Growth and Mortality in a Population of Fucus distichus L. emend. Powell INTRODUCTION The use of an appropriate state variable to describe demographic parameters such as growth, mortality, reproduction, and recruitment, is of fundamental importance in understanding the dynamics of a population (Caswell 1989). Because of the plastic morphology of many clonal organisms, e.g. scleractinian corals and bryozoans, and modular characters of higher plants, demographic theories and concepts developed based on solitary individuals and using age as a state variable are often inadequate when applied to them. (e.g. Hughes 1984, Hughes and Jackson 1985). Demographic parameters of these organisms are more often size-related, rather than age-related. Size can therefore more accurately predict the fate of these organisms than age (Harper 1977, Hughes 1984, Hughes and Jackson 1985, Caswell 1989). Many algae exhibit modular construction similar to that of higher plants. Although the population ecology of many algae has been examined, the question on the appropriateness of any state variable used to describe algal demographic parameters is seldom addressed. Many algal population studies are concerned with seasonal changes in plant size and growth rate (Kaliaperumal and Kalimuthu 1976, Mathieson et al. 1976, Niemeck and Mathieson 1976, Chennubhotla et al. 1978, Lobban 1978, Kain 1979, Dion and Delipine 1983, Sideman and Mathieson 1983, Thorn 1983, De Wreede 1984, Keser and Larson 1984, Ang 1985a, Klein 1987, Nelson 1989, van Tussenbroek 1989). Size has been expressed in terms of length (Sideman and Mathieson 1983, Ang 1985a, Klein 1987, Nelson 1989), area of the thallus (Kain 1976a, 1976b), volume (Gunnill 1985), biomass wet weight (Kain 1976a, 1976b, van Tussenbroek 1989), dry Chapter 2 Growth and Mortality p.52 weight (Sheppard et al. 1978, Nelson 1989), percent cover (Keser and Larson 1984) or other parameters unique to the species or population [e.g. bushiness in Gelidiella acerosa (Forskal) Feldmann et Hamel (Thomas et al. 1975), number of dichotomies in Chondrus crispus Stackhouse (Pringle and Semple 1988), or number of nodes on the fronds of Macrocystispyrifera (L.) C.Ag. (van Tussenbroek 1989)]. Growth is usually expressed in absolute terms as a change in size over a fixed time period. It can also be expressed in relative terms as a change in size with respect to the initial size of the individual per unit time (Bird and McLachlan 1976, Kain 1976a, 1976b, 1987). Studies that deal with survivorship (or mortality) in algae are relatively fewer. Survivorship has been evaluated with respect to age, i.e., in a depletion curve (e.g. Chapman 1984a, Dayton et al. 1984) or in a life table analysis (e.g. Gunnill 1980a, Coyer and Zaugg-Haglund 1982, Dayton et al. 1984). More rarely, it has also been assessed with respect to frond size (e.g. Bhattacharya 1985). The different variables used in algal population studies, such as age, length, wet weight, and dry weight, may all be important parameter descriptors. However, destructive sampling is necessary in order to obtain information about most of them. Individual plants have to be sacrificed in a destructive sampling. This reduces the sample size and changes the structure of the population under study. "Destructive" variables such as weight and volume are thus limited in their utility as descriptors of demographic parameters. However, many of these variables are inter-related. For example, Gunnill (1985) found damp weight (fresh weight) of Pelvetia fastigiata (J. Ag.) de Toni to be strongly and positively related to dry weight, length and displacement volumes. Cheshire and Hallam (1989), citing Cheshire (1985), mentioned a highly significant allometric relationship between stipe circumference and palm thickness in Durvillaea potatorum (La Billardiere) Areschoug. De Wreede (1984) and Hymanson et al. (1990) found stipe length of Pterygophora californica Ruprecht to be Chapter 2 Growth and Mortality p.53 significantly correlated with age, though the relationship is also site-dependent. Hence, it may be possible to make use of the "non-destructive" or "less-destructive" variables like age, length and area to assess population change. Plant age can be assessed by following plants through time (Dayton, et al. 1984), although this is a tedious process. Other methods of age determination, such as counting growth rings, are destructive (De Wreede 1984, Hymanson et al. 1990). Area may be a better measure of frond size, e.g. in Laminaria hyperborea (Gunn.) Fosl. (Kain 1976a), but accurate measurement of area in situ is unlikely to be possible given the morphology of most algae. Thallus length (or width) appears to be logistically the simplest non-destructive way to measure a plant. In Chapter 1, plant length was found to be a better predictor of reproductive events than plant age in a population of Fucus distichus L. emend. Powell. This was also the conclusion by Chapman (1986b) for Laminaria longicruris Pyle. Chapman (1984a) found survivorship to be significantly affected by initial plant size in L. longicruris but not in L. digitata (Huds.) Lamour. In a subsequent study on L. longicruris, however, Chapman (1986b) found that within age classes, size was not related to survivorship, and only within one size class (301-400 cm length) was survivorship significantly affected by age. In another population of L. longicruris, Smith (1985) found no relationship between plant size and survivorship among plants > 50 cm long. Black (1974) found a positive relationship between growth rate and initial length in Egregia laevigata (Setchell). Sheppard et al. (1978) mentioned the positive relationship between age and growth in L. hyperborea and L. ochroleuca Pyl., but it is not clear how they estimated plant age or determined the growth-age relationship. In this chapter, seasonal patterns of change in plant age structure and plant length of Fucus distichus are presented. Growth rate and mortality (survivorship) are then evaluated with respect to plant age and plant length using correlation and log linear Chapter 2 Growth and Mortality p.54 analyses and analysis of simple, multiple and partial association to assess which of the state variables is a better descriptor of these parameters. MATERIALS AND METHODS Age, Size (Length), and Absolute Growth Rates Three 50 x 50 cm permanent quadrats were randomly set up in the Fucus zone. All plants within each quadrat were mapped monthly, and thus aged, from July 1985 to November 1987 (except August 1985 and November 1986) as described in Chapter 1. A plant was designated as age 1 at the time when it first appeared in the quadrat. Monthly mean frequency (%) distribution of age classes was calculated based on the number of plants in each monthly age class over the total number of plants of known age in each quadrat. Linear sizes of these plants were measured to the closest mm from the base of the holdfast to the tip of the longest branch. Mean frequency (%) size class distribution was then calculated based on the number of plants in each size class over the total number of plants in each quadrat. Size classes were designated as follow: size class 1 included plants < 1 cm long; size class 2, > 1 to < 2.5 cm; size class 3, > 2.5 to < 4.5 cm; size class 4, > 4.5 to < 9.5 cm; and size class 5 included plants > 9.5 cm long. Growth of individuals was monitored by changes in plant length. Detailed length measurements were recorded only for plants > 1 cm. Absolute growth rate (AGR) was calculated as an increase (or decrease) in length over a time period (usually one month) using the equation: (L*2 "  Lti) AGR = ( h - h ) where L f i is the length of the plant at time 1 (tj), and Lt2 is the length of the plant at time 2 (t2). For comparison purposes, any decrease in plant length over time due to Chapter 2 Growth and Mortality p.55 attrition or degeneration (die back) is referred to as negative growth, so values of AGR can be positive or negative. Mortality and Survivorship The fate of each individual was monitored based on monthly mappings. Any individual that disappeared from the permanent quadrats was considered dead. Mortality was measured as a percentage of plants lost over time (usually one month) by the equation: (N,2 - N„) M = * 100 where M is the percent mortality, Ntl is the number of plants per quadrat at time 1 and N r 2, the remaining number of plants per quadrat at time 2, excluding the new recruits. Percent survivorship (S) is given as: S = 100% - M . All plants, including those < 1 cm in length were monitored in the mortality study. The minimal detectable size was around 1 mm. Plants that were first detected in each quadrat in each month were considered as new recruits (see Chapter 1) and each set of new recruits was monitored as a monthly cohort. When permanent quadrats were first set up in July 1985, a set of plants < 1 cm long was present. This set of plants was included in the analysis as a monthly cohort. It is not known how many of these plants were actually new recruits for July 1985. Thus, this cohort included all plants that recruited on or before July 1985 and were < 1 cm at the time of sampling. Quadrats were not checked in August 1985, so plants that were Chapter 2 Growth and Mortality p.56 recorded as new in September 1985 actually represented individuals that recruited in either August or September. Age vs. Size as the Descriptor (Predictor) of Growth and Mortality Growth rates were correlated separately with plant age and size from each quadrat at each month of the monitoring period from September 1985 to October 1987. Furthermore, as in Chapter 1, log linear analyses and simple, multiple and partial associations were used to evaluate age versus size as a predictor of absolute growth rate and of mortality. Log linear analysis evaluates qualitatively, and association analysis quantitatively, the contribution of age versus size to the knowledge of growth rates and mortality. More details about these two methods are described in Chapter 1 and in Caswell (1989). For purposes of these evaluations, only plants of known age were used. To minimize the number of sparse cells in the contingency table, plants of different ages were grouped into the following age classes: age class 1 for plants 1 to 2 months old; age class 2, 3 to 4 months old; age class 3, 5 to 6 months old; age class 4, 7 to 9 months old; and age class 5 for plants > 9 months old. Likewise, these plants were grouped into the different size classes designated earlier. Based on absolute growth rates, plants were also divided into 4 categories: plants that died were given a growth rate of -100 cm/month, a rate that no plant could actually attain, and grouped as AGR 1; AGR 2 for plants with a growth rate > -100 to < 0 cm/month; AGR 3, > 0 to 2 cm/month; and AGR 4 for plants with a growth rate > 2 cm/month. In addition, plants were classified into 2 groups, those that died and those that survived. The range of categories used to partition plants with different growth rates were obtained based on the distribution of data points in growth vs. length and growth vs. Chapter 2 Growth and Mortality p.57 age scatter plots. Further division of the categories into smaller ranges resulted in more than 20% of cells in the contingency tables having a value less than 5. To evaluate the effect of age versus size on growth rates, size class 1 and age class 1 were not included in the analyses. Plants of age class 1 (1 to 2 months old) were usually < 1 cm long. Their length was not recorded in detail, hence information on their growth rates was not available. Although these plants may have experienced a high mortality rate, because they were mostly < 1 cm long, their exclusion should not affect the analyses on age- or size-dependence. AGR 1 was included in the evaluation of the respective effects of age versus size on mortality. Statistical Analyses Data were first tested for normality (Lilliefor's test) and homogeneity of variances (Barlett's test) before application of parametric statistical analyses. If necessary, data were transformed to meet the parametric assumptions. Distribution free statistics were used if data transformation was unsuccessful. Pearson's linear correlation or Spearman rank-order correlation were used to relate the patterns of change in length, growth rate and mortality among cohorts, time, age and size classes. Analysis of covariance (ANCOVA) was used to evaluate the effect of time on the survivorship of plants of each cohort. All analyses were performed using SYSTAT (Wilkinson 1988). RESULTS Overall Seasonal Trend Mean length and growth rate of the Fucus population at False Creek were negatively correlated (Spearman rank-order correlation, ry=-0.453, P< 0.001, n=74). Largest plants were initially recorded in summer 1985. Mean length subsequently declined from fall-winter 1985-86 to level off in the summer of 1986, then increased through winter Chapter 2 Growth and Mortality p.58 1986 and declined again in the summer of 1987 (Fig. 2.1). Mean growth rate showed an opposite trend, with higher growth rates in the spring and summer and lower growth rates in the fall and winter (Fig. 2,1). Age Distribution, Length and Growth For all months, mean frequency (%) of age distribution for plants of known age in the permanent quadrats was highly skewed, with most of the plants in the younger age classes (Fig. 2.2). Age class distributions presented for November 1985 through July 1986 did not represent the true age structure of all the plants within the quadrats. Ages of the plants which were already present at the beginning of sampling in July 1985, and which survived through this period, were not known. Nevertheless, recruits of < 1 cm in size (« 1 month old) were usually the most numerous among the total number of plants (see the section on size class distribution below), hence the true age class distributions of all the plants within the quadrats during this period were most likely to be highly skewed as well. For each monthly cohort, plant length generally increased with plant age (Table 2.1, Spearman rank-order correlation between age and length) but the increase was not monotonic (Fig. 2.3). At any one time, the longest plants were not necessarily the oldest ones. The pattern of change in mean growth rate among cohorts was less consistent over time (Fig. 2.3). Cohorts from April to July 1986 tended to show a negative correlation, and those from other months a positive correlation, between plant age and growth rate (Table 2.1). This means that compared to older plants, younger plants tended to show higher growth rates between late spring and early summer of 1986 and lower growth rates during other times. It is not known if this pattern holds for monthly cohorts initiated beyond May 1987 and through the summer months of 1987. Monitoring of the quadrats were terminated in November 1987, hence Chapter 2 Growth and Mortality p.59 insufficient data were available about these cohorts to provide a meaningful analysis of the pattern observed. Plants of the same age differed in their mean length at different times (Fig. 2.4). The mean length of 3 to 7 months old plants was longer between summer and fall of 1986, shorter between winter and spring of 1987, and became longer again in the fall of 1987. Patterns for plants > 8 months old were more irregular. A decrease in plant length was usually preceded by a decrease in growth rates (Fig. 2.4). However, most plants did not exhibit any consistent pattern of change in their growth rates over time. Size Class Distribution, Age and Growth Mean monthly size class distribution of the plants of known age was monitored from the time they were first detected in the permanent quadrats. Early on, only young and small plants were of known age. This explains the high proportion of plants in size class 1 up to July 1986 (Fig. 2.5). By August 1986, more than 90% of the plants in the quadrats were of known age. The pattern of distribution from August 1986 onward is therefore a better representation of the actual frequency distribution of the population. Except for the last 2 months of the monitoring, plants in size class 1 were consistently the most numerous, ranging from 40 to 60% of the total population (Fig. 2.5). For plants > 1 cm, monthly data from 61.5% (40 out of 65) of the quadrats showed a significant positive correlation between plant length and growth rate (Table 2.2), suggesting that growth rate is largely size-dependent. This is further shown in cohort data, with 63.8% (37 out of 58) of the cohorts showing a positive correlation between plant length and growth rate (Table 2.3). Mean monthly plant length within the different size classes showed considerable variation (Fig. 2.6). This was especially so in size class 5. Given that this size class Chapter 2 Growth and Mortality p. 60 included plants in a wider range of sizes, a wider range of variation of monthly mean plant length was expected. Within this size class, plants were longer during summer and shorter between fall and winter. This pattern was not consistent in other size classes, although a decrease in plant length was mainly associated with late spring and summer months. Plants in the larger size classes were generally older than those in the smaller size classes, although there were considerable overlaps of mean plant ages among them (Fig. 2.6). The presence of younger plants in size classes 2 to 4 early on was partly an artifact of sampling, where only the younger plants were of known ages. The increase in the mean plant age in all size classes starting in October 1986 was related to the degeneration (negative growth) of terminal branches among older and larger plants (cf. Figs. 2.6 and 2.7). The subsequent loss of these plants in different size classes at different times caused the decline in the mean plant age (see section on mortality below). Mean growth rates were generally lower during winter and higher during summer (Fig. 2.7). This trend was less distinct in size class 4 where lower growth rates were also recorded in the summer months of 1987. Plants in size class 5 experienced negative growth rates in summer, and higher positive growth rates in spring and fall. Patterns of change in mean plant length over time were generally not significantly correlated with those of mean age and growth rates within each size class (Spearman rank-order correlation, rs > 0.05). Mortality and Survivorship The survivorship of different monthly cohorts from July 1985 to October 1986, when expressed in a log scale, generally assumes a straight line. This suggests a constant rate of survivorship among these cohorts over time. However, mortality frequently Chapter 2 Growth and Mortality p.61 increased when the plants became older (Fig. 2.8). Results of the ANCOVA (Table 2.4A) indicate that not all survivorship curves have the same slope, i.e., not all cohorts have the same survival rate over time. Cohorts of July, September, and October 1985, and of January and February of 1986 do not differ significantly in their survival rate (Table 2.4B). Calculated from a regression line on pooled data, these cohorts have a survival rate of 89% per month (Linear regression Log Y = 1.831 - 0.050X, 1^ =0.535, /><0.001, n=218). Monthly cohorts of March to June 1986 can also be pooled (Table 2.4C) and show a survival rate at 81% per month (Linear regression Log Y = 2.654 - 0.092X, r^O.874, P<0.001, n=196). Cohorts of November and December 1985, which have very short life span (< 12 months) are grouped with cohorts of June 1986 to May of 1987 (Table 2.4D). These latter cohorts were not followed to the end of their life span. The resulting regression line from the pooled data indicates a high survival rate of 91.6% per month (Linear regression Log Y = 1.957 -0.038X, 1^ =0.193, i><0.001, n=367). However, although the regression is significant, it accounts for only 20% of the variation within the pooled data. Ages of plants that either died or survived in each month were significantly different among the 3 quadrats (Kruskal-Wallis One Way ANOVA by Rank, P<0.05). Based on mean values for each quadrat (Fig. 2.9A), results from paired Mests indicate that the mean age of plants that survived was significantly different from the mean age of those that died (r=-2.128, df=65, P=0.037). This is mainly because plants that died from May to August 1987 were significantly older than those that survived (Mest, r=2.842, df=22, P=0.009). Lengths of plants that either died or survived in each month were not significantly different among quadrats (Kruskal-Wallis One Way ANOVA by Rank, P>0.05). Monthly data from the 3 quadrats were therefore pooled. Over the whole sampling period (Fig. 2.9B), the mean length of plants that survived was not significantly Chapter 2 Growth and Mortality p.62 different from that of those that died (paired Mest, t=0.757, df=22, P=0.457). However, on a month to month basis, the difference was significant (Mann-Whitney U test, P<0.05) in February, April, June, and September 1986 to January 1987 where plants that died were smaller than those that survived, and from May to June 1987, where larger plants were the ones that died. Plants 1 month old generally suffered greater mortality («40%) than older plants (Fig. 2.10), although plants > 9 months old occasionally had mortality exceeding 80%. There was an increase in mortality among plants 1 to 4 months old between fall 1986 and winter of 1986-87. If examined by seasons (Fig. 2.11), some of the older plants (> 9 months) suffered very high mortality in summer and fall (up to 100%), much higher than that experienced by younger plants. In the winter and spring of 1987, younger plants appeared to suffer greater mortality than did the older plants. However, the patterns observed for 1986 were not similar to those observed for 1987, suggesting significant interannual variation in mortality among plants of different ages. When grouped by size, plants in size class 1 (< 1 cm long) generally exhibited a greater mortality («40%) than those in other size classes (Fig. 2.12). However, plants in other size classes suffered higher than 40% mortality at times. The overall patterns were similar only between plants in size classes 2 and 3, and in size classes 3 and 5 (Spearman rank-order correlation, P<0.05 for both tests). Mortality was generally higher (40 - 60%) for size class 1 in most seasons except summer when mortality in size classes 3 to 5 could be as high as 60 to 70% (Fig. 2.13). Log Linear and Association Analyses on Age vs. Size as the Descriptor of Growth and Mortality Growth and mortality rates were significantly different among plants from different quadrats at different times of the year (Kruskal-Wallis One-way ANOVA by Rank, Chapter 2 Growth and Mortality p.63 P<0.05). If all the plants monitored are considered, irrespective of seasonality and their spatial location among quadrats, results of log linear analyses (Table 2.5) indicate a highly significant effect of age and/or size (as length) on growth, with or without the effect of mortality. The effects of age or size may be taken together (age x size x growth) or considered alone (age x growth or size x growth), or the effect of age on growth may be evaluated given the known contribution of size (age x growth/ size) or vice versa (size x growth/ age). Similarly, the effect of age and/or size on mortality is also highly significant except in the case where the effect of age on mortality is evaluated given the known contribution of size (Table 2.5C). When data were pooled to reflect seasonality and differences among plants in each quadrat, the effect of size on growth with or without the effect of mortality, and on mortality alone, is significant in a greater number of cases than is the effect of age. This is true either when size or age is considered alone, or when the contribution of age or size respectively is known. Detailed results of these analyses are given in Appendix A. Association analyses indicate that on average among the 3 quadrats, size is more important than age by 9.3% (± 4.1% S.E.) as a predictor of growth when the effect of mortality is considered, and by 24.0% (± 8.9%) without the effect of mortality (Fig. 2.14). Size is also a better predictor of mortality than age by 12.7% (+ 4.7%) (Fig. 2.14). Based on pooled seasonal data from each quadrat, there are a few cases when age is more important than size as a descriptor of growth or mortality. However, no consistent pattern is present to indicate any seasonal trend. Detailed results of association analyses on seasonal data are also given in Appendix A. DISCUSSION For the population of Fucus distichus at False Creek, the decrease in plant mean length from fall-winter 1985-86 to summer 1986 suggests either an increase in the Chapter 2 Growth and Mortality p.64 number of smaller plants or a greater loss of larger plants or both at this time. The significant increase in the number of recruits in the quadrats between March and July 1986 (see Chapter 1, Fig. 1.13) may explain the decrease in the mean length of the population during this same period. However, there was no corresponding increase in the number of recruits in the second summer, i.e., between July and September of 1987, but the population still experienced a decrease in mean length. Plants that died between fall and early winter of 1986 were smaller, but between late spring and summer of 1987 were larger, than those that survived (see Figs. 2.9 and 2.13). Thus, changes in the mean length of the population from October (1986) to the end of the monitoring period in November (1987) could be explained by the variation in survival of different sizes of plants. While the increase in the number of recruits may account for the decrease in the mean size of the population in the spring and summer of 1986, mortality of the larger plants contributed to this decline as well. Seasonal patterns of change in the growth rate of the Fucus population from False Creek are comparable to those reported for Fucus distichus L. edentatus (Pyl.) Powell (Sideman and Mathieson 1983) and F. vesiculosus L. var. spiralis Farl. (Keser and Larson 1984) from the northeastern coast of the United States. However, the maximum absolute growth rate of 1.4 cm/month in September 1987, is much lower than that reported for other Fucus species, e.g. 2.5-4.0 cm/month for F. distichus edentatus from Maine (Keser and Larson 1984), 3.5 cm/month for the same species from New England (Sideman and Mathieson 1983), 4 to 6.0 cm/month for F. vesiculosus var. spiralis from Maine (Keser and Larson 1984), 3.5 cm/month for F. vesiculosus from New Hampshire and Maine (Mathieson et al. 1976), and 1.9 to 2.8 cm/month for F. spiralis L. from New Hampshire (Niemeck and Mathieson 1976). The generally lower mean maximum and minimum growth rates recorded for the population that I observed, compared to other published data, may be due to different Chapter 2 Growth and Mortality p.65 study techniques. All the plants in my quadrats were mapped and sizes of the plants > 1 cm were measured in detail. Growth rates were then calculated based on changes in the length of all plants measured. In some other studies, growth rates were calculated based on plants randomly or haphazardly selected and tagged. Changes in the sizes of the tagged plants were then monitored over time. New plants were tagged from time to time depending on the loss rate of the tags. Assuming that the plants randomly tagged truly represent the size variation within the population, monitoring of plants tagged at one or a few times alone would result in missing newly recruited (younger and smaller) plants, unless recruitment is strongly seasonal. If these young plants have significantly different growth rates than those of the older or larger tagged plants, then results from monitoring the tagged plants alone would be very different from results that included the young plants. Comparing my study with that by Sideman and Mathieson (1983) where only plants 1 year or older (and > 10 cm) were tagged and monitored, the maximum growth rate of 3.5 cm/month that they reported for Fucus distichus ssp. edentatus is comparable to that of my plants in size classes 4 and 5 at 2.9 and 3.2 cm/month, respectively. Inclusion of plants from size classes 2 and 3, which have lower growth rates, lowers the overall mean growth rate calculated for the population in False Creek. It seems obvious that changes in the size structure of a plant population can be inferred from an understanding of the growth dynamics of the individuals. The failure to include smaller plants in growth rate studies could result in an under or over-estimation of the growth dynamics and hence, the dynamics of the population size structure. How serious this under or overestimation may be will depend on how dominant these smaller plants are and how different their growth patterns are from the larger plants. From my observations, some Fucus plants may be lost altogether between sampling periods. Among other plants, terminal branches that formed receptacles became Chapter 2 Growth and Mortality p.66 necrotic after shedding of eggs. Thus, plants could experience an initial decrease in size due to the decay of the reproductive terminal branches but could eventually increase in size when branches that did not form receptacles continued to grow. This process was also observed by Knight and Parker (1950) for Fucus vesiculosus. If receptacles were formed on all terminal branches, then the whole plant eventually decayed. The whole plant may also be torn, leaving a small stump or holdfast which eventually disappeared. Regeneration from the stump or holdfast was not observed in F. distichus except in very young plants. Reduction in size due to necrosis of terminal branches was the main reason for the negative growth recorded for plants in all size classes in the fall and winter of 1986. The loss of whole plants, leaving small stumps or holdfasts, explains the negative growth exhibited by plants in size class 5 in the summers of 1986 and 1987 (Fig. 2.7). Most studies on fucoids did not show any negative mean growth in their populations, except perhaps for Keser and Larson (1984) for Fucus vesiculosus and Gunnill (1985) for Pelvetia fastigiata. In some of these studies, it is possible that tags on plants with significant tissue erosion were lost, such that these plants were recorded (in error) as dead (or lost) rather than as exhibited a negative growth. However, it is also possible that most of these fucoid populations may not have experienced extensive erosion or attrition of individual thalli. Because of the modular character of fucoid plants, non-reproductive and reproductive terminal branches within the same plant could have different growth patterns. While the longest terminal branches are usually reproductive, formation of receptacles eventually terminates growth in these branches. Non-reproductive branches could then grow over time to become the longest branch(es) before any die back of the older reproductive branches sets in. In that case, any decrease in plant length will not be detected. The absence of any negative growth, therefore, could indicate a fast turnover of longest terminal branches and thus, an Chapter 2 Growth and Mortality p.67 increase in the reproductive potential of the plant as terminal branches eventually become reproductive. The few cases of significant correlations between age and growth and variations in growth rate associated especially with older plants strongly suggest that growth rate is only occasionally age-dependent. Such variations also explain the more consistent seasonal pattern of change in growth rate discernable only among plants < 8 months old. While seasonal patterns of mean plant length and mean growth rate are negatively correlated (Fig. 2.1), within each month or each cohort, patterns of plant length and absolute growth are mainly positively correlated (Tables 2.2 and 2.3). This suggests that while growth rate is very often size-dependent, it is also season-dependent. A seasonal pattern becomes more obvious only when plants are grouped by size rather than by age. Similar results were obtained if growth rate was expressed in relative terms with respect to initial plant length. The skewed age structure observed in the Fucus population from False Creek is similar to that observed for some populations of Laminaria hyperborea (Kain 1963), L. setchellii Silva (Dayton et al. 1984) and Ascophyllum nodosum (L.) Le Jolis (Keser et al. 1981). Other populations of L. hyperborea and/4, nodosum, however, showed a bimodal age structure (Kain 1963, Keser et al. 1981). A unimodal, approximately normal distribution of age structure has been reported for other algal populations, e.g., Pterygophora californica (Dayton et al. 1984, De Wreede 1984). Skewed age structure appears to be typical of dense, all-aged population (Cousens 1985) and its maintenance throughout the year in the False Creek population is probably a result of the continuous influx of new recruits. It is also a result of the near constant rate of mortality among the recruited plants (Fig. 2.8). Chapter 2 Growth and Mortality p.68 The critical stage for survival in many algae is probably the microscopic germling or sporeling stage (Chapman 1984a, Reed 1990a, see also Chapter 4). Once recruits become large enough to be visible, the risk of mortality becomes less. This appears to be typical of many perennial populations. Populations of Pelvetia fastigiata (Gunnill 1980a), Laminaria digitata (Chapman 1984a), L. longicruris (Chapman 1984a, 1986b), and Chondrus crispus (Bhattacharya 1985) all showed such a pattern. Some variations do exist. De Wreede (1986) found age-specific survivorship of P. californica to be variable. One population that he monitored had a relatively constant age-specific survivorship, but in another population there was a greater mortality among younger plants. Annuals such as Leathesia difformis (L.) Areschoug showed a high survivorship for younger plants and a high mortality for older plants (Chapman and Goudey 1983). For the False Creek population, the probability of mortality is not uniform for plants of the same age or size at different times of the year. Seasonal effects appear to outweigh the effect of age and/or size such that greater risk of mortality was experienced by older and larger plants in summer but not in winter and spring. Only older, but not necessarily larger, plants suffered greater mortality in the fall. During summer, long exposure at daytime low tide is likely to be one of the main causes of mortality for the bigger plants. Smaller plants are covered and hence possibly protected by the canopy. Fucus plants do not usually die abruptly and disappear from the population. The whole thallus may be torn away but it usually takes 1 to 2 months for the remaining stump or holdfast to be eroded and lost. In the fall, older and dying plants first became much smaller before being considered as dead (lost). This explains the apparent discrepancy observed, i.e., the greater probability of mortality for older, but not necessarily the larger, plants during this time. If plants which had lost a considerable part of their thallus were considered as dead, then the mortality rate of the larger plants in the fall would have been much higher. Chapter 2 Growth and Mortality p . 6 9 During winter, low tide occurs at night. In contrast to what was observed in summer, the retention of moisture under the overlying canopy appeared to cause softening of the tissues of understory plants and their eventual decay. This scenario is analogous to decay of fallen leaves, where those at the bottom tend to be moist and to decay first. This decay may be facilitated by detritus feeders and grazers like amphipods and littorines. In this sense, it may be speculated that herbivory also contributed to the higher mortality of the smaller plants. Crowding (Black 1 9 7 4 ) may also affect mortality. Because all the plants monitored in my study were in the same permanent quadrats, density effects experienced by plants of different age or size classes should be comparable. There may be compounding effect of crowding on age- or size-specific mortality, e.g. shading of light or alteration of water flow pattern. The effect of density on the population is treated in greater detail in Chapter 4 . Because tips of Fucus plants could be eroded and growth of understory plants may be suppressed by the canopy, the relationship between age and length is not always a positive or a direct one. Although in most cases the correlation between these two variables is positive and significant, variation in this relationship is indicated by the relatively low correlation coefficients ( r y < 0 . 7 ) . Such variation was also observed by Gunnill ( 1 9 8 5 ) for the population of Pelvetia fastigiata, and Keser and Larson ( 1 9 8 4 ) for Fucus spp. Given that a significant correlation exists between age and length, it is not surprising to find that both these state variables are significant as predictors of growth and mortality, as indicated by the log linear analysis. However, it is interesting to note that age is not significant as a predictor of mortality when the contribution of size (length) is known. Furthermore, size is consistently shown to be more important than age as a predictor for both parameters in the association analyses. This clearly indicates that both growth and mortality are more size-dependent than age-dependent. Given that Chapter 2 Growth and Mortality p.70 plant length is also significantly related to reproduction (Chapter 1) and plant biomass (Chapter 3), the use of plant length as a state variable is definitely more desirable than the use of age in demographic analyses of the Fucus population from False Creek. However, it is still premature to make a generalization about the importance of plant length in other algal populations. Other size parameters, such as width and biomass, may be used as state variables. Evaluation of the relative significance of these size parameters as well as age versus size as a state variable should be carried out in future algal population ecological studies to ascertain the appropriateness of the state variable employed. Chapter 2 Growth and Mortality p.71 Table 2.1 Fucus distichus. Matrix of Spearman rank-order correlation coefficients between age and growth rate (AGR), and age and length in different cohorts in each quadrat (Q). n = sample size. Cohorts Q n AGR Length Cohorts Q n AGR Length Sep 85 1 123 0.357* 0.817* 2 71 0.574* 0.762* Oct 85 1 9 0.783* 0.937* 2 41 -0.267 0.554* 3 151 0.020 0.549* Nov 85 1 30 0.496* 0.832* 2 62 0.252* 0.761* 3 41 -0.156 0.743* Dec 85 1 29 0.412* 0.887* 2 57 0.166 0.757* Jan 86 1 31 0.070 0.966* 2 70 0.086 0.684* 3 13 -0.361 0.588* Feb 86 1 39 -0.049 0.628* 2 239 0.003 0.606* 3 49 0.172 0.355* Mar 86 1 194 0.077 0.703* 2 349 0.039 0.734* 3 122 0.203* 0.654* Apr 86 1 216 -0.149* 0.631* 2 185 -0.049 0.484* 3 62 0.025 0.660* May 86 1 229 -0.159* 0.630* 2 138 -0.053 0.585* 3 106 -0.233* 0.528* Jun 86 1 350 -0.125* 0.728* 2 134 -0.176* 0.466* 3 67 0.265* 0.709* Jul 86 1 331 0.047 0.406* 2 77 -0.103 0.410* 3 21 -0.526* 0.644* Aug 86 1 108 0.065 0.491* 2 65 0.278* 0.419* 3 14 0.135 0.768* Sep 86 1 49 0.504* 0.573* 2 46 0.114 0.543* 3 21 0.722* 0.742* Oct 86 1 38 0.646* 0.682* 2 23 0.516* 0.306 3 20 0.684* 0.879* Dec 86 1 46 0.197 0.406* 2 16 -0.099 0.258 3 11 0.159 0.348 Jan 87 1 69 0.039 0.414* 2 4 0.316 0.833 3 23 0.415* 0.734* Feb 87 1 118 0.241* 0.551* 2 9 0.375 0.491* 3 42 0.531* 0.704* Mar 87 1 42 0.307* 0.592* 2 33 0.532* 0.797* 3 24 0.395* 0.564* Apr 87 1 95 0.322* 0.552* 2 60 0.468* 0.591* 3 30 0.229 0.802* May 87 1 29 0.224 0.515* 2 44 0.026 0.759* 3 65 -0.028 0.504* *P < 0.05 Chapter 2 Growth and Mortality p.72 Table 2.2 Fucus distichus. Matrix of Spearman rank-order correlation coefficients between plant length and growth rate (AGR) per quadrat (Q) over different time periods, n = sample size. Time Q n AGR Time Q n AGR Dec 85 1 14 -0.369 Dec 86 1 143 0.254* 2 14 0.312 2 112 0.190* 3 52 0.075 Jan 86 1 19 0.097 Jan 87 1 102 0.392* 2 18 -0.046 2 79 0.340* 3 23 -0.383 3 49 0.011 Feb 86 1 20 -0.357 Feb 87 1 90 0.152 2 30 0.363* 2 63 0.185 3 23 0.427* 3 40 0.113 Mar 86 1 34 0.160 Mar 87 1 88 0.702* 2 49 0.025 2 54 0.656* 3 25 0.525* 3 43 0.512* Apr 86 1 36 0.134 Apr 87 1 119 0.582* 2 83 0.478* 2 52 0.688* 3 27 0.637* 3 44 0.374* May 86 1 82 0.341* May 87 1 104 0.290* 2 166 0.315* 2 45 0.309* 3 45 0.191 3 40 0.306 Jun 86 1 136 0.306* Jun 87 1 100 0.477* 2 196 0,379* 2 32 -0.104 3 42 0.121 3 35 0.246 Jul 86 1 97 0.405* Jul 87 1 78 -0.086 2 113 0.385* 2 37 0.060 3 50 0.171 3 36 0.310 Aug 86 1 179 0.425* Aug 87 1 80 0.519* 2 165 0.524* 2 50 0.205 3 58 0.388* 3 61 0.192 Sep 86 1 319 0.457* Sep 87 1 115 0.380* 2 172 0.505* 2 61 0.459* 3 63 0.555* 3 94 0.550* Oct 86 1 197 0.252* Oct 87 1 176 0.440* 2 134 0.299* 2 114 0.420* 3 59 0.326* 3 101 0.420* *P < 0.05 Chapter 2 Growth and Mortality p.73 Table 2.3 Fucus distichus. Matrix of Spearman rank-order correlation coefficients between plant length and growth rate (AGR) in different cohorts in each quadrat (Q). n = sample size. Cohorts Q n AGR Cohorts Q n AGR Sep 85 1 123 0.321* 2 71 0.518* Oct 85 1 9 0.711* 2 41 0.133 3 151 0.250* Nov 85 1 30 0.344 2 62 0.496* 3 41 0.135 Dec 85 1 29 0.430* 2 57 0.312* Jan 86 1 31 0.095 2 70 0.263* 3 13 0.077 Feb 86 1 39 0.369* 2 239 0.291* 3 49 0.111 Mar 86 1 194 0.190* 2 349 0.175* 3 122 0.264* Apr 86 1 - 216 0.089 2 185 0.400* 3 62 0.284* May 86 1 229 0.188* 2 138 0.257* 3 106 -0.077 Jun 86 1 350 0.142* 2 134 0.121 3 67 0.299* Jul 86 1 331 0.383* 2 77 0.116 3 21 -0.136 Aug 86 1 108 0.225* 2 65 0.254* 3 14 0.416 Sep 86 1 49 0.528* 2 46 -0.186 3 21 0.618* Oct 86 1 38 0.485* 2 23 0.086 3 20 0.576* Dec 86 1 46 0.175 2 16 -0.130 3 11 0.828* Jan 87 1 69 0.437* 2 4 0.632 3 23 0.503* Feb 87 1 118 0.262* 2 9 0.775* 3 42 0.465* Mar 87 1 42 0.400* 2 33 0.420* 3 24 0.130 Apr 87 1 95 0.418* 2 60 0.266* 3 30 0.254 May 87 1 29 0.247 2 44 0.255 3 65 0.281* *P < 0.05 Chapter 2 Growth and Mortality p.74 Table 2.4 Fucus distichus. Results of ANCOVA on the effect of time on the survivorship of plants of each cohort. The covariates are the cohorts listed in the table. Source of Variation df MS F P A. Al l monthly cohorts from July 1985 to May 1987 Time 1 35.476 696.05 < 0.001 Cohorts 23 1.090 21.38 < 0.001 Time x Cohorts 23 0.560 10.99 < 0.001 Error 811 0.051 B. Cohorts of July, September, October 1985, January, February 1986 Time 1 23.415 366.85 < 0.001 Cohorts 4 0.045 0.70 0.592 Time x Cohorts 4 0.151 2.37 0.054 Error 208 0.064 C. Monthly cohorts of March to June 1986 Time 1 44.389 1560.14 < 0.001 Cohorts 3 0.092 3.24 0.023 Time x Cohorts 3 0.035 1.24 0.295 Error 188 0.028 D. Monthly cohorts of November, December 1985, and June 1986 to May 1987 Time 1 37.914 950.59 < 0.001 Cohorts 11 0.450 11.28 < 0.001 Time x Cohorts 11 0.046 1.15 0.324 Error 343 0.040 Chapter 2 Growth and Mortality p.75 Table 2.5 Fucus distichus. Results of log linear analysis on the effect of age vs. size on growth, with or without the effect of mortality, and on mortality alone. See text for explanation of the models. Models df G P A. Age vs. size on growth with the effect of mortality Age x Size x Growth 27 94.04 < 0.0001 Age x Growth 9 250.28 < 0.0001 Size x Growth 9 940.06 < 0.0001 Age x Growth/ Size 9 189.30 < 0.0001 Size x Growth/ Age 9 879.08 < 0.0001 B. Age vs. size on growth without the effect of mortality Age x Size x Growth 18 54.04 < 0.0001 Age x Growth 6 230.20 < 0.0001 Size x Growth 6 900.48 < 0.0001 Age x Growth/ Size 6 194.50 < 0.0001 Size x Growth/ Age 6 864.78 < 0.0001 C. Effect of age vs. size on mortality Age x Size x Mortality 12 63.80 < 0.0001 Age x Mortality 3 76.68 < 0.0001 Size x Mortality 4 307.88 < 0.0001 Age x Mortality/ Size 3 5.62 0.1316 Size x Mortality/ Age 4 236.82 < 0.0001 Chapter 2 Growth and Mortality p.76 C o o UJ < O o 9; 7-o 5-X i 1— o 3-7 UJ 1 -1 - 1 • • — • MEAN LENGTH ± S.E. O — O MEAN GROWTH RATE ± S.E. \ \ •.T/V T •.t T . . . \ >, s°-o-oo-°o T T" T 1——i r J A O D F A J A O D F A J A O D 1985 1986 1987 TIME Figure 2.1 Fucus distichus. Seasonal patterns of change in mean (+ S.E.) plant length and absolute growth rates of the population from False Creek. Error bars < 0.4 cm (for length) or cm/month (for growth rate) not shown. Chapter 2 Growth and Mortality p.77 60 40 20 >3 60 Z UJ 4 0 O 20 or b_ 0 ^ 60 X NOV 85 DEC 85 JL 4 0 2 0 0 60 40 20 JAN 86 0 > 8 0 g 6 0 3 4 0 O UJ 2 0 or b_ 0 FEB 86 Daft. MAR 86 u5 60 4 0 2 0 0 APR 86 % - ~ ^ t -MAY86 JUN 86 Jlk JUL 86 AUG 86 L SEP 86 OCT 86 DEC 86 JAN 87 FEB 87 1Tr>TrfT>fV1 ^ MAR 87 APR 87 ttb MAY 87 JUN 87 JUL 87 "too* AUG 87 SEP 87 OCT 87 NOV 87 0 2 4 6 8 10 0 2 4 6 8 1 0 1 2 1 4 1 6 0 4 8 12 16 2 0 0 4 8 12 16 2 0 A G E ( MONTHS ) A G E ( MONTHS ) Figure 2.2 Fucus distichus. Monthly mean (+ S.E.) age structure of the population. Data are from means of three quadrats. Chapter 2 Growth and Mortality p.78 c o — E UJ C C o o 20, SEP 85 COHORT i 5 ] ; 10 5 0 -5 • •* • -5 15 12 9 6 3 0 -:3 OCT 85 COHORT 12, NOV 85 COHORT 9 6 3 nl • M ? -c o i> o 35 t=y 25 5 DEC 85 COHORT 6 4 2 0 -2 JAN 86 COHORT z § 15 iSo-15 jjj 1 5 , FEB 86 COHORT 2 12 Po 20- MAR 86 COHORT 15 10 5 12, APR 86 COHORT 9 6 3 0 -3 9 6 3 0 -3 •••••• ••»• X SNJMMJSNJMMJSN 1985 1986 1987 6 3 • 0 -3 2Q. MAY 86 COHORT 13 6 -1 - 8 -15 1 2 . JUN 86 COHORT 9 6 3 0 • - 3 i t JUL 86 COHORT .oo AUG 86 COHORT I • A J A O D F A J A O 1986 1987 T I M E OCT 86 COHORT 1 DEC 86 COHORT. g JAN 87 COHORT 6 / 1 5 FEB 87 COHORT 4 3 2 1 0 J 5, MAR 87 COHORT 4 3 2 1-0. 0 D F A J A 0 1986 1987 Figure 2.3 FMCWJ distichus. Patterns of change in mean (+ S.E.) length and growth rates of cohorts from the 3 permanent quadrats over time. Date in each graph indicates the time when the cohort was first detected in the population. Error bars < 2.0 cm or cm/month not shown. Chapter 2 Growth and Mortality p.79 12, AGE = 11 MONTHS 9 c o — E !> —' X z ^ ul o 2 o r . o 1$ 2 AGE = 4 MONTHS TP 0J{ - 1 -g AGE = 8 MONTHS 5 2 -1 17 • • • - 3 AGE =13 MONTHS -1 AGE = 5 MONTHS o°o° S N J M M J S N J M M J S N 1985 1986 1987 T I M E t. - 3 AGE = 9 MONTHS 8 5 2 -1 14, AGE = 10. MONTHS 11 8 5 2 -1 21 . AGE = 14 MONTHS 17 1 , ,>r. i * . . . - 6 i g , AGE > 14 MONTHS 14 9 4 J M M J S N J M M J S N J A O D F A J A O 1986 1987 1986 1987 T I M E T I M E Figure 2.4 Fucus distichus. Mean (± S.E.) length and growth rates of plants of the same age at different times during the monitoring period from September 1985 to November 1987. Error bars < 2.0 cm or cm/month not shown. Due to differences in the longevity of monthly cohorts, plants of all ages are not always present at all times. Chapter 2 Growth and Mortality p. 80 >-O z LU ZD O LU < LU 100 80-60-40-20-0 A - — A SC.1. ( < 1 cm ) • - - • SC 2 ( 1 - < 2.5 c m ) A - - A SC 3 ( 2.5 - < 4.5 cm o- • - o SC 4 ( 4.5 - < 9.5 cm SC 5 (..> 9.5 c m ) ATA A - A V \ i'\-M/t'^ l V _ A L ' J. A ft T 'v J i V-T T/\ 1 4 2-« • V " • ft'6""* A A A A 0 D F A J A 0 D F A. J A 0 D 1985 1986 1987 T I M E Figure 2.5 Fucus distichus. Mean frequency (% + S.E.) size class distribution of the plants of known age. Data are from mean values of the 3 permanent quadrats. Error bars < 2.5% not shown. Chapter 2 Growth and Mortality p.81 E u 2.5 2.0 1.5 SIZE CLASS 2 • I T T T • • • * T J & 9 4.5 7 4.0 5 3.5 3 3.0 1 2.5 SIZE CLASS 3 12 10 6 -g 4 E LU < SIZE CLASS 5 18 3 O D F A J A O D F A J A O 0 D F A J A 0 D F A J A 0 1985 19B6 1987 1985 1986 1987 T I M E 15 _ 12 r 9 . 6 3 Figure 2.6 Fucus distichus. Seasonal patterns of change in mean (+ S.E.) age and length of plants in different size classes. Data are from mean values of the 3 permanent quadrats. Error bars < 2.5 months or 0.04 cm not shown. Chapter 2 Growth and Mortality p. 82 1.5i _c c 1.0 o E •— 0.5 E 0 o -0.5 -UJ 1 LY. 5i T. 4-3 O LYL 2 1 Z 0 - U 0 SIZE CLASS 2 ?» 1 V 1 I I 1 2.5 2.0 1.5 1.0 0.5 0 —0.5 SIZE CLASS 4 5 2 -1 - 4 -71 - 10 SIZE CLASS 3 * i i i i SIZE CLASS 5 • - y 1985 1986 1987 1985 1986 T I M E 1987 Figure 2.7 Fucus distichus. Seasonal patterns of change in mean (+ S.E.) growth rate of plants in different size classes. Data are from mean values of the 3 permanent quadrats. Error bars < 0.25 cm/month not shown. if Chapter 2 Growth and Mortality p. 83 o o _J 2.0-j -^^  CL X CO en 1.0-o > > -cc ZD CO 0.0-\— z LU o or: -1.0-LU Q_ z iS J i n m m io m to co <5 co (ococo <o<o<o 00 CO 03 CD 00 CO CO »0 00 03 03 QQ CO 03 CD -i 1 1 — i 1 1 r T T — r 1985 1986 1987 TIME Figure 2.8 Fucus distichus. Mean survivorship curves (logjn) of different cohorts in the 3 permanent quadrats. Data for July 1985 included all plants < 1 cm which were present in July 1985. Error bars not shown. Chapter 2 Growth and Mortality p. 84 O D F A J A ' O D F A J A O 1985 1986 1987 T l M E Figure 2.9 Fucus distichus. A. Mean age of plants that survived and died during the monitoring period. Data are mean values for each permanent quadrat. Mean age of plants that survived (- ) or died (....) from the 3 quadrats are also given. Error bars not shown. B. Mean (+ S.E.) length of plants that survived and died during the same period. Data are from mean values of the 3 permanent quadrats. Error bars < 0.16 cm not shown. Chapter 2 Growth and Mortality p. 85 80 60 40 20 o 80 60 ^ 2 0 ^-^ 0 80 60 < h— 40 LY. O 20 AGE = 1 MONTH AGE = 6 MONTHS AGE = 2 MONTHS o 80 60 40 20 0 80 60 40 20 0 AGE = 3 MONTHS i * • AGE = 4 MONTHS AGE = 5 MONTHS V A O D F A J A O D F A J A O 1985 1986 1987 AGE = 11 MONTHS AGE = 7 MONTHS AGE - 8 MONTHS AGE =13 MONTHS AGE = 9 MONTHS AGE = 14 MONTHS in A1 AGE = 10 MONTHS AGE > 14 MONTHS V A O D F A J A O D F A J A O 1985 1986 1987 TIME A J A O D F A J A O 1986 1987 Figure 2.10 Fucus distichus. Mean probability of mortality (% ± S.E.) of plants of the same age over time. Data are from mean values of the permanent quadrats. Error bars < 8.5% not shown. Due to differences in the longevity of monthly cohorts, plants of all ages are not always present at all times. Chapter 2 Growth and Mortality p. 86 WINTER o — o DEC 85 A A JAN 86 • • FEB 1986 >-• < I— LY. O < 80 60 40 20 0 100 80 60-. 40 204 0 100 80 6 0 i 40 20 0 SPRING O O MAR A - A APR • • MAY 1 A V'<t> DVD A • •1 * b -• SUMMER o — o JUN A A JUL • • AUG • h / \f - " G j A A A T/ T/M : i i g • FALL o — o . SEP A A OCT A A T • 9 - 6 1 'M ' ? \ * A WINTER o — o DEC 86 A A JAN 87 • Q FEB 1 80 60 40 20 0 FALL o — o SEP A A OCT o. i o 7 9 11 -13>14 " -1 3 5 A G E ( M O N T H S ) ' 7 O O Q" 11 13 >14 Figure 2.11 Fucus distichus. Monthly mean probability of mortality (% + S.E.) of plants of different ages. Data are from mean values of the permanent quadrats. Error bars < 3.0% not shown. Chapter 2 Growth and Mortality p. 87 80 60 40 20 0 SIZE CLASS 1 80n i 60 i < 40 MO 20 z 0 iS 80i 60 40-20 0 A 0 D F A J A 0 D F A J AO SIZE CLASS 2 SIZE CLASS 3 T SIZE CLASS 4 • • 1 i . A A • SIZE CLASS 5 M 1985 1986 1987 1985 T I M E 1986 1987 Figure 2.12 Fucus distichus. Mean probability of mortality (% + S.E.) of plants from the same size class over time. Data are from mean values of the permanent quadrats. Error bars < 2.5% not shown. Chapter 2 Growth and Mortality p. 88 WINTER 1987 o — o DEC 86 A • • A JAN 87 D- - • FEB 4 5 SIZE CLASS Figure 2.13 Fucus distichus. Monthly mean probability of mortality (% + S.E.) of plants from different size classes. Data are from mean values of the permanent quadrats. Error bars < 3.0% not shown. Chapter 2 Growth and Mortality p. 89 LU O < to > Ld N CO • • _ l < h-LY. < CL O O 0.400 0.300 0.200 0.100 0.000 -0.100 -0.200 MEAN + S.E. ABSOLUTE GROWTH W/MORT W/0 MORT MORTALITY Figure 2.14 Fucus distichus. Mean (+ S.E.) ratio of log partial association coefficient (T) of size vs. age as a state variable in describing growth rates with or without the effect of mortality, and in describing mortality. Data are based on mean values for the permanent quadrats. A ratio > 0 indicates that size is more important than age as a predictor of the demographic parameter. p. 90 CHAPTER 3 Cost of Reproduction in Fucus distichus L. emend. Powell INTRODUCTION Reproductive effort is the amount of resources allocated to reproduction over a defined period of time (Begon et al. 1990). This is one of the central concepts in life history theory. There is, however, an unresolved controversy as to how this effort can be measured, especially in plants (Harper and Ogden 1970, Abrahamson and Gadgil 1973, Harper 1977, Bell 1980, Thompson and Steward 1981, Abrahamson and Caswell 1982, Bazzaz and Reekie 1985, Goldman and Willson 1986, Reekie and Bazzaz 1987a, 1987b, 1987c, Chapin 1989). Conventionally, reproductive effort is expressed in terms of the ratio between the dry weight of reproductive biomass and that of the whole plant, although the question of what constitutes the reproductive biomass remains debatable (see Bazzaz and Reekie 1985 for discussion). Bell (1980) argued that any measurement of reproductive effort could be of evolutionary significance only if it is translated into units of fitness. The concept of the cost of reproduction, defined as the effect of a given quantity of present reproduction on the expectation of future survival, is more relevant. What is important is not how much of the resource(s) or energy is allocated to reproductive or non-reproductive structures, but how reproduction could reduce the future chance of survival of the adult (survival cost), and/or future reproduction (fecundity cost) (Bell and Koufopanou 1986). The question on the cost of reproduction has seldom been addressed in algal studies. Many phenological observations have indicated a close link between growth (increase in length) and reproduction, where rapid growth is concurrent with or followed by the onset of reproduction (see review by De Wreede and Klinger 1986). In many cases, the blades or erect thalli become necrotic and die back after the discharge of reproductive Chapter 3 Cost of Reproduction p.91 propagules like gametes or spores (e.g. Kain 1975, Ang 1985a). This seems to suggest a survival cost associated with reproduction. However, exceptions have also been observed in which vegetative blades decayed without formation of any reproductive structures (e.g. Klein 1987). In addition, reproduction might occur just prior to the time of natural die-back of the plants as a response to changing environmental conditions; in that case, reproduction itself is not the cause of such die-back. Bell and Koufopanou (1986) stated two basic ways of measuring the cost of reproduction: by analysis of causality by experiments and by analysis of correlation by observations. Inherent with the difficulties in manipulating reproduction in algae, e.g. experimentally reducing reproductive output from a thallus, the first approach has not been attempted nor is there currently a feasible way to do it. The second approach is simpler, though it is not without its limitations. Correlation between components of fitness, say reproductive output and mortality, may be significant but may be spurious due to covariation with a third factor. Nevertheless, observation of the pattern in the natural populations, i.e., phenotypic correlation, may provide some basic information that can point to the direction of future research on the topic of cost of reproduction in algae. In this chapter, reproductive effort of individual plants of Fucus distichus L. emend. Powell is given as a ratio between dry weight of the receptacles and that of the total plant. Several hypotheses on the cost of reproduction (sensu Bell 1980) are tested based on monitoring the fate of reproductive and non-reproductive plants within the population. If reproduction has a significant survival cost, then one or all of the following phenomena should be observed: the mortality rate of reproductive plants should be higher than that of non-reproductive plants, reproductive plants should have a shorter longevity (months to live) and should experience slower growth than the non-reproductive plant. Chapter 3 Cost of Reproduction p.92 It is not possible to evaluate directly and independently the fecundity cost of reproduction. Egg production (reproductive output) has been shown to be correlated with plant size in Chapter 1, so fecundity cost is inferred from the effect of reproduction on changes in plant size, hence presumably on reproductive output. Reproduction is both age- and size-dependent in Fucus (Chapter 1), but size is a better descriptor of reproductive events, and of growth and mortality, than is age (see Chapters 1 and 2). The cost of reproduction is therefore evaluated only with respect to the size of the individuals. MATERIALS AND METHODS Four to seven 10 x 10 cm quadrats were randomly placed in the Fucus bed each month from October 1985 to November 1987 (except November 1986). All plants within the quadrats were collected and brought back to the laboratory. Sizes of the plants were measured to the closest mm as length from the base of the holdfast to the tip of the longest branch. Each plant was then blotted dry on a paper towel and wet weight was measured on a Mettler PB300 top loading balance. Each plant was placed in an oven at 105° C for 6 hours (Brinkhuis 1985) and then weighed again to obtain its dry weight. For fertile plants, the reproductive tips (receptacles) were excised and dried separately from the remaining vegetative part. The dry weight of fertile parts is expressed as a proportion of the total dry weight and is referred to as the reproductive effort. Dry weight data were log (x + 1) transformed and the proportion data were arcsin square root (x + 3/8) transformed (Zar 1984 Chapter 14) to meet the assumptions of normality (Lilliefor's Test) and homogeneity of the variances (Bartlett's Test) of parametric statistics. Analysis of Covariance (ANCOVA) was used to compare the relationship among plant size, plant dry weight, dry weight of the receptacles and the reproductive effort at different time periods. Chapter 3 Cost of Reproduction p.93 Cost of reproduction was measured in terms of the probability of mortality due to reproduction, and the effect of reproduction on longevity (i.e., number of months a plant survived after becoming reproductive) and growth rate. Three 0.25 m2 permanent quadrats were set up in the Fucus bed and plants within each quadrat were mapped and monitored monthly. Only plants > 4.5 cm in length were considered because plants < 4.5 cm never became reproductive (see Chapter 1). Information gathered included the plants' reproductive status, whether they survived in the following month of sampling (mortality); if they survived, how long (months) they lived before they died or disappeared from the quadrat (longevity), and changes in plant length between samplings (growth rate). Because the number of reproductive plants per quadrat was very small (< 6) at certain times of the year, not all monthly data can be used in the subsequent analyses. Monthly data used were those that roughly represented the four seasons of the year: fall (October 1985), winter (January 1986 and 1987), spring (May 1986 and April 1987), and summer (August 1986). Different data transformations (Zar 1984 Chapter 14) were attempted but were not successful in achieving normality and homogeneity of variances in the data, so the distribution-free contingency table analysis was used to assess the relationship between reproduction, mortality, longevity and growth rate. Heterogeneity chi-square tests were carried out among contingency tables from different time periods. If the results of the chi-square tests were not significant (P>0.05), then monthly data were pooled and analyzed in a single contingency table (Zar 1984). The effect of plant size on the relationship between reproduction and other demographic events was assessed using log linear analysis in a three-way contingency table. The G-statistic was employed in all contingency table analyses and log linear analyses (Sokal and Rohlf 1981). Reproductive plants may remain reproductive for a number of months after the initial formation of receptacle(s), or the plant may become vegetative after the decay or loss Chapter 3 Cost of Reproduction p.94 of the receptacle. To further evaluate the effect of reproduction on longevity, the number of months a plant remained reproductive, given as a ratio over the number of months a plant survived after first becoming reproductive (longevity), was regressed against longevity of the reproductive plant. No data transformation was necessary to achieve normality and homogeneity of variances in this ratio. ANCOVA was used to assess the relationship between this ratio (i.e. the fertility/longevity ratio) and plant longevity as well as the effect of plant size on this ratio over time. All statistical analyses were performed using SYSTAT (Wilkinson 1988). RESULTS Considering only the fertile plants, the relationship between plant dry weight and plant size is not significantly different over time (Table 3.1). Based on pooled data, this relationship is linear and positively significant (Fig. 3.1). The same can be said of the relationship between receptacle dry weight and plant size (Table 3.2A and Fig. 3.2A). The relationship between receptacle dry weight and plant dry weight is significantly different over time (Table 3.2B). Based on pooled data from October 1985 to April 1987, except those from May and June 1986 (Table 3.2C), the relationship is positively significant (Fig. 3.2B). Only selective data can be pooled to show the effect of plant size (Table 3.3A) and plant dry weight (Table 3.3B) on reproductive effort. The reproductive effort is negatively related to plant size (Fig. 3.3B). Although this relationship is significant, it accounted for only 3% of the variation within the pooled data. The relationship between reproductive effort and plant dry weight is not significant (Fig. 3.3B). This means that the proportion of plant dry weight allocated to reproduction (receptacle) can not be predicted based on plant dry weight or plant size. On average, about 12.7% + 0.0.1% S.E. of the plant dry weight is allocated to receptacles. Chapter 3 Cost of Reproduction p.95 Contingency tables of reproduction versus mortality based on data from October 1985, January, May 1986, January and April 1987 are homogeneous (chi-square = 1.527, df=4, P=0.822). Pooled data suggest that there is a greater chance of mortality for non-fertile plants than for fertile plants (Table 3.4). Longevity was first grouped into 3 categories to minimize the presence of sparse cells in the contingency table. These categories are: survival for 1 to 2 months, 3 to 4 months, or greater than 4 months. A heterogeneity test indicated that contingency tables of reproduction versus longevity for data from all sampling periods are not significantly different (chi-square = 10.449, df=10, P=0.402). Based on the pooled data, fertile plants had about equal chances of surviving in each longevity category, but non-fertile plants either survived only for 1 to 2 months or greater than 4 months but more rarely between 3 to 4 months (Table 3.5). To further test this relationship, the actual number of months a plant survived was used in the analysis. The results (Table 3.6) indicate that 53% of the non-fertile plants survived for 1 to 3 months. Proportionally, a greater number of them also survived more than 7 months, compared to the fertile plants. Most fertile plants (88%) survived from 1 to 6 months. As a general trend, most fertile and non-fertile plants (52%) survived for 1 to 3 months, and the number surviving beyond 3 months diminished nearly monotonically. For the reproduction versus growth rate contingency table, growth rate was also grouped into 3 categories: negative to 0 growth, > 0 to 2 cm/month and > 2 cm/month. As indicated by pooled data (Table 3.7), most fertile plants (52%) exhibited negative or no growth, and most non-fertile plants (50.3%) exhibited positive growth of < 2 cm/month. Proportionally, there were also more non-fertile than fertile plants that exhibited growth > 2 cm/month. The potential influence of plant size on the patterns observed above was assessed by log linear analyses on 3-way contingency tables that include plant size (Table 3.8). Chapter 3 Cost of Reproduction p.96 Plant sizes were grouped into 3 classes: 4.5 to 11 cm, > 11 to 17 cm, and > 17 cm. The interaction among reproduction, size and mortality is not significant (Table 3.8A). Chances of mortality were not significantly different among size classes, irrespective of whether plants were fertile or not. But within each size class, fertile plants had a better chance of surviving than the non-fertile plants. Proportionally, more fertile plants were in the larger size classes. Interaction among reproduction, size, and longevity is also not significant (Table 3.8B). The pattern of longevity appears to be consistent among non-fertile plants of different size classes; in each case a greater number of plants survived either for 1 to 2 months or greater than 4 months, but more rarely for 3 to 4 months. Fertile plants of the smallest size class survived relatively longer, whereas longevity was about the same among those in the larger size classes. The interaction among reproduction, size, and growth rate is significant (Table 3.8C), suggesting that differences in growth rates were not only dependent on the reproductive status of the plants, but also on their sizes. The pattern observed earlier between reproduction and growth rate (Table 3.7) is consistent with that of plants in the first size class. However, plants in the second and third size classes showed a less consistent pattern. Both non-fertile and fertile plants in the second size class exhibited a greater chance of positive growth, whereas only fertile plants > 17 cm exhibited a greater chance of negative growth. Fertile plants > 17 cm were far more likely (69.9%) to exhibit negative growth than were non-fertile plants of the same size class (50%). There is no significant difference in the relationship between the fertility/longevity ratio and plant longevity over time (Table 3.9A), as well as between this ratio and plant size at different times (Table 3.9B). Both relationships are non-significant (linear regression, df=l,57, P>0.05, n=59). The mean ratio is not different among times (ANOVA F=0.804, df=4,54, P=0.528, n=59). On average, from the time a plant Chapter 3 Cost of Reproduction p.97 first became fertile, it would remain fertile 65.7% (± 4.4% S.E.) of the time before it died. The longest time a plant remained fertile was 10 months. DISCUSSION Early works (e.g. Baardseth 1970b) measured the proportion of reproductive biomass over biomass of the whole plant without referring to the concept of reproductive effort. Vernet and Harper (1980) were probably the first to introduce the idea in the algal literature. In their attempt to find some answers to the evolutionary question on the cost of sex in algae, they estimated that the eggs of various species of Fucus constituted only about 0.1 to 0.4% of the total plant weight. Ford et al. (1983) and Edyvean and Ford (1984) found up to 25% by volume of yearly growth in asexual thalli and 55% in sexual thalli of the coralline red alga Lithophyllum incrustans Phil, to be made up of conceptacles. Klinger (1984) reported mean sorus surface area to be 13.2 to 31.7% of the total blade area in Laminaria ephemera Setchell, and 1.28 - 30.48% in L. setchellii Silva. The ratios varied with time and locality. Novaczek (1984b), using an estimated 5 mg cm-2 as the dry weight of sporangia and accessory structures, calculated that fertile tissue constituted about 20% of the yearly tissue production in Ecklonia radiata (C. Ag.) J. Ag. at shallow depth (7 m), and 10% of the production at 15 m. Schiel (1985a) argued that for Sargassum spp. and Cystoseira spp., reproductive structures developed along the entire length of the annual growth which is about 80-90% of the plant biomass. The true cost of reproduction must take into account this whole vegetative structure that supports the fertile material. Cousens (1986) made a distinction between reproductive effort and reproductive proportion in Ascophyllum nodosum (L.) Le Jollis, the former being a ratio of weight of receptacle over the quantity of net annual production and the latter, a ratio of weight of receptacle over total standing crop. He estimated reproductive dry weight biomass in A. nodosum to be 41.4 - 70.4% of the annual growth or 10-29% of the total standing crop. He also found reproductive effort Chapter 3 Cost of Reproduction p.98 to differ along exposure gradients, but not along vertical nor latitudinal distribution in Nova Scotia. It is interesting to note that while there are only a few studies on algal reproductive effort, each study measured reproductive effort in a different way, making comparisons difficult. This is partly because of the very different morphology and phenology of the plants studied. Reproductive effort in the population of Fucus from False Creek is independent of plant size and total plant dry weight over time. It remains to be seen if this pattern holds for other Fucus, or other algal, populations. The allocation of a relatively constant proportion of resource to different parts of the algal thallus, regardless of their size, has been reported for Durvillaea antarctica (Chamisso in Choris) Hariot (Lawrence 1986) and Postelsia palmaeformis Ruprecht (Lawrence and McClintock 1988). However, none of these authors reported allocation specifically to reproductive parts. The mean allocation of only 12.7% of its total dry weight biomass to reproduction in Fucus is relatively small compared to the highest allocation of 67% recorded for some individuals within the population. These plants do not become reproductive when < 4.5 cm in size (see Chapter 1). Whether there is any physiological reason for this minimum size requirement is not known. Weiner (1988) suggested that given a minimum size for reproduction and a linear relationship between reproductive and vegetative weights, the relationship between percent reproductive allocation (i.e., reproductive effort) and total or vegetative weight will be a decreasing slope approaching a constant percent reproductive allocation. While this is intuitively sound, it is not demonstrated in the present study. This is mainly because of the large variation in the reproductive effort of the plants sampled. Chapter 3 Cost of Reproduction p. 99 Although individuals of Fucus distichus can live longer than one year, reproduction involves different receptacles in different branches. New receptacles continue to form while the old ones are dying or decaying, giving the impression of continuous reproduction in the whole plant. This continuity is interrupted only if the formation of new receptacles does not catch up with the decay of the old ones, thus giving an impression of iteroparity. Once a receptacle is developed, it eventually occupies more than half the length of the branch. If each branch is considered separately as a module, a larger reproductive effort within the module would likely be detected. The modular character of the Fucus plant implies that there could be two levels of mortality: mortality of the modules versus that of the whole plant. A branch inevitably dies after the decay of the receptacle (per. obs.). Each module may thus be considered as semelparous in its reproduction, though the eggs may not all be discharged simultaneously. The entire plant may continue to survive if at least one terminal branch remains vegetative. This phenomenon is not infrequent in this Fucus population and it has also been observed by Knight and Parke (1950) for Fucus vesiculosus L. and F. serratus L. However, Edelstein and McLachlan (1975) observed that in F. distichus ssp. distichus, new branches can still develop even if all terminal branches have become fertile. The failure to detect a significantly greater probability of mortality in fertile than in non-fertile plants may be related to the modular character of the plants. Mortality, of the modules may not be associated with that of the whole plant. Even if all the terminal branches become fertile, it will take a few months before the natural attrition of the terminal branches is complete. Hence, the plant will not die immediately after reproduction. However, during this period when the terminal branches are being eroded, the plant may die from causes unrelated to reproduction. The non-significant effect of size on mortality suggests that among these factors, size is not one of them. Chapter 3 Cost of Reproduction p. 100 Other things being equal, the lack of interaction among reproduction, longevity and size suggests that any cost of reproduction on longevity, coupled with the effect of size, is difficult to detect. However, the negative effect of reproduction and size on growth is easier to discern. A large proportion of fertile plants, especially those in the largest size class, has a negative or zero growth. Decay and erosion of receptacles is the main reason for this negative growth. As reflected in the phenology of the Fucus population, plant length is positively correlated with reproduction (Pearson's linear correlation coefficient r=0.60, P=0.001, n=26; see also Chapter 1, Fig. 1.6), but is negatively correlated with growth rate (Chapter 2, Fig. 2.1). Reproduction takes place at a time when plants reach their maximum size. Plant growth rate is further slowed because of reproduction. It thus appears that reproduction in Fucus does not entail a cost in terms of greater mortality and decreased longevity of the fertile plants, but possibly does in terms of growth. Given that the reproductive output is positively correlated with plant size (Chapter 1), reduced, or negative, growth could lead respectively to a slow increase, or decrease, in plant size. This in turn may result in decreased future reproductive output. This close association between reproduction and growth has also been reported in other algae. For example, Dion and Delepine (1983) reported that autumn-winter recruited fronds of Gigartina stellata (Stackhouse) Batters stopped growing and started to degenerate only if cystocarps occupied frond apices, as occurred in fronds recruited earlier in the season. Fronds recruited later in the year had fewer reproductive structures and apices not occupied by cystocarps continued to grow into the following season without degeneration. On the other hand, Klein (1987) observed that decay of fronds of Dumontia contorta (Gmel.) Rupr. was not always preceded by reproduction. Production of reproductive and non-reproductive biomass was measured by McCourt (1984) in three species of Sargassum from Baja California. He suggested the existence Chapter 3 Cost of Reproduction p. 101 of an energy trade off between growth and reproduction and between the alternate strategies of sexual reproduction by way of receptacle formation and asexual reproduction by way of investment in the holdfast where new shoots are initiated. The absence of a survival cost of reproduction, or even the presence of a positive effect of reproduction (as in fertile plants having a lower mortality than non-fertile plants in Fucus distichus), may also be related to the fact that reproductive parts in many algae are photosynthetic. This may indicate a reduced dependence of these reproductive parts on the vegetative part for much of their nutrition. The dependence may also be much more localized, i.e., within the module. However, it has been shown in larger algae, like kelps, that reproductive parts are a sink for resources or photoassimilates generated elsewhere in the plant [see reviews by Schmitz (1981) and Buggeln (1983)]. Reed (1987) reported that vegetative biomass has a great influence on zoospores production in Macrocystis pyrifera (L.) C. Ag. The removal of 75% of vegetative fronds in this kelp led to a significant reduction in sporophyll production. Among fucoid algae, movement of photoassimilates from lower parts of the branch towards the apex was demonstrated by Diouris and Floc'h (1984). Their autoradiographs also showed that translocation was localized within a branch or bifurcation, i.e. assimilates did not move around from one branch to another. There was also no downward movement of assimilates from the apices as well as no upward movement of assimilates from the holdfast in Fucus serratus. In higher plants, Bazzaz and Reekie (1985) suggested that there may be an increased respiration cost of reproduction due to uptake and transport of nutrients required for reproduction, even if reproductive parts of some of these plants are photosynthetic. For fucoids, it remains to be demonstrated if formation of a receptacle from the apical branch would increase the rate of assimilate translocation or other physiological rates either for the whole plant or for the specific branch that bears the receptacle. Any increase only in localized Chapter 3 Cost of Reproduction p. 102 translocation or other physiological rates would suggest a lack of interdependence among modules and that reproduction is very much an activity at the modular level. The significance of the modular character of algae has been pointed out only by Klinger (1988) in her studies on the cost of reproduction in Dictyota binghamiae J. Ag., an isomorphic haplodiplontic alga. She found no evidence of survival cost nor reproductive cost in terms of reduced future reproduction. She argued that the cost of reproduction may be at the modular level, hence may be manifested only in reduced reproductive output, rather than in terms of mortality of the whole plant. Other studies have not distinguished the interactions among modular levels and the results on the cost of reproduction are more equivocal. Bhattacharya (1985) reported that vegetative fronds of Chondrus crispus Stackhouse survived longer than those that bore sori in fall and winter, but both gametophytes and sporophytes have higher or equal survivorship than vegetative thalli in spring and summer. Chapman (1986b) found no relationship between sorus area (reproductive output) and subsequent survival in Laminaria longicruris Pyle. Pfister (1990) found no cost of reproduction in terms of resource allocation in plants of Alalia nana Schrader, but those with sporophylls have a 44 % survivorship compared to 68% in those without. Fecundity cost of reproduction in Fucus distichus has not been assessed. At the modular level, it is not known if the number of oogonia in each conceptacle is fixed. Each oogonium can produce 8 eggs. The presence of underdeveloped oogonia in spent conceptacles suggests that additional eggs can still develop and be discharged (see Chapter 1), i.e., there can still be future reproductive output. But if the number of oogonia within a conceptacle is fixed, then any reduction in future reproductive output may be related more to reproductive determinism (sensu Bell and Koufopanou 1986) than to cost of reproduction. It is unlikely that the number of eggs discharged from one conceptacle will be affected by those discharged from the others, or that the number Chapter 3 Cost of Reproduction p. 103 discharged at one time in one conceptacle will affect the number that will be discharged from other conceptacles in the future. Unless there is translocation of limited resources or other growth substances among them, conceptacles are probably physiologically independent from each other. Evidences of translocation in fucoid algae have indicated only apical translocation of photoassimilates from lower parts of the branches (Floc'h and Penot 1972, Floc'h 1982, Diouris and Floc'h 1984, Penot et al. 1985, Diouris 1989). It is not known if there is any localized movement between conceptacles. At the whole plant level, there is no evidence that receptacle formation in one branch would reduce the chances of receptacle formation in other branches. This suggests that reduction in future reproduction is probably minimal. Cost difference between sexes in F. distichus can not be assessed as the plants are monoecious. The present study and all other studies on algae so far have only been concerned with phenotypic correlations among unmanipulated individuals. Bell and Koufopanou (1986) emphasized the importance of an experimental approach combined with genetic correlation of fitness components in evaluating the cost of reproduction. It has been shown that mortality in semelparous plants like soybean can be delayed by removal of the flower buds (Leopold 1961). Such an approach, however, could induce stress on the plants. Reekie (1989) manipulated photoperiod to induce or suppress flowering in Plantago. This approach can avoid the potential artifact associated with physical injuries of removing flower and seed buds and may be adaptable for use in algae. Fritsch (1945) reported that some fucoids growing in a salt marsh propagate only vegetatively, although some have non-functional female reproductive structures. These are potential materials for genetic analysis and comparison with fully functional individuals. Klinger (1988) argued that the existence of a low cost of reproduction may explain the persistence of a biphasic life history in algae, wherein there are two reproductive events, sporogenesis and gametogenesis. If there is a high cost in Chapter 3 Cost of Reproduction p. 104 reproduction, then selection should favour a reduction in the number of reproductive events, as in a monophasic life history. It is interesting to note that Fucus, having a monophasic life history, has also shown a low cost in reproduction. Further studies, especially on members of the Fucales, using experimental approaches and genetic correlation are needed to elucidate the significance of the cost of reproduction on the evolution of life history strategies in algae. Chapter 3 Cost of Reproduction p. 105 Table 3.1 Fucus distichus. Results of ANCOVA on the effect of plant size on plant dry weight with sampling time as the covariate. Data represent monthly samples from October 1985 to November 1987. Plant size and plant dry weight were log (x + 1) transformed. Source of Variation df MS Size 1 9.421 172.72 < 0.001 Time 24 0.060 1.11 0.336 Size x Time 24 0.065 1.19 0.256 Error 245 0.055 Chapter 3 Cost of Reproduction p. 106 Table 3.2 Fucus distichus. Results of ANCOVA on the effect of A. plant size, B. and C. plant dry weight, on dry weight of receptacles with sampling time as the covariate. Monthly samples included in each analysis are indicated. All data were log (x + 1) transformed. Source of Variation df MS F P. A. October 1985 to November 1987 Size 1 8.575 37.881 < 0.001 Time 24 0.276 1.218 0.226 Size x Time 24 0.271 1.196 0.246 Error 245 0.226 B. October 1985 to November 1987 Dry Weight 1 13.107 80.422 < 0.001 Time 24 0.775 4.753 < 0.001 Dry Weight xTime 24 0.357 2.187 0.002 Error 245 0.163 C. October 1985 to April 1987 except May and June 1986 Dry Weight 1 15.662 98.812 < 0.001 Time 16 0.817 5.153 < 0.001 Dry Weight xTime 16 0.254 1.602 0.069 Error 223 0.158 Chapter 3 Cost of Reproduction p. 107 Table 3.3 Fucus distichus. Results of ANCOVA on the effect of A. plant size, and B. plant dry weight on proportion of dry weight allocated to receptacles (reproductive effort), with sampling time as the covariate. Monthly samples included in each analysis are indicated. Plant size, dry weight were log (x + 1) transformed and reproductive effort was arcsin square root (x + 3/8) transformed. Source of Variation df MS F P A. November 1985 to August 1987 except May, June 1986 and June 1987 Size 1 0.016 0.593 0.442 Time 17 0.038 1.456 0.113 Size x Time 17 0.036 1.382 0.147 Error 224 0.026 B. November 1985 to May 1987 except May and June 1986 Dry Weight 1 0.001 0.055 0.815 Time 15 0.146 5.728 < 0.001 Dry Weight xTime 15 0.043 1.709 0.051 Error 209 0.025 Chapter 3 Cost of Reproduction p. 108 Table 3.4 Fucus distichus. Contingency table on the relationship between reproduction and mortality based on pooled data from October 1985, January, May 1986, January, April 1987. Row percentage given in parentheses. Reproductive Status Mortality Died Survived Total Non-fertile Fertile Total 45 (10.2%) 9 (5.2%) 54 (8.8%) G = 8.342 df = 1 399 (89.8%) 164 (94.8%) 563 (91.3%) P < 0.001 444 (100%) 173 (100%) 617 (100%) Chapter 3 Cost of Reproduction p. 109 Table 3.5 Fucus distichus. Contingency table on the relationship between reproduction and longevity based on pooled data from October 1985, January, May, August 1986, January, and April 1987. Column percentage given in parentheses. Longevity Reproductive Status Non-fertile Fertile Total 1-2 months 3-4 months > 4 months Total 194 (41.5%) 98 (20.9%) 176 (37.6%) 468 (100%) G = 20.538 df = 2 51 (32.3%) 53 (33.5%) 54 (34.2%) 158 (100%) P < 0.001 245 (39.1%) 151 (24.1%) 230 (36.7%) 626 (100%) Chapter 3 Cost of Reproduction p. 110 Table 3.6 Fucus distichus. Contingency table on the relationship between reproduction and longevity based on pooled data from different time periods as given in Table 3.5. Column percentage given in parentheses. Longevity Reproductive Status Total Non-fertile Fertile 1 month 92 (19.7%) 26 (16.5%) 118 (18.9%) 2 months 102 (21.8%) 25 (15.8%) 127 (20.3%) 3 53 (11.3%) 26 (16.5%) 79 (12.6%) 4 45 (9.6%) 27 (17.1%) 72 (11.5%) 5 56 (12.0%) 13 (8.2%) 69 (11.0%) 6 34 (7.3%) 22 (13.9%) 56 (9.0%) 7 25 (5.3%) !0 (6.3%) 35 (5.6%) 8 17 (3.6%) 2 ( 1.3%) 19 (3.0%) 9 22 (4.7%) 4 (2.5%) 26 (4.2%) > 9 22 (4.7%) 3 ( 1.9%) 25 (4.0%) Total 468 (100%) 158 (100%) 626 (100%) G = 48.722 df = 9 P < 0.001 Chapter 3 Cost of Reproduction p. 111 Table 3.7 Fucus distichus. Contingency table on the relationship between reproduction and growth rate (cm/month) based on pooled data from different time periods as given in Table 3.5. Column percentage given in parentheses. Growth Rate Reproductive Status Non-fertile Fertile Total Negative to 0 growth > 0 to 2 cm/mo. > 2 cm/mo. Total 142 (30.3%) 236 (50.3%) 91 (19.4%) 469 (100%) G = 54.384 df = 2 90 (52.0%) 66 (38.2%) 17 (9.8%) 173 (100%) P < 0.001 Heterogeneity Test for Pooled Data Chi-square = 9.18 df = 15 P = 0.868 232 (36.1%) 302 (47.0%) 108 (16.8%) 642 (100%) Chapter 3 Cost of Reproduction p. 112 Table 3.8 Fucus distichus. Contingency tables and results of Log linear analyses on the relationship among reproduction, size and A . mortality, B. longevity, and C. growth rate. Row percentage in parentheses. A. Reproductive Size Mortality Status Died Survived Total Non-fertile 4.5-11 cm 30 (9.4) 291 (90.6) 321 (100) > 11-17 cm 11 (12.0) 81 (88.0) 92 (100) >17 cm 4 (13.0) 27 (87.1) 31 (100) 45 (10.1) 399 (89.9) 444 (100) Fertile 4.5-11 cm 0 (0.0) 16 (100) 16 (100) > 11-17 cm 3 (3.7) 79 (96.3) 82 (100) >17cm 6 (8.0) 69 (92.0) 75 (100) 9 (5.2) 164 (94.8) 173 (100) Total 54 (8.8) 563 (91.2) 617 (100) Log linear models: 1. Test for interdependence among reproduction (A), size (B) and mortality (C) In (expected frequency) = constant + A + B + C + AB + AC + BC G A B C = 1-04 df = 2 P = 0.595 2. Test of independence between size and mortality given the level of reproduction (BC = 0) GBC(A) = 5.48 df = 4 P = 0.241 GBC(A) " ° A B C = 4.44 df = 2 P = 0.109 3. Test of independence between reproduction and mortality given the level of size (AC = 0) G A C ( B ) = 11.50 df = 3 P = 0.009 G A C ( B ) - G A B C = 10.46 df = 1 P = 0.001 4. Test of independence between reproduction and size given the level of mortality (AB = 0) G A B C Q = 469.38 df = 4 P < 0.001 GAB(C) - G A B C = 468.34 df = 2 P < 0.001 Chapter 3 Cost of Reproduction p. 113 Table 3.8 Fucus distichus. Continued. B. Reproductive Size Longevity Status 1-2 mo. 3-4 mo. > 4 mo. Total Non-fertile 4.5-11 cm 134 (37.9) 78 (22.0) 142 (40.1) 354 (100) > 11-17 cm 46 (52.9) 15 (17.2) 26 (29.9) 87 (100) >17cm 14 (51.9) 5 (18.5) 8 (29.6) 27 (100) 194 (41.5) 98 (20.9) 176 (37.6) 468 (100) Fertile 4.5-11 cm 1 (7.7) 5 (38.5) 7 (53.8) 13 (100) > 11-17 cm 28 (35.4) 28 (35.4) 23 (29.1) 79 (100) >17cm 22 (33.3) 20 (30.3) 24 (36.4) 66 (100) 51 (32.3) 53 (33.5) 54 (34.2) 158 (100) Total 245 (39.1) 151 (24.1) 230 (36.7) 626 (100) Log linear models: 1. Test for interdependence among reproduction (A), size (B) and longevity (C) In (expected frequency) = constant + A + B + C + AB + AC 4- BC G A B C = 3.96 df = 4 P = 0.411 2. Test of independence between size and longevity given the level of reproduction (BC = 0) GBC(A) = 25.76 df = 8 P = 0.001 G B C ( A ) - G A B C = 21.80 df = 4 P< 0.001 3. Test of independence between reproduction and longevity given the level of size (AC = 0) GAC(B) = 32.98 df = 6 P < 0.001 GAC(B) - G A B C = 29.02 df = 2 P < 0.001 4. Test of independence between reproduction and size given the level of longevity (AB = 0) GAB(C) = 510.90 df = 6 P < 0.001 GAB(C) - G A B C = 506.94 df = 2 P < 0.001 Chapter 3 Cost of Reproduction p. 114 Table 3.8 Fucus distichus. Continued. C . Reproductive Size Growth rate (cm/month) Status negative > 0 - 2 > 2 Total Non-fertile 4.5-11 cm 98 (27.5) 192 (53.9) 66 (18.5) 356 (100) > 11-17 cm 30 (35.3) 38 (44.7) 17 (20.0) 85 (100) >17cm 14 (50.0) 6 (21.4) 8 (28.6) 28 (100) 142 (30.3) 236 (50.3) 91 (19.4) 469 (100) Fertile 4.5-11 cm 9 (52.9) 7 (41.2) 1 (5.9) 17 (100) > 11-17 cm 30 (36.1) 40 (48.2) 13 (15.7) 83 (100) >17cm 51 (69.9) 19 (26.0) 3 (4.1) 73 (100) 90 (52.0) 66 (38.2) 17 (9.8) 173 (100) Total 232 (36.1) 302 (47.0) 108 (16.8) 642 (100) Log linear model: Test for interdependence among reproduction (A), size (B) and growth rate (C) In (expected frequency) = constant + A + B + C + AB + AC + BC G A B C = 15.0 df = 6 P = 0.020 Chapter 3 Cost of Reproduction p. 115 Table 3.9 Fucus distichus. Results of ANCOVA on the effect of A. longevity and B. plant size on the ratio between number of months a plant remained reproductive and number of months a plant survived after becoming reproductive (fertility/longevity ratio), with sampling time as the covariate. Source of Variation df MS F P A. B. Longevity 1 0.104 0.890 0.350 Time 4 0.104 0.898 0.472 Longevity x Time 4 0.129 1.111 0.362 Error 49 0.116 Size 1 0.012 0.105 0.748 Time 4 0.060 0.504 0.733 Size x Time 4 0.074 0.622 0.649 Error 49 0.119 Chapter 3 Cost of Reproduction p. 116 O _-j 5 j r i ( i i ~ J *0 .5 0.7 0.9 1.1 1.3 1.5 LOG SIZE ( c m ) Figure 3.1 Fucus distichus. Linear regression of plant dry weight vs. plant size. Only reproductive plants (plants > 4.5 cm) were included. Chapter 3 Cost of Reproduction p. 117 cn O LU >-LY. Q LU < Q_ l_U O LU O O 1.0 0.5-I 0.0 •0.5 •1.0 -1.5--2.0-- 2 . 5 1.0 0.5-0.0--0.5 -1.0 -1.5 -2.0-I - 2 . 5 Y = 1.999X - 3.100 r 2 = 0.245 n = 295 p < 0.001 • • - .v: *' * V ^ > A 0.5 0.7 0.9 1.1 1.3 1.5 LOG PLANT SIZE ( c m ) Y = 0.869X - 0.977 r 2 = 0.448 n = 257 P < 0.001 B - 1 . 5 - 1 . 0 - 0 . 5 0.0 0.5 1.0 1.5 LOG PU\NT DRY WEIGHT ( g ) Figure 3.2 Fucus distichus. Linear regression of dry weight of receptacle vs. A. plant size, and B. Plant dry weight. Chapter 3 Cost of Reproduction p. 118 1.3 " > 0.7 7 0.4 c 'w 0.1 - 0 . 2 LY O Ld > O ZD Q O LY Q_ LU 1.3i 1.0 0.7 0.4 0.1 - 0 . 2 Y = 0.596 - 0.207X r 2 = 0.029 n = 260 P = 0.006 . . A • •«. .> • • • i — 0.5 0.7 0.9 1.1 1.3 1.5 LOG PLANT SIZE ( c m ) Y = 0.378 - 0.046X r 2 = 0.014 n = 241 P = 0.066 • . % • % • . t. • I. _ l^u • . • . , • • . * • • *. . \ *• \'&f • ' .. * . * • • •"* . •., - 1 . 5 - 1 . 0 - 0 . 5 0.0 0.5 1.0 1.5 LOG PLANT DRY WEIGHT•( g ) '. Figure 3.3 Fucus distichus. Linear regression of reproductive effort (proportion of receptacle dry weight over total plant dry weight) vs. A. plant size, and B. plant dry weight. p. 119 CHAPTER 4 Experimental Evaluation of Density-Dependence in a Population of Fucus distichus L. emend. Powell INTRODUCTION The effect of density on mortality and growth has been assessed in a number of studies on algal populations. Mortality is generally found to be positively correlated with density (Black 1974, Chapman and Goudey 1983, Chapman 1984a, Schiel 1985b, Dean et al. 1989, Reed 1990b). Both positive (Schiel and Choat 1980, Schiel 1985b) and negative relationships (Dean et al. 1989, Reed 1990b) with growth have been reported. Fewer studies have looked at the effect of density on reproduction and the results are not consistent (e.g. compare Schiel 1985b vs. Reed 1990b). Most of these studies, however, involved plant recruits which were visible to the unaided eye. Density effect at the microscopic stage is little known. Reed et al. (1991) pointed out the importance of detailed information on density-dependent processes. Only with an understanding of the response of different algal developmental stages to density can their responses to other environmental factors be better evaluated. In this chapter, I report on an experiment in which settling blocks were seeded with different known densities of germlings, and on clearings with naturally occurring recruits of different densities, and address questions on the effect of density on mortality and growth in Fucus distichus L. emend. Powell, both at the microscopic and macroscopic stages. None of the experimental plants became reproductive during this part of the study. However, given a significant correlation of reproduction with plant size (see Chapter 3), an indirect evaluation of density-dependent regulation of reproduction is assessed through the effect of density on plant size (length) mediated through growth. Chapter 4 Density-Dependence p. 120 MATERIALS AND METHODS Seeded Density Blocks Settling blocks of 5 x 5 cm were made out of chips of granite collected from the seawall around the study area in False Creek. These chips were cemented together with Poly Cement (Le Page's Limited, Bramalea, Ontario, Canada) and washed in seawater and freshwater as described in Chapter 1. Receptacles from plants haphazardly collected in the field in July, November 1986, and May 1987 were cut and placed in a mesh bag suspended above the settling blocks in the aquaria with filtered seawater and kept in the growth chamber at 16h light: 8h dark, at 15°C, under low light (40 uE m"2 s"1). To achieve different settling densities of the germlings on the blocks, the number of receptacles placed in the mesh bags was varied. The actual number of receptacles placed in any mesh bag, however, was not counted. The water was aerated to create some water motion within the aquaria. Germlings were discharged from the receptacles within 2 to 3 days. Each block was examined under the stereo-microscope for density of settled germlings. As expected, distribution of germlings on the blocks was uneven. Different number of germlings settled on different blocks. As much as possible, the number of all germlings on each block was counted with a grid divided into 25 1-cm2 squares. However, blocks with a very high density of germlings were subsampled: only 2 to 3 randomly chosen 1-cm2 squares were counted. The mean from these subsamples was taken as representing the density in the block. Based on the range of settling densities, 21 blocks were selected and grouped into three groups with 7 replicates each to represent low [5.75 ± 1.64 germlings cm-2 (mean ± S.E.)], mid (165.43 + 31.26 germlings cm-2) and high Chapter 4 Density-Dependence p. 1 2 1 ( 2 , 5 5 5 . 2 9 ± 5 1 2 . 9 9 germlings cm"2) settling densities. Initial size (length in / i m ) of 3 to 2 0 germlings in each block was measured under the stereo-microscope. These density blocks were then outplanted to the Fucus bed and placed in cement holding molds (Chapter 1 ) in 7 sets. Each set had 4 blocks: high, mid, low density blocks plus a control, unseeded block. The control blocks served as a measure of natural recruitment. The first set of 2 1 seeded density blocks was outplanted in July 1 9 8 6 but none of the germlings survived the summer. The second set was outplanted in November 1 9 8 6 , and many of the germlings survived through the subsequent winter, spring and summer 1 9 8 7 . A third set was outplanted in May 1 9 8 7 , but only a few germlings survived through July, and none survived through September 1 9 8 7 . All the analyses reported here are therefore based on data from the second set of density blocks. Every 2 months, from November 1 9 8 6 to November 1 9 8 7 , the blocks were taken back to the laboratory to be examined for changes in the density and sizes of the germlings (plants). After November 1 9 8 7 , sizes of the surviving plants were large enough so monitoring of these blocks was continued in situ. Monitoring was terminated in June 1 9 8 9 after the last plant disappeared from the block. Natural Density Squares Fourteen 5 0 x 5 0 cm permanent plots in the Fucus bed were cleared and burned using a propane torch in September 1 9 8 5 to remove all plants and animals. Recruits > 1 mm long started to appear in February 1 9 8 6 , but were not even in their distribution within the plot. The distribution of plants among different plots was also not the same. Some plots had more patches of recruits than the others. Each cleared plot was divided into 2 5 , 1 0 x 1 0 cm squares. Only the inner 9 squares were used to minimize 'edge' effect. By April 1 9 8 6 , many squares among the 1 4 plots were still completely devoid of Chapter 4 Density-Dependence p. 122 visible recruits and were therefore dropped from further examination. Only 31 remaining squares with visible recruits were further monitored for the change in plant density and size. The number of plants in most squares increased from April to July 1986. Based on July density, the squares were grouped arbitrarily into 2 categories, 23 of them as high density (> 0.25 plant cm-2) and 8 as low density (< 0.25 plant cm"2) squares. It was not possible to have an even distribution of number of high and low density squares within each plot. Since patches of recruits were likely to have settled randomly into each plot and the size of each patch was defined by the 10 x 10 cm square, each square was treated as an independent sample. To test the response of plants to thinning, the density of recruits in 9 high density squares was artificially thinned in July to 0.25 plant cm-2 (or 1 plant per 2x2 cm). This was achieved by further dividing the squares into 25, 2 x 2 cm subplots and then scraping off all except one plant in each subplot. As much as possible, sizes of all plants in each square were measured. In cases where this was not practical, e.g. density was too high, at least 20 plants from each square were randomly selected and measured. All density squares were monitored every 2 to 3 months from April 1986 to November 1987. Statistical Analyses Mortality is expressed as a percentage difference in the density of germlings (plants) between 2 consecutive times in each density block or square. Growth is expressed as the difference in the mean length of germlings (plants) between 2 times. Because the time intervals between sampling were not always equal, both mortality and growth data were standardized to a time interval of 2 months. Chapter 4 Density-Dependence p. 123 All data were tested for normality (Lilliefor's test) and equality of variances (Bartlett's test). If necessary, data were transformed to meet the assumptions of the parametric statistics. Two-level nested analysis of variance (ANOVA) was used to test the difference in the mean size of plants among density blocks or squares. Analysis of covariance (ANCOVA) was used to compare separately the regressions between mortality, length, growth and density over time as well as over different initial densities. Where results of ANCOVA indicated non-significant differences in their slopes, data from different time periods or different density blocks or squares were pooled for regression analyses. In most cases, density data were log-transformed to improve the linear fit of the regression curve. Other statistical analyses used are described in the results. All statistical analyses were performed using SYSTAT (Wilkinson 1988). RESULTS Seeded Density Blocks The Fucus population from False Creek experienced a high recruitment rate in the month of November 1986 (see Chapter 1, Fig. 1.13). When the seeded blocks were outplanted during that time, they were also settled by new recruits from the field. This was confirmed by the presence of recruits on the control blocks. Although the locations of the original germlings on the density blocks were mapped, the presence of new recruits occasionally presented some problems in the identification of the original germlings. However, the older germlings were generally bigger than the new recruits on the control blocks. None of the latter was > 320 /xm in length. When there was doubt in determining whether a germling was an old one or a new recruit, the size of 320 jwm was used as a cut off. All plants considered to be new recruits were not counted and were subsequently physically removed from the block. Doing this may Chapter 4 Density-Dependence p. 124 have also excluded some of the older but smaller germlings and would result in the overestimation of mortality. However, this problem was probably minimal as a decision like this was made < 25% of the time. This was a problem only from November 1986 to March 1987 and only with respect to mid and low density blocks. After March, the original germlings on the density blocks had grown big enough to be easily distinguished from any new recruits. In high density blocks, because the germlings were so close to each other, there was probably no room for new recruits to settle, and none was assumed to have done so. Plant density declined gradually over time (Fig. 4.1). From September 1987 on, the density among blocks was no longer significantly different (Kruskal-Wallis one-way ANOVA, df=2, P=0.356). Results of ANCOVA indicate that the effect of density on mortality rate is not significantly different among sampling times (Table 4.1 A). If mortality data for November 1986 to January 1987 are excluded from the analysis, the effect becomes even much less significant (P=0.892, Table 4. IB). At the initial phase of development, i.e. from November 1986 to January 1987, as density increased mortality rate of the plants (germlings) declined (Fig. 4.2A). This relationship is reversed after January. From January to November 1987, plants in low density blocks suffered lower mortality than those in high density blocks (Fig. 4.2B). Plants from mid density blocks suffered intermediate rate of mortality throughout this period. Although the regression line describing this density relationship is very significantly different from 0 (Fig. 4.2B), it accounts only for 12% of the variation within the pooled data. Polynomial regression did not significantly improve the fit of the regression. Hence, although mortality is positively density-dependent, the effect of density on mortality is not strong. Mean mortality rates among plants in the 3 density blocks are not significantly different most of the times, except from November 1986 to March 1987 (ANOVA, P<0.05). Chapter 4 Density-Dependence p. 125 There is no significant relationship between plant length and plant density in each bimonthly sampling time from November 1986 to November 1987 (Linear regression, P>0.05) except for September 1987, where the positive relationship is marginally significant (Linear regression: log length=0.978 + 0.243 log density, n = 10, 1^ =0.412, P=0.045). When first seeded in November 1986, the initial lengths of the plants (germlings) in all density blocks were not significantly different (Table 4.2A). However, variation in the mean plant size increased over time and sizes of the plants among density blocks became significantly different in January 1987, just 2 months after seeding (Table 4.2B). This difference was mainly due to increased variation in the plant size among high density blocks. At this time, sizes of the plants among the high density blocks were significantly different (ANOVA, F 5 6 6 =9.793, P< 0.001), whereas sizes of the plants among either the mid or low density blocks were not (ANOVA, F 6 > 6 3 =0.87, P=0.522 for mid density blocks; F2>10=0.534, P=0.597 for low density blocks). Sizes of the plants among the mid density blocks became significantly different 2 months later in March 1987 (ANOVA, F 6 1 7 3 =4.918, P<0.001), and those among low density blocks another 4 months later in July 1987 (ANOVA, F5>58=2.541, P=0.038). Plants from different density blocks remained significantly different in sizes until November 1987 (Table 4.2C). There was no consistent pattern that plants in high density blocks were larger than those in the mid or low density blocks (Fig. 4.3). By April 1988, only one high density block remained so no comparison can be made between the sizes of the plants in high versus those in mid and low density blocks. Mean sizes of the remaining plants in mid (57.8 ±13.5 mm, mean ± S.E.) and low (78.1 ± 25.9 mm) density blocks did not differ significantly (two-level nested ANOVA, Between Densities, F 1 3 6 = 1.938, P=0.172). The pattern of change in plant length for plants in all 3 density blocks followed a negative slope as plant density declined over time (Fig. 4.3). The differences among Chapter 4 Density-Dependence p. 126 these slopes, which are measures of rates of change, are only marginally significant (Table 4.3A). The difference occurred mainly between plants in the high and low density blocks (Table 4.3B - D), The distribution of plant length among and within each set of density blocks was highly variable (Fig. 4.4), ranging from being negative to positively skewed at the early germling stage in November 1986 to generally more normal to positively skewed towards spring (March to May 1987). The distribution became more variable again towards summer and fall of 1987. This pattern was the same in all 3 densities. Mean growth rate of plants from different initial densities increased from November 1986 to February 1988, and then showed some decline after June 1988 (Fig. 4.5). The effect of density on growth rates is not significantly different among times from November 1986 to July 1987 (Table 4.4A), but is significantly different among times if a longer sampling period from November 1986 to November 1987 is considered (Table 4.4B). This suggests that the difference is mainly due to increased variation in the growth rate at later times. However, multiple regression analysis indicates that plant growth rate is not significantly related to plant density, but is significantly related to plant length (Table 4.5). The effect of density alone accounts for only 5% of the variation, whereas plant length alone accounts for about 19% of the variation in plant growth. Similar results are obtained if growth rate is expressed as a relative proportion of increase of plant size. Natural Density Squares The effect of density on mortality in plants in the cleared plots (density squares) is not significantly different over time (Table 4.6A), nor among the 3 sets of squares with different initial densities (Table 4.6B). The relation between plant density and mortality is significantly positive only for the pooled data from July 1986 to January 1987 (Fig. Chapter 4 Density-Dependence p. 127 4.6). However, only 21% of the variation of the pooled data is accounted for by this regression. Polynomial regression did not improve the fit of the curve. There is no significant relationship between plant density and mortality for the data from January to May 1987. Plants in all 3 density squares exhibited a wide range of sizes (Table 4.7A). In July 1986, mean lengths of plants in density squares with similar initial density (i.e. among squares), as well as among squares with different initial densities (i.e. among densities) were significantly different (Table 4.7B). However, by March 1987, these differences were no longer significant (Table 4.7C). Size distribution among plants in all 3 density squares was highly variable, ranging from normal to positively skewed in summer (July 1986) to becoming negative to positively skewed in fall to winter (Fig. 4.7). There was no significant difference in the effect of plant density on plant length over time (Table 4.8A). Similar to that observed in density blocks, plants increased in length as plant density declined (Fig. 4.8). However, the difference in the slopes relating plant length with plant density is marginally significant among the 3 density squares (Table 4.8B). Only in the high and the thinned density squares was the negative slope significantly different from 0 (Fig. 4.8). The effect of plant density on mean plant growth rate was significantly different over time (Table 4.9) so the data can not be pooled. The relationship between plant density and mean plant growth rate varied over time (Fig. 4.9). DISCUSSION The range of densities of germlings seeded in the mid and low density blocks is within that observed in natural settling experiments (see Chapter 1). However, the range of density in the high density blocks has not been observed in the field. Nevertheless the Chapter 4 Density-Dependence p. 128 range of density in the high density blocks a few months after germlings were seeded is similar to ranges of density of small plants observed in the cleared plots, as well as in the permanent quadrats (Chapters 1 and 2). This suggests that the density range of germlings initially seeded in the high density blocks is probably realistic. It is conceivable that a high density of eggs could be discharged in clusters especially during re-submergence of fertile plants by the incoming tide. Newly seeded germlings on the density blocks were microscopic. They became visible 4 months later in March 1987 when they had grown to be > 1 mm in length. Based on this information, macrorecruits that started to appear in February 1986 in the plots cleared in September 1985 were likely to have been recruited into the population at least 4 months earlier in November 1985. The timing of recruitment would have coincided with the peak period of fertility of the population (Chapter 1, Fig. 1.5). Subsequent appearances of new plants from April to July 1986 may have resulted from continuous recruitments or from the growth of germlings from the "germling bank" (Chapter 1). Recruitment is believed to be one of the processes that regulate population structure (Roughgarden et al. 1988, Hughes 1990). Depending on whether the system is closed or open, reproductive phenology within the local population may or may not be coupled with the recruitment event. Algal reproductive products (i.e. spores, gametes, or zygotes) usually have a short dispersal range (Hoffman 1987). This would suggest that the algal system is closed. However, Amsler and Searles (1980) found spores of the green alga Enteromorpha 35 km away from the nearest known population. In contrast, Vadas and Wright (1986) found no successful recruitment of the brown alga Ascophyllum nodosum (L.) Le Jolis over 20 years, despite the presence of reproductive plants within the population during the same period. Chapter 4 Density-Dependence p. 129 There is a good indication that the Fucus population from False Creek is a closed system. The pattern of recruitment has been shown to follow the reproductive phenology (see Chapter 1). Within a closed system, population size can be regulated either through a density-dependent mortality of the recruits, or through a density-dependent regulation on the production of recruits, i.e., through reproduction. Crowding appeared to have conveyed some advantages to the Fucus germlings at the early months of their development, as survivorship was better at high than at low densities (Fig. 4.2A). Schonbeck and Norton (1978) observed that intertidal fucoids dried out more slowly at low tide and survived slightly better when in clumps than as individuals. Hruby and Norton (1979) reported that the spores of various intertidal species survived better at high densities. Germlings of Fucus are tuft-like especially at high densities. Perhaps this offers the same advantage against desiccation and herbivory as was suggested for other tuft-forming algae. Hay (1981) showed that tuft-forming algae survived better in intertidal habitats because they suffered less physiological damage due to desiccation and lost relatively less biomass to herbivory than non-tuft-forming algae. In contrast, in a study to test the survival of the zygotes of Ascophyllum nodosum exposed to simulated intertidal water movement, Vadas et al. (1990) found zygotes survived better at medium and low densities, than at high density, at different setting times (sensu Vadas et al. 1990: time allowed for the zygote to attach to the substratum). They suggested that this may be partly due to an enchanced bacterial growth that was associated with high zygote densities, especially at longer setting times. However, survivorship, as used in their context, is mainly an indication of the number of zygotes that was not dislodged from the pottery chips (settling plates) after being exposed to simulated water movement for 1 min, compared to those on the control chips that were placed in calm water. Their results do not indicate a density-dependent response over time and therefore can not be compared with those in my Chapter 4 Density-Dependence p. 130 study. Nevertheless, their results indicate that it was perhaps more difficult for the zygotes to attach more firmly to the substratum (settling plate) at high densities. Fucus germlings seeded in spring or summer did not seem to have benefited from crowding. None of them survived through the summer months. Prolonged exposure to high temperature and desiccation during summer low tide appeared to be a strong density-independent factor that eliminated whatever advantage crowding may have on early germling survival. The positive effect of density on mortality (Fig. 4.2B) for plants more than 2 months old suggests that competition probably became more important once the plants had grown beyond the initial stage. A negative effect of density on mortality was not detected in plants from the density squares. Other density studies on algae likewise did not observe any negative effect (Black 1974, Schiel and Choat 1980, Chapman and Goudey 1983, Chapman 1984a, Dean et al. 1989). These studies were mainly based on plants already quite large, i.e., beyond the germling stage. Presumably, if such a negative effect were to occur only during early development, it would have been missed in these studies. This is likely to be the case for the plants in the density squares. Fucus plants in the density squares showed a significant relationship between density and mortality only in the first few months. Similar observations have been made by Black (1974). He reported that a significant positive effect of density on mortality in Egregia laevigata (Setchell) was detected only in the first few months beyond which mortality became density-independent. The density of plants among my density blocks became non-significantly different beyond September 1987 so any difference in mortality beyond this period would not have been due to density. Other than density, many other factors such as physiology and intrinsic growth rate could also affect the mortality rate of Fucus plants. This is reflected in the low variation accounted Chapter 4 Density-Dependence p. 131 for by the regression line describing this relationship in both the density blocks and density squares. In higher plants, mortality rate usually increases with increasing density (e.g. Harper 1977, Antonovics and Levin 1980, Weiner and Thomas 1986). The effect of density is also often expressed in terms of plant yield. Watkinson (1985) noted that only about 20% of the variation in individual plant yield can be accounted for by size and proximity of neighbouring plant(s). He further noted that the different measures used to estimate the level of crowding, like number of neighbours within a given area, assume that competition between plants is two-sided. In reality, competition is often asymmetrical and a plant that managed to become bigger earlier than the others tend to exert considerably more effect on smaller plants, and not vice versa, thus leading to dominance and the suppression of these smaller plants. It is not difficult to understand that a similar mechanism of dominance-suppression (Schmitt et al. 1986, 1987) can be operating in algal populations resulting in size inequality within the populations and increased mortality of the smaller plants. Competition among individual algal plants is conceivably less complicated than in higher plants simply because of the absence of a below-ground component. Although in some cases, holdfasts may compete for space with neighbouring plants. Dean et al. (1989) and Reed (1990b) suggested that the effect of shading by an algal canopy was one of the key factors influencing growth and survival in subtidal algal populations of Macrocystispyrifera (L.) C. Ag. and Pterygophora californica Ruprecht respectively, through dominance and suppression. Other research has been less supportive of this mechanism. Chapman (1984a, 1986b) did not find smaller plants of Laminaria longicruris Pyl. to suffer a significantly greater mortality than larger plants. Higher growth rate at higher density was also reported for Sargassum sinclairii Hook, et Harv. (Schiel and Choat 1980, Schiel 1985b) and Carpophyllum maschalocarpum (Turn.) Chapter 4 Density-Dependence p. 132 Grev. (Schiel 1985b). Shading is likely to be a key factor in intertidal algal competition as well, especially for relatively large algae like Fucus. Light may be important for growth between fall and early winter of 1986 such that shading reduced the growth rates of more crowded plants in the density squares. This suppression was apparently released in mid winter, when presumably growth was more limited by other factors and plants at higher density were able to cope with them better than those at lower density. Over this same period, plants on the settling blocks were in a different stage of development. It is interesting to note that these germlings also responded positively to crowding, but with higher survivorship rather than with higher growth rate. Whether this response could be attributed directly to shading is, however, less clear. During summer low tide, canopy shading may play a different role for the understory individuals by providing protection from desiccation. As suggested in Chapter 1, this mechanism could improve the chances of survival of Fucus germlings and make possible the existence of a "germling bank". On the other hand, prolonged exposure during summer low tide may exert a heavy toll on the larger plants (Chapter 2). The sizes of the plants in the high density blocks became significantly different at the very early stage of development, whereas the plants on mid and low density blocks became different in size at a much later time. While the initial advantage of crowding may be in increasing the chances of survival, competition probably took place, and dominance-suppression was in effect earlier when the plants were more crowded. There was a large variation in size inequality, measured by skewness (Ford 1975, Schiel 1985b but see Weiner and Solbrig 1984, Watkinson 1985), in both the density blocks and density squares (Figs. 4.5 and 4.9). In the absence of selective mortality, dominance-suppression should further exaggerate size inequality and lead to greater positive skewness, i.e. fewer large and more smaller individuals. Selective mortality of either the larger or smaller plants would tend to obscure this pattern. There appeared to Chapter 4 Density-Dependence p. 133 be a general trend towards positive skewness in density blocks from winter to spring, but the trend became less consistent in summer probably due to increased mortality of the larger plants. This seems to be the case for the density squares as well. Turner and Rabinowitz (1983) argued that size inequality in an even-aged population may simply be a result of inherent differences in the intrinsic growth rate among individuals. When the density blocks were initially set out in the field in November 1986, some germlings were already observed to be slightly bigger than the others. These could be the ones that eventually dominated the others. However, because the blocks were seeded over a period of at least a week during which different pulses of eggs would have settled, it is not certain whether these bigger germlings were bigger because they were discharged and settled earlier, hence had more time to grow, or that they grew faster than the others because of their inherent genetic make up. Both the quality of the germlings and timing of settlement are probably important in determining the size structure of the population, which may then be further modified through the process of dominance and suppression. In both the density blocks and density squares, the populations started out with different densities but eventually converged to a similar final density. This final density may indicate the carrying capacity for a given surface area. Only a few large plants of about similar sizes survived till the end of the experiment. Density studies on algal populations are usually evaluated at the population level rather than at the level of the individuals. Density is rarely expressed in terms of distance from the nearest neighbour (but see Reed 1990b), but rather in terms of a mean value. This is largely because of the difficulty in experimentally manipulating the desired distance between plants. It is possible that plants in populations of a lower mean density may be experiencing as much interference from their neighbours as plants Chapter 4 Density-Dependence p. 134 growing in higher mean densities, especially if the distribution of the plants is clustered. Individuals in the thinned density squares were more or less kept equi-distant from their neighbours. They showed as much variation in size and chances of mortality as those in low and high density squares. Further studies emphasizing neighbourhood relationship are needed to clarify the effect of density at the individual level. The plastic response of higher plants to density is usually a developmental phenomenon. Under crowded conditions, increased mortality results in thinning and reduction in mean size results in a constant final yield. A similar response has been documented in algae (e.g. Adams and Austin 1979, Harger and Neushul 1983, Neushul and Harger 1985). A different but nonetheless interesting response has been shown in sea urchins where large urchins responded to overcrowding by becoming smaller (Levitan 1989). It is not known if a similar response is possible in algae. It may be that if an algal population becomes more crowded, it is the new recruits that would become suppressed in growth. Increased crowding did not seem to affect the bigger or already well established individuals (pers. obs. on permanent quadrats). While individuals of Fucus from False Creek do not exhibit periodic die back, it would be interesting to examine how those other species with perennating holdfasts respond to crowding. Regeneration from a perennating holdfast may be more advantageous than from new recruits, as in Sargassum (Ang 1985b, 1985c) where new shoots started to develop well before the older erect parts died back or new plants had a chance to be recruited. Dominance by the regenerated plant is thus maintained. Individuals on the density blocks formed an even-aged stand. Those on the density squares were more probably of mixed age. Although the results from the density blocks and density squares were generally similar, intercohort interactions may account for part of the variations observed in the density squares. However, details of these interactions, if any, were not detectable with my experimental designs. Intercohort Chapter 4 Density-Dependence p. 135 interactions may effect a lower recruitment rate as reported in some subtidal algal populations (Dayton et al. 1984, Reed 1990b). Reproductive output of Fucus has been shown to be size-dependent (Chapter 3). None of the plants in the density blocks or density squares were reproductive at the time when the density among blocks or squares became non-significantly different. Less than 10 of those that remained eventually became reproductive in the following year. The absence of significant size difference among plants from the density blocks during the later part of the experiment suggests that reproductive output is probably independent of the initial density. This conclusion can only be tentative because of the small sample size and is in contrast to the negative effect of density on reproduction observed in Pterygophora californica sporophytes (Reed 1990b). Except for a recent study by Reed et al. (1991) which showed that female gametophytes of P. californica and Macrocystis pyrifera matured later at higher settlement density and never produced gametes at extremely high density of ~ 3000 mm-2, it is not known if density would affect other aspects of algal reproduction like timing and mode (vegetative vs. sexual) similar to that observed in some higher plants (Weiner 1988). The effect of herbivores has not been evaluated in these experiments. The main grazers are littorines and amphipods. Brawley and Adey (1981) found that micrograzers like amphipods significantly altered the algal community structure of a coral reef microcosm. Reed (1990b) however, found that while the abundance of macrograzers such as sea urchins and sea hares may be correlated with Pterygophora density, the amount of plant tissue lost due to grazing and/or abrasion probably was not. Herbivory has been considered to be a key factor in structuring some intertidal and subtidal algal communities (see reviews by Lubchenco and Gaines 1981, Hawkins and Hartnoll 1983). Responses of herbivores to algal density and the direct or indirect effects of these responses on performance of the algae remain to be clarified. Chapter 4 Density-Dependence p. 136 Results from my study indicate that regulation of the Fucus population in False Creek is more likely to be mediated through a density-dependent mortality of the recruits, rather than through a density-dependent production of the recruits. Futhermore, the former would be important probably only at the initial stages of plant development. However, given the large variation indicated in the data (i.e. low percentage of variation accounted for by most regression lines), these results should be taken in the light of Strong's (1986) argument that there is hardly a simple and explicit density relationship with demographic performances in any real population. Both physical and biological factors are likely to add to the variance of any density relationship and introduce vagueness into the relationship. Such density-vague relationships differ from density-dependent relationships in suggesting a strong stochastic element in population regulation. Further experimentation is necessary to explore the characteristics of this relationship. Chapter 4 Density-Dependence p. 137 Table 4.1 Fucus distichus. Results of ANCOVA on the effect of density on mortality of plants over time in the settling blocks seeded initially with different densities of germlings and with sampling time as the covariate. Sampling periods included in each analysis are indicated. Mortality data were arcsine squareroot transformed and density data were log transformed. Source of Variation df MS F P A. November 1986 to November 1987 Density 1 0.652 6.245 0.014 Time 5 0.696 6.664 < 0.001 Density x Time 5 0.201 1.921 0.098 Error 94 0.104 B. January to November 1987 Density 1 0.959 7.620 0.007 Time 4 0.552 4.384 0.003 Density x Time 4 0.035 0.277 0.892 Error 75 0.126 7r Chapter 4 Density-Dependence p. 138 Table 4.2 Fucus distichus. Results of two-level nested ANOVA on the difference in the mean length of plants among blocks seeded in November 1986 with different initial densities of germlings. Sampling periods included in each analysis are indicated. Sources of variation are among blocks with different initial seeding densities (among densities) and among plants within blocks with similar initial density (among blocks). Length data were log transformed. Source of Variation df MS F P A. November 1986 Among Densities 2 0.006 0.617 0.541 Among Blocks 18 0.009 0.935 0.531 Error 189 0.010 B. January 1987 Among Densities 2 Among Blocks 13 Error 139 C. November 1987 Among Densities 2 Among Blocks 8 Error 136 0.345 20.969 < 0.001 0.049 2.811 0.001 0.016 0.457 3.234 0.042 0.383 2.706 0.009 0.141 Chapter 4 Density-Dependence p. 139 Table 4.3 Fucus distichus. Results of ANCOVA on the effect of plant density on mean plant length over time in the settling blocks with the initial seeding density as the covariate. Data included in each analysis are indicated. Sampling period is from November 1986 to November 1987. Density and length data were log transformed. Source of Variation df MS F P A. Al l 3 density blocks Density 1 27.999 141.713 < 0.001 Initial Density 2 4.500 22.775 < 0.001 Density x Initial Density 2 0.628 3.177 0.046 Error 110 0.198 B. High and mid density blocks Density 1 19.986 110.583 < 0.001 Initial Density 1 2.850 15.771 < 0.001 Density x Initial Density 1 0.115 0.639 0.427 Error 78 0.181 Chapter 4 Density-Dependence p. 140 Table 4.3 Fucus distichus. Continued. Source of Variation df MS F P C. High and low density blocks Density 1 18.351 87.757 < 0.001 Initial Density 1 8.179 39.112 < 0.001 Density x Initial Density 1 1.255 6.001 0.017 Error 69 0.209 D. Mid and low density blocks Density 1 18.874 92.222 < 0.001 Initial Density 1 3.263 15.942 < 0.001 Density x Initial Density 1 0.676 3.304 0.073 Error 73 0.205 Chapter 4 Density-Dependence p. 141 Table 4.4 Fucus distichus. Results of ANCOVA on the effect of plant density on mean plant growth rate over time in the settling blocks with sampling time as the covariate. Sampling periods included in each analysis are indicated. Density data were log transformed. Source of Variation df MS F P A. November 1986 to July 1987 Density 1 0.033 0.041 0.840 Time 3 1.871 2.305 0.086 Density x Time 3 0.276 0.339 0.797 Error 62 0.812 B. November 1986 to November 1987 Density 1 1.390 0.561 0.456 Time 5 89.189 35.983 < 0.001 Density x Time 5 19.576 7.898 < 0.001 Error 77 2.479 Chapter 4 Density-Dependence p. 142 Table 4.5 Fucus distichus. Results of Multiple Regression on the effect of mean density and mean length on mean absolute growth over time among plants on the settling blocks. Variables df b r2 P Density + Length Density Length 2,67 1,68 -0.173 1,68 0.919 0.193 0.001 0.052 0.057 0.192 < 0.001 Chapter 4 Density-Dependence p. 143 Table 4.6 Fucus distichus. Results of ANCOVA on the effect of density on mortality of plants over time in the cleared plots. The covariate in each analysis is indicated. Sampling period is from July 1986 to May 1987. Density data were log transformed. Source of Variation df MS F P A. Sampling time Density 1 1668.681 2.085 0.152 Time 3 1707.841 2.134 0.100 Density x Time 3 447.173 0.559 0.643 Error 104 800.400 B. Initial plant density in July 1986 Density 1 4920.206 5.101 0.026 Initial Density 2 4757.260 4.932 0.009 Density x Initial Density 2 929.438 0.964 0.385 Error 106 964.481 Chapter 4 Density-Dependence p. 144 Table 4.7 Fucus distichus. A.) Mean length (cm + S.E.) of plants among the density squares at different times. Number of squares (n) for each density is given in the parentheses. B.) and C.) Results of two-level nested ANOVA on the difference in the mean length of plants among density squares with different initial densities of recruits. Sampling periods included in each analysis are indicated. Sources of variation are among squares with different initial densities of recruits (among densities) and among plants within squares with similar initial density (among squares). Length data were log transformed. A: Dates Density Squares High Low Thinned Jul 86 1.12 ± 0.09 (14) 0.65 ± 0.07 (8) 0.96 ± 0.10 (9) Sep 86 2.87 ± 0.21 (14) 1.87 ± 0.26 (8) 2.67 ± 0.21 (9) Jan 87 4.07 ± 0.49 (14) 6.16 ± 0.86 (8) 6.08 ± 0.91 (9) Mar 87 11.50 ± 0.85 (8) 9.52 ± 0.76 (6) 8.93 ± 2.04 (9) May 87 12.93 ± 0.58 (7) 6.98 ± 1.73 (5) 12.20 ± 1.21 (5) Source of Variation df MS F P B. July 1986 Among Densities 2 0.940 12.719 < 0.001 Among Squares 28 0.381 5.151 < 0.001 Error 605 0.074 C. March 1987 Among Densities 2 0.165 1.211 0.308 Among Squares 12 0.127 0.934 0.523 Error 42 0.137 Chapter 4 Density-Dependence p. 145 Table 4.8 Fucus distichus. Results of ANCOVA on the effect of plant density on mean plant length over time in the cleared plots. The covariate in each analysis is indicated. Sampling period is from July 1986 to May 1987. Density and length data were log transformed. Source of Variation df MS F P A. Sampling time Density 1 0.038 0.898 0.345 Time 4 0.845 19.761 < 0.001 Density x Time 4 0.013 0.304 0.875 Error 121 0.043 B. Initial plant density in July 1986 Density 1 6.216 57.376 i < 0.001 Initial Density .2 0.819 7.556 0.001 Density x Initial Density 2 0.339 3.128 0.047 Error 125 0.108 Chapter 4 Density-Dependence p. 146 Table 4.9 Fucus distichus. Results of ANCOVA on the effect of plant density on mean plant growth rate over time in the cleared plots with sampling time as the covariate. Sampling period is from July 1986 to May 1987. Density data were log transformed. Source of Variation df MS F P Density 1 15.971 2.689 0.104 Time 3 48.026 8.086 < 0.001 Density x Time 3 29.740 5.007 0.003 Error 91 5.940 Chapter 4 Density-Dependence p. 147 CM O c cn o CO LU Q 2-0-- 2 § DENSITY BLOCKS o HIGH o MID * LOW A A A i 1 8 8 • H a A 5 o h~ B A A B H -A A~ B • l l A • "A SEP JAN MAY SEP JAN MAY SEP JAN MAY 1986 1987 1988 1989 TIME Figure 4.1 Fucus distichus. Density of the plants in each density block over time. Dotted lines are curves fitted by second order polynomial for high density blocks and third order polynomial for mid and low density blocks to indicate the general pattern of decline in density among the 3 groups of density blocks. Chapter 4 Density-Dependence p. 148 < O 1.5 1.3 1.1 0.9 0.7 0.5 0.3 CO 2.0-1 1.5-1.0-0.5 0.0 T I M E o N0V86 - JAN87 * MAY87 - JUL87 • JAN87 - MAR87 • JUL87 - SEP87 A MAR87 - MAY87 • SEP87 - N0V87 Oo° Y = 1.273 -0.085X r 2 = 0.330 n = 21 P = 0.006 0 1 2 Y = 0.726 + 0.122X r 2 = 0.124 n = 85 P = 0.001 • A D • • B - 1 . 5 - 0 . 5 0.5 1.5 2,5 3.5 DENSITY ( l o g n o . / c m 2 ) Figure 4.2 Fucus distichus. Linear regression of plant mortality vs. plant density in the density blocks at different time periods. A.) November 1986 to January 1987, B.) January 1987 to November 1987. Chapter 4 Density-Dependence p. 149 LEGEND O L U O N0V86 A MAR87 • JUL87 v N0V87 • JAN87 A MAY87 n S E P 8 7 1.5 1.0' 0.5 0.0 - 0 . 5 - 1 . 0 - 1 . 5 A Y = 1.073 - 0.509X r 2 = 0.599 n = 39 P < 0.001 HIGH DENSITY BLOCKS 0.0 ^ 2.5-CD 1.5-O ^ 0.5 JZ - 0 . 5 1.5 1.0 2.0 3.0 4.0 B Y = 0.391 - 0.593X r 2 = 0.577 n = 43 P< 0.001 MID DENSITY B L O C K S .5 -0.5 0.5 1.5 2.5 2.5i 1.5-0.5 -0.5 -1.5 C Y = -0.088 - 0.870X r 2 = 0.559 n = 34 P < 0.001 A A A A V LOW DENSITY B L O C K S . 5 -1 .0 -0 .5 0.0 0.5 1.0 1.5 DENSITY ( log n o . / c m 2 ) Figure 4.3 Fucus distichus. Pattern of change in plant length with the decline in plant density in each group of density blocks over time Chapter 4 Density-Dependence p. 150 GO GO UJ GO 3 2 1 0 •1. 2 HIGH DENSITY BLOCKS 3 2 1 0 •1 2 3 2\ 1 0 •1 •2 • I a" • A O • V A X • MID DENSITY BLOCKS A V A A i o s • v X v A LOW DENSITY BLOCKS 8 • A B 5 • • 9 _ o N J M M J S N 1986 1987 SAMPLING PERIOD Figure 4.4 Fucus distichus. Changes in the size distribution of the plants among the density blocks measured as zero-centered skewness. Each symbol represents the same block over different times. The dotted line connects the mean values for each sampling period. Chapter 4 Density-Dependence p. 151 o O l_U cn sz c o E CN o CO m < E E-60 n 45 30-15-0-, -15-- 3 0 DENSITY BLOCKS o HIGH — • MID - -A L O W ••• • • \ 2 \ • OCT FEB JUN OCT FEB JUN OCT FEB JUN 1986 1987 1988 1989 TIME Figure 4.5 Fucus distichus. Changes in the absolute growth rate of the plants in each density block over time. Curve lines are fitted by second order polynomial for high density blocks and third order polynomial for mid and low density blocks to indicate the general pattern of change in mean growth rates among respective density blocks. Chapter 4 Density-Dependence p. 152 Y = 40.68 + 17.0X r 2 = 0.21 n = 63 P < 0.001 TIME U i •—• —r-e a* 1 1 1 1 - 2 . 0 - 1 . 5 - 1 . 0 - 0 . 5 0.0 0.5 1.0 1.5 DENSITY ( log n o . / c m 2 ) Figure 4.6 Fucus distichus. Linear regression of plant mortality vs. plant density in the density squares. Only data from July 1986 to January 1987 were pooled. Chapter 4 Density-Dependence p. 153 3 2 1 0 -1 cn LU CO 3i 2 CO co M LU 0 2 1 0 HIGH DENSITY SQUARES • v • '"I LOW DENSITY SQUARES o v. 6 • s I THINNED DENSITY SQUARES • • JUL SEP JAN MAR 1986 1987 SAMPLING PERIOD Figure 4.7 Fucus distichus. Changes in the size distribution of plants in the density squares over time measured as zero centered skewness. Each symbol represents the same block over different times. The dotted line connects the mean values for each sampling period. Chapter 4 Density-Dependence p. 154 LEGEND O JUL 86 A JAN 87 • MAY 87 HIGH DENSITY SQUARES - 2 . 5 - 1 . 5 - 0 . 5 0.5 1.5 LOW DENSITY SQUARES , Q THINNED DENSITY SQUARES ° -0.5-1 < — • ;  - 2 . 0 - 1 . 5 - 1 . 0 - 0 . 5 DENSITY ( l o g n o . / c m 2 ) Figure 4.8 Fucus distichus. Changes in plant length with the decline in plant density over time in each group of density squares. Chapter 4 Density-Dependence p. 155 o DC O UJ co sz c o E CM O GO OQ < E o 1-2-1 9-6-3-0-: - 3 - 6 - 9 A ^ A * A Ax A • /A A. • A* A « A 4 ^ •A* A» TIME o JUL - SEP86 • SEP86-JAN87 A JAN - MAR87 A MAR - MAY87 . o J ^ o ' _ _ _ - 2 . 0 - 1 . 5 - 1 . 0 - 0 . 5 0.0 0.5 1.0 DENSITY ( log n o . / c m 2 ) Figure 4.9 Fucus distichus. Changes in the mean absolute growth rate of the plants in each density square oyer time. The regression lines relating the mean growth rate to density for each period are indicated. Regressions for Jul-Sep86 and Mar^ May87 are non-significant (P>0.05). Regression for Sep86-Jan87: growth=0.694 - 1.236 log density, n=30, r2=0.257, P=0.004. Regression for Jan-Mar87: growth=11.213 + 6.647 log density, n=23, r2=0.179, P=0.044. CHAPTER 5 p. 156 Matrix Models for Algal Life History Stages INTRODUCTION Studies on algal demographic events, e.g. survival, mortality, recruitment and fecundity of individual plants and of the population, have received far less attention than studies on algal biomass production. Only in a few cases have these events been correlated with algal state variables like age, size, or stage. Chapman (1986b) showed that for the sporophytic stage of Laminaria longicruris Pyle., size was not related to mortality but was clearly related to reproduction. Age was only partially related to mortality, but was unrelated to reproduction. Several studies have shown that large algae like kelps can be aged by using growth rings found in the stipe (e.g. Frye 1918, Kain 1963, De Wreede 1984, Klinger and De Wreede 1988). Cousens (1984) suggested that in the brown alga Ascophyllum nodosum (L.) Le Jol., air vesicles are formed annually. Powell (1964) indicated that blades of the red alga Constantinea are probably also formed annually, and so could be used to age the plant. There has been no other known way to reliably age algae, except by following a cohort through time. Following cohorts of algae is difficult and has many technical problems, such as recognizing the same individuals over time. Even if these problems can be overcome, the question remains as to the most appropriate state variable that can be used in an algal demographic study. Plant size has been shown to be more closely correlated to demographic events than is plant age in many higher plants and clonal animals (see review by Caswell 1986, 1989). Fecundity data for many algae are based on the number of reproductive structures per unit area of the reproductive thallus. Reproductive output are therefore Chapter 5 Matrix Models p. 157 related to thallus size (Kain 1975, De Wreede 1986). Using log linear analysis and association analysis, size is shown to be a better descriptor for reproduction, mortality and growth in the Fucus population from False Creek (Chapters 1 and 2). Further studies are necessary to establish the relative significance of size as a state variable. But given the modular character of many algae, it is likely that algal demographic events can best be described based on size. The complex life histories characteristic of many algae, their isomorphic or heteromorphic stages and their having monoecious or dioecious thalli, poses other potential difficulties in algal demographic analysis. Three basic algal life history patterns, namely monophasic, diphasic and triphasic life histories, are commonly recognized. In the monophasic life history, only a haploid gametophytic stage or a diploid sporophytic stage is present. The diphasic life history is characterized by alternation of gametophytic and sporophytic stages, with either stage being physically dominant or both stages being co-dominant. The triphasic life history is typical of many red algae where a third stage, a carposporophytic stage, forms on the gametophytic blade. The female gametophyte with the attached carposporophytic stage is referred to in this paper as a cystocarpic plant (or stage). Apogamy and apospory are found among some species. Recent reviews have noted many variations in these three types of life history among members of the three major groups of macrobenthic algae, the Chlorophyta (Tanner 1981), Phaeophyta (Pederson 1981, Peters 1987), and Rhodophyta (West and Hommersand 1981, Hawkes 1990). Figure 5.1 shows the different stages of a diphasic life history based on size, considering most of the possible variations that could occur. While these variations may not all be found in a single species, the complexity of some algal life histories is obvious. Some of these stages are rare, or are microscopic and transient, and are unlikely to be traceable in the field, making a complete demographic study of algae Chapter 5 Matrix Models p. 158 difficult. Some stages may be more important than the others, e.g., while apogamy or apospory may occur, they probably do so in only a small fraction of the population and their effect on the different demographic events may thus be a minor one. Figure 5.2 shows what could be the dominant pathways in the three life history patterns. Some of these stages may not be measurable directly, but a close approximation can be made based on relevant criteria. As long as these limitations are kept in mind, and necessary adjustments made to account for them, demographic analysis using only these dominant stages can yield meaningful information about the population. In this chapter, three matrix models, i.e. monophasic, diphasic and triphasic models, that describe these three basic types of algal life history based on size and stage are presented. Using field data for two species of brown algae, namely Sargassum siliquosum J. Ag. and Laminaria longicruris, the utility of the first two of these models are demonstrated. These models explore the relative importance of the different life history stages or size classes to the population growth of each of these species. Use of a modified triphasic model to analyze potential harvesting strategies for a red algal population of Iridaea splendens (Setchell et Gardner) Papenfuss is given in Ang et al. (1990). Applications of the matrix model in the analysis of Fucus population dynamics are presented in Chapter 6. THE MODELS As stated in the General Introduction, the basic projection matrix model is given as N , + 1 = A N , . In the case of a Leslie matrix, N, is a column vector whose elements represent the number of individuals in each age class at time t, N , + 1 represents number of individuals in each age class at time t+l, and A is the transition matrix describing the Chapter 5 Matrix Models p. 159 change in the population from t to t+1. Where the state variable is size and/or stage, N, and N, + 1 represent vectors whose elements are numbers of individuals in each size class, or in each size class of each stage, at the respective time. Plants of different sizes may have different rates of growth. It is possible for some individuals to move across more than one size class within a given period of time. Algae are also subject to erosion from waves, herbivory, or, as a periodic phenomenon, some species die back after the reproductive period. Hence, it is also possible for them to return to a smaller size class (cf. Hughes 1984 for corals). Thus, the transition matrix A that describes these phenomena needs not have the non-zero values confined only to the elements in the first row and the principal subdiagonal, as in the Leslie matrix. Because many algae go through different phenological phases within a year, it would be appropriate to generate transition matrices that correspond to these phenological events. The time interval covered by these matrices would then depend on the duration of these events. It is likely that any algal population would first be sampled at regular intervals, e.g. biweekly or monthly for a year, before its phenology could be established. Thus, transition matrices could be generated with a transition time interval equal to that of the sampling interval. In both cases, the product of the matrices, whether based on phenological or sampling events, would then describe a projection interval equivalent to one year. Algae also exhibit sexuality. However, because males do not really contribute to population growth, for simplicity, only females are considered in the following models. In a dioecious sporophytic or gametophytic population, fecundity or recruitment rates would have to be adjusted based on the ratio between male and female, e.g. these values must be halved if male to female ratio is one. Males could still be included, and their inclusion would constitute an extension of these models. Monophasic Model Chapter 5 Matrix Models p. 160 For a monophasic life history, the transition matrix is analogous to the one proposed by Hughes (1984). In a matrix for algae with only the diploid sporophytic stage, the R terms in the first row represent recruitment rate (Table 5.1A). Recruits are usually the products of sexual reproduction and, less frequently, those of asexually produced spores. Recruitment rate is therefore a measure of fecundity and of the survival probability of zygotes or spores becoming recruits. The probability that a plant will stay in the same size class within a unit of time is given by the P terms. The term G describes the probability of moving from one size class to a larger size class (i.e. growth) and D, that of moving to smaller size class (i.e. degeneration). The P, G, and D terms have values ranging from 0 to 1. The term V describes the probability of die back and subsequent regeneration from the holdfast. This resembles vegetative reproduction (sensu Sarukhan and Gadgil 1974), especially if more than one plant axis is regenerated from the holdfast that eventually leads to the formation of more than one individual. Regenerating holdfasts are grouped with juveniles because in general, they are bigger in size and have a higher probability of survival than the recruits. The transition matrix for algae with a dioecious sporophytic stage or a haploid gametophytic stage is analogous to that described above when only female plants are considered. Diphasic Model The matrix model for a diphasic life history (Table 5. IB) is analogous to the one presented by Law (1983). But instead of age and size, the model consists of stage and size, where stage refers to either the sporophytic or gametophytic stage. The transition matrix can be reduced to its submatrices given as: Chapter 5 Matrix Models p. 161 A D C B where A and B are transition matrices of the sporophytic and gametophytic stages respectively, and C and D describe the transition from one stage to the other. The transition elements within A and B are similar to those in the monophasic model. These submatrices can be analyzed separately and need not be of the same size. In many algae, either sporophyte or gametophyte may be microscopic; in such cases, the microscopic stage would be placed in a single size class. The model may then be reduced to one analogous in form to the monophasic model. Triphasic Model In the triphasic algal life history three stages are involved, the sporophytic (or tetrasporophytic), gametophytic, and the cystocarpic stages (Table 5.1C). This triphasic model can also be reduced to its component submatrices: A 0 F D B 0 0 E C where A, B and C are the transition matrices of the three stages; D, E and F are the transition matrices between stages. Where no transition is possible, e.g. from sporophytic stage to cystocarpic stage, the matrix is a zero matrix. The triphasic model is an expansion of the diphasic model. However, apart from the presence of an additional stage, the cystocarpic stage, the transition from a gametophytic to a cystocarpic stage does not have to pass through a juvenile stage. A Chapter 5 Matrix Models p. 162 female gametophyte becomes cystocarpic after successful fertilization and the growth of the attached carposporophytic stage. Hence, a female gametophyte belonging to a certain size class will transform to become a cystocarpic stage of the same size class, except when there is growth or erosion of its thallus. Contributions of cystocarpic plants to sporophytic recruits are indicated by R c l and in Table 5.1C. Sensitivity and Elasticity Analyses To be biologically meaningful, all the models presented above are non-negative. In some plant and many animal populations, there are individuals that eventually cease to contribute to future generations. Algae do not exhibit such a phenomenon. In all the three life histories, there exists a pathway by which each size class or stage can contribute sexually or vegetatively to individuals of another size class or stage. Thus, matrices describing algal populations are irreducible. Furthermore, the presence of at least one positive diagonal element in the matrices, representing the possibility of an individual remaining in a size class or stage, means that the matrices are also primitive. This implies the existence of a real dominant eigenvalue (lambda(m)) with positive right ( w ) and left ( v ) eigenvectors (Caswell 1986, 1989). The population will thus converge on a stable size distribution described by w and growing at a rate equivalent to lambda .^ The left eigenvector v describes the reproductive value of the different size classes, i.e., the contribution of each size class to future generations (Leslie 1948, Caswell 1986, 1989). Various authors have tested the sensitivity of their matrix models numerically by evaluating the effect of varying proportionally the matrix entries on the intrinsic rate of increase (e.g. Usher 1966). This process, however, could be tedious especially where a large matrix is involved. Caswell (1978) derived a general formula for the sensitivity analysis of lambda(m) to changes in the entries of the projection matrix that can be Chapter 5 Matrix Models p. 163 readily applied to the algal models. This sensitivity measures the absolute change in lambda(m) caused by a small change in the matrix entries. It is also possible to calculate the elasticity, or the proportional change in lambda(m) caused by a change in the matrix entries (de Kroon et al. 1986, Caswell 1986). These elasticities have the additional advantage of measuring the relative contribution of the matrix entries to lambda^ ) (Caswell 1986, 1989). EXAMPLES Most demographic studies of algae reported in the literature do not lend themselves to matrix analysis. Two examples are given to.demonstrate the utility of the monophasic and diphasic models. In both examples, missing parameters have been estimated based on some fundamental assumptions about the life histories of these algae. In each case, these assumptions are given and the way the parameters are estimated is briefly described. Because these missing parameters have had to be estimated, these examples should not be taken as representing the absolute dynamics of the two populations modelled. Example 1 Sargassum is a brown alga with a monophasic life history. Plants are sporophytic (sensu Jensen 1974) and may be monoecious or dioecious, annual or perennial. Ang (1985a) showed the growth pattern of Sargassum siliquosum J. Ag. to be characterized by a regenerative and slow growth phase, a fast growth phase, a reproductive phase and a die-back and recruiting phase. This species is monoecious and pseudoperennial, i.e., only the holdfast, not the whole plant, persists through several years. Data used in this example were collected from Balibago, Calatagan, Philippines (Ang, unpublished). Plants in four 1-m2 quadrats were measured every other month from December, 1979 to November, 1980. In each case, the quadrats were haphazardly selected. The same Chapter 5 Matrix Models p. 164 plants were not followed over the observation period. For the purpose of this exercise, it is assumed that the population structure obtained from the haphazardly selected quadrats would not be significantly different from what would have been obtained by following the same plants over time. The population sampled was divided into seven size classes: the recruits, size class one of juveniles and regenerating holdfasts of not more than 20 cm in length, and 5 other size classes each with size intervals of 20 cm. Based on information obtained from selected tagged plants used in growth studies (Ang 1985a), it is estimated that 60% of the surviving individuals remained in the same size class, and 40% moved to the next higher size class between each sampling interval during the period of slow growth. All surviving individuals moved at least one size class higher during the period of fast growth. Growth among larger plants declined during the reproductive period, so that only individuals in size classes one and two experienced growth. All of the plants except those in size class one experienced die-back during the die-back period. Hence, those that survived eventually ended up in size class one with the juveniles. The number of eggs produced per plant during the reproductive period was not measured, nor was the mortality rate between the eggs and recruits. Only the actual number of recruits per 0.25-m2 was measured (Ang 1985b). It is assumed that the number of recruits produced per 0.25-m2 is proportional to the volume of the plant, which then is allometrically related to its length (cf. Fucus distichus L. emend. Powell, Chapters 1 and 3). Recruitment values were thus estimated as the average number of recruits produced per plant of each size class as a function of plant length, i.e. the longer the plant, the larger its volume, the more recruits it produces. Six matrices were constructed, each covering a time interval of 2 months. The first two matrices correspond to the regeneration and slow growth phase, the second two to the fast growth phase, and the last two to the reproductive phase and the die back and Chapter 5 Matrix Models p. 165 recruiting phases respectively. Each matrix gives the resulting population structure that conforms to that observed in the field at that particular time interval. The product of these six matrices is a matrix S with all non-zero, non-negative elements (Table 5.2), with a period of operation equivalent to one year. Matrix analysis could be performed on each of the six matrices to show the dynamics of the population within each phenological phase. However, only the results of the analysis on matrix S are presented here. This analysis shows that the rate of increase of the population is only slightly above unity (lambda(m) = 1.0264), indicating that the population is very stable. Fig. 5.3A shows the stable size distribution and the reproductive values of the different size classes in log scale. The proportion of the number of recruits in a stable distribution is extremely small and most of the plants (about 76%) are in size classes one (juvenile) to three. This is not unusual for a size-structured population (Caswell 1986). As expected, the reproductive values of the plants vary in direct proportion to their sizes. The sensitivity matrix S s (Table 5.2) shows the trend for population growth rate to be more sensitive to transitional changes from smaller to larger size classes, as indicated by the increasing values of the elements from rows one to seven within each column. However, transition from recruits to larger size classes (ssc,2), i = 2 - 7) appears to be unimportant. Except for this, sensitivity values tend to decrease progressively across the rows from left to right. This trend is analogous to that observed for teasel Dipsacus sylvestris Huds. and was interpreted by Caswell and Werner (1978) to indicate the importance of early reproduction and faster developmental rates on the overall growth rate of the population. In the case of Sargassum, early reproduction would refer to vegetative reproduction, i.e., regeneration from holdfasts. The insignificant contribution to the population growth rate by recruits, compared to the contribution of each of the other size classes, is further shown in the elasticity matrix E s (Table 5.2), where the production of recruits (eS(i j), j = 2 classes (e i^), i = 2 - 7) are all close to zero. Chapters Matrix Models p. 166 - 7) and their transitions to larger size The results of the sensitivity and elasticity analyses appear to reflect the population dynamics of Sargassum reasonably well. The damping ratio, which is the ratio between the largest and the next largest eigenvalues, is very much larger than 1, suggesting that a stable size distribution was attained very rapidly and in the present example, within 1 operation of the matrix (=1 year cycle). Because the plants die back every year, "new" plants arise not only from the recruits but also from regeneration of the holdfasts. The latter appears to be more important than the former. This is readily observed in the field. New recruits are infrequently observed except during the first 2 or 3 months immediately after reproduction (Ang, 1985b). Although recruits may appear in large numbers in those few months, on an annual basis changes in their numbers do not seem to have a significant effect on the overall population growth rate. Example 2 Laminaria is a common brown alga of north temperate seas. Its life history is characterized by an alternation of macroscopic sporophytic and microscopic free living gametophytic stages. Reproduction is seasonal and normally occurs after a period of rapid growth. Reproductive structures are known as sori, and are formed on both sides of the blades producing billions of spores per season (Kain 1963, Klinger 1984). In some species, reproductive blades eventually become eroded and new growth starts again from the basal part of the blade (Kain 1963, 1976a, 1977). Spores give rise to male and female gametophytes in equal ratio (Schreiber 1930 cited in Chapman 1984a). Each female gametophyte is believed to produce one egg which, when fertilized, gives rise to a new sporophyte (Liining 1980). Gametophytes can persist over long periods, and can grow vegetatively and become fragmented, giving rise to new clonal Chapters Matrix Models p. 167 gametophytes (Hsiao and Druehl 1973). Chapman (1984a, 1986b) made a detailed study of spore production, recruitment, and survival rates of sporophytic plants of Laminaria longicruris in eastern Canada. Based on data from that research, a transition matrix is constructed. Other information on the gametophytic stage, sex ratio, sporophytic population structure and growth of this eastern Canadian population are incomplete. Some assumptions have to be made regarding them and these assumptions are based on data from other populations of Laminaria. The gametophytic stage, being microscopic, is grouped in only one size class. The sporophytic stage can be divided into the smallest size class of recruits, juveniles of not more than 100 cm in length, and three other larger size classes in 100 cm length intervals. It is assumed that the sporophytic population has a bimodal distribution, i.e., there are more individuals in smaller and larger size classes than in the middle size class as was observed in Laminaria populations around the Isle of Man, the west mainland of Scotland and the southern outer Hebrides (Kain, 1977). It is further assumed that members of the middle size class tend to grow faster when the canopy opens up as a result of higher mortality of larger plants in fall and winter. Six matrices are constructed to correspond to the six two-month periods of a year. In each matrix, the spores were not included as a size category. Only the number of female gametophytes is considered, and it is assumed that it takes 2 months for a spore to be formed, released and to become a gametophyte, and another 2 months for an egg produced by the gametophyte to be fertilized and to become a sporophytic recruit large enough to be detected by eye in the field. This assumption is based on the observations of Klinger (1984) and Chapman (1984a) on the germination of spores and the laboratory examination on the growth of new sporophytic recruits. The number of female gametophytes produced is assumed to be 2.5% of the number of spores produced, and is proportional to the size of the sporophytes. In other words, it is Chapter 5 Matrix Models p. 168 assumed that the spores suffer a 95 % mortality and only 5 % ever become gametophytes after 2 months. Of these, half are female. Based on the observation of Chapman (1984a, Tables 3 and 4), it is estimated that about 1 % (Aug-Oct) to 20% (Dec-Feb) of the fertilized eggs produced from the female gametophytes eventually become sporophytic recruits. High mortality of recruits has been observed by Chapman (1984a) and only about 0.0001% of the recruits ever become juveniles. The transition elements in the matrix are estimated from the cohort life table (Table 1, Chapman 1986b) and the mean length of all plants in the cohort (Fig. 2, Chapman 1986b). Laminaria longicruris appears to experience a fast growth period, a period of reproduction followed by erosion of the old blades, and a period of new growth. Plants less than 150 cm in length probably continue to grow throughout the year, and move to the next size class in about 4 months. Larger plants suffer some erosion of their blades after reproduction, hence becoming smaller during November through January. As is the case with the Sargassum matrices, each matrix covering every two-month period gives a resulting population structure that conforms to that observed in the field. The product of these six matrices is the projection matrix L, for the whole year (Table 5.3). Based on this matrix the population is growing at a rate lambda(m) = 1.04, and with a damping ratio very much greater than 1. This is consistent with the observation of Chapman (1984a) that the total number of plants in the population does not appear to be changing. The greatest proportion of the plants is in the gametophytic stage and the number of plants in the larger size classes decreases rapidly (Fig. 5.3B). The actual number of gametophytes in the field has been difficult to ascertain but, given the number of spores produced by the sporophytes and their ability to reproduce asexually, such a high number is expected. On the other hand, the correspondingly low number of plants in the sporophyte size classes suggests a very high mortality in the transition from gametophyte to sporophytic recruits, and from recruits to juveniles. The bimodal Chapter 5 Matrix Models p. 169 size structure of the population is not distinct at the stable distribution. The pattern of the reproductive value is typical, where larger plants have a larger share in the contribution to future generations. The sensitivity matrix SL (Table 5.3) shows a similar trend to that observed in the Sargassum matrix. Sensitivity to gametophyte and recruit production appears to be extremely small. However, it should be remembered that these production values are measured on a different scale than all the other elements in the transition matrix. The sensitivity values for the transition from the gametophyte and the recruits to larger size classes, (sL(i,i), i = 3 - 6) and (sL(i,2), i = 3 - 6) respectively, are extremely high, suggesting the great impact it would have to the population growth rate if the development of gametophytes and recruits to maturity were speeded up. The elasticity matrix E L (Table 5.3) shows the relative contributions of the different size and stage classes to population growth rate in the same scale. The transition from gametophyte to 6 recruits and to plants of larger size classes ( E eL(i,i)) contributes about 21% to the i=2 population growth rate, whereas the transition from recruits to plants of larger size 6 classes ( E ei.(i,2)) accounts for only 1 %. This shows the relative importance of i=3 the gametophytic stage to the dynamics of this population. With millions of gametophytes being formed from the even larger number of spores produced by the sporophytes, the number that eventually become sporophytic recruits is not critical (as indicated by ei.(2,i)=0.008) as long as some of them eventually reach maturity (cf. CL(6,I)=0.078). On the other hand, 53% of the population growth rate is accounted for 6 6 by the transitions of the plants within the last three size classes ( E E CLOJ) )• This Chapter 5 Matrix Models p. 170 suggests that although large plants may be present in only very small number (Fig. 5.3B), they are more important in the maintenance of the population growth rate than the gametophytes and plants of smaller sizes. DISCUSSION In both the examples examined, the dominant stage is sporophytic (sensu Jensen 1974), followed by either a microscopic gametophytic stage, as in Laminaria or, in the case of Sargassum, with the gametophytic stage being absent. These are clearly among the simplest life histories in macro-algae. While it is theoretically possible to construct a more elaborate matrix to include all the possible transitional pathways depicted in Fig. 5.1, this would be intractable. Although inclusion of more of the transitional parameters would undoubtedly improve the resolution of the model, this advantage may be overshadowed by the fact that such parameters are often difficult to measure and hence are subject to greater measurement errors. Given these limitations, assumptions have to be made regarding these parameters. Sensitivity and elasticity analyses of the matrix indicate how accurately these parameters must be estimated, and how important these estimates are to the overall population growth rate. In the case of Sargassum, the recruitment rate and the survival probability of the recruits are difficult to estimate in the field. But these terms are less critical than others (e.g. survival probability of the larger plants) to the population growth rate, as indicated by their near zero values in both the sensitivity matrix Ss and the elasticity matrix Es (Table 5.2). Reasonably accurate analysis of the population would thus be possible as the other parameters of greater importance can all be estimated with greater confidence in the field. Because the production of Laminaria gametophytes and their survival and vegetative growth are relatively important to the population growth rate but are difficult to estimate in the field, there will always be a limit to the accuracy by which the dynamics of a Laminaria population can be analyzed. Any assumptions or estimates relating to Chapter 5 Matrix Models p. 171 gametophytes must therefore be made with care. Given that the other parameters can be estimated more accurately, manipulation of the parameters related to gametophytes can be used to provide additional information on their effects on the population. Many algae exhibit discrete episodes of growth, reproduction, die back and regeneration. Discrete models like matrix models may thus be an appropriate tool for studying such algal populations. The time interval through which a matrix operates depends on the biological phenomena associated with the population being modelled. There is usually strong seasonality among algae, therefore, a projection model operating within a shorter time interval may be able to describe such populations more accurately. Woodward (1982) pointed out that a limitation of the Leslie model and its modified form put forward by Usher (1966) is that the models assume the fecundity and transition probability terms (and by extension, all the other terms in the present models) to apply equally to all individuals within the respective age or size class within each operation of the matrix. Woodward proposed that this limitation could be overcome by considering the age distribution among individuals within an age or size class. For most algae, however, determination of age is. extremely difficult. Furthermore, since size is probably a better descriptor of algal demographic events than age, the inclusion of age distribution may not add much information to what can already be derived by knowing the size distribution. Nevertheless, the probability distribution of a transition event and the distribution within a size class should be of interest in future investigations. An algal gametophyte can produce more gametophytes, and/or at the same time contributes to sporophyte production. Such a case resembles life history case C in Caswell (1982, 1986), where there would be fecundity terms (or in the present case, recruitment terms) among stages. As pointed out by Klinger (1984), such complexity in the algal life history is not the same as the complexity exhibited by higher plants with Chapter 5 Matrix Models p. 172 their seed bank (Schmidt and Lawlor 1983). Seeds in the seed bank do not produce more seeds. Most population models consider only females in their analysis. However, where the sex ratio or the interaction between the two sexes is known, the models of Meagher (1982) may be adapted, since these models can show the importance of the contribution of each sex to the population structure and growth. Other extensions of the Leslie matrix model, including those incorporating density effects (e.g. Solbrig et al. 1988) and stochastic events (e.g. Pollard 1966), are worth considering with respect to algal population dynamics. Chapter 5 Matrix Models p. 173 Table 5.1. Matrix models of algae with A. monophasic, B. diphasic, and C. triphasic life history, and their corresponding column vector. Symbols follow those used in Fig. 5.2 and correspond to the transition elements in the respective life cycle graph. B. PrS 0 Rsi RS2 GrS Pjs Vsi V S 2 0 G j s Psi DS2 0 0 Gsi PS2 Recruit Juvenile Sporophyte-1 Sporophyte-2 —' PrS 0 0 0 0 0 R g l R g 2 G r S Pjs Vsi V S 2 0 0 0 0 0 G j S Psi DS2 0 0 0 0 0 0 Gsi PS2 0 0 0 0 0 0 Rsi RS2 Prg 0 0 0 0 0 0 0 Grg Pig Vgl Vg2 0 0 0 0 0 Gjg Pgl D g 2 0 0 0 0 0 0 Ggl Pg2 PrS 0 0 0 0 0 0 0 G r S Pjs Vsi V S 2 0 0 0 0 0 Gjs Psi DS2 0 0 0 0 0 0 Gsi PS2 0 0 0 0 0 0 Rsi RS2 Prg 0 0 0 0 0 0 0 Grg Pjg Vgl Vg2 0 0 0 0 0 Gjg Pgl D g 2 0 0 0 0 0 0 Ggl Pg2 0 0 0 0 0 0 Ggcl 0 0 0 0 0 0 0 0 Ggc2 Rel 0 0 0 0 0 Pel Recruit-S Juvenile-S Sporophyte-1 Sporophyte-2 Recruit-G Juvenile-G Gametophyte-1 Gametophyte-2 Rc2 0 0 0 0 0 0 0 DC2 Pc2 Recruit-S Juvenile-S Sporophyte-1 Sporophyte-2 Recruit-G Juvenile-G Gametophyte-1 Gametophyte-2 Cystocarp-1 Cystocarp-2 Chapter 5 Matrix Models p. 174 Table 5.2. Projection matrix S for the population of Sargassum siliquosum with a monophasic life history, and its corresponding sensitivity matrix S s and elasticity matrix E s . The Column vector shows the arrangement of the size classes. S = 0.6xl0-9 O.lxlO"4 0.3X10-4 1.4X10-4 4.1x10-4 7.1x10-4 12.1x10-4 O.lxlO"4 0.190 0.571 2.360 6.986 12.070 20.486 0.9xl0-5 0.168 0.504 2.083 6.164 10.650 18.076 0.002 0.434 0.648 1.767 4.671 8.041 13.667 0.005 0.813 0.784 0.957 1.435 2.424 4.181 0.005 0.674 0.634 0.798 1.244 2.168 3.792 0.002 0.090 0.028 0.122 0.362 0.858 1.677 0.6xl0"7 0.0010 0.0009 0.0008 0.0004 0.0003 0.0001 0.8xl0'5 0.1284 0.1133 0.0942 0.0475 0.0404 0.0091 0.8xl0-5 0.1277 0.1126 0.0937 0.0472 0.0402 . 0.0091 1.4xl0-5 0.2328 0.2054 0.1709 0.0861 0.0733 0.0165 3.0xl05 0.5079 0.4481 0.3727 0.1879 0.1599 0.0360 0.0001 0.9118 0.8045 0.6691 0.3373 0.2871 0.0647 0.0001 1,5954 1.4077 1.1708 0.5902 0.5023 0.1132 3.8x10" 18 O.lxlO'8 0.3xl08 l.OxlO8 1.6xl0-8 2.3X108 0.9x10-8 0.8x10 11 0.0024 0.0063 0.0217 0.0323 0.0475 0.0182 0.7x10" 11 0.0021 0.0055 0.0190 0.0284 0.0417 0.0159 0.3x10 8 0.0098 0.0130 0.0294 0.0392 0.0574 0.0220 1.5x10-8 0.0402 0.0342 0.0348 0.0263 0.0378 0.0147 2.4x10 8 0.0599 0.0497 0.0521 0.0409 0.0606 0.0239 2.1x10-8 0.0140 0.0039 0.0140 0.0208 0.0420 0.0185 Recruits Juveniles (Size Class 1) Size Class 2 Size Class 3 Size Class 4 Size Class 5 Size Class 6 Chapter 5 Matrix Models p. 175 Table 5.3. Projection matrix.L for a population of Laminaria longicruris with a diphasic life history, and its corresponding sensitivity matrix S l and elasticity matrix E L . The column vector Lvr shows the arrangement of the stage and size classes. (Based on data from Chapman 1984a, 1986b). 3.390 2.8xl02 0.6xl08 1.5xl08 3.5xl08 6.6xl08 0.005 0.393 0.9x10s 0.8x10s 1.2X105 1.8x10s l.OxlO7 0.9xl0"s 2.031 4.035 5.587 5.547 0.8xl0"10 0.3xl0-15 0.051 2.020 4.621 8.681 0.4xl0"8 0.3xl0"6 0.099 1.813 4.257 8.084 l.OxlO8 0.8X10-6 0.180 0.425 0.964 1.822 0.021 1.8x10s 0.5xl0"9 O.lxlO9 O.lxlO"9 0.6xl010 1.737 0.001 0.4xl0"7 O.lxlO"7 O.lxlO"7 0.5xlO"8 0.4xl06 0.4X103 0.010 0.003 0.003 0.001 2.0xl06 1.7X103 0.047 0.014 0.014 0.006 4.5xl06 3.9X103 0.104 0.031 0.030 0.013 8.3xl06 7.1X103 0.191 0.056 0.056 0.023 0.070 0.005 0.030 0.022 0.049 0.038 0.008 0.001 0.003 0.001 0.001 0.001 0.042 0.003 0.019 0.011 0.015 0.007 1.5X10"4 0.4xl0"n 0.002 0.027 0.061 0.047 0.016 0.001 0.010 0.053 0.124 0.098 0.078 0.005 0.033 0.023 0.052 0.041 LN= Gametophytes Recruits Juveniles Size Class 2 Size Class 3 Size Class 4 Chapter 5 Matrix Models p. 176 Juvenile-fp-. Zoospore-d Asexual spore nile-as -* metophyte-f2->.— / ^-*-Gametophyte-f 1— ore 0 G a m - e t e - , "N \ / ^Gamete At \ Sporophyte-2 -Juvenile-z Sporophyte-1 Figure 5.1. Flow diagram of a diphasic algal life history showing most of the possible transitions from stage to stage, or within the different size classes. Numbers denote size class number, as: asexual, d: diploid, f: female, m: male, p: parthenogenetic, z: zoosporic. Chapter 5 Matrix Models p. 177 Figure 5.2. Simplified flow diagram of (A) monophasic life history with sporophyte as the only dominant stage, (B) diphasic life history and (C) triphasic life history. In (B) and (C), only the female gametophytes are shown. D: degeneration, R: recruitment, G: growth, P: probability of staying in same stage or size class, V: vegetative regeneration, c: cystocarpic, g: gametophytic, j: juvenile, r: recruit, s: sporophytic, numbers: size class number. Chapter 5 Matrix Models p. 178 A. SARGASSUM SILIQUOSUM LOG 1 0--1--2 -3--4--5 o Stable distribution • - - • Reproductive Value R J S2 S3 S4 S5 S6 B. LAMINARIA LONGICRURIS LOG 2i 0--2--4 -6 -8-I -10 _ — • G R J S2 S3 S4 STAGE / SIZE CUSS Figure 5.3. Stable size distribution and reproductive values as a function of the stage/size classes for (A) Sargassum siliquosum and (B) Laminaria longicruris. G: gametophyte, R: recruits, J: juvenile (size class 1), S number: size class number. p. 179 CHAPTER 6 Simulation and Analysis of the Dynamics of a Population of Fucus distichus L. emend. Powell INTRODUCTION Mathematical models are tools used to provide insights into the observed natural patterns of various populations. They can help point out gaps in our understanding of the dynamics of these populations and hence suggest future directions for research. Attempts to model algal populations were often associated with the need to exploit algae as a resource and to provide a basis for sound management of this resource. Several approaches have been made each utilizing different types of models. Anderson (1974) modelled the seasonal growth of the giant kelp Macrocystis pyrifera (L.) C. Ag. Silverthorne (1977) developed an optimal harvesting strategy for Gelidium robustum (Gardn.) Hollenberg et Abbott. Seip (1980) used a logistic model to evaluate the optimal harvesting for Ascophyllum nodosum (L.) Le Jol. Smith (1986) utilized a stochastic model to predict the outcome of annual harvesting on the interaction between Laminaria longicruris De la Pylaie and L. digitata (Hudson) Lamouroux and on the yield of Laminaria biomass using different harvesting strategies. Jackson (1987) modelled the growth and biomass yield of Macrocystis pyrifera. Ang (1987) and Ang et al. (1990) used projection matrix models to assess harvesting strategies for Sargassum spp. and Iridaea splendens (Setchell et Gardner) Papenfuss respectively. In recent years, models were also developed to evaluate the basic biology and ecology of algal populations. Jackson et al. (1985) assessed the morphological relationships among fronds of Macrocystis pyrifera. Nisbet and Bence (1989) developed a family of models depicting a simplified relationship between juvenile recruitment and adult Chapter 6 Fucus model p. 180 population density of this same species, incorporating a recruitment inhibitory factor represented by a random variable. They found that despite the overly simplified assumptions in their models, they were able to produce patterns of fluctuation in the population density very similar in range to those observed in the field. Their models indicate that factors affecting recruitment may be very important in determining the dynamics of the giant kelp population. Burgman and Gerard (1990) developed a more comprehensive model of M. pyrifera, incorporating life history stages, environmental and demographic stochasticity, and density-dependent interactions. Their model can predict the monthly changes in the density of each stage of the population for up to 20 years. Demographic characteristics of other species of kelps have also been modelled, e.g. De Wreede (1986) used a matrix model to evaluate changes in the age class distribution of Pterygophora californica Ruprecht. In Chapter 5,1 presented matrix projection models based on size and stage that can be used with algae having different basic types of life history. Matrix models for Sargassum siliquosum J. Ag. and Laminaria longicruris were developed to show the utility of these models. In these models, the populations are projected to grow based on parameters defined by the matrix. The question that can be asked is what would happen to the population if the conditions defined by the matrix remain unchanged? By comparing the "fates" of the population subjected to the constraints of different matrix functions, the significance of the different transition probabilities experienced by the population at different times can be evaluated. The population growth rate (dominant eigenvalue or lambda), stable distribution, reproductive values and relative contribution of each matrix parameter to population growth rate evaluated by way of elasticity analysis, are some measures of the fate of the population. In this chapter, a general matrix model based on recruitment stages and plant size is developed for the False Creek Fucus population. Transition matrices were constructed Chapter 6 Fucus model p. 181 to represent monthly time intervals, and product matrices from these monthly matrices to represent seasonal and yearly time periods. Based on these models, the importance of recruitment and the relative contribution of each matrix parameter to population growth rate were assessed. Population growth was simulated by running random combinations of monthly, seasonal, and yearly matrices, to resemble different fluctuating environments defined by the respective matrices. The characteristics of the transition probabilities and the effect of these on population growth rates and size structure were evaluated and compared. THE MODEL A monophasic matrix model would be appropriate to describe Fucus populations because Fucus plants exhibit a monophasic life history without an alternation of generations (Chapter 5). Detailed monthly monitoring of the fate of individual plants within 3 permanent quadrats (0.25 m2) from July 1985 to November 1987 provided the basic information on the dynamics of the population. Twenty-six matrices were constructed each representing a transition period of 1 month (except for one representing the 2-month period from July to September 1985 and another one, from October to December 1986). Log linear and association analyses carried out in Chapters 1 and 2 to assess the relative importance of size vs. age as descriptors of demographic parameters were based on plants divided into 6 size classes. Hence, the matrix models constructed herein were also based on plants divided into 6 size classes. This provided a more uniform distribution of transition probabilities among the size classes. In addition, data on settling blocks set out in the field provided information on the recruitment of germlings, i.e. microrecruits, as distinguished from the recruitment of macroscopic plantlets (macrorecruits) into the permanent quadrats (Chapter 1). There was a 4-month lag between the release of gametes by the reproductive plants and the time when the germlings became visible macrorecruits (Chapter 4). Hence, 3 stages Chapter 6 Fucus model p. 182 of the recruits were also represented in each matrix to account for this transition, with a fourth stage equivalent to macrorecruits in size class 1 (Table 6.1). The basic 9x9 transition matrix is therefore more complex than the monophasic matrix described in Chapter 5 and is of the form: M = 0 0 F 3 F 4 F 5 F 6 Ri 0 0 0 R2 G : 0 0 0 0 0 0 0 0 R3 : P n P12 Pi6 • 0 : P21 • 6 6 : Pei Pee where R is the probability of moving from 1 recruitment stage to the next, with R3 representing the probability of microrecruits becoming a visible macrorecruit. G is the probability of staying as microrecruits, i.e. of staying in the germling bank. F is the fecundity value for each size class and P , the probability of moving from one size class to the other. Where transition is not possible, it is represented by a 0. As indicated by the dotted line, the transition matrix M can be partitioned into 4 submatrices as: M = A C B D where A describes the transition among the recruits, and B, the transition from microrecruits to macrorecruits in size class 1, as well as to larger size classes. C describes the fecundity, i.e. the contribution of larger plants to microrecruits and D, the transition among plants in different size classes. Chapter 6 Fucus model p. 183 The basic column vector, given as matrix N, represents the distribution of the individuals in the different recruit stages and size classes (Table 6.1). Growth of the population is then defined by: N r + 1 = MN, where t is time. PARAMETER ESTIMATION Transition Among the Size Classes (P) Any plant in any size class can become longer within a time period t to t +1 due to growth and move to a larger size class, or become shorter and move to a smaller size class due to die back or degeneration of receptacles or terminal branches. The plant may also stay in the same size class if growth or die back is not large enough. It is theoretically possible for a plant to move from 1 size class to another in either direction, and across 1 or > 1 size classes over a single time period. Individual plants in 3 permanent quadrats (0.25 m2) were mapped separately and measured each month from the base of the holdfast to the tip of the longest branch. They were sorted into 6 size classes defined in the column vector N. Their "fate" over each month was scored according to whether they survived and, if they did, whether they became larger, smaller or showed no change in size. The probability of moving into different size classes was then calculated and given as P. A separate matrix was constructed for each quadrat for each month (Appendix B, Table B.l). The mean of each transition probability of the 3 matrices for each month was calculated and used as the submatrix D of the final monthly matrix M. Chapter 6 Fucus model p. 184 Fecundity (F) The potential number of eggs produced by the plant is size-dependent, but the actual number produced is not. The latter was demonstrated based on the number of egg clusters released from receptacles of known sizes (Chapter 1). The number of eggs (zygotes) entering the population as new recruits is therefore independent of the plant size. Plants in size classes 1 and 2 never became reproductive, their fecundity values were therefore always nil. Fecundity values for plants in the other 4 size classes can be calculated in terms of the number of microrecruits recorded on settling blocks every month. The number of microrecruits produced per reproductive plant (Z) is given as: R Z = — for / = 3,4,5,6, E ( P , * n i ) where R is the mean number of microrecruits recorded on settling blocks, P,- is the mean probability of being reproductive, and n,-, the mean number of individuals in each size class'/. The fecundity value F,- for size class / is therefore calculated as: Z * P, * n,-F, = —— or F,- = Z * P,-. F is in effect a function of the mean probability of the individual plants being reproductive in each reproducing size class. The actual number of microrecruits was recorded only starting in November 1985. The numbers of microrecruits for September and October 1985 were calculated as a mean of the number of microrecruits of the same months in the following 2 years. The number of microrecruits in July 1985 was back-calculated based on the data of macrorecruits in November 1985. The mean number of microrecruits for July 1986 and 1987 was too small to account for the number of macrorecruits in November 1985, Chapter 6 Fucus model p. 185 hence could not be used to fit the model. Between April and August 1986, and July and August 1987, no microrecruits were recorded in the settling blocks (Chapter 1). In order to maintain the irreducibility of the transition matrices representing these months (i.e., to avoid having one row of the matrices with all 0 values), fecundity for each of the 4 size classes was given a very small value of 1 x 10"10. Transition Among Microrecruits (Ri and R2) Survivorship of the microrecruits at the initial stages is positively density-dependent, although this relationship is relatively weak (Chapter 4). Twenty-two percent of the microrecruits survived the first two months after being seeded in the density blocks in November 1986 (Chapter 4). Estimates of microrecruit survivorship (Rr and R2) at different time periods were based on a factor of 22%, taking into account the positive effect of density. Since only the number of microrecruits, based on the settling blocks, and that of macrorecruits, based on the permanent quadrats, were actually known from field observation, the number of recruits between these stages (i.e., microrecruit-2 and 3) can only be hypothetical values. The number of microrecruit-3's in July 1985 was set at 1000. This is approximately the smallest value that can account for the number of macrorecruits recorded in the permanent quadrats in September 1985, given a survivorship of approximately 3% (Chapter 1). The number of microrecruit-2's and 3's in the subsequent months was calculated empirically, based on the estimated survivorship for each stage. Transition from Microrecruits to Macrorecruits (R3) It is assumed that only a microrecruit-3 can become a macrorecruit. This transition probability was estimated as a ratio between the number of microrecruit-3's and the Chapter 6 Fucus model p. 186 number of macrorecruits. A few macrorecruits were > 1 cm when first detected, so that it is possible for a microrecruit-3 to become a member of size class 2 within a single transition period. Germling Bank (G) The presence of a germling bank was suggested in Chapter 1 to account for the continuous presence of macrorecruits in the permanent quadrats throughout the year despite the absence of any microrecruits in summer. It is assumed that microrecruits stay in the germling bank only after they reach stage 3. The probability of staying in the germling bank was estimated based on a factor of 22%, similar to that used in the estimation of the probability of transitions from Rx to R2 and R2 to R3. METHODS OF ANALYSES AND SIMULATION Construction of the transition matrices is an attempt to describe the dynamics of the population as realistically as possible in mathematical terms. Both the elements of the submatrix D and those of the column vector are mean values estimated from the 3 quadrats and, therefore, have variances around their respective means. However, fecundity values and transitions among microrecruits and from micro- to macrorecruits can not be estimated from the 3 quadrats separately. All 3 quadrats were located within the same population and strictly localized recruitment within micro-patch, while possible, was unlikely. Furthermore, the micro-recruitment data on the settling blocks represented recruitment for the whole population, and not for any particular quadrat. Macro-recruitment data, however, were based on individual quadrats. Under these constraints, elements of the submatrix D, using the mean values, and the fecundity values were assumed to be fixed for each matrix. Transition values of the microrecruits and that from micro- to macrorecruits were then fine-tuned in order to achieve a resulting population distribution within ± 1 standard error of the mean value of the Chapter 6 Fucus model p. 187 actual distribution estimated from the 3 quadrats. This was largely successful except for the months of May to June and June to July 1986 where the simulated population size is much larger than that of the actual field population (Fig. 6.1). This discrepancy is mainly due to a larger simulated size class 1 population over this time period. Each monthly matrix M and the corresponding column vector are presented in Table 6.1. These monthly matrices can be considered as realistic in their depiction of Fucus population dynamics and further analyses can therefore be made on them to understand these dynamics. These matrices represent information on a total of 58,402 observations made over the sampling period. Analysis of the Model Monthly Matrix A population undergoing changes as defined by a transition matrix will eventually grow at a constant growth rate (lambda). This growth rate can be calculated as the dominant eigenvalue of the transition matrix (Leslie 1948, Caswell 1989, see also Chapter 5). Matrix M, which includes all the matrix parameters (i.e. P, F, R, and G), can be compared with submatrix D, which includes only the matrix parameter P. The dominant eigenvalue for matrix M estimates the overall population growth rate, that for submatrix D the population growth rate due to the survival and transition of plants in the size classes (P) alone. By comparing the 2 eigenvalues, the relative effect of recruitment and reproduction versus survival of plants on population growth can be assessed. The dominant eigenvalue was calculated for each monthly M and D to evaluate differences in the population growth rate at any point in time. It was also calculated for each monthly matrix with G set to 0. This is to assess the relative effect of the absence of a germling bank on the population growth. A dominant eigenvalue Chapter 6 Fucus model p. 188 > 1 indicates that the population is growing, a value < 1 indicates that the population is declining. An eigenvalue = 1 suggests that the population is stable. Elasticity analysis (de Kroon et al. 1986, see also Chapter 5) measures the relative contribution of each matrix entry to population growth. The sum of all contributions equals 1. This technique was used to assess the relative contribution of each matrix parameter to population growth at each month, i.e. the proportional sensitivity of population growth rate to each matrix entry. When the population is growing at a constant growth rate (lambda), a stable distribution characterized by a constant relative proportion of each recruit stage and size class is attained. The stable distribution is the right eigenvector corresponding to the dominant eigenvalue of each matrix (Caswell 1989, see also Chapter 5). The stable distribution for each monthly matrix M was calculated and then compared with the observed distribution of the plants in the field to assess the relative stability of the plant distribution. The reproductive value for each monthly matrix M was also calculated. The reproductive value is the left eigenvector corresponding to the dominant eigenvalue (Leslie 1948, Caswell 1989, see also Chapter 5). It is a measure of the relative contribution or importance of each recruit stage or size class to future generations of the population. Yearly Matrix A yearly matrix Y was constructed by obtaining the product of monthly matrices corresponding to a period of 1 year, e.g. July 1985 to July 1986. Starting from July 1985 and then each month subsequently, 16 yearly matrices were obtained. The last yearly matrix covers the period from December 1986 to November 1987, the end of the sampling period (Table 6.2). Chapter 6 Fucus model p. 189 The relative fate of individuals within a year, beginning at different months, was assessed using the yearly matrix. The dominant eigenvalue of each yearly matrix, as well as that of the product of the submatrix D corresponding to a period of 1 year, was calculated. In addition, the eigenvalue of each yearly matrix, derived from monthly matrices with G set to 0, was also calculated. These different eigenvalues were compared. Elasticity analysis, stable distribution and reproductive values of each yearly matrix were also calculated. Simulation and Projection The product of all the monthly matrices is a matrix T describing the transition of the population over the whole sampling period from July 1985 to November 1987. The population may be projected to grow following the parameters defined by this matrix. Population growth rate is then given by the dominant eigenvalue of matrix T. This assumes that population growth follows a cycle defined invariably by the 28-month period sampled. This undoubtedly represents only one of the possible patterns that may be exhibited by the population. Other possible patterns of growth may be defined by the monthly, seasonal, or yearly matrices. These patterns may be simulated by a randomized combination of the different matrices projected over a fixed period of time. Randomized Monthly Matrices Within the sampling period, there were 2 complete 12-month cycles covering the period from November 1985 to November 1987. Each month within a 12-month cycle can therefore be represented by 2 matrices. To project the growth of the population, one of the 2 matrices was selected at random using the built-in random number generator with uniform distribution in SYSTAT (Wilkinson 1988). The chronological sequence of the 12-month cycle from November to November was not changed. The growth of the population was projected over a 60-month period (5 years) 100 times. Chapter 6 Fucus model p. 190 The growth rate for each projection was calculated, and the mean growth rate of these 100 replicates, the standard deviation, and the highest and lowest growth rates were recorded. Randomized Seasonal Matrices The dynamics of population growth may be related to seasonality. To simulate this, monthly matrices were grouped to represent the 4 seasons. Each seasonal matrix S is a product of 3 monthly matrices, e.g. a winter matrix is represented by the product of December to January, January to February and February to March matrices. Given that 2 complete years were covered by the sampling period, there are 2 matrices representing each season. Either 1 of the 2 matrices for each season is selected at random following the seasonal sequences of winter, spring, summer and fall. The growth of the population was projected over 5 years (20 seasons) arid 10 years (40 seasons), each replicated 100 times. The growth rate for each projection was calculated and the mean, standard deviation, and highest and lowest growth rates among the replicates were recorded. Randomized Yearly Matrices The population was simulated to grow following yearly cycles. Yearly matrices are products of 12 monthly matrices. Each of the 2 yearly matrices was selected at random and the population simulated to grow following the combinations of these yearly matrices. The growth of the population was projected for 5 and 10 years, each replicated 100 times. The growth rate for each projection was likewise calculated and the mean, standard deviation, and the highest and lowest growth rates among replicates were recorded. Chapter 6 Fucus model p. 191 RESULTS Analysis of the Model Monthly Matrix Plants in size class 1 generally had a lower survivorship than those in other size classes (Fig. 6.2). Most plants suffered a greater mortality during spring and summer of 1986 than during fall and winter of 1986. Plants in size classes 3 to 6 also showed a high mortality in the summer of 1987, but this pattern was less distinct for smaller plants. Plants in size class 6 suffered consistently high mortality (> 60%) in all 3 summers from 1985 to 1987. If there were no reproduction and recruitment, then population growth rate would be dependent on the survivorship of the plants alone. Patterns of plant survival are reflected in the submatrix D. If the population were to grow under the conditions described by D, in most cases, the population would not be able to maintain itself. This is indicated by the small ( < 1) eigenvalues for most of the monthly submatrices D (Fig. 6.3). In the few cases where eigenvalue « 1, it is mainly due to the high survivorship of larger plants, notably plants in size class 6. The inclusion of reproduction and recruitment increased the population growth rate in many cases, but the increase is not always large enough to prevent the decline of the population. However, in some instances, e.g. September to October 1986, the population experienced a sharp increase in growth rate (Fig. 6.3). At very low fecundity (late spring of 1986 and summers of 1986, 1987), population growth rate would be dependent on the survival of the plants alone. The absence of a germling bank would lower the population growth rate, but only by about 4%. Chapter 6 Fucus model p. 192 Results of the elasticity analysis indicate that plant survival is the single most important parameter and contributes at least 50% to the population growth rate at any time (Fig. 6.4). In those months when contributions from other parameters are also important, the proportional contribution from each of them follows generally a similar pattern, being lower in early winters of 1985, 1986, and in late spring to mid summer of 1986, 1987 than in the rest of the year. In general, the germling bank contributes the least to population growth. Plants in size classes 1 and 2 never became reproductive, so their contribution to population growth rate was only through their survivorship (Fig. 6.5). This contribution could be very large (> 60%) at times. The contributions of reproduction from the other size classes are comparable and are usually small. There is a lot of variation in the way different size classes contribute to population growth. In a few cases, the contribution is mainly from a single size class (e.g. January to February 1987 from size class 5). These are the times when very low mortality was experienced by that particular size class. Detailed results of elasticity analyses are given in Appendix B, Table B.2. When the population was projected to grow based on the estimated matrix functions and attained a stable distribution, a very high proportion of the plants would be in the form of recruits, e.g. as high as 99% in December to January 1987 (Fig. 6.6). The stable distribution would have more large plants than recruits only if fecundity was low or negligible. The number of recruits projected in the stable distribution included those recruits of intermediate stages. There are no actual field data on microrecruit-2's and 3's. Hence, when comparing the projected stable distribution of the plants in the size classes with the observed size class distribution, it is more appropriate to compare the pattern of the Chapter 6 Fucus model p. 193 distribution rather than the absolute proportion of each size class. In most cases, the projected stable distribution is very different from the distribution recorded from field observations (Figs. 6.7A-C). There are, however, a few cases where the patterns are comparable, e.g. July to September 1985, September to October 1985, November to December 1985, February to March 1987, March to April 1987, September to October 1987, and October to November 1987. Size class 6 usually has the highest reproductive value but, from summer of 1985 to the fall of 1986, reproductive values of the 4 largest size classes are comparable (Fig. 6.8). The total reproductive values are positively related to population growth rate. The extremely high reproductive value (> 103) of size class 6 in February to March and August to September 1987 is related to its high survival rate (« 1). Yearly Matrix Transitions among the recruits and across different size classes are possible in a yearly matrix (Table 6.2), hence all the matrix elements are non-zero. The zero elements in OCT 86 - OCT 87 and DEC 86 - NOV 87 matrices are due to the absence of plants in size class 6 during October and November 1987. Initial populations recorded at different months in 1985 to 1986 would decline rapidly if they were to be maintained by the survivorship of the plants alone (Fig. 6.9). In 50% of the cases, reproduction and recruitment only slowed down the rate of decline. In other cases, i.e. JUL 85 - JUL 86, OCT 86 - OCT 87 to DEC 85 - DEC 86, MAY 86 -MAY 87 and JUN 86 - JUN 87, the population growth rate became positive in the presence of reproduction and recruitment. The population would be relatively stable if it were to grow following JAN 86 - JAN 87 and APR 86 - APR 87 matrices. In the absence of a germling bank, all of the populations would decline and experience from 45% to 83% reduction in the growth rate (Fig. 6.9). Chapter 6 Fucus model p. 194 There is a discernible seasonal pattern in the relative contribution of the different demographic parameters to population growth within each year (Fig. 6.10). Contribution of plant survival is inversely related to contribution from other matrix parameters, particularly those of transition from plant to microrecruits and from micro-to macrorecruits. In general, survival of microrecruits contributed the least to population growth rate, though it could be more important than the germling bank in matrices beginning in spring. Certainly, it contributed the most to growth rate in APR 86 - APR 87 matrix. Contribution of plant survival to growth rate is mainly attributable to contributions from plants in size classes 2 to 4 (Fig. 6.11); contributions from the remaining size classes are « < 15%. For the years starting from February to July 1986, the contribution of the transition from plant to microrecruits is generally the most important. In contrast, plant survival is more important at other times. This is consistent in all size classes with fecundity usually being the least important. Although plants in size classes 1 and 2 never became fertile, over a year's period, some of them would have grown larger and become fertile, hence, could also contribute to fecundity. However, this contribution is generally low. Only in the JUL 85 - JUL 86 matrix does the stable distribution have more macro-plants than recruits (Fig. 6.12). At all other times, recruits dominate. There is no clear pattern between the proportion of recruits and population growth rate, i.e., having more recruits does not guarantee a growth rate > 1. Reproductive values for size classes 5 and 6 are the highest of all categories in JUL 85 - JUL 86 to JAN 86 - JAN 87 and AUG 86 - AUG 87 to DEC 86 - NOV 87 matrices. At other times, values for size classes 3 and 4 are comparable or higher than those for size classes 5 or 6 (Fig. 6.13). This suggests that all these size classes are important in contributing to future generations of the population. Chapter 6 Fucus model p. 195 Simulation and Projection The overall matrix T has a dominant eigenvalue = 0.6992, indicating that the population would eventually go extinct if its growth were to be defined by the 28-month cycle. However, if the population were to continue to grow for another year based on 1985 to 1986 matrices, then the population could recover and attain a positive growth rate. Simulations using random combinations of different matrices projected over different periods of time all yielded very wide ranges of growth rates (Table 6.3). In the simulation using random combinations of monthly matrices projected over 5 years, only 13 of the 100 replicates yielded a growth rate > 1. Seasonal matrices (Table 6.4) indicate a projected increase in the population during fall, and a decline during spring and summer in both 1986 and 1987. Growth during winter is more variable, declining in 1986 but increasing in 1987. Simulations using random combination of seasonal matrices generally yielded a growth rate < 1 (Table 6.3). Several combinations of yearly matrices could be used in the simulation, e.g. JUL 85 - JUL 86 vs. JUL 86 - JUL 87. The DEC 85 - DEC 86 and DEC 86 - NOV 87 matrices were chosen to be consistent with the other simulations using monthly and seasonal matrices. The DEC 86 - NOV 87 matrix was further multiplied with the monthly matrix for October to November 1985 in order to obtain a matrix that covers a full year. Results of the simulation using random combination of these 2 DEC - DEC matrices generally yielded very low growth rates, although occasionally very high growth rates were also obtained (Table 6.3). Chapter 6 Fucus model p. 196 Simulations based on seasonal or yearly matrices over different fixed periods of time did not yield consistent results. Both mean growth rates greater or lesser than 1 were obtained (Table 6.3). In general, however, a negative growth rate was obtained in > 60% of the simulation runs. DISCUSSION Variabilities in the physico-chemical and biological environment can easily affect the survival, growth and reproduction of individual plants. These effects are reflected in the transition probabilities of the matrix models representing different time periods. In general, the attempt to depict realistically the behaviour of the Fucus population using matrix models has been successful. It was, however, not possible to get an exact fit between the sizes of the total population simulated from the models and estimated from field observations (Fig. 6.1). Since field observations were based on 3 quadrats, variations among samples would always be expected. The number of plants in size class 1 projected from the model, especially for the months from June to August 1986, has had to be larger than that observed in order to keep the simulated number of plants in other size classes of later months as close to that observed as possible. Some of the inaccuracies in the model parameters are likely to be due to error or variation in the estimate of the number of macrorecruits, or to the lack of information on the transition of the intermediate microrecruit stages. Nevertheless, the number of individuals in these stages, though largely hypothetical, is within a realistic range indicated by the number of microrecruits on the settling blocks. The inclusion of intermediate recruit stages (microrecruit-2 and 3) is necessary to provide the time-delay between micro- and macro-recruitments. This makes the model more realistic. With this time-delay, it became possible to separate and evaluate the different stages between the transition from plant reproduction to recruitment. Chapter 6 Fucus model p. 197 Specifically, there are at least 2 steps in this sequence, from reproduction to microrecruits, and from microrecruits to visible macrorecruits. Size class 1 included new macrorecruits entering the population, as well as older macrorecruits that did not grow into the next size class. It also included die-back or remnants of older plants. These categories are represented by different matrix entries, hence their relative contribution to population growth can be assessed separately. This minimizes the potential problem of having to deal with complex parameters which are the sum or product of different demographic traits. The model is realistic within the time period sampled, and thus should be able to reveal information about the dynamics of the population within that period. However, what is equally interesting is that the models can also be used to simulate the dynamics of the population into the future. One of the inherent properties of the matrix model is time-invariance of the matrix parameters. This, as suggested by Cohen (1979), can be partly overcome by simulating the growth of the population with random combinations of matrices. This technique has been used with some success in higher plants, e.g. Arisaema triphyllum (L.) Torr. (Bierzychudek 1982), Plantago lanceolata L. (van Groenendael and Slim 1988) and Carex bigelowii Torr. ex Schwein. (Carlsson and Callaghan 1991). Although sampling for this Fucus population covered a period of more than 2 years, the observed data do not suggest any recurring pattern with respect to the distribution and size of the population. Variations in matrix transition probabilities among months and between years are large, hence it appears that the population never behaved in any cyclical pattern. However, the population was starting to increase in size towards the end of the sampling period (Fig. 6.1). This could suggest that the sampling period covered represented only a fraction of the population cycle. Several cohorts within the population had been followed to their extinction (Chapters 1 and 2). While the Chapter 6 Fucus model p. 198 phenomena of recruitment, growth, reproduction, and death were the same for each cohort, the presence of cohorts overlapping in time could easily dampen any cyclical pattern exhibited by these biological phenomena. Depending on the time period covered by the matrix, different assumptions are made when using random combinations of matrices to simulate population change. In general, however, cyclic behaviour of the population is not assumed. Random combinations of monthly matrices assume that other than a constant temporal sequence, month to month phenomena are independent from each other. Any change in the population within a month, defined by the matrix functions, is not related to changes in the previous or subsequent months. Random combinations of seasonal matrices assume a close relationship among months within the same season but not between seasons. Any change in the population within a month, e.g. April 1986, is followed by changes in May and June 1986, the subsequent months within the same spring season. What follows, however, could either be defined by summer matrices of 1986 or those of 1987. Similarly, random combinations of yearly matrices assume a close relationship among months within the same year. To represent the dynamics of a population over an extended sampling period, both the mean matrix (e.g. Werner and Caswell 1977) and product matrix (e.g. Huenneke and Marks 1987) have been used. In the former approach, transition values of different matrices representing different time periods were averaged. This approach assumes that variability among time periods is not important. A product matrix results from matrix multiplication of individual matrices. This approach takes into account variabilities between time periods. With monthly monitoring on individuals within the quadrats, very detailed information on the behaviour of the Fucus population became available. Seasonal and yearly matrices were constructed as a product of monthly matrices. This is especially advantageous because variability among months is considerable. Chapter 6 Fucus model p. 199 A matrix model summarizes the information about current population behaviour. Despite the constraints of being deterministic in its prediction, considerable information about the population can be inferred from the analysis. Fucus did not exhibit any vegetative reproduction, i.e. regeneration from the holdfast was not observed. The population therefore can not be maintained by the existing individuals alone because mortality would certainly occur. Recruitment is essential for the continuity of the population. Positive growth (eigenvalues > 1) for the population can only be attained in the presence of reproduction and recruitment (Figs. 6.3 and 6.9). The importance of recruitment to the stability (or instability) and growth of marine benthic populations has increasingly been recognized in recent years both in algal (e.g. Reed et al. 1988, Nisbet and Bence 1989) and animal populations (e.g. Roughgarden et al. 1988, Pascual and Caswell 1991). The reduction in the relative importance of plant survival to population growth rate indicated by the yearly matrices is compensated for by the increased importance of other parameters such as the survival of macrorecruits to juvenile and reproductive size classes and the contribution of plant reproduction to microrecruit stages. These parameters, however, actually represent the contribution of new individuals that entered the population over the course of a year. The relative importance of plant survival measured by the elasticity analyses represents mainly the contribution of the older plants that existed at the start of the period. These plants suffered increased mortality, hence, their contribution to the population growth rate also decreased over time. A large contribution of plant survival to population growth rate is characteristic of long-lived plants like trees (Hartshorn 1975, Enright and Ogden 1979). This suggests that even in the absence of any recruitment, the decline of the population would not be abrupt. In such a case, the chances are high that at some time the population may recover from a continuous decline as a result of a sudden influx of pulses of recruits. Chapter 6 Fucus model p.200 In the simulation, each month, season or year, was chosen from 2 matrices, each having an equal probability of being included in each run. One of the 2 matrices (the "good" matrix) projects a higher growth rate, thus depicts a "good" month, season or year, than the other (the "bad" matrix). An extremely high growth rate could be obtained, or vice versa, if the "good" or the "bad" matrix is continuously being chosen over the period simulated. In reality, a "good" or "bad" month, season, or year described respectively by the "good" or "bad" matrix may not recur over a prolonged period. These extreme growth rates are therefore very unlikely. It can not be ascertained which of the 3 ways of randomly combining matrices used in the simulation is more realistic. This needs to be tested with a longer term of sampling, i.e. beyond the 2 years covered by this study. Nevertheless, while this Fucus population is declining, it may recover in the future. The population is probably being maintained by an occasional pulse of a large number of recruits. The year 1986 may be an example of such a good year. On a monthly basis, the presence of a germling bank had little effect on population growth rate. However, if there were no germling bank for the whole year, the effect could be more significant. None of the yearly matrices showed a growth rate > 1 if the probability of microrecruits being present in the germling bank was set to 0. The germling bank appears to compensate for the lack of fecundity, as indicated by a negative relationship between the contributions of fecundity and the germling bank to growth rate. The seed bank of higher plants has a stabilizing effect on population growth rate (Schmidt and Lawlor 1983). The germling bank in algae, if it exists, is likely to play a similar role. How significant this role is, to this Fucus, as well as to other algal populations, remains to be shown in the field (see also review by Santelices 1990). Chapter 6 Fucus model p.201 Many algae produce a large number of propagules (Hoffmann 1987, Santelices 1990), but only a small fraction of this is recruited into the population. An even smaller fraction of this ever survives and becomes large enough to contribute to future reproduction. Hence, a stable distribution with a large proportion of the plants in the recruit stage is probably typical of many algae. This is not true for another brown alga Sargassum where the proportion of recruits at the stable distribution is small (Chapter 5). However, in Sargassum, new laterals regenerate from the holdfast every year. This mode of vegetative reproduction is therefore far more important than sexual reproduction to population growth of Sargassum. Current size distribution is a reflection of past events. Stable distributions calculated from the monthly matrices are, in general, different from the current size distribution of the Fucus population. This indicates that the population is unstable. This instability is reflected in the highly variable transition probabilities that governed the population and the relative contributions of each size class to population growth. If the population were being maintained by occasional influxes of recruits, as suggested earlier, then the influx could serve as a disturbance that keeps the population in a non-equilibrium state. Bierzychudek (1982) argued that the attainment of a constant growth rate is based on the assumption of the existence of a constant environment. In reality, the environment is never constant and a constant growth rate will never be attained. A population may therefore be much more influenced by its size structure than by its growth rate. This argument may be particularly relevant to this Fucus population. The existence of a large number of recruits in this population, especially those in the intermediate stages, remains to be verified. Further analyses incorporating these stages should prove to be interesting in elucidating the stability and the possible influence of the environment on current size structure in this population. Chapter 6 Fucus model p.202 Low reproductive values for recruits and size classes 1 and 2 are expected as they do not contribute directly to fecundity. For the other 4 size classes, a positive relationship between reproductive values and plant size classes is discernible. Although the number of microrecruits originating from each reproductive plant may be the same, i.e. the actual number of eggs produced per plant may be independent of plant size, but because the probability of being reproductive is higher for larger plants, there is therefore a positive relationship between fecundity value and plant size, hence between reproductive values and plant size classes. However, there is no theoretical basis to assume that reproductive value is always positively related to plant size class. There are examples in higher plants where this relationship does not hold (e.g. Carex bigelowii, Carlsson and Callaghan 1991). This is largely a reflection of a different functional relationship between the state variable (plant size or age) and fecundity. The life span of Fucus is about 2-3 years (Chapters 1 and 2). With a high mortality of the recruits, iteroparity should be favoured (Charnov and Schaffer 1973). Iteroparity in Fucus appears to be achieved by the formation of receptacles at different terminal branches at different times (Chapter 3). This enables other non-reproductive terminal branches of the plant to continue to grow, thus minimizing the cost of reproduction (Chapter 3). This must have a significant advantage for Fucus. Reduction in mortality rate and increase in plant size both increase the importance of the plant to population growth rate, the latter through an increase in reproductive value, and hence increased contribution to recruitment. The matrix models developed here reflect the dynamics of the Fucus population. Given that both age and size are significant state variables in describing the demographic parameters of a Fucus population (Chapters 1 and 2), further improvement of the models may include age as an additional state variable. Density-dependent survivorship and stochasticity of recruitment are probably two important Chapter 6 Fucus model p.203 factors that control the outcome of any population change. Variation within the population has not been accounted for in this study. The information on population dynamics was based on mean data from three quadrats. It is possible that spatial heterogeneity may allow patches of the population to exhibit different dynamics. If this is true, then there could be variation in the dispersal of propagules resulting in spatial heterogeneity in recruitment. This should make the study of Fucus in particular, and algal population dynamics in general, even more challenging. Chapter 6 Fucus model p.204 Table 6.1 Fucus distichus. Monthly transition matrices for the Fucus population. Transition elements are mean values from the transition matrices of the 3 permanent quadrats. Where no transition is possible, it is indicated by a 0. Mean monthly density (per 0.25 m2) of the population is given as a column vector with the respective categories defined in the matrix N. N = Microrecruits Microrecruit-2 Microrecruit-3 Size class 1 ( < 1 cm ) Size class 2 ( 1 - < 4.5 Size class 3 ( 4.5 - < 9 Size class 4 ( 9.5 -Size class 5 ( 14.5 cm) 5 cm) < 14.5 cm) < 19.5 cm) Size class 6 ( > 19.5 cm ) JUL - SEP 85 0 0 0 0 0 7.705 51.924 94.604 163.737 0.219 0 0 0 0 0 0 0 0 0.219 0.219 0.219 0 0 0 0 0 0 0 0.177 0.007 0.184 0 0.039 0.088 0.045 0 0 0 0.000 0.344 0.461 0.035 0 0.045 0 0 0 0.016 0 0.137 0.250 0.011 0.015 0 0 0 0 0 0 0.192 0.318 0.045 0 0 0 0 0 0 0.013 0.141 0.212 0 0 0 0 0 0 0.013 0.041 0.394 0.389 JUL 85 535.59 894.89 1000.00 198.23 61.05 63.80 42.53 30.18 14.41 SEP - OCT 85 0 0 0 0 0 41.707 151.788 199.971 243.964 0.438 0 0 0 0 0 0 0 0 0 0.219 0.219 0 0 0 0 0 0 0 0 0.400 0.458 0 0.056 0 0 0.042 0 0 0.030 0.117 0;699 0.028 0 0 0 0 0 0 0 0:033 0.639 0.076 0.021 0 0 0 0 0 0 0.111 0.491 0.063 0 0 0 0 0 0 0 0.253 0.500 0 0 0 0 0 0 0 0 0.375 0.840 SEP 85 7913.64 117.19 531.79 209.24 98.79 24.70 28.12 17.83 17.15 Table 6.1 Fucus distichus. Continued. Chapter 6 Fucus model p.205 OCT - NOV 85 OCT 85 0 0 0 0 0 1.241 13.129 14.753 27.240 0.438 0 0 0 0 0 0 0 0 0 0.328 0.004 0 0 0 0 0 0 0 0 0.740 0.519 0.085 0 0.033 0.020 0 0 0 0.000 0.135 0.816 0.082 0 0 0 0 0 0 0 0.009 0.861 0.231 0 0.020 0 0 0 0 0 0.021 0.641 0.565 0 0 0 0 0 0 0.019 0.020 0.263 0.395 0 0 0 0 0 0 0 0.086 0.586 13390.91 3463.04 142.00 157.24 168.62 37.26 20.83 11.47 21.29 NOV - DEC 85 0 0 0 0 0 4.224 125.700 105.829 231.540 0.219 0 0 0 0 0 0 0 0 0 0.328 0.328 0 0 0 0 0 0 0 0 0.103 0.501 0.149 0.029 0.025 0 0.056 0 0 0 0.039 0.728 0.061 0 0 .0.050 0 0 0 0 0.018 0.757 0.025 0 0 0 0 0 0 0 0.121 0.683 0.026 0 0 0 0 0 0 0 0.217 0.796 0.261 0 0 0 0 0 0 0 0.151 0.533 NOV 85 1079.17 5859.92 1137.20 226.98 168.21 39.13 20.33 14.76 12.93 DEC 85 - JAN 86 0 0 0 0 0 33.781 479.241 598.040 623.038 0.328 0 0 0 0 0 0 0 0 0 0.219 0.328 0 0 0 0 0 0 0 0 0.050 0.500 0.058 0 0 0 0 0 0 0.050 0.079 0.720 0.115 0.180 0 0.071 0 0 0 0 0.076 0.644 0.029 0 0 0 0 0 0 0 0.070 0.610 0.024 0 0 : 0 0 0 0 0 0.121 0.952 0.071 0 0 0 0 0 0.038 0 0.024 0.714 DEC 85 7308.33 236.12 2172.07 223.01 79.59 19.90 17.15 19.89 9.60 JAN - FEB 86 0 0 0 0 0 74.804 164.935 236.878 287.598 0.660 0 0 0 0 0 0 0 0 0 0.328 0.219 0 0 0 0 0 0 0 0 0.431 0.510 0.053 0.048 0.033 0.016 0 0 0 0.020 0.084 0.747 0.0714 0.100 0.067 0.042 0 0 0 0 0.036 0.778 0.100 0.111 0 0 0 0 0 0 0.085 0.686 0.064 0.042 0 0 0 0 0 0 0.048 0.727 0.083 0 0 0 0 0 0 0 0.016 0.750 JAN 86 26625.00 2398.62 764.55 200.68 148.75 38.26 14.84 18.42 8.32 Table 6.1 Fucus distichus. Continued. Chapter 6 Fucus model p.206 FEB - MAR 86 0 0 0.547 0 0 0.656 0 0 0 0 0 0 0 0 0 0 0 0 MAR- APR 86 0 0 0.219 0 0 0.438 0 0 0 0 0 0 0 0 0 0 0 0 APR - MAY 86 0 0.219 0 0 0 0 0 0 0 MAY - JUN 86 0 0 0.219 0 0 0.219 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.219 0 0 0 0 0 0 0 0 0 1.457 3.393 0 0 0 0 0 0.219 0 0 0 0 0.606 0.461 0.052 0.030 0 0.001 0.139 0.711 0.114 0 0 0 0.080 0.598 0.056 0 0 0 0.215 0/719 0 0 0 0 0.200 0 0 0 0 0 0 0 0 0.201 2.019 0 0 0 0 0 0.656 0 0 0 0 0.075 0.501 0.029 0.028 0.061 0.012 0.063 0.802 0.039 0.030 0 0 0.036 0.724 0.037 0 0 0 0.161 0.616 0 0 0 0 0.226 0 0 0 0 0 0 0 0 1.0E-10 1.0E-10 0 0 0 0 0 0.656 0 0 0 0 0.062 0.287 0.007 0 0 0.001 0.093 0.445 0 0 0 0 0.111 0.304 0.014 0 0 0.002 0.221 0.329 0 0 0 0.067 0.310 0 0 0 0 0 0 0 0 1.0E-10 1.0E-10 0 0 0 0 0 0.547 0 0 0 0 0.176 0.510 0.025 0 0 0.004 0.093 0.754 0.072 0 0 0 0.063 0.646 0.148 0 0 0 0.127 0.519 0 0 0 0 0.278 0 0 0 0 0 FEB 86 14.499 12.871 11347.37 0 0 17476.84 0 0 954.52 0.076 0.111 368.71 0.020 0 138.81 0 0 42.08 0.133 0 15.76 0.638 0.178 14.72 0.094 0.644 6.49 MAR 86 2.981 3.407 407.69 0 0 6207.08 0 0 11680.77 0.056 0.083 769.26 0 0 161.68 0 0 34.47 0 0 22.79 0.528 0 12.47 0.389 0.750 6.03 APR 86 1.0E-10 1.0E-10 114.29 0 0 89.20 0 0 10383.58 0 - 0 1616.45 0.066 0 396.01 0.018 0 51.43 0 0 27.82 0.277 0.194 16.13 0.206 0.569 10.19 MAY 86 1.0E-10 1.0E-10 0.00 0 0 25.01 0 0 6835.38 0 0.048 1199.35 0.037 0.111 264.64 0 0 44.29 0.074 0 19.59 0.439 0.167 15.80 0.280 0.468 7.40 Table 6.1 Fucus distichus. Continued. Chapter 6 Fucus model p.207 JUN - JUL 86 JUN 86 0 0 0 0 0 1.0E-10 1.0E-10 1.0E-10 1.0E-10 0.219 0 0 0 0 0 0 0 0 0 0.219 0.438 0 0 0 0 0 0 0 0 0.242 0.444 0.022 . 0 0 0 0 0 0 0.019 0.127 0.689 0.061 0 0.048 0 0 0 0 0 0.051 0.616 0.083 0 0.111 0 0 0 0 0 0.161 0.417 0.056 0.056 0 0 0 0 0 0 0.148 0.587 0 0 0 0 0 0 0 0 0.206 0.778 0.00 0.00 3744.46 1414.48 325.83 47.82 18.67 14.01 8.36 JUL - AUG 86 0 0 0 0 0 1.0E-10 1.0E-10 1.0E-10 1.0E-10 0.219 0 0 0 0 0 0 0 0 0 0.219 0.438 0 0 0 0 0 0 0 0 0.290 0.271 0.007 0.020 0.048 0 0.067 0 0 0.088 0.134 0.403 0 0.048 0.083 0.150 0 0 0 0 0.037 0.529 0 0.222 0 0 0 0 0 0 0.116 0.330 0.083 0 0 0 0 0 0 0 0.141 0.056 0 0 0 0 0 0 0 0 0.306 0.200 JUL 86 0.00 0.00 1638.59 1349.75 444.88 48.57 16.72 11.23 10.73 AUG - SEP 86 0 0 0 0 0 7.051 412.764 940.104 1019.845 0.219 0 0 0 0 0 0 0 0 0 0.219 0.438 0 0 0 0 0 0 0 0 0.243 0.338 0.012 0 0.042 0 0 0 0 0.219 0.219 0.699 0.070 0 0 0 0 0 0 0 0.123 0.601 0.042 0 0 0 0 0 0 0 0.220 0.417 0 0 0 0 0 0 0 0 0.175 0.833 0 0 0 0 0 0 0 0 0 0.286 AUG 86 0.00 0.00 717.06 920.68 522.77 61.02 16.79 4.97 10.63 SEP - OCT 86 0 0 0 0 0 22.996 736.830 0.547 0 0 0 0 0 0 0 0.219 0.219 0 0 0 0 0 0 0.598 0.439 0.010 0.018 0.026 0 0 0.000 0.180 0.692 0.039 0.083 0 0 0 0 0.109 0.627 0 0 0 0 0 0 0.227 0.448 0 0 0 0 0 0 0.315 0 0 0 0 0 0 0 0 0 0 0 0 0 0.667 0.333 0 0 0 0 0 0 0.250 0.500 SEP 86 12200.00 0.00 313.79 563.63 599.22 96.09 20.58 5.84 5.66 Chapter 6 Fucus model p. 208 Table 6.1 Fucus distichus. Continued. OCT - DEC 86 OCT 86 0 0 0 0 0 0 34.759 69.652 135.538 0.328 0 0 0 0 0 0 0 0 0.328 0.328 0.219 0 0 0 0 0 0 0 0.328 0.055 0.291 0.022 0 0 0 0 0 0 0.025 0.098 0.509 0.040 0 0 0 0 0 0.055 0 0.039 0.541 0.042 0.056 0 0 0 0 0 0 0.136 0.642 0 0 0 0 0 0 0 0 0.066 0.639 0 0 0 0 0 0 0 0 0 0.500 21645.45 6673.47 68.66 474.05 498.88 123.47 31.10 11.81 4.33 DEC 86 - JAN 87 0 0 0 0 0 9.424 44.838 95.181 131.934 0.219 0 0 0 0 0 0 0 0 0 0.328 0.328 0 0 0 0 0 0 0 0 0.008 0.316 0.059 0.031 0.021 0 0 0 0 0.001 0.056 0.516 0.128 0.066 0.067 0 0 0 0 0 0.012 0.653 0.037 0 0 0 0 0 0 0 0.096 0.658 0.233 0 0 0 0 0 0 0 0.108 0.567 0 0 0 0 0 0 0 0 0.133 1.000 DEC 86 1890.91 7104.11 9309.39 329.17 296.50 85.56 35.44 9.62 0.77 JAN - FEB 87 0 0 0 0 0 22.644 254.850 529.219 529.219 0.328 0 0 0 0 0 0 0 0 0 0.219 0.328 0 0 0 0 0 0 0 0 0.021 0.507 0.121 0.009 0 0 0 0 0 0.000 0.078 0.578 0.063 0.039 0 0 0 0 0 0 0.036 0.668 0.070 0 0.667 0 0 0 0 0 0.121 0.768 0 0 0 0 0 0 0 0 0.081 1.000 0 0 0 0 0 0 0 0 0 0.333 JAN 87 3418.18 413.74 5386.97 192.60 211.80 60.27 33.93 8.76 2.32 FEB - MAR 87 0 0 0 0 0 148.075 683.513 1535.056 1674.607 0.547 0 0 0 0 0 0 0 0 0 0.219 0.219 0 0 0 0 0 0 0 0 0.080 0.525 0.018 0.028 0.048 0.194 0 0 0 0.001 0.102 0.684 0.023 0.024 0 0 0 0 0 0 0.072 0.732 0.072 0 0 0 0 0 0 0 0.067 0.672 0 0 0 0 0 0 0 0 0.048 0.500 0 0 0 0 0 0 0 0 0 1.000 FEB 87 15990.91 1121.86 1858.55 241.45 133.49 50.37 34.06 11.72 0.77 Chapter 6 Fucus model p.209 Table 6.1 Fucus distichus. Continued. MAR - APR 87 MAR 87 0 0 0 0 0 5.815 47.133 134.983 202.475 50945.45 0.656 0 0 0 0 0 0 0 0 8747.12 0 0.438 0.219 0 0 0 0 0 0 652.12 0 0 0.145 0.380 0.006 0 0 0 0 277.99 0 0 0.003 0.186 0.723 0.026 0,067 0 0 120.62 0 0 0 0 0.094 0.465 0 0 0 49.29 0 0 0 0 0 0.408 0.499 0 0 26.89 0 0 0 0 0 0 0.334 0.722 0 7.35 0 0 0 0 0 0 0 0.222 1.000 0.77 - MAY 87 APR 87 0 0 0 0 0 1.828 5.382 15.478 13.905 2740.00 0.219 0 0 0 0 0 0 0 0 33440.95 0 0.547 0.328 0 0 0 0 0 0 3970.47 0 0 0.047 0.504 0.028 0.010 0.058 0 0 200.67 0 0 0.002 0.147 0.732 0.028 0 0 0 157.83 0 0 0 0 0.072 0.649 0.024 0 0 34.80 0 0 0 0 0 0.179 0.497 0 0 30.93 0 0 0 0 0 0 0.244 0.611 0 13.85 0 0 0 0 0 0 0 0.139 0.750 1.37 MAY - JUN 87 MAY 87 0 0 0 0 0 0.636 . 6.809 11.322 31.492 520.00 0.219 0 0 0 0 0 0 0 0 599.52 0 0.219 0.438 0 0 0 0 0 0 19595.52 0 0 0.007 0.297 0.021 0.037 0.015 0 0 292.66 0 0 0.000 0.156 0.723 0.036 0 0.015 0 149.19 0 0 0 0 0.038 0.493 0.015 0.015 0 33.76 0 0 0 0 0 0.096 0.431 0.015 0 20.83 0 0 0 0 0 0 0.162 0.523 0 16.55 0 0 0 0 0 0 0 0.030 0.625 2.74 - JUL 87 JUN 87 0 0 0 0 0 0.038 0.128 0.219 0.933 509.09 0.219 0 0 0 0 0 0 0 0 113.78 0 0.219 0.329 0 0 0 0 0 0 8706.27 0 0 0.014 0.442 0.017 0 0 0.024 0 225.84 0 0 0.000 0.159 0.595 0.032 0.109 0 0 152.68 0 0 0 0 0.075 0.308 0.111 0 0 23.95 0 0 0 0 0 0.105 0.160 0 0 12.97 0 0 0 0 0 0 0.103 0.190 0 11.56 0 0 0 0 0 0 0 0.135 0.167 2.74 Chapter 6 Fucus model p.210 Table 6.1 Fucus distichus. Continued. JUL - AUG 87 JUL 87 0 0 0 0 0 1.0E-10 1.0E-10 1.0E-10 1.0E-10 0.219 0 0 0 0 0 0 0 0 0 0.219 0.328 0 0 0 0 0 0 0 0 0.063 0.372 0.021 0 0 0 0 0 0 0.010 0.317 0.605 0.124 0 0.250 0 0 0 0 0 0.065 0.473 0.350 0 0.250 0 0 0 0 0 0.067 0.450 0 0 0 0 0 0 0 0 0.200 0.167 0 0 0 0 0 0 0 0 0.083 0 8.33 111.39 2882.32 237.23 133.22 21.24 5.11 5.49 2.33 AUG - SEP 87 AUG 87 0 0 0 0 0 21.890 490.339 689.539 919.386 0.00 0.219 0 0 0 0 0 0 0 0 1.82 0 0.219 0.438 0 0 0 0 0 0 970.36 0 0 0.199 0.356 0.009 0.056 0 0 0 268.66 0 0 0.022 0.375 0.772 0.043 0 0 0 184.92 0 0 0 0 00.075 0.641 0 0 0 23.16 0 0 0 0 0.072 0.750 0 0 3.74 0 0 0 0 0 0 0 0.500 0 1.83 0 0 0 0 0 0 0 0 1.000 0.46 - OCT 87 SEP 87 0 0 0 0 0 0 899.871 933.200 1866.400 3627.27 0.328 0 0 0 0 0 0 0 0 0.00 0 0.219 0.328 0 0 0 0 0 0 425.03 0 0 0.330 0.187 0.008 0 0 0 0 291.06 0 0 0.140 0.533 0.706 0 0.071 0 0 277.06 0 0 0 0 0.161 0.585 0 0 0 31.68 0 0 0 0 0 0.252 0.286 0 0 4.61 0 0 0 0 0 0 0.143 0.500 0 0.91 0 0 0 0 0 0 0 0 0 0.46 -NOV 87 OCT 87 0 0 0 0 0 17.850 58.042 217.656 1.0E-10 5136.36 0.438 0 0 0 0 0 0 0 0 1190.48 0 0.328 0.109 0 0 0 0 0 0 139.50 0 0 0.570 0.340 0.006 0 0 0 0 212.55 0 0 0.149 0.425 0.798 0.025 0 0 0 417.52 0 0 0 0 0.063 0.812 0 0 0 61.04 0 0 0 0 0 0.078 0.733 0.333 0 12.56 0 0 0 0 0 0 0.125 0.333 0 1.37 0 0 0 0 0 0 0 0 0 0.00 Table 6.1 Fucus distichus. Continued. Chapter 6 Fucus model p.211 NOV 87 1733.33 793.66 0.00 146.90 422.46 71.65 14.43 1.83 0.00 Chapter 6 Fucus model p.212 Table 6.2 Fucus distichus. Transition matrices of one-year cycles derived from the multiplication of monthly transition matrices. The inclusive time period represented by each matrix is indicated. Transition probability < 0.0001 is indicated by 0.0000. JUL 85 - JUL 86 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0025 0.0102 0.1076 0.0027 0.0105 0.1093 0.0024 0.0062 0.0330 0.0007 0.0018 0.0034 0.0003 0.0008 0.0012 0.0002 0.0005 0.0008 0.0001 0.0003 0.0007 SEP 85 - SEP 86 0.0707 0.2677 0.6653 0.0000 0.0000 0.0000 0.0000 0.0003 0.0019 0.0001 0.0005 0.0032 0.0004 0.0015 0.0054 0.0002 0.0007 0.0017 0.0001 0.0003 0.0006 0.0000 0.0001 0.0003 0.0000 0.0000 0.0001 OCT 85 - OCT 86 0.2882 0.2611 1.8364 0.0961 0.0884 0.6693 0.0000 0.0000 0.0003 0.0001 0;0001 0.0019 0.0008 0.0007 0.0053 0.0004 0.0004 0.0026 0.0002 0.0002 0.0013 0.0001 0.0001 0.0008 0.0000 0.0000 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1449 1.0599 5.4751 0.1456 1.0739 5.6054 0.0533 0.3251 1.7120 0:0103 0.0354 0.1528 0.0046 0.0136 0.0453 0.0031 0.0095 0.0263 0.0020 0.0074 0.0247 2.3032 8.8009 49.8703 0.0000 0.0000 0.0000 0.0087 0.0761 1.2263 0.0140 0.1207 1.9417 0.0212 0.1576 2.4150 0.0058 0.0309 0.3764 0.0020 0.0077 0.0555 0.0008 0.0031 0.0166 0.0002 0.0010 0.0058 3.3896 13.5969 77.3307 1.3322 5.5479 27.9711 0.0015 0.0104 0.2810 0.0094 0.0634 1.6909 0.0155 0.0898 2.0938 0.0058 0.0283 0.5007 0.0023 0.0099 0.1064 0.0014 0.0054 0.0281 0.0004 0.0018 0.0086 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 10.0580 16.6903 10.1412 10.3431 17.1883 10.4806 3.2356 5.4142 3.4240 0.2900 0.4839 0.3339 0.0787 0.1261 0.0892 0.0395 0.0592 0.0396 0.0404 0.0672 0.0431 99.0444 138.4946 142.0626 0.0000 0.0000 0.0000 3.1622 5.0136 4.9893 5.0261 7.9674 7.9370 6.3469 10.0396 10.0530 0.9959 1.5564 1.5754 0.1411 0.2104 0.2184 0.0356 0.0495 0.0513 0.0096 0.0131 0.0131 170.3570 223.2289 257.9201 46.5502 57.6782 64.5500 0.7920 1.1065 1.2970 4.7784 6.6750 7.8280 6.0059 8.3842 9.8565 1.4354 1.9975 2.3514 0.2960 0.4076 0.4798 0.0613 0.0796 0.0918 0.0141 0.0172 0.0192 Table 6.2 Fucus distichus. Continued. Chapter 6 Fucus model p.213 NOV 85 - DEC 86 0.0089 0.0455 0.0546 0.0412 0.2161 0.2611 0.0529 0.2882 0.3495 0.0012 0.0073 0.0090 0.0003 0.0010 0.0011 0.0002 0.0006 0.0007 0.0001 0.0004 0.0005 0.0000 0.0002 0.0002 0.0000 0.0000 0.0000 DEC 85 - DEC 86 0.0148 0.0409 0.1385 0.0621 0.1882 0.6585 0.0758 0.2415 0.8782 0.0016 0.0055 0.0224 0.0011 0.0013 0.0030 0.0005 0.0007 0.0020 0.0002 0.0005 0.0014 0.0001 0.0002 0,0006 0.0000 0.0000 0.0001 JAN 86 - JAN 87 0.0751 0.0659 0.2246 0.0072 0.0099 0.0409 0.0722 0.1379 0.6446 0.0032 0.0037 0.0176 0.0051 0.0023 0.0058 0.0018 0.0010 0.0024 0.0008 0.0006 0.0019 0.0002 0.0002 0.0007 0.0000 0.0000 0.0002 FEB 86 - FEB 87 0.2235 0.5375 0.9409 0.0156 0.0375 0.0659 0.0081 0.0385 0.1445 0.0019 0.0058 0.0156 0.0025 0.0051 0.0052 0.0011 0.0022 0.0025 0.0006 0.0013 0.0019 0.0001 0.0003 0.0007 0.0000 0.0000 0.0000 0.1696 1.0850 6.6824 0.8138 5.1062 25.2195 1.1105 7.2043 34.7639 0.0306 0.2295 1.4763 0.0040 0.0518 1.1948 0.0024 0.0205 0.3553 0.0016 0.0109 0.1297 0.0008 0.0047 0.0245 0.0001 0.0010 0.0045 0.2370 1.3155 5.2501 1.1403 6.2688 21.2886 1.5336 8.8459 30.6111 0.0397 0.2764 1.2736 0.0041 0.0515 0.7743 0.0030 0.0220 0.2315 0.0022 0.0124 0.0864 0.0011 0.0057 0.0197 0.0002 0.0013 0.0044 0.3068 1.2958 6.8936 0.0602 0.2781 1.1041 0.9917 4.8750 18.2938 0.0279 0.1485 0.7323 0.0072 0.0303 0.3895 0.0027 0.0093 0.1121 0.0025 0.0095 0.0613 0.0010 0.0044 0.0180 0.0004 0.0019 0.0079 1.6266 7.0598 16.8680 0.1146 0.5016 1.2223 0.3515 1.8930 6.2762 0.0370 0.2066 0.7446 0.0073 0.0341 0.1150 0.0031 0.0112 0.0218 0.0027 0.0102 0.0181 0.0014 0.0061 0.0146 0.0001 0.0007 0.0027 22.2338 27.5483 24.6229 74.5005 89.6323 81.3657 94.1946 113.0180 101.3990 4.1123 5.1876 4.4022 4.9801 6.5766 5.6036 1.4796 1.9369 1.6704 0.5306 0.6849 0.6004 0.0787 0.0953 0.0868 0.0089 0.0104 0.0089 21.0743 26.9198 26.4051 69.4048 89.3408 82.6228 88.0194 109.4808 102.6416 4.0134 5.2247 4.9583 4.9507 6.6692 6.7781 1.4555 1.9486 1.9789 0.5145 0.6813 0.6900 0.0735 0.0918 0.0895 0.0084 0.0102 0.0088 11.0967 14.1506 15.9604 1.4298 1.5679 1.5960 21.4432 21.1196 19.5486 0.9929 1.0813 1.0881 0.7600 1.0456 1.2310 0.2286 0.3239 0.3872 0.1106 0.1503 0.1756 0.0251 0.0296 0.0318 0.0092 0.0088 0.0080 16.9414 12.9657 10.9889 1.2405 0.9502 0.8071 7.1876 5.5034 4.8092 0.9036 0.7230 0.6434 0.1489 0.1333 0.1211 0.0238 0.0229 0.0204 0.0165 0.0141 0.0120 0.0139 0.0098 0.0081 0.0033 0.0026 0.0022 Table 6.2 Fucus distichus. Continued. Chapter 6 Fucus model p.214 MAR 86 - MAR 87 0.2052 1.4051 2.7101 0.0323 0.2235 0.4479 0.0013 0.0095 0.0253 0.0004 0.0032 0.0098 0.0005 0.0036 0.0064 0.0003 0.0018 0.0031 0.0001 0.0009 0.0016 0.0000 0.0002 0.0004 0.0000 0.0000 0.0000 APR 86 - APR 87 0.0139 0.0502 0.1716 0.1701 0.6157 2.1076 0.0177 0.0659 0.2282 0.0004 0.0016 0.0060 0.0007 0.0022 0.0075 0.0002 0.0008 0.0027 0.0002 0.0008 0.0027 0.0001 0.0003 0.0009 0.0000 0:0000 0.0001 MAY 86 - MAY 87 0.0040 0.0136 0.0477 0.0039 0.0139 0.0502 0.1249 0.4519 1.6382 0.0013 0.0049 0.0183 0.0009 0.0027 0.0092 0.0003 0.0010 0.0032 0.0002 0.0007 0.0025 0.0001 0.0005 0.0017 0.0000 0.0001 0.0003 JUN 86 - JUN 87 0.0018 0.0178 0.0606 0.0004 0.0040 0.0136 0.0175 0.2537 0.9178 0.0004 0.0058 0.0209 0.0006 0.0040 0.0130 0.0001 0.0009 0.0028 0.0001 0.0006 0.0019 0.0001 0.0005 0.0017 0.0000 0.0001 0.0003 3.6629 21.0215 50.5170 0.6820 4.1501 10.9550 0.0661 0.5158 1.9238 0.0293 0.2491 1.0437 0.0066 0.0447 0.1833 0.0026 0.0125 0.0287 0.0018 0.0087 0.0160 0.0006 0.0038 0.0098 0.0001 0.0007 0.0032 0.2297 1.2616 3.1739 2.8535 15.4373 36.7698 0.3558 2.1327 5.7322 0.0191 0.1793 0.7238 0.0104 0.0846 0.3509 0.0023 0.0110 0.0322 0.0026 0.0108 0.0215 0:0012 0.0064 0.0139 0.0002 0.0016 0.0058 0.0592 0.2494 0.7798 0.0696 0.3268 1.1514 2.3144 10.9314 37.7796 0.0306 0.1930 0.9399 0.0120 0.0826 0.4840 0.0033 0.0146 0.0609 0.0027 0.0098 0.0259 0.0021 0.0085 0.0243 0.0004 0.0023 0.0096 0.0687 0.2359 1.0158 0.0156 0.0535 0.2207 1.1777 4.5856 21.8315 0.0275 0.1181 0.6907 0.0144 0.0715 0.6101 0.0026 0.0091 0.0587 0.0019 0.0058 0.0218 0.0019 0.0061 0.0221 0.0004 0.0015 0.0085 44.2665 31.5741 29.0794 9.9289 7.1329 6.5973 1.9887 1.5329 1.4471 1.1347 0.9076 0.8633 0.2137 0.1833 0.1763 0.0300 0.0260 0.0248 0.0131 0.0099 0.0091 0.0083 0.0055 0.0050 0.0036 0.0028 0.0027 3.2746 1.8651 2.3061 36.0068 20.0581 24.3607 5.9876 3.3532 4.1514 0.9196 0.5487 0.7183 0.4695 0.2915 0.3867 0.0418 0.0273 0.0361 0.0223 0.0144 0.0182 0.0127 0.0071 0.0084 0.0069 0.0039 0.0050 0.8619 0.6293 0.4245 1.2897 0.8917 0.5816 39.6881 26.0836 16.8869 1.3151 1.0058 0.6535 0.8167 0.6931 0.4600 0.1005 0.0888 0.0605 0.0309 0.0260 0.0184 0.0237 0.0164 0.0112 0.0124 0.0088 0.0056 0.9460 1.0475 0.5651 0.1901 0.2063 0.1107 18.4745 17.4104 8.6486 0.7127 0.7430 0.3873 0.8403 1.0108 0.5614 0.0827 0.1069 0.0613 0.0228 0.0300 0.0175 0.0170 0.0191 0.0105 0.0090 0.0091 0.0046 Table 6.2 Fucus distichus. Continued. Chapter 6 Fucus model p.215 JUL 86 - JUL 87 0.0000 0.0001 0.0013 0.0005 0.0018 0.0178 0.0068 0.0266 0.3846 0.0005 0.0020 0.0286 0.0005 0.0021 0.0158 0.0001 0.0005 0.0029 0.0000 0.0001 0.0009 0.0000 0.0001 0.0007 0.0000 0.0000 0.0004 AUG 86 - AUG 87 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0091 0.0107 0.0417 0.0024 0.0029 0.0113 0.0014 0.0027 0.0102 0.0001 0.0005 0.0018 0.0000 0.0001 0.0004 0.0000 0.0000 0.0002 0.0000 0.0000 0.0000 SEP 86 - SEP 87 0.0199 0.1775 0.4570 0.0000 0.0000 0.0000 0.0001 0.0183 0.0214 0.0001 0.0124 0.0147 0.0006 0.0099 0.0156 0.0001 0.0009 0.0023 0.0000 0.0002 0.0005 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 OCT 86 - OCT 87 0.0376 0.0543 1.0742 0.0077 0.0119 0.2663 0.0000 0.0000 0.0274 0.0000 0.0001 0.0385 0.0008 0.0008 0.0738 0.0003 0.0003 0.0097 0.0001 0.0001 0.0013 0.0000 0.0000 0.0002 0 0 0 0;0013 0.0039 0.0209 0.0183 0.0545 0.2695 0.4412 1.5274 8.9547 0.0327 0.1164 0.7534 0.0150 0.0541 0.5080 0.0025 0.0077 0.0675 0.0008 0.0019 0.0103 0.0007 0.0019 0.0081 0.0004 0.0011 0.0055 0.0000 0.0000 0.0000 0.0003 0.0015 0.0064 0.1226 0.8651 4.3942 0.0330 0.2344 1.2343 0.0226 0.1361 0.8396 0.0031 0.0126 0.0809 0.0007 0.0024 0.0107 0.0003 0.0013 0.0045 0.0001 0.0003 0.0010 0.5485 2.2895 8.5764 0.0000 0.0000 0.0000 0.0169 0.2195 1.8310 0.0117 0.1491 1.2471 0.0145 0.1267 1.0052 0.0026 0.0127 0.0764 0.0006 0.0024 0.0088 0.0001 0.0006 0.0022 0.0000 0.0002 0.0011 0.6540 2.5897 11.9081 0.1530 0.6259 2.9086 0.0017 0.0266 0.4925 0.0025 0.0375 0.6923 0.0095 0.0817 1.3154 0.0029 0.0145 0.1630 0.0008 0.0028 0.0175 0.0001 0.0005 0.0024 0 0 0 0.0292 0.0287 0.0093 0.3289 0.3206 0.0970 9.9646 8.1462 1.6896 0.9778 0.8362 0.2144 1.0340 1.0117 0.3699 0.1497 0.1545 0.0605 0.0196 0.0221 0.0090 0.0084 0.0094 0.0031 0.0060 0.0057 0.0016 0.0000 0.0000 0.0000 0.0103 0.0206 0.0089 5.7714 9.8165 2.1891 1.7337 3.0255 0.7835 1.7292 3.3684 1.4744 0.2336 0.4849 0.2707 0.0299 0.0622 0.0384 0.0086 0.0169 0.0105 0.0012 0.0020 0.0010 25.6437 43.1022 44.1697 0.0000 0.0000 0.0000 3.6774 5.0788 3.1018 2.5788 3.6043 2.2720 2.7007 4.1377 3.2379 0.3052 0.5155 0.4853 0.0377 0.0664 0.0689 0.0041 0.0063 0.0063 0.0014 0.0017 0.0013 15.6819 17.2666 18.0636 3.4736 3.4909 3.7926 1.2842 1.9668 1.0114 1.8084 2.7710 1.4311 3.4726 5.3350 2.9172 0.4273 0.6560 0.4038 0.0402 0.0600 0.0463 0.0029 0.0031 0.0034 0 0 0 Table 6.2 Fucus distichus. Continued. Chapter 6 Fucus model p.216 DEC 86 - NOV 87 0.0044 0.0141 0.0184 0.1997 0;6794 4.7667 13.5211 23.9351 20.0634 0.0059 0.0207 0.0295 0.4292 1.6476 7.2926 8.8207 10.5450 14.1991 0.0009 0.0031 0.0046 0.0734 0.2966 1.4247 1.6603 1.9110 2.4740 0.0000 0.0000 0.0001 0.0013 0.0155 0.5232 1.7644 3.2289 2.1554 0.0003 0.0009 0.0011 0.0110 0.0590 1.4125 4.8224 8.8405 6.1192 0.0001 0.0004 0.0005 0.0046 0.0165 0.2150 0.7272 1.3312 0.9924 0.0000 0.0001 0.0001 0.0014 0.0044 0.0280 0.0812 0.1449 0.1248 0.0000 0.0000 0.0000 0.0002 0.0008 0.0035 0.0076 0.0126 0.0126 0 0 0 0 0 0 0 0 0 Chapter 6 Fucus model p.217 Table 6.3 Fucus distichus. Results of the simulation showing the mean + S.D., and highest and lowest growth rates (lambda) recorded from using different combinations of transition matrices projected over different fixed periods of time. The mean value is based on 100 replicates. Models Growth Rate Mean ± S.D. Highest Lowest Monthly Matrix 5 years 0.503 ± 0.076 5.800 0.012 Seasonal Matrix 5 years 1.094 ± 0.123 8.043 0.034 10 years 0.911 ± 0.134 6.460 0.007 Yearly Matrix 5 years 0.899 ± 0.179 16.060 0.035 10 years 1.471 ± 0.555 52.093 0.008 \ Chapter 6 Fucus model p.218 Table 6.4 Fucus distichus. Dominant eigenvalues of the seasonal matrices. Season Winter Spring Summer Fall 1986 0.6469 0.6455 0.5695 1.7755 1987 1.4984 0.4646 0.6894 1.7423 Chapter 6 Fucus model p.219 2000i 1600 1200 800 CNl 400 E 0 m 800-1 CN 600 • o \ 400 Ul L 200 r z 0 160i CL It 120 a 1 o 80 40 LU m 0 ZD SIZE GLASS 1 SIZE CLASS 4 SIZE CLASS 3 25n 20 SIZE CLASS 6 2500 2000 1500 1000 500 0 JAODFAJAODFAJAOD TOTAL JAODFAJAODFAJAOD 1985 1986 1987 TIME Figure 6.1 Fucus distichus. Mean number of plants in each size class and total number of plants recorded from field observations over time, compared with the number simulated from the matrix models. Dotted outlines indicate the upper and lower boundaries of ± S.E. respectively, of the field estimates. Chapter 6 Fucus model p.220 40T RECRUITS 301 20 10 0 100 80 60 _ 40 Q_ 20 ° rr 100 | 80 > 60 40 20 0 100 80 60 40 20 0 J A O D F A J A O D F A J A O D A~vv\ / V SIZE CLASS 1 SIZE CLASS 4 CO SIZE CLASS 2 ' '?"• "'T 1 I 1 1 I 1 SIZE CLASS 5 i" • i i i i V SIZE CLASS 3 /v \ ft / \ I - . 4 . / \ SIZE CLASS 6 J A O D F A J A O D F A J ' A O D J A O D F A J A O D F A J A O D 1985 1986 1987 1985 1986 1987 TIME Figure 6.2 Fucus distichus. Survivorship of recruits and plants in different size classes over time as estimated from the matrix models. Chapter 6 Fucus model p.221 LU !< LY O LY O 1.4-1 1.2-1.0-0.8-0.6-0.4 o o W/0 RECRUITMENT A A W/ RECRUITMENT : A A A \/ A. o o T r T 1 1 r J A O D F A J A O D F A J A O D 1985 1986 1987 TIME Figure 6.3 Fucus distichus. Dominant eigenvalue (population growth rate) calculated for each monthly matrix M (with recruitment) and monthly submatrix D (without recruitment). Dotted horizontal line indicates eigenvalue = 1. Chapter 6 Fucus model p.222 241 20 1 16 1 12-LU O 8 rr i. i 4-LU Q_ 0 161 12-8 4-°i PLANT SURVIVAL 100 80 60 40 20 0 J A O D F A J A O D F A J A O D RECRUITS SURVIVAL GERMLING BANK MACRORECRUITS FECUNDITY 1985 1986 1987 1985 TIME 1986 1987 Figure 6.4 Fucus distichus. Relative contribution (%) of different matrix parameters in each monthly matrix M to population growth rate, as estimated from elasticity analysis. Chapter 6 Fucus model p. 223 0 - - 0 SURVIVAL * 14i SIZE CLASS 1 12 10 8 6 0 :Q O a a • 30 25 20 <y° 15 10 5 0 •o FECUNDITY SIZE CLASS 4 OOo<* ? 9 od oQ 100T SIZE CLASS 2 80 60 z UJ 40 g 20 80 60 40 201 o 9 100 801 60 40 °o° 20 SIZE CLASS 5 Q • p ; o SIZE CLASS 6 9 ? 06 Ql r?oxxPi3E& J A O D F A J A O D F A J A O D 1985 1986 1987 : : *P A O D F A J A O D F A J A O D 1985 1986 1987 TIME Figure 6.5 Fucus distichus. Relative contribution (%) of survivorship and fecundity of each size class to population growth rate, as estimated from elasticity analysis on each monthly matrix M. Chapter 6 Fucus model p.224 nn R E C R U I T S M A C R O — P L A N T S O I— Q: o o_ o rr 100 i 80-60-40 20-0 i " i L J A O D F A J A O D F A J A O D 1985 1986 1987 TIME Figure 6.6 Fucus distichus. Proportion (%) of all recruits vs. other plants in the size classes at stable distribution calculated for each monthly matrix M. Recruits included all intermediate stages of microrecruits and other plants included all plants from size classes 1 (with macrorecruits) to 6. Chapter 6 Fucus model p.225 JUL-SEP85 la Ji f l l r\B LZ3 STABLE DIST. FIELD NOV—DEC85 20 i 15 10 5 •Ji nM flu rv—. 0 FEB—MAR86 » q a R SEP—OCT85 I 1.5 1.0 0.5 J J u o OCT-NOV85 u 2 3 4 5 6 1 L DEC85-JAN86 JAN—FEB86 2 3 4 5 6 SIZE CLASS 15 12 9 6 3 • 0 60 40 20 0 MAR-APRB6 l i x a. APR—MAY86 1 2 3 4 5 6 Figure 6.7A Fucus distichus. Proportion (%) of plants in different size classes at stable distribution calculated for each monthly matrix M from Jul-Sep 85 to Apr-May 86, compared with the corresponding observed monthly distribution of the plants in the field. Chapter 6 Fucus model p.226 o^ LY. O CL O LY. CL 50 40 30 20 10 0 40 30 20 10 0 50 40 30 20 10 0 MAY-JUN86 1 1- n n n A JUN—JULB6 I JUL—AUG86 I 1 2 3 4 5 6 STABLE DIST. I AUG—SEP86 A r j FIELD 2.5 2.0 1.5 1.0 0.5 < 0 SEP-0CT86 OCT—DEC86 1 2 3 4 5 6 SIZE CLASS DEC86—JAN87 —a, 1.5 1.2 0.9 0.6 0.3 - 0 2.0 1.5 1.0 0.5 - 0 JAN—FEB87 J 1 J i n . . . FEB—MAR87 2 3 4 5 6 Figure 6.7B Fucus distichus. Proportion (%) of plants in different size classes at stable distribution calculated for each monthly matrix M from May-Jun 86 to Feb-Mar 87, compared with the corresponding observed monthly distribution of the plants in the field. Chapter 6 Fucus model p.227 3 2 1 0 5 4 3 2 1 0 30 20 10 0 II MAR-APR87 CZI STABLE DIST. 69i FIELD 46 23 I r\- ry n,—0, , Q 1 2 3 4 5 6 JUN-JULB7 -JQX. J n APR—MAY87 L I . f i n f MAY—JUN87 »-!!—a,—a, , , 60 40 20 0 8 6 4 2 0 I JUL-AUG87 L AUG—SEP87 -01-1 2 3 4 5 6 SIZE CLASS 8 6 4 2 0 10 8 6 4 2 0 SEP-0CT87 _ J _ n OCT—N0VB7 1 2 3 4 5 6 Figure 6.7C Fucus distichus. Proportion (%) of plants in different size classes at stable distribution calculated for each monthly matrix M from Mar-Apr 87 to Oct-Nov 87, compared with the corresponding observed monthly distribution of the plants in the field. Chapter 6 Fucus model p.228 o R E C R U I T S LU ID LU > CD Q O Q_ LU LY 6i 4 2 0 - 2 • - - • S C 1 A A S C 2 A - - - A S C 3 S C 4 «-—o S C 5 v v S C 6 J A O D 1985 A J A O D 1986 TIME F A J A 0 D 1987 Figure 6.8 Fucus distichus. Reproductive values (log) of all recruits and plants in each size class calculated for each monthly matrix M. Chapter 6 Fucus model p.229 < LY O LY O 2.0 1.6-1.2-0.8-0.4-0.0 o W/0 RECRUITMENT A W/ RECRUITMENT A W/0 GERMLING BANK • A A o o o A * A 9 9 9 9 0 0 90 T T ^ A A A Q O O O *T"—"r J S 0 N D J F M A M J J A S 0 D 1985 1986 TIME Figure 6.9 Fucus distichus. Dominant eigenvalue (population growth rate) calculated for each yearly matrix S (with recruitment), yearly submatrix D Y (without recruitment), and yearly matrix S with transition from microrecruit to germling bank set to 0 (without germling bank). Only the starting month of each yearly matrix is indicated in the x axis. Dotted horizontal line indicates eigenvalue = 1. Chapter 6 Fucus model p.230 100i 80 60 40 20 0 ^7 0 ^ ^ 60 ^ 5 0 f— 40 Ld 3 0 O 20 80i 60 40 20 0 PLANT SURVIVAL In it 1 MICRORECRUIT SURVIVAL 40 30 20 10 - 0 40 30 20 10 MACRORECRUITS JAM GERMLING BANK PI •P 111 . 0 40 30 20 10 • 0 i i i i l l l i i i PLANT TO MICRORECRUIT Bill FECUNDITY Lj j l . JS0NDJ FMAMJJAS0D JJSONDJFMAMJJAS0D 1985 1986 1985 1986 TIME Figure 6.10 Fucus distichus. Relative contribution (%) of different matrix parameters in each yearly matrix Y to population growth rate, as estimated from elasticity analysis. X axis legend as in Fig. 6.9. Chapter 6 Fucus model p.231 UJ o Cd U J Q_ 25 20 15 10 5 0 50 40 30 20 10 0 60 50 40 30 20 10 SIZE CLASS 1 o SURVIVAL A PLANT TO MICRO n FECUNDmr • TOTAL 40 30 20 Pi 1 0 SIZE CLASS 2 15 12 SIZE CLASS 4 ° | o | SIZE CLASS 3 J J S O N D 1985 9 6 3 0 6 5 4 3 2 1 0 SIZE CLASS 5 fir 3 o 0 M -SB PI On -0*1-, SIZE CLASS 6 J F M A M J J A S O D 1986 TIME V J S O N D J F M A M J J A S O D 1985 1986 Figure 6.11 Fucus distichus. Relative contribution (%) of survivorship, fecundity and transition from plant to microrecruits of each size class to population growth rate, as estimated from elasticity analysis on each yearly matrix Y. X axis legend as in Fig. 6.9. Chapter 6 Fucus model p. 232 100-. 80 O 60-LY O Q_ O LY Q_ 40-20-0 CZ1 RECRUITS mm MACRO—PLANTS L I I I I J J S O N D J F M A M J J A S O D 1985 1986 TIME Figure 6.12 Fucus distichus. Proportion (%) of all recruits vs. other plants in the size classes at stable distribution calculated for each yearly matrix Y. X axis legend as in Fig. 6.9. Recruits included all intermediate stages of microrecruits and other plants included all plants from size classes 1 (with macrorecruits) to 6. Chapter 6 Fucus model p.233 LU < > LU Q O O L o o RECRUITS - - • SC1 SC4 4 i A A SC2 o - — o SC5 A - - - - A SC3 v v SC6 3-2-1 O-l 1 * A - A -A- ^ - A - © •'X ^ o V—V. - • J A- ^7 A . . o o i i T r T r J J S O N D J F M A M J J A S O D 1 9 8 5 1 9 8 6 TIME Figure 6.13 Fucus distichus. Reproductive values (log) of all recruits and plants in each size class calculated for each yearly matrix Y. X axis legend as in Fig. 6.9. p.234 SUMMARY DISCUSSION An understanding of algal population dynamics is essential to our understanding of the organization of the rocky intertidal and subtidal communities. Algal populations are important structural components of intertidal and subtidal rocky shores in themselves, and they also provide the structure on which other organisms depend on. One of the fundamental questions about studies on algal populations is which state variable best describes their demographic parameters. In this thesis, I addressed the prediction of these parameters (specifically reproduction, growth and mortality) of Fucus distichus L. emend. Powell as a function of plant size (length) versus that of plant age (months). Using log linear and association analyses, I concluded that size is a better descriptor of these parameters than age, although age is also significant. Other state variables, such as biomass or number of bifurcations of Fucus, may also be important descriptors of demographic parameters. More studies are needed to ascertain the significance of these other variables. It is at present premature to extend the results from these studies on Fucus to other algal populations and to conclude that size is the most important descriptor of algal demographic parameters. Each algal species needs to be assessed separately, as some state variables may be unique to a particular algal species. It is only by evaluating the relative importance of different state variables that the population dynamics of any algal population can be better understood. One other topic that has currently received much attention among plant and animal ecologists is recruitment. To date, most recruitment studies on algal populations are based on the visible recruits. Information on the microscopic stage, the stage when dispersing propagules first settle on the substratum, is scarce but is beginning to be addressed. Most recently, different aspects of algal recruitment, notably microclimate experienced by algal propagules (Amsler et al. 1991); diversity and functional significance of algal reproductive structures (Clayton 1991); settlement, attachment Summary Discussion p. 235 characteristics and responses of algal propagules to external stimuli (Fletcher 1991); competitive interactions between germlings of different algal groups (Vadas 1991), as well as relative merits of short and long distance dispersal of algal propagules (Norton 1991) are being evaluated. In this thesis, I assessed seasonal variation of recruitment and reproduction in a Fucus population. Both the microscopic and the macroscopic stages of recruits were monitored. Reproductive plants and macrorecruits were present in the population throughout the sampling period from May 1985 to November 1987. However, microrecruits were absent in the settling blocks in the summers of 1986 and 1987. There were pulses of large numbers of microrecruits in the winter and fall of 1986, and the spring of 1987. It is significant to note that contrary to what one would expect, these large pulses of microrecruits were not always followed by an increase in the number of macrorecruits observed in the permanent quadrats. This is indicative of the seasonal and annual variations in the survival of the microrecruits. Pulses of a large number of microrecruits do not guarantee an increase in the number of individuals that would eventually become part of the population. This increase is not only dependent on the presence of microrecruits, but more importantly on how these recruits survive through the "environmental sieve". Factors associated with this "environmental sieve" may be density-related. Microrecruits survived better at higher density than at low density in the first 2 months after settlement on the substratum. When these recruits became older, the effect of density was reversed. Similar to that observed among macrorecruits, plants growing at higher density experienced a higher mortality. Eventually, however, plant survival became density-independent. This relationship suggests the importance of clustering at the early microrecruitment stage. It also points out that the environment encountered by the microrecruits is conceivably very different from that experienced by the larger Summary Discussion p.236 plants. Growth is more related to plant size than to plant density. The mechanism of dominance-suppression and difference in the intrinsic growth rate or timing of settlement probably all contributed to the inequality in the size distribution. The potential number of eggs produced by Fucus plants, measured in terms of the number of eggs per conceptacle in a receptacle, was found to be size-dependent. However, the actual number of eggs released from each conceptacle, measured in terms of the number of eggs within egg clusters released from the receptacle, is not related to plant size. This means that the number of microrecruits developed from fertilized eggs can not be accurately predicted from knowing the size of the plants. Recruitment may be uncoupled with reproductive phenology and thus, the number of eggs released from the plants at any specific time may itself be a source of variation that affects the number of recruits that would eventually entering the population. The presence of a "germling bank" may account for the continuous presence of macrorecruits even in the absence of any significant microrecruitment into the population during summer. The possible existence of a "germling bank" among other algal populations has been previously suggested and is now beginning to receive more attention from algal ecologists (Hoffman and Santelices 1991, Santelices et al. 1991). The significance of a "germling bank", if it exists and if it could contribute significantly to the number of macrorecruits, would be to stabilize any fluctuations in the size of the population. From an evolutionary viewpoint, the relationship between growth, reproduction, and mortality, can be evaluated in the light of the resource allocation theory. I observed that the cost of reproduction in Fucus is manifested by reduced growth, rather than in greater mortality or shorter longevity of the fertile plants. The failure to detect decreased survival as a cost of reproduction may be related to the modular organization Summary Discussion p.237 of the plants, where cost occurs at the level of the modules (branches) rather than at the level of the whole plant. The absence of a cost of reproduction may also explain the ability of the plant to produce large numbers of eggs or propagules continuously without suffering an increased mortality. In this sense, the plants have both the advantage of producing lots of propagules for colonizing any new area, as well as the capacity to persist in areas already colonized. The production of large numbers of recruits could compensate for any uncertainty associated with recruitment. The information on the population dynamics of Fucus obtained from field studies were synthesized in matrix models. Both monthly and yearly matrices were constructed each corresponding respectively to a monthly and yearly transition time-step within the sampling period. The models quantified the relative importance of the different demographic parameters, such as recruitment, survival of the adults, and the "germling bank", on the population growth rate. These models also pointed out gaps in our information about these populations, notably data on germling bank, survival from microrecruit to macrorecruits, and on density-dependent survival of recruits. Simulation of the models suggested that a significant decline may be experienced by the population from time to time, but the trend could be reversed by pulses of recruits which may then be responsible for the maintenance of the population. This hypothesis needs to be tested with further long term monitoring of the population. But now that a base line information is available, further monitoring could be continued to better understand the natural variation in population demographics. This thesis represents a very detailed analysis of the population dynamics of a common intertidal brown alga, Fucus distichus. Although various aspects of its population ecology have been addressed, results from this study also pointed to areas where important information is still lacking. The role of recruitment in maintaining the population needs to be studied in greater depth. Microclimate experienced by the Summary Discussion p.238 recruits and its effect on their survival needs to be examined. 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H. (1984). Biostatistical analysis. Second Edition. Prentice-Hall, Inc., Englewood Cliffs, N.J., U.S.A. p.253 APPENDIX A Age vs. Size as the Descriptor of Growth and Mortality in Fucus distichus L. emend. Powell Log linear analysis tests the significance of a state variable like age or size, or both, as a descriptor of a demographic parameter in a population. Association analyses quantify the contribution of these state variables to the demographic parameter and allow an assessment of the relative importance of one state variable versus the other as a descriptor or predictor of the parameter. Age and size were assessed as descriptors of growth and mortality in a population of Fucus distichus L. emend. Powell from False Creek, Vancouver, Canada using these 2 methods. Presented in this appendix are detailed results from these analyses. Fucus plants were monitored monthly in 3 permanent quadrats from July 1985 to November 1987. They were divided into 5 age classes, 5 size classes, and 4 growth categories as described in Chapter 2. Monthly data were initially used to test for the relative importance of age vs. size on growth and mortality. However, this approach resulted in greater than 20% of the cells in the contingency table having a value less than 5, making the statistical analysis doubtful. To remedy this problem, pooling of data was attempted. Kruskal-Wallis One Way ANOVA by Rank was used to test for significant difference in the growth and mortality rates among the permanent quadrats at different months. Data from the 3 permanent quadrats were not pooled as they were tested to be significantly different in some months. For each quadrat, monthly growth and mortality data were pooled only when tested to be insignificantly different. As much as possible, data were pooled to reflect seasonal patterns. Appendix A p.254 Log Linear Analysis i When growth is considered with mortality, the combined effect of age and size on growth (ASG) is significant in only 3 out of 14 seasons in all 3 quadrats (Table A.l A). The contribution of age alone (AG) is significant in 11 out of 14 seasons and that of size alone (SG) is always significant. The contribution of age, given the known contribution of size (ASG/AG), is significant in 9 out of 14 seasons. In comparison, the contribution of size, given the known contribution of age (ASG/SG) is significant in all but one season. When mortality is not considered (Table A. IB), the combined effect of age and size on growth (ASG) is significant in only 1 season. Age alone (AG) is significant as a descriptor of growth in 8 out of 15 seasons, and size (SG), 13 out of 15 seasons. The contribution of age, given the known contribution of size (ASG/AG), is significant in 6 out of 15 seasons, and that of size, given the known contribution of age (ASG/SG), is significant in all except 2 seasons. On an annual basis, the significant effect of age or size, or both, on growth does not follow any discernible seasonal pattern. Among the 3 quadrats, combined effect of age and size on mortality (ASM) is significant in 7 out of 12 seasons (Table A.2). The effect of age alone (AG) is significant also in 7 out of 12 seasons, and that of size (SG), in all except 2 seasons. The effect of age, given the known effect of size (ASM/AG), is significant in 6 out of 12 seasons. That of size, given the known effect of age (ASM/SG), is significant in 8 out of 12 seasons. The significant effect of age or size, or both on mortality does not follow any overall seasonal trend. Association Analyses Simple, multiple and partial associations were tested on growth and mortality data from each quadrat similarly pooled by seasons. As described in Chapter 1, the relative Appendix A p.255 importance of size vs. age as a descriptor of growth or mortality is given as a log ratio between the association coefficients (T) of size and age. A ratio > 0 indicates that size is more important than age as a descriptor of the demographic parameter being associated with. For the Fucus data, size is in most cases more important than age as a descriptor of growth when mortality is also considered (Fig. A.l A). Size could be 191.6% more important than age as in March to April 1987 in quadrat 2 or 42.4% less important than age, as in October 1986 to January 1987 in quadrat 3. The relative importance of size is more obvious when mortality is not included in the analyses (Fig. A. IB). Except for the extreme case where size is less important than age by 173% in February to March 1986 in quadrat 1, in all other seasons, size is more important than age from 18.5% in February to August 1987 in quadrat 3 to as high as 549% in March to April 1987 in quadrat 2. Size is also a better descriptor of mortality than age, when mortality is considered alone (Fig. A.2). Although size may be less important than age by 13.3% in November 1985 to June 1986 in quadrat 1, in most other cases, size is more important than age by a range from 19.4% in February to March 1987 in quadrat 1 to 178.7% in October to December 1986 in quadrat 2. Appendix A p.256 Table A. 1 Fucus distichus. Results of the log linear analyses on the effect of age vs. size on growth, with or without the effect of mortality, in different seasons. Values given as G statistic. Degrees of freedom in parentheses. See text for explanation of the models. SEASONS LOG LINEAR MODELS ASG AG SG ASG/AG ASG/SG A. Growth Rate with the Effect of Mortality Quadrat 1 Feb-Jun 86 32.84* (18) 27.38** (9) 50.90** (6) 17.24* (9) 40.76** (6) Oct-Dec 86 39.88** (18) 130.14** (9) 124.04** (6) 75.22** (9) 69.12** (6) Jan-Feb 87 14.54 (18) 51.54** (9) 59.68** (6) 30.98** (9) 39.12** (6) May-Jul 87 27.80 (18) 60.98** (9) 79.84** (6) 19.38* (9) 38.24** (6) Quadrat 2 Feb-Apr 86 11.32 (12) 28.80** (6) 54.02** (6) 23.22** (6) 48.44** (6) Jun-Jul 86 37.50** (18) 26.90** (9) 74.80** (6) 10.16 (9) 58.06** (6) Oct 86 - Feb 87 22.16 (18) 58.64** (9) 102.62** (6) 32.92** (9) 76.90** (6) Mar-Apr 87 17.32 (18) 9.68 (9) 55.72** (6) 6.66 (9) 52.70** (6) Jul, Aug, Oct 87 22.30 (18) 43.02** (9) 52.86** (6) 30.38** (9) 40.22** (6) Quadrat 3 Feb-May 86 10.36 (12) 9.76 (6) 40.10** (6) 13.38* (6) 43.72** (6) Aug-Sep 86 19.16 (18) 9.78 (9) 30.56** (6) 13.32 (9) 34.10** (6) Oct 86 - Jan 87 10.18 (18) 17.48* (9) 13.24* (6) 13.20 (9) 8.96 (6) Feb, Apr - Jul 87 18.28 (18) 27.34** (9) 36.90** (6) 21.92** (9) 31.48** (6) Aug-Sep 87 17.42 (18) 25.04** (9) 38.92** (6) 13.84 (9) 27.72** (6) Appendix A p.257 Table A.l Fucus distichus. Continued. SEASONS LOG LINEAR MODELS ASG AG SG ASG/AG ASG/SG B. Growth Rate without the Effect of Mortality Quadrat 1 Feb-Mar 86 1.48 (2) 1.74 (2) 0.80 (1) 1.36 (2) 0.42 (1) Apr-Aug 86 13.24 (12) 53.40** (6) 122.94** (4) 13.74* (6) 83.28** (4) Dec 86 - Feb 87 29.76** (12) 30.06** (6) 45.40** (4) 27.42** (6) 42.76** (4) Mar, Aug-Sep 87 30.62** (12) 61.76** (6) 188.90** (4) 24.52** (6) 151.66** (4) Apr-Jun 87 12.72 (12) 67.92** (6) 108.12** (4) 7.90 (6) 48.10** (4) Quadrat 2 Feb-Mar 86 5.36 (8) 11.76* (4) 21.20** (4) 10.42* (4) 19.76** (4) Jun-Jul 86 29.68** (12) 25.40** (6) 62.66** (4) 8.78 (6) 46.04** (4) Oct 86 - Feb 87 14.56 (12) 13.12* (6) 62.10** (4) 9.80 (6) 58.78** (4) Mar-Apr 87 11.48 (12) 6.04 (6) 51.22** (4) 2.24 (6) 47.42** (4) May-Jun 87 9.68 (12) 6.86 (6) 11.04* (4) 6.64 (6) 10.82* (4) Quadrat 3 Feb-Apr 86 7.16 (8) 2.96 (4) 33.96** (4) 1.10 (4) 32.10** (4) May-Jun 86 8.84 (8) 10.70* (4) 13.42** (4) 15.22** (4) 17.94** (4) Aug-Sep 86 10.24 (12) 8.36 (6) 30.36** (4) 10.40 (6) 32.40** (4) Oct-Dec 86 4.32 (12) 3.16 (6) 5.56 (4) 3.12 (6) 5.52 (4) Feb, Apr, May-Aug 87 11.40 (12) 9.28 (6) 17.40** (4) 15.64* (6) 23.76** (4) **P «£ 0.01 * 0.01 < P <, 0.05 Appendix A p.258 Table A.2 Fucus distichus. Results of the log linear analyses on the effect of age vs. size on mortality at different seasons in each quadrat. Values given as G statistic. Degrees of freedom in parentheses. See text for explanation of the models. SEASONS LOG LINEAR MODELS ASM AG SG ASM/AG ASM/SG Quadrat 1 Nov 85 - Jun 86 9.10 (9) 10.02* (3) 7.46 (3) 8.52* (3) 5.96 (3) Feb-Mar 87 19.74 (12) 6.34 (3) 29.20** (4) 4.70 (3) 27.56** (4) May-Jul 87 26.72** (12) 13.44** (3) 9.80* (4) 10.82* (3) 7.18 (4) Quadrat 2 Nov 85 - Mar 86 9.88 (6) 0.16 (2) 20.86** (3) 0.88 (2) 21.58** (3) Jul-Sep 86 14.52 (12) 9.08* (3) 36.46** (4) 5.32 (3) 32.70** (4) Oct-Dec 86 24.28* (12) 36.22** (3) 70.52** (4) 9.40* (3) 43.70** (4) Jan-May, Jul 87 33.60** (12) 6.78 (3) 16.92** (4) 4.64 (3) 14.78** (4) Aug-Oct 87 21.56* (9) 2.92 (3) 10.76* (3) 2.38 (3) 10.22* (3) Quadrat 3 Jan-Mar 86 2.64 (3) 3.90* (1) 6.24 (3) 2.74 (1) 5.08 (3) Jun-Oct 86 22.60* (12) 32.20** (3) 62.56** (4) 12.28** (3) 42.64** (4) Jan-Jul 87 21.70* (12) 6.98 (3) 11.30* (4) 8.98* (3) 13.30** (4) Aug-Oct 87 33.92* (12) 26.08** (3) 18.04** (4) 16.00** (3) 7.96 (4) ** P <S 0.01 * 0.01 < P <, 0.05 Appendix A p.259 UJ O < CO > LU M CO _ l < < Q_ O O 0.500i 0.250 0.000 •0.250 1.000 0.500 0.000 •0.500 A GROWTH WITH MORTALITY B GROWTH WITHOUT MORTALITY • QUADRAT 1 LZ] QUADRAT 2 EX] QUADRAT 3 N J M M J 1986 S N TIME J M M J 1987 Figure A.l Fucus distichus. The relative importance of size vs. age in describing plant growth rate with or without considering the effect of mortality in the analysis. The results are based on pooled data for each quadrat representing different times of the year. Relative importance is given as a ratio of log association coefficients. Ratio > 0 indicates that size is more important than age and vice versa. Appendix A p.260 O - 0 . 1 0 0 - J . 1 - i . 1——. • , 1 - i - r O N J M M J S N J M M J S 1986 1987 T I M E Figure A.2 Fucus distichus. The relative importance of size vs. age in determining the probability of plant mortality in each quadrat at different times of the year. p.261 APPENDIX B Transition Matrices from Permanent Quadrats and Elasticity Analysis on Monthly and Yearly Matrices A transition matrix was constructed based on the fate of each individual mapped and monitored in each of the 3 50 x 50 cm permanent quadrats. A total of 32,894 individuals were censused over the period from July 1985 to November 1987. Individuals were divided into 6 size classes as indicated in the matrix N in Table 6.1. Their fate was scored according to whether they survived and, if they did, whether they became larger, smaller, or did not change in size significantly. Theoretically, it is possible for any plant to move to any size class within a single time-step of one month. Division of the plants into 6 size classes provided a more uniform distribution of the transition probabilities such that, in general, an individual plant only moved 1 size class below or above, or stayed in the same size class, per unit time-step. Each transition probability in the matrix is a mean value for all plants in the same size class. The matrix model assumes that individuals in each size class have similar behaviour and experience the same fate. Each matrix in Table B. 1 represents only the dynamics of the plants in each permanent quadrat over each month (except those for July to September 1985 and October to December 1986). Each column of the matrix represents the monthly survivorship of the plants in the corresponding size class. The sum of all transition probabilities in each column is therefore < 1. Elasticity analysis is a measure of the proportional sensitivity of population growth rate to each matrix entry. The sum of all elements in an elasticity matrix = 1. It is therefore superior to sensitivity analysis in that it allows comparison of the relative importance of different demographic traits, e.g. fecundity, survival of the adults etc., Appendix B p.262 to population growth rate to be made directly. Different demographic traits are measured in different scales, e.g. fecundity is measured in terms of hundreds of propagules or recruits produced whereas survivorship value will always be < 1. Their relative importance to the population can not be deciphered readily based on sensitivity analysis. Elasticity analysis was originally developed by de Kroon et al. (1987) and their paper should be consulted for more details about this technique. The results of elasticity analysis on each monthly and yearly matrix are presented in Tables B.2 and B.3 respectively. Appendix B p.263 Table B. 1 Fucus distichus. Monthly transition matrix for each permanent quadrat. Where no plant was present for a particular size class, the transition element is indicated by a dot (.). QUADRAT 1 JUL - SEP 85 0.27451 0 0 0.18137 0.46154 0.01818 0 0.05769 0.23636 0 0 0.20000 0 0 0 0 0 0 SEP - OCT 85 0.34615 0 0.05556 0.16026 0.56716 0 0 0.01493 0.77778 0 0 0 0 0 0 0 0 0 OCT - NOV 85 0.66197 0.10448 0 0 0.74627 0.11111 0 0 0.77778 0 0 0 0 0 0.05556 0 0 0 NOV - DEC 85 0.61039 0.07407 0 0.03896 0.79630 0.06250 0 0 0.75000 0 0 0.12500 0 0 0 0 0 0 0 0 0 0 0 0 0.02222 0.03030 0 0.40000 0 0 0.22222 0.42424 0 0.02222 0.24242 0.33333 0 0 0 0 0 0 0.06897 0.04167 0 0.48276 0.12500 0 0.17241 0.50000 0 0 0.25000 0.84615 0 0.05882 0 0 0 0 0.05882 0 0.05882 0.82353 0.29412 0 0.05882 0.58824 0.41176 0 0.05882 0.52941 0.05000 0 0 0 0 0.10000 0.05000 0 0 0.70000 0.05263 0 0.10000 0.84211 0.30000 0 0.05263 0.60000 Table B.l Fucus distichus. Continued. Appendix B p.264 QUADRAT 1 DEC 85 - JAN 86 0.52632 0.04082 0 0.10526 0.69388 0.23077 0 0.12245 0.53846 0 0 0.07692 0 0 0 0 0 0.07692 JAN - FEB 86 0.45082 0.09804 0.14286 0.06557 0.66667 0.07143 0 0.01961 0.71429 0 0 0.07143 0 0 0 0 0 0 FEB - MAR 86 0.34109 0.06667 0 0.20155 0.68889 0.16667 0 0.06667 0.58333 0 0 0.16667 0 0 0 0 0 0 MAR - APR 86 0.47977 0.04348 0.08333 0.06936 0,79710 0 0 0.02899 0.66667 0 0 0.16667 0 0 0 0 0 0 0 0 0 0.23529 0 0 0.05882 0 0 0.47059 0.04762 0 0.11765 0.90476 0 0 0.04762 0.85714 0.10000 0.04762 0.00000 0.10000 0 0.12500 0.10000 0 0 0.60000 0.19048 0.12500 0 0.71429 0.25000 0 0.04762 0.50000 0 0.11765 0 0 0.05882 0 0.16667 0 0 0.50000 0.17647 0 0.25000 0.47059 0.20000 0 0.05882 0.60000 0.09091 0.16667 0.25000 0.09091 0 0 0 0 0 0.54545 0 0 0.18182 0.58333 0 0 0.16667 0.75000 Table B.l Fucus distichus. Continued. Appendix B p.265 QUADRAT 1 APR - MAY 86 0.21344 0 0 0.05172 0.10969 0 0 0.01280 0.14583 0 0 0.02083 0 0 0 0 0 0 MAY - JUN 86 0.48795 0 0 0.10723 0.64901 0.06250 0 0.09272 0.50000 0 0 0.12500 0 0 0 0 0 0 JUN - JUL 86 0.40824 0 0 0.19060 0.67672 0.08696 0 0.07759 0.52174 0 0 0.21739 0 0 0 0 0 0 JUL - AUG 86 0.18384 0 0.03125 0.18384 0.19172 0 0 0.03268 0.28125 0 0 0.12500 0 0 0 0 0 0 0 0 0 0 0.05263 0 0.04167 0.05263 0 0.20833 0 0 0.04167 0.21053 0.25000 0 0 0.37500 0 0 0 0 0 0.33333 0 0 0 0.33333 0 0 0.50000 0.42857 0 0 0.28571 0.33333 0 0 0 0 0 0 0.25000 0 0.33333 0.25000 0.16667 0 0 0.33333 0 0 0.33333 0.66667 0.14286 0 0 0.14286 0 0 0 0.50000 0 0.14286 0 0 0 0 0 0 0 0 Appendix B p.266 Table B. 1 Fucus distichus. Continued. QUADRAT 1 AUG - SEP 86 0.38473 0 0 0 0.31756 0.78571 0.04000 0 0 0.08791 0.60000 0 0 0 0.20000 0.40000 0 0 0 0.40000 0 0 0 0 SEP - OCT 86 0.39332 0.19794 0 0 0 0 0 0.67102 0.11111 0 0 0 0 0 0.56522 0.30435 0 0 0 0 0 0.28571 0.71429 0 0 0 0 0 0.50000 0.50000 OCT - DEC 86 0.22420 0.08185 0 0 0 0 0.00286 0.36571 0.03714 0 0 0 0 0.04110 0.53425 0.06849 0 0 0 0 0.12500 0.68750 0.12500 0 0 0 0.16667 0 0.50000 0 0 0 0 0 0 1 DEC 86 - JAN 87 0.22680 0.06395 0.01852 0.06250 0 0.07216 0.41279 0.07407 0 0.20000 0 0.01744 0.62963 0 0 0 0 0.07407 0.62500 0.20000 0 0 0 0.12500 0.20000 0 0 0 0 0.40000 0 0 0 0 0 1 Table B.l Fucus distichus. Continued. Appendix B p. 267 QUADRAT 1 JAN - FEB 87 0.42727 0.21705 0.02703 0.05455 0.35659 0.05405 0 0.03876 0.59459 0 0 0.13514 0 0 0 0 0 0 FEB - MAR 87 0.51471 0 0 0.08088 0.71698 0.06897 0 0.01887 0.86207 0 0 0.06897 0 0 0 0 0 0 MAR - APR 87 0.41667 0.01887 0 0.20370 0.62264 0 0 0.18868 0.33333 0 0 0.58333 0 0 0 0 0 0 APR-MAY 87 0.41958 0.01587 0.03030 0.14685 0.81746 0 0 0.07143 0.69697 0 0 0.12121 0 0 0 0 0 0 0 0 0 0 0 0 0.06667 0 0.66667 0.80000 0 0 0.06667 1 0 0 0 0.33333 0 0.25000 0 0 0 0 0 0 0 0.94444 0 0 0 0.50000 0 0 0 1 0 0 0 0 0 0 0 0 0 0.52632 0 0 0.31579 0.50000 0 0 0.50000 1 0.03125 0 0 0 0 0 0 0 0 0.56250 0 0 0.37500 0.83333 0 0 0.08333 0.50000 Table B. 1 Fucus distichus. Continued. Appendix B p.268 QUADRAT 1 MAY - JUN 87 0.32743 0.03150 0 0.04545 0 0 0.15929 0.69291 0.03030 0 0.04545 0 0 0.06299 0.60606 0.04545 0.04545 0 0 0 0.21212 0.22727 0.04545 0 0 0 0 0.31818 0.31818 0 0 0 0 0 0.09091 0.50000 JUN - JUL 87 0.43421 0.21053 0 0 0 0 0.01739 0.60870 0.09565 0 0 0 0 0.09677 0.45161 0.06452 0 0 0 0.07692 0 0.23077 0.30769 0 0.07143 0 0 0 0.57143 0.07143 0 0 0 0 0 0.33333 JUL - AUG 87 0.45000 0.21000 0 0 0 0 0.04301 0.54839 0.03226 0 0 0 0 0.04000 0.72000 0 0 0 0 0 0.20000 0.40000 0.40000 0 0 0.25000 0 0 0.16667 0.08333 0 0 0.50000 0 0 0 AUG - SEP 87 0.39080 0.36782 0 0 0 0 0 0.74390 0.08537 0 0 0 0 0.13043 0.56522 0.21739 0 0 0 0 0 1 0 0 0 0 0 0 0.50000 0 0 0 0 0 0 1 Table B.l Fucus distichus. Continued. Appendix B p.269 QUADRAT 1 SEP - OCT 87 0.23005 0.56338 0 0 0 0 0.00719 0.73381 0.11511 0 0 0 0 0 0.35000 0.40000 0 0 0 0.14286 0 0.57143 0.28571 0 0 0 0 0 0.50000 0 0 0 0 0 0 0 OCT - NOV 87 0.35542 0.56627 0 0 0 0 0.00405 0.86235 0.05668 0 0 0 0 0 0.87500 0.08333 0 0 0 0 0 0.66667 0.25000 0 0 0 0 0.33333 0.33333 0 QUADRAT 2 JUL - SEP 85 0.09412 0.50588 0 0 0 0 0 0.45946 0.21622 0 0 0 0.07895 0.05263 0.26316 0.18421 0.02632 0.02632 0.17647 0 0 0.23529 0.05882 0.05882 0.09091 0.09091 0 0.09091 0 0.54545 0 0 0 0 0 0.44444 SEP - OCT 85 0.57047 0.07383 0 0 0 0 0 0.83117 0.05195 0 0 0 0.05556 0.05556 0.50000 0.22222 0 0 0 0 0.08333 0.50000 0.33333 0 0 0 0 0 0.50000 0.50000 0.08333 0 0 0 0 0.83333 Table B.l Fucus distichus. Continued. Appendix B p. 270 QUADRAT 2 OCT - NOV 85 0.39444 0.02632 0 0.07222 0.90789 0.07143 0 0.01316 0.92857 0 0 0 0 0 0 0 0 0 NOV - DEC 85 0.39234 0.22353 0.05882 0.03828 0.65882 0.05882 0 0.03529 0.76471 0 0 0.11765 0 0 0 0 0 0 DEC 85 - JAN 86 0.46957 0.07463 0 0.05217 0.74627 0 0 0.02985 0.75000 0 0 0.06250 0 0 0 0 0 0 JAN - FEB 86 0.61579 0.03125 0 0.08947 0.78125 0.14286 0 0.01563 0.78571 0 0 0.07143 0 0 0 0 0 0 0.10000 0 0 0 0 0 0.30000 0 0 0.60000 0.40000 0 0 0.20000 0.27273 0 0.20000 0.72727 0 0 0.11111 0 0 0 0 0 0 0.66667 0 0 0.33333 0.75000 0.22222 0 0.25000 0.66667 0 0 0 0.12500 0 0.14286 0 0 0 0.75000 0 0 0.12500 1 0.14286 0 0 0.57143 0 0 0 0 0.20000 0 0 0 0 0.85714 0 0 0.14286 0.80000 0 0 0 0.75000 Appendix B p.271 Table B.l Fucus distichus. Continued. QUADRAT 2 FEB - MAR 86 0.49630 0.05479 0 0 0.11111 0.33333 0.12346 0.64384 0.08333 0 0 0 0 0.12329 0.66667 0 0 0 0 0 0.25000 0.85714 0.22222 0 0 0 0 0.14286 0.44444 0.33333 0 0 0 0 0.22222 0.33333 MAR - APR 86 0.53358 0.07960 0 0 0 0 0.01010 0.80808 0.03030 0 0 0 0 0.11765 0.70588 0.11765 0 0 0.09091 0 0 0.63636 0.27273 0 0 0 0 0 0.66667 0.33333 0 0 0 0 0 1 APR - MAY 86 0.32831 0.12312 0 0 0 0 0.02013 0.57047 0.10067 0.00671 0 0 0 0 0.26667 0.26667 0.20000 0 0 0 0 0.44444 0.44444 0 0 0.14286 0 0 0.28571 0.28571 0 0 0 0 0 1 MAY - JUN 86 0.52955 0.09891 0 0 0 0 0.02510 0.74477 0.04603 0 0 0 0 0.05263 0.78947 0.10526 0 0 0 0 0.33333 0.55556 0.11111 0 0 0.11111 0 0.22222 0.22222 0.22222 0.14286 0 0 0 0 0.57143 Table B.l Fucus distichus. Continued. Appendix B p.272 QUADRAT 2 JUN - JUL 86 0.43595 0.12603 0 0 0 0 0.02273 0.68939 0.06061 0 0 0 0 0.03448 0.62069 0.20690 0 0 0 0 0 0.44444 0.11111 0 0 0 0 0 1 0 0 0 0 0.16667 0 0.66667 JUL - AUG 86 0.13019 0.11560 0 0 0 0 0.00627 0.27273 0.04702 0 0 0 0.02941 0 0.38235 0.14706 0 0 0 0 0 0.18182 0.09091 0 0 0.25000 0 0.25000 0 0.25000 0 0.25000 0 0 0 0 AUG - SEP 86 0.26073 0.22112 0 0 0 0 0.00485 0.60680 0.14078 0 0 0 0 0.03571 0.53571 0.39286 0 0 0.12500 0 0.12500 0.25000 0.12500 0 0 0 0 0 1 0 0 0 0 0 0 0 SEP - OCT 86 0.40212 0.20635 0 0 0 0 0.01429 0.67143 0.09048 0 0 0 0 0.06522 0.63043 0.21739 0 0 0.07692 0 0 0.30769 0.23077 0 0 0 0 0 0.50000 0.50000 Table B. 1 Fucus distichus. Continued. Appendix B p.273 QUADRAT 2 OCT - DEC 86 0.29714 0.01563 0 0 0 0.08000 0.50000 0.07843 0 0 0 0.01563 0.47059 0 0 0 0 0.19608 0.57143 0 0 0 0 0.07143 0.75000 0 0 0 0 0 DEC 86 - JAN 87 0.40000 0.07438 0.07407 0 0 0.03200 0.51240 0.07407 0.05556 0 0 0 0.74074 0.11111 0 0 0 0.03704 0.77778 0.50000 0 0 0 0.05556 0.50000 0 0 0 0 0 JAN - FEB 87 0.42697 0.04494 0 0 0 0 0.02857 0.65714 0 0 0 0 0 0.04545 0.68182 0.13636 0 0 0 0.11765 0 0.64706 0.17647 0 0 0 0 0 1 0 FEB - MAR 87 0.52564 0.06410 0 0 0 0 0 0.75472 0.03774 0 0 0 0 0 0.66667 0.13333 0 0 0 0.07143 0.07143 0.35714 0.14286 0 0 0 0 0 0.66667 0 Table B. 1 Fucus distichus. Continued. Appendix B p.274 QUADRAT 2 MAR - APR 87 0.40909 0 0 0 0 0.15909 0.76596 0.07692 0 0 0 0 0.46154 0 0 0 0 0.30769 0.57143 0 0 0 0 0.28571 0.66667 0 0 0 0 0.16667 APR-MAY 87 0.50495 0.24752 0 0 0 0 0 0.71250 0.10000 0 0 0 0 0 0.66667 0.33333 0 0 0 0 0.07143 0.21429 0.35714 0 0 0 0 0 0.33333 0.33333 0 0 0 0 0 1 MAY - JUN 87 0.25600 0.20800 0 0 0 0 0.03297 0.64835 0.02198 0 0 0 0 0.07692 0.53846 0.07692 0 0 0 0 0 0.40000 0 0 0 0 0 0 0.25000 0 0 0 0 0 0 0.75000 JUN - JUL 87 0.36782 0.12644 0 0 0 0 0.03371 0.46067 0.03371 0 0 0 0 0 0.22222 0 0 0 0 0 0.33333 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Appendix B p.275 Table B. 1 Fucus distichus. Continued. QUADRAT 2 JUL - AUG 87 0.29670 0 0 0.37363 0.58491 0.33333 0 0.05660 0.50000 0 0 0 0 0 0 0 0 0 AUG - SEP 87 0.38037 0.01333 0.16667 0.25153 0.76000 0 0 0.04000 0.50000 0 0 0 0 0 0 0 0 0 SEP - OCT 87 0.12139 0 0 0.55491 0.63725 0 0 0.20588 0.83333 0 0 0 0 0 0 0 0 0 OCT - NOV 87 0.29808 0 0 0.37500 0.79592 0.03846 0 0.06122 0.76923 0 0 0.07692 0 0 0 0 0 0 Table B. 1 Fucus distichus. Continued. Appendix B p.276 QUADRAT 3 OCT - NOV 85 0.50000 0.33333 0 0 0 0 0.12329 0.79452 0.01370 0 0 0 0 0.06250 0.87500 0.06250 0 0 0 0 0.33333 0.50000 0 0 0 0 0 1 0 0 0 0 0 0 0.50000 0.50000 JAN - FEB 86 0.46341 0.09756 0 0 0 0 0.02941 0.79412 0.07353 0 0 0 0 0 0.83333 0.11111 0 0 0 0.20000 0.20000 0.60000 0 0 0 0 0.33333 0 0.66667 0 0 0 0 0 0 1 FEB - MAR 86 0.54545 0.09091 0 0 0 0 0.03333 0.80000 0.05000 0 0 0 0.09091 0.09091 0.54545 0.22727 0 0 0 0 0 0.80000 0.20000 0 0 0 0 0 1 0 0 0 0 0 0 1 MAR - APR 86 0.48837 0.04070 0 0 0 0 0.03333 0.80000 0.05000 0 0 0 0 0 0.80000 0.20000 0 0 0 0 0.11111 0.66667 0.22222 0 0 0 0 0 0.33333 0.66667 0 0 0 0 0 0.50000 Table B. 1 Fucus distichus. Continued. Appendix B p.277 QUADRAT 3 APR - MAY 86 0.31925 0 0 0.10329 0.65455 0 0 0.21818 0.50000 0 0 0.37500 0 0 0 0 0 0 MAY - JUN 86 0.51309 0.04918 0 0.07330 0.86885 0.10000 0 0.04918 0.65000 0 0 0.15000 0 0 0 0 0 0 JUN - JUL 86 0.48649 0.04286 0 0.06486 0.70000 0.05882 0 0.01429 0.70588 0 0 0.05882 0 0 0 0 0 0 JUL - AUG 86 0.50000 0.01587 0 0.10127 0.74603 0 0 0.03175 0.92308 0 0 0.07692 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.33333 0 0 0.44444 0.33333 0.33333 0 0.33333 0.33333 0 0 0 0 0 0 0.11111 0 0 0.66667 0 0 0.22222 0.66667 0.50000 0 0.33333 0.50000 0 0 0 0 0.14286 0 0 0 0 0.55556 0 0 0.33333 0.42857 0 0 0.28571 1 0 0 0.20000 0 0 0.20000 0 0.16667 0 0.66667 0 0 0.33333 0.16667 0 0 0.66667 0.60000 Table B.l Fucus distichus. Continued. Appendix B p.278 QUADRAT 3 AUG - SEP 86 0.36765 0.03125 0 0.11765 0.70313 0.13333 0 0.14063 0.66667 0 0 0.06667 0 0 0 0 0 0 SEP - OCT 86 0.52273 0.01563 0.05263 0.13636 0.73438 0.05263 0 0.12500 0.68421 0 0 0.15789 0 0 0 0 0 0 OCT - DEC 86 0.35165 0.04839 0 0.13187 0.66129 0 0 0.06452 0.61905 0 0 0.14286 0 0 0 0 0 0 DEC 86 - JAN 87 0.32258 0.03774 0 0.06452 0.62264 0.23529 0 0.01887 0.58824 0 0 0.17647 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.60000 0 0 0 0.66667 0 0 0 0.57143 0 0 0 0.25000 0 0 0 0 0 0.75000 0 0 0 1 0.25000 0 0 0.50000 0 0 0 0 0 0 0 0 0 0.66667 0 0 0 0.66667 0 0 0 0 0 0 0.14286 0 0 0 0.57143 0 0.14286 1 0 0 Table B. 1 Fucus distichus. Continued. Appendix B p.279 QUADRAT 3 JAN - FEB 87 0.66667 0.13333 0 0 0 0 0.11628 0.72093 0.06977 0 0 0 0 0.09091 0.72727 0.09091 0 0 0 0 0.14286 0.85714 0 0 0 0 0 0 1 0 FEB - MAR 87 0.53571 0.16071 0 0 0 0 0.05263 0.57895 0.15789 0 0 0 0.08333 0 0.66667 0 0 0 0.14286 0 0.14286 0.71429 0 0 0.33333 0 0 0 0 0 MAR - APR 87 0.31522 0.19565 0 0 0 0 0 0.78125 0.09375 0 0 0 0 0 0.60000 0.33333 0 0 0 0.20000 0 0.40000 0.40000 0 0 0 0 0 1 0 APR - MAY 87 0.58730 0.04762 0 0 0 0 0.06667 0.66667 0.04444 0 0 0 0 0.08333 0.58333 0.08333 0 0 0.14286 0 0 0.71429 0 0 0 0 0 0 0.66667 0 Table B. 1 Fucus distichus. Continued. Appendix B p.280 QUADRAT 3 MAY - JUN 87 0.30769 0 0.11111 0 0.10000 0.82857 0 0 0 0.02857 0.33333 0 0 0 0 0.66667 0 0 0 0.16667 0 0 0 0 0 0 0 0 1 0 JUN - JUL 87 0.52336 0.14019 0 0 0 0 0 0.71429 0.09524 0 0 0 0 0 0.25000 0.25000 0 0 0 0.25000 0 0.25000 0 0 0 0 0 0 0 0.33333 JUL - AUG 87 0.36792 0.36792 0 0 0 0 0.02128 0.68085 0.10638 0 0 0 0 0 0.20000 0.20000 0 0 0 0 0.50000 0.50000 0 0 0 0 0 0 0 0 AUG - SEP 87 0.29630 0.50617 0 0 0 0 0.01250 0.81250 0.10000 0 0 0 0 0 0.85714 0 0 0 0 0 0 0.50000 0 0 Table B. 1 Fucus distichus. Continued. Appendix B p.281 QUADRAT 3 SEP - OCT 87 0.20988 0.48148 0 0 0 0 OCT - NOV 87 0.36508 0.33333 0 0 0 0 0.01695 0 0 0.74576 0 0 0.16102 0.57143 0 0 0.35714 0 0 0 0 0 0 0 0.01316 0 0 0.73684 0.03704 0 0.07237 0.66667 0 0 0.07407 0.80000 0 0 0 0 0 0 Appendix B p.282 Table B.2 Fucus distichus. Results of elasticity analyses on monthly transition matrices showing the proportional contribution of each transition element to population growth. Contributions < 0.0001 are indicated by 0.0000. JUL - SEP 85 0 0 0 0 0 0.0206 0.0446 0.0206 0.0472 0.0750 0 0 0 0 0 0 0 0 0.0580 0.0137 0.0221 0 0 0 0 0 0 0 0.0613 0.0037 0.0166 0 0.0011 0.0008 0.0001 0 0 0 0 0.0669 0.0681 0.0021 0 0.0002 0 0 0 0.0680 0 0.0693 0.0509 0.0007 0.0003 0 0 0 0 0 0 0.0927 0.0491 0.0018 0 0 0 0 0 0 0.0111 0.0378 0.0145 0 0 0 0 0 0 0.0107 0.0105 0.0260 0.0340 - OCT 85 0 0 0 0 0 0.0067 0.0068 0.0053 0.0271 0.0459 0 0 0 0 0 0 0 0 0 0.0459 0.0141 0 0 0 0 0 0 0 0 0.0116 0.0118 0 0.0004 0 0 0.0002 0 0 0.0343 0.0121 0.1438 0.0007 0 0 0 0 0 0 0 0.0471 0.1137 0.0038 0.0006 0 0 0 0 0 0 0.0437 0.0537 0.0040 0 0 0 0 0 0 0 0.0372 0.0435 0 0 0 0 0 0 0 0 0.0273 0.2588 r - NOV 85 0 0 0 0 0 0.0038 0.0061 0.0017 0.0008 0.0125 0 0 0 0 0 0 0 0 0 0.0125 0.0001 0 0 0 0 0 0 0 0 0.0125 0.0243 0.0064 0 0.0001 0.0000 0 0 0 0 0.019 0.1854 0.0056 0 0 0 0 0 0 0 0.0182 0.5310 0.0213 0 0.0001 0 0 0 0 0 0.0147 0.0677 0.0152 0 0 0 0 0 0 0.0155 0.0025 0.0084 0.0032 0 0 0 0 0 0 0 0.0041 0.0072 Table B.2 Fucus distichus. Continued. Appendix B p.283 NOV - DEC 85 0 0 0 0 0 0.0000 0.0009 0.0044 0.0036 89 0 0 0 0 0 0 0 0 0 0.0089 0.0027 0 0 0 0 0 0 0 0 0.0089 0.0113 0.0007 0.0000 0.0000 0 0.0001 0 0 0 0.0097 0.0381 0.0004 0 0 0.0007 0 0 0 0 0.0101 0.0518 0.0019 0 0 0 0 0 0 0 0.0117 0.0749 0.0158 0 0 0 0 0 0 0 0.0246 0.4953 0.0615 0 0 0 0 0 0 0 0.0657 0.0875 - JAN 86 0 0 0 0 0 0.0054 0.0129 0.0249 0.0127 59 0 0 0 0 0 0 0 0 0 0.0559 0.0249 0 0 0 0 0 0 0 0 0.0068 0.0072 0.0014 0 0 0 0 0 0 0.0491 0.0082 0.1301 0.0038 0.0010 0 0.0003 0 0 0 0 0.0610 0.0944 0.0007 0 0 0 0 0 0 0 0.0330 0.0481 0.0029 0 0 0 0 0 0 0 0.0213 0.2598 0.0096 0 0 0 0 0 0.0195 0 0.0031 0.0460 JAN - FEB 86 0 0 0 0 0 0.0439 0.0218 0.0044 0.0003 0.0703 0 0 0 0 0 0 0 0 0 0.0703 0.0181 0 0 0 0 0 0 0 0 0.0538 0.0508 0.0018 0.0002 0.0000 0.0000 0 0 0 0.0165 0.0560 0.1741 0.0023 0.0007 0.0001 0.0000 0 0 0 0 0.0736 0.2141 0.0062 0.0010 0 0 0 0 0 0 0.0344 0.0627 0.0008 0.0000 0 0 0 0 0 0 0.0065 0.0139 0.0001 0 0 0 0 0 0 0 0.0004 0.0009 FEB - MAR 86 0 0 0 0 0 0.0041 0.0097 0.0253 0.0058 0.0448 0 0 0 0 0 0 0 0 0 0.0448 0.0124 0 0 0 0 0 0 0 0 0.0446 0.0403 0.0023 0.0003 0 0.0005 0.0002 0 0 0.0002 0.0479 0.1270 0.0046 0 0.0005 0 0 0 0 0 0.0509 0.0862 0.0082 0 0 0 0 0 0 0 0.0502 0.1727 0.0194 0 0 0 0 0 0 0 0.0516 0.1015 0.0073 0 0 0 0 0 0 0 0.0132 0.0234 Table B.2 Fucus distichus. Continued. Appendix B p.284 MAR - APR 86 0 0 0 0 0 0.0004 0.0028 0.0027 0.0101 0160 0 0 0 0 0 0 0 0 0 0.0160 0.0495 0 0 0 0 0 0 0 0 0.0084 0.0216 0.0024 0.0007 0.0010 0.0006 0.0029 0 0 0.0076 0.0159 0.3843 0.0057 0.0028 0 0 0 0 0 0 0.0296 0.1778 0.0058 0 0 0 0 0 0 0 0.0286 0.0699 0 0 0 0 0 0 0 0 0.0163 0.0252 0 0 0 0 0 0 0 0 0.0130 0.0823 - MAY 86 0 0 0 0 0 0.0000 0.0000 0.0000 0.0000 0000 0 0 0 0 0 0 0 0 0 0.0000 0.0000 0 0 0 0 0 0 0 0 0.0000 0.0000 0.0000 0 0 0 0 0 0 0.0000 0.0000 0.0139 0 0 0.0073 0 0 0 0 0.0071 0.0092 0.0003 0.0040 0 0 0 0 0 0.0002 0;0085 0.0082 0 0 0 0 0 0 0 0.0028 0.0084 0.0880 0.1168 0 0 0 0 0 0 0 0,1168 0.6083 - JUN 86 0 0 0 0 0 0.0000 0.0000 0.0000 0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0075 0.0034 0 0 0 0.0014 0 0 0 0.0048 0.3654 0.0189 0 0.0052 0.0118 0 0 0 0 0.0373 0.2099 0.0250 0 0 0 0 0 0 0 0.0433 0.0920 0.0134 0 0 0 0 0 0 0 0.0317 0.0511 0.0147 0 0 0 0 0 0 0 0.0279 0.0353 JUL 86 0 0 0 0 0 0.0000 0.0000 0.0000 0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0003 0.0002 0 0 0 0 0 0 0 0.0002 0.0238 0.0038 0 0.0011 0 0 0 0 0 0.0048 0.1064 0.0086 0 0.0245 0 0 0 0 0 0.0342 0.0531 0.0042 0.0150 0 0 0 0 0 0 0.0448 0.1058 0 0 0 0 0 0 0 0 0.0395 0.5296 Table B.2 Fucus distichus. Continued. Appendix B p.285 JUL - AUG 86 0 0 0 0 0 0.0000 0.0000 0.0000 0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0058 0.0004 0.0024 0.0029 0 0.0009 0 0 0 0.0065 0.0485 0 0.0066 0.0031 0.0046 0 0 0 0 0.0205 0.6474 0 0.0383 0 0 0 0 0 0 0.0564 0.0833 0.0057 0 0 0 0 0 0 0 0.0526 0.0056 0 0 0 0 0 0 0 0 0.0055 0.0029 3 - SEP 86 0 0 0 0 0 0.0016 0.0296 0.0416 0 0.0728 0 0 0 0 0 0 0 0 0 0.0728 0.0469 0 0 0 0 0 0 0 0 0.0552 0.0242 0.0006 0 0.0002 0 0 0 0 0.0177 0.0559 0.1281 0.0031 0 0 0 0 0 0 0 0.0761 0.0909 0.0020 0 0 0 0 0 0 0 0.0733 0.0436 0 0 0 0 0 0 0 0 0.0416 0.1222 0 0 0 0 0 0 0 0 0 0 - OCT 86 0 0 0 0 0 0.0037 0.0311 0.0330 0.0149 0.0827 0 0 0 0 0 0 0 0 0 0.0827 0.0165 0 0 0 0 0 0 0 0 0.0825 0.0414 0.0003 0.0001 0.0000 0 0 0 0 0.0002 0.0829 0.0932 0.0008 0.0005 0 0 0 0 0 0 0.0841 0.0761 0 0 0 0 0 0 0 0 0.0795 0.0408 0 0 0 0 0 0 0 0 0.0479 0.0579 0.0088 0 0 0 0 0 0 0 0.0237 0.0145 r - D E C 86 0 0 0 0 0 0 0.0913 0.0303 0 0.0296 0 0 0 0 0 0 0 0 0.0920 0.0292 0.0325 0 0 0 0 0 0 0 0.0004 0.0012 0.0006 0.0000 0 0 0 0 0 0 0.0039 0.0016 0.0061 0.0008 0 0 0 0 0 0.1161 0 0.0062 0.1394 0.0037 0.0008 0 0 0 0 0 0 0.1261 0.2065 0 0 0 0 0 0 0 0 0.0311 0.0504 0 0 0 0 0 0 0 0 0 0 Table B.2 Fucus distichus. Continued. Appendix B p. 286 DEC 86 - JAN 87 0 0 0 0 0 0.0000 0.0000 0.0000 0.0000 0.0001 0 0 0 0 0 0 0 0 0 0.0001 0.0000 0 0 0 0 0 0 0 0 0.0000 0.0000 0.0000 0.0000 0.0000 0 0 0 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0 0 0 0 0 0.0000 0.0000 0.0000 0 0 0 0 0 0 0 0.0000 0.0000 0.0000 0 0 0 0 0 0 0 0.0000 0.0000 0 0 0 0 0 0 0 0 0.0000 0.9997 1 - FEB 87 0 0 0 0 0 0.0000 0.0000 0.0024 0 0.0024 0 0 0 0 0 0 0 0 0 0.0024 0.0012 0 0 0 0 0 0 0 0 0.0024 0.0026 0.0001 0.0000 0 0 0 0 0 0.0000 0.0025 0.0035 0.0000 0.0000 0 0 0 0 0 0 0.0025 0.0055 0.0003 0 0 0 0 0 0 0 0.0027 0.0088 0 0 0 0 0 0 0 0 0.0024 0.9584 0 0 0 0 0 0 0 0 0 0 I - MAR 87 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 R - APR 87 0 0 0 0 0 0.0011 0.0055 0.0130 0.0333 0.0529 0 0 0 0 0 0 0 0 0 0.0529 0.0127 0 0 0 0 0 0 0 0 0.0493 0.0251 0.0002 0 0 0 0 0 0 0.0035 0.0495 0.0966 0.0005 0.0008 0 0 0 0 0 0 0.0542 0.0379 0 0 0 0 0 0 0 0 0.0526 0.0416 0 0 0 0 0 0 0 0 0.0463 0.0819 0 0 0 0 0 0 0 0 0.0333 0.2554 Table B.2 Fucus distichus. Continued. Appendix B p.287 APR - MAY 87 0 0 0 0.0297 0 0 0 0.0297 0.0191 0 0 0.0275 0 0 0.0022 0 0 0 0 0 0 0 0 0 0 0 0 MAY-JUN 87 0 0 0 0.0011 0 0 0 0.0011 0.0016 0 0 0.0010 o o o.oooi 0 0 0 0 0 0 0 0 0 0 0 0 JUN -JUL 87 0 0 0 0.0002 0 0 0 0.0002 0.0002 0 0 0.0002 0 0 0.0000 0 0 0 0 0 0 0 0 0 0 0 0 JUL - AUG 87 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0021 0 0 0 0 0 0 0.0527 0.0047 0.0007 0.0351 0.2855 0.0044 0 0.0369 0.1350 0 0 0.0323 0 0 0 0 0 0 0 0 0.0001 0 0 0 0 0 0 0.0089 0.0094 0.0026 0.0133 0.9015 0.0071 0 0.0118 0.0243 0 0 0.0025 0 0 0 0 0 0 0 0 0.0001 0 0 0 0 0 0 0.0512 0.0206 0 0.0212 0.8252 0.0115 0 0.0209 0.0220 0 0 0.0111 0 0 0 0 0 0 0 0 0.0000 0 0 0 0 0 0 0.0173 0.0153 0 0.0153 0.4465 0.0459 0 0.0551 0.2000 0 0 0.0499 0 0 0 0 0 0 0.0033 0.0101 0.0142 0 0 0 0 0 0 0.0021 0 0 0 0 0 0.0026 0 0 0.0469 0 0 0.0243 0.0652 0 0 0.0142 0.1195 0.0003 0.0004 0.0003 0 0 0 0 0 0 0.0003 0 0 0. 0.0007 0 0.0002 0.0002 0 0.0036 0.0001 0 0.0017 0.0040 0 0 0.0003 0.0016 0.0001 0.0000 0.0000 0 0 0 0 0 0 0 0.0004 0 0.0088 0 0 0.0018 0 0 0.0038 0 0 0.0004 0.0002 0 0 0.0000 0.0000 0.0000 0.0000 0.0000 0 0 0 0 0 0 0 0 0 0 0.0092 0 0.0394 0 0.0013 0.0898 0 0 0.0105 0.0033 0 0 0.0013 0 Table B.2 Fucus distichus. Continued. Appendix B p.288 AUG - SEP 87 0 0 0 0 0 0.0103 0.0568 0 0 0.0670 0 0 0 0 0 0 0 0 0 0.0670 0.0484 0 0 0 0 0 0 0 0 0.0559 0.0303 0.0012 0.0015 0 0 0 0 0 0.0112 0.0586 0.2047 0.0022 0 0 0 0 0 0 0 0.0707 0.1125 0 0 0 0 0 0 0 0 0.0568 0.1451 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SEP - OCT 87 0 0 0 0 0 0 0.0906 0.0160 0 56 0 0 0 0 0 0 0 0 0 0.1066 0.0346 0 0 0 0 0 0 0 0 0.0556 0.0091 0.0006 0 0 0 0 0 0 0.0510 0.0562 0.1201 0 0.0006 0 0 0 0 0 0 0.1072 0.0831 0 0 0 0 0 0 0 0 0.1072 0.0291 0 0 0 0 0 0 0 0 0.0160 0.0095 0 0 0 0 0 0 0 0 0 0 OCT - NOV 87 0 0 0 0 0 0.0366 0.0257 0.0148 0 71 0 0 0 0 0 0 0 0 0 0.0771 0.0081 0 0 0 0 0 0 0 0 0.0515 0.0220 0.0007 0 0 0 0 0 0 0.0256 0.0522 0.1813 0.0011 0 0 0 0 0 0 0 0.0782 0.1902 0 0 0 0 0 0 0 0 0.0405 0.0824 0.0058 0 0 0 0 0 0 0 0.0206 0.0085 0 0 0 0 0 0 0 0 0 0 Appendix B p.289 Table B.3 Fucus distichus. Results of elasticity analyses on yearly transition matrices showing the proportional contribution of each transition element to population growth. Contributions < 0.0001 are indicated by 0.0000. JUL 85 - JUL 86 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0086 0.0000 0.0000 0.0195 0.0000 0.0000 0.0272 0.0000 0.0000 0.0125 0.0000 0.0000 0.0083 0.0000 0.0000 0.0093 0.0000 0.0000 0.0048 SEP 85 - SEP 86 0.0034 0.0000 0.0006 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0001 0.0026 0.0000 0.0006 0.0139 0.0000 0.0021 0.0149 0.0000 0.0019 0.0083 0.0000 0.0012 0.0014 0.0000 0.0003 OCT 85 - OCT 86 0.0272 0.0084 0.0004 0.0081 0.0025 0.0001 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000 0.0040 0.0011 0.0001 0.0240 0.0071 0.0003 0.0309 0.0093 0.0004 0.0239 0.0074 0.0003 0.0073 0.0023 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0118 0.0273 0.0158 0.0264 0.0614 0.0360 0.0447 0.0860 0.0508 0.0390 0.0424 0.0205 0.0320 0.0296 0.0111 0.0357 0.0343 0.0107 0.0149 0.0171 0.0064 0.0031 0.0149 0.0143 0.0000 0.0000 0.0000 0.0001 0.0011 0.0031 0.0006 0.0062 0.0170 0.0041 0.0384 0.1000 0.0113 0.0767 0.1584 0.0100 0.0485 0.0593 0.0064 0.0297 0.0273 0.0019 0.0098 0.0096 0.0043 0.0227 0.0335 0.0015 0.0083 0.0108 0.0000 0.0001 0.0008 0.0001 0.0013 0.0091 0.0011 0.0081 0.0490 0.0043 0.0276 0.1262 0.0046 0.0255 0.0713 0.0037 0.0192 0.0258 0.0014 0.0073 0.0092 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0104 0.0110 0.0053 0.0238 0.0252 0.0122 0.0344 0.0366 0.0184 0.0139 0.0148 0.0081 0.0069 0.0070 0.0040 0.0057 0.0055 0.0029 0.0038 0.0040 0.0020 0.0052 0.0024 0.0007 0.0000 0.0000 0.0000 0.0015 0.0008 0.0002 0.0080 0.0041 0.0012 0.0477 0.0245 0.0075 0.0761 0.0387 0.0119 0.0274 0.0133 0.0042 0.0106 0.0048 0.0015 0.0029 0.0013 0.0004 0.0184 0.0081 0.0026 0.0045 0.0019 0.0006 0.0005 0.0003 0.0001 0.0064 0.0030 0.0010 0.0349 0.0164 0.0054 0.0900 0.0422 0.0138 0.0493 0.0229 0.0075 0.0140 0.0061 0.0020 0.0038 0.0016 0.0005 Table B.3 Fucus distichus. Continued. Appendix B p.290 NOV 85 - DEC 86 0.0000 0.0006 0.0010 0.0007 0.0142 0.0229 0.0010 0.0226 0.0364 0.0001 0.0018 0.0029 0.0001 0.0017 0.0024 0.0006 0.0099 0.0151 0.0014 0.0255 0.0397 0.0007 0.0151 0.0242 0.0001 0.0023 0.0037 DEC 85 - DEC 86 0.0001 0.0008 0.0037 0.0007 0.0097 0.0452 0.0031 0.0420 0.2030 0.0001 0.0016 0.0088 0.0004 0.0022 0.0070 0.0009 0.0062 0.0219 0.0020 0.0173 0.0665 0.0007 0.0088 0.0400 0.0001 0.0012 0.0068 JAN 86 - JAN 87 0.0042 0.0006 0.0325 0.0004 0.0001 0.0063 0.0170 0.0054 0.3895 0.0011 0.0002 0.0155 0.0082 0.0006 0.0240 0.0133 0.0012 0.0458 0.0091 0.0011 0.0536 0.0020 0.0004 0.0230 0.0003 0.0001 0.0080 FEB 86 - FEB 87 0.1259 0.0213 0.0840 0.0213 0.0036 0.0143 0.0198 0.0066 0.0560 0.0083 0.0018 0.0111 0.0528 0.0076 0.0176 0.0627 0.0092 0.0232 0.0391 0.0061 0.0194 0.0069 0.0013 0.0060 0.0001 0.0000 0.0003 0.0001 0.0005 0.0009 0.0025 0.0103 0.0165 0.0040 0.0174 0.0270 0.0003 0.0017 0.0036 0.0003 0.0027 0.0200 0.0017 0.0097 0.0540 0.0041 0.0191 0.0736 0.0026 0.0105 0.0178 0.0004 0.0020 0.0028 0.0002 0.0005 0.0008 0.0024 0.0068 0.0081 0.0110 0.0323 0.0392 0.0005 0.0017 0.0028 0.0003 0.0019 0.0099 0.0010 0.0038 0.0142 0.0033 0.0096 0.0234 0.0021 0.0058 0.0069 0.0004 0.0012 0.0015 0.0014 0.0028 0.0053 0.0003 0.0006 0.0009 0.0189 0.0447 0.0586 0.0008 0.0020 0.0034 0.0009 0.0019 0.0085 0.0017 0.0027 0.0115 0.0022 0.0040 0.0090 0.0010 0.0022 0.0031 0.0004 0.0010 0.0014 0.0182 0.0325 0.0299 0.0031 0.0056 0.0053 0.0171 0.0378 0.0483 0.0033 0.0076 0.0105 0.0031 0.0059 0.0076 0.0036 0.0054 0.0041 0.0035 0.0055 0.0037 0.0014 0.0026 0.0024 0.0001 0.0003 0.0004 0.0012 0.0004 0.0001 0.0200 0.0058 0.0008 0.0300 0.0087 0.0013 0.0041 0.0012 0.0002 0.0342 0.0109 0.0015 0.0921 0.0291 0.0040 0.1233 0.0384 0.0054 0.0234 0.0068 0.0010 0.0023 0.0007 0.0001 0.0014 0.0005 0.0001 0.0119 0.0043 0.0007 0.0510 0.0185 0.0028 0.0040 0.0015 0.0002 0.0287 0.0113 0.0019 0.0404 0.0158 0.0026 0.0630 0.0243 0.0040 0.0117 0.0043 0.0007 0.0013 0.0005 0.0001 0.0056 0.0023 0.0009 0.0008 0.0003 0.0001 0.0455 0.0143 0.0044 0.0031 0.0011 0.0004 0.0110 0.0048 0.0019 0.0156 0.0071 0.0028 0.0108 0.0047 0.0018 0.0029 0.0011 0.0004 0.0011 0.0003 0.0001 0.0194 0.0053 0.0004 0.0035 0.0009 0.0001 0.0358 0.0097 0.0007 0.0083 0.0023 0.0002 0.0064 0.0020 0.0002 0.0029 0.0010 0.0001 0.0022 0.0007 0.0000 0.0015 0.0004 0.0000 0.0003 0.0001 0.0000 o o o o p p o o o b b b b b o o o g o ^ - 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O O O O O t O U i H - v o O Q H-U10OVOU1OOOK-O O O §§ p p p 0 O b b b d b 0 0 0 »—» 0 0 to Ul VO 0 ON to O O O O O O O O O b b b g g g o o o p p o o p p b o b b b b o ' o ~ — ~ 8 o o © © o O O © © P— O H |0 M U p p p p p p p 0 0 0 0 0 0 0 - O O O O O O O o o o o o t o - 0 0 I— OOOOOOl— ^ t U l t O p O O p 0 p p 0 b b b b b U l b 0 U l U l U l 0 to U l 0 ON to to 1—» to ~ J U l ON to U l t—» U l p p p p p O p p b b b b b b b 0 0 U l 0 to to to 00 0 U l U l U l 00 - J to U l 0 C O O N 00 pppppppp 8 2 2 S 8 8 S 8 ( O O O l — O O U I - J t O U l - o t o o o o - o v o u i t o O 1— ^ to o to O N 0 p 0 p p p p 0 0 b b b b b b b b b 0 0 0 3^ 0 © 0 0 0 0 0 0 5 0 0 Ul 00 0 0 to U l U l 00 Ul J >  to p p p p p p p p p b b b b b b b b b O Q O O O O O i — o o > — t o t o ^ - t o u i o 0 * v U l * H U l l ) l O t O 0 p p p p p p 0 p b b b b b b b b b 0 0 0 0 0 0 »—» Ul 0 0 0 t o U l t o - j 0 t o - j 0 VO U l 0 J > VO p p 0 p O O O O 0 b 0 b 0 b 0 b 0 8 b 0 8 b U l s 0 U l U l ON U l 00 l O N to J>. 00 Ov U l 8 p p O p p p O p b b b b b b b b 0 0 0 0 0 to 0 0 1—» o\ to Ul •p>. 0 *>. 1—» U l U l Ul Ov OV 0 0 p p p p p p O b b b b b b b b b 0 0 0 0 Ul to 0 to 0 0 Ul V O O N J > to O N 00 V O to to p O p p p O p O O p p p 0 p p 0 b b b b b b b b b b b b b b b b 0 0 0 0 1—» to 0 0 0 0 0 0 0 0 H— 00 to Ul Ul 0 0 0 to ov U l o\ - J ^* VO  •0 0 ON to U l 0 U l to J > 00 U l U l 0 0 0 8" 0 0 0 _ o 0 o _ O O O H -» H u V i 00 O O O O O O O O O 8 8 8 8 8 _ _ _ l-» I— H - U l tO h - M U l U H U h - O O O O O O O O O § 0 0 b b b b ' 8 8 8 8 8 8 . O O H W M U l 00 O O O O O O O O O o o o o o o o o o O O — i " o o o o d d n M in 5 ~ ~ (S M O O — o o o o d d CO vO ov CN oo CM m CO CN cs o O o o o O d d d d o •<* CO ^4 m m o o r- o o CO VO o Q cs 00 r- o o o o ov CN VO CO o S CN o o Q o o o o o o o CO CN o o o O O o O O o o o o o o o o O o o d d d d d d d d d d d d d d d d d o d o CN OO m CN oo o o o CO r- OV Ov o 00 i—( o o VO i n co CN CN o o o CN OV CO o o o r- o « ^ O o o o o CN 00 i-H O o o o p o O o o o o o o o o O o o o d d d d d d d d d d d d d d d d d d o CN VO CO ON o oo in o o OV OV o VO oo 00 o O VO VO OV OV co CN o o o o OV CO m VO CN o o t- o o Q o o o o o r~- CO CN VO CN CN o o o o o o o O o o o o o o o o o o d d d d d d d d d d d d d d d d d d o - * o \ o v v o o \ o r - - c o O O c o p p p O O O O O O O O O O O O o o o o o o o o o CN o ~* o Ov >/•> Ov o o 00 Ov CN Ov Ov o o o O CN <N o o o o o o O O O q o o d d d d d d d d d o CN co 00 CN •<* CO o o •* 00 Ov <n o VO CO CN CO O CN CO o o Ov r- r- O 00 o Q CO VO r- CO CN o o o o CN o o o o o o O o o o o o o o o O o o d d d d d d d d d d d d d d d d d d oo vo oo oo a < i VO OO o o o o o o o o o o O O O O O O O O O O O O O O O O O O -O O O O O O O O O ^ • Q t " - i n o o o O O c o > - i 8 8 8 8 S o S 8 § p p o o o p p p o d o d d d o d o o O O O O O O O O O 0011 ,0000 0029 0022 0155 0127 0048 0007 0002 0005 1000 0024 0010 0102 0132 0030 CN O o o o o o o o o o o o o o o o o d ,0031 ,0000 ,0078 ,0505 .0374 .0135 0024 ,0007 U034 0009 0112 0048 0466 ,0603 0141 in o o o o o o o o o o o o O o o o o o o d o r- CN >n Ov CO CN Ov C- VO Ov r- o VO o CN co VO 00 r- CO oo in OV CN CN Ov CN OO o o CO CN >n o O o CN cs m o o q o o o o o o o o o q '—' o o d d d d d d d d d d d d d d d d d 00 o o CO o VO in o r- o CN in o in «n CO r- 00 VO r- CN CO o CO CN CO oo o CN o o m OV o o o o O o o o o o o o p o o O d d d d d d d d d d d d d d d d d o Ov CN VO Ov 00 CN CN T f o CN CN VO OV CO CO O o o o < o o o o o o o o o o o o o d d d d d d d d d d O CO OV VO -H o o p o o o o o o o o o o o Q o OV CO VO Ov o •* CO Ov in o m •* in m VO m CO •<t VO CN »—< o o o o CN CN o o o o o o CN o o o o o o O o o o o p o o o o o o o d d o" d d d d d d d d d d d d d d oo a. W C/3 VO 0O W L C/3 o o g o o o o o o o o _ _ _ Q p O O O © o o o o o o - o o O O O O O O O O O CN O CN O 8 8 O O O O O m Ov t-- CO m 00 o »—i o 8 o o o o d d d d r-oo H U O VO OO H U o o in o Ov vo 00 CN o o o r-~ 8 o o o o o o o o d d d d d d d OV CO CO m o o Ov r~ o p p o o CN o o p p p o O d d d d d d d o o o C~ CN Table B.3 Fucus distichus. Continued. Appendix B p.293 DEC 86 - NOV 87 0.0001 0.0003 0.0001 0.0002 0.0020 0.0025 0.0011 0.0003 0 0.0003 0.0014 0.0004 0.0014 0.0156 0.0120 0.0023 0.0004 0 0.0000 0.0003 0.0001 0.0003 0.0036 0.0030 0.0006 0.0001 0 0.0000 0.0000 0.0000 0.0001 0.0020 0.0117 0.0063 0.0016 0 0.0006 0.0029 0.0007 0.0018 0.0274 0.1149 0.0630 0.0157 0 0.0028 0.0141 0.0033 0.0081 0.0834 0.1895 0.1030 0.0257 0 0.0023 0.0117 0.0028 0.0076 0.0711 0.0783 0.0365 0.0089 0 0.0006 0.0030 0.0007 0.0022 0.0219 0.0179 0.0062 0.0014 0 0 0 0 0 0 0 0 0 0 

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