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Modelling studies on a marine plankton community : biological, temporal and spatial structure Christian, James Robert 1988

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a p p e n d l& . A , " B ,C .  MODELLING STUDIES ON A MARINE PLANKTON COMMUNITY: BIOLOGICAL, TEMPORAL AND SPATIAL STRUCTURE by JAMES ROBERT  CHRISTIAN  B.Sc. (Honours) 1986, University of British Columbia  A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E REQUIREMENTS FOR T H E D E G R E E OF MASTER OF SCIENCE  in T H E F A C U L T Y O F G R A D U A T E STUDIES The Department of Zoology  We accept this thesis as conforming to the required standard  T H E U N I V E R S I T Y O F BRITISH C O L U M B I A 9 September 1988 (c) James R o b e r t C h r i s t i a n ,  1988  In presenting this thesis in partial fulfilment of degree at the  the  University of British Columbia, I agree that the  freely available for reference and or  by  his  or  her  representatives.  be  permission.  Department The University of British Columbia Vancouver, Canada  DE-6  (2/88)  Library shall make it  flc-U^^ym  granted by  It is understood  publication of this thesis for financial gain shall not  Date  advanced  study. I further agree that permission for extensive  copying of this thesis for scholarly purposes may department  requirements for an  be  the that  head of  my  copying  or  allowed without my  written  - ii Abstract  The SELECT model (Frost, 1982) is analyzed, criticized, and extended to embrace new information about the feeding behaviour of copepods and the structure of the planktonic food web in a series of alternative models. Diel variations in photosynthesis, grazing, and predation on copepods (temporal structure) and patchiness of zooplankton and their predators (spatial structure) are modelled in other variants. It is observed that the vertical, temporal, and (horizontal) spatial structure of the planktonic ecosystem are important components of ecosystem models that can not safely be ignored. It is further observed that a convincing mechanism for the termination of diatom blooms is lacking and should be a subject of intensive research, and that the status of chlorophyll-containing microflagellates as phototrophs is questionable and should be reconsidered.  - iii Table of Contents Abstract  ii  Table of Contents  iii  List of Tables  v  List of Figures  vi  Acknowledgements  vii  1 Introduction  1  2 Methods and Materials  5  2.1 Computer Simulation  5  2.2 The SELECT Model  6  2.3 Sensitivity Analysis  10  2.4 Similarity Index  11  2.5 Random Number Generator  12  3 Results and Discussion 3.1 Sensitivity Analysis  13 13  3.1.0 Introduction  13  3.1.1 Attenuation coefficient and photosynthetic rate  19  3.1.2 Euphotic zone depth  20  3.1.3 Half-saturation for nutrient uptake  20  3.1.4 Mixing rate  21  3.1.5 Sinking rate  22  3.1.6 Chlorophyll-to-carbon ratio  23  3.1.7 Respiration rate of phytoplankton  23  3.1.8 Zooplankton assimilation efficiency  24  3.1.9 Zooplankton basal metabolic rate  25  3.1.10 Size selection of cells by grazers 3.1.11 Carnivore predation  26 28  3.2 Deviation from mass-dependence 3.3 Phytoplankton and copepods - Alternative models 3.3.1 Photosynthetic rates of diatoms and flagellates 3.3.2 Vertical migration of dinoflagellates 3.3.3 Chemosensory grazing Toxicity Nutritional state of cells 3.3.4 Selection of prey cells by Pseudocalanus sp. 3.3.5 Copepod carnivory 3.4 Protozooplankton and the "microbial loop" 3.4.0 Introduction 3.4.1 Some definitions 3.4.2 Protozooplankton growth rates Trophic phasing 3.4.3 Pathways of energyflowand succession 3.4.4 Extracellular metabolism 3.4.5 Protozooplankton herbivory 3.4.6 Phytoflagellate bacterivory 3.4.7 Nutrient regeneration 3.4.8 Seasonal succession 3.5 Temporal structure and vertical migration 3.6 Spatial structure - the stochastic predation model 4 Conclusions Literature Cited Appendix A (stored separately) Appendix B (stored separately) Appendix C (stored separately)  -  V  -  List of Tables I. List of input variables for the SELECT model. 9 II. Summary of sensitivity analysis results. 15 in. Similarity indices for biomass spectra of phytoplankton and stage distributions of zooplankton with random deviationsfrombase values of phytoplankton submodel parameters (comparison to standard simulation). 31 IV. Values of half-saturation function for nutrient uptake. 40 V. Maximum biomass of Calamts sp. and selection models for Pseudocalanus  Pseudocalanus sp. 52  sp.  under alternative prey  VI. Initial phases for parameters undergoing sinusoidal variation over 24 hours in the temporally structured model. 67 VII. Zooplankton biomass and chlorophyll and nutrient concentrations under alternative models of vertical migration of Pseudocalanus sp. 69  - vi -  List of Figures 1. Schematic diagram of possible outcomes in sensitivity analysis. 11 2. Development of the plankton community over 100 days as depicted by the SELECT model. 14 3. Prey selection curve for adult female Pseudocalanus sp. 27 4. Phytoplankton biomass spectra (Dav 50) for constant and variable random deviationsfrombase value of the maximum photosynthetic rate. 33 5. Phytoplankton biomass spectrum (Day 50) with an increased photosynthetic rate for diatoms. 36 6. Phytoplankton biomass spectrum (Day 60) with two size classes exempted from nutrient limitation by vertical migration. 38 7. Phytoplankton biomass spectrum (Day 30) with reduced predation on two size classes. 43 8. Phytoplankton biomass spectrum (Day 60) with grazing rate depending on the nutritional state of the cells. 45 9. Phytoplankton biomass spectrum (Day 50) with random deviation from base value of half-saturation constant for nutrient uptake and grazing rate depending on the nutritional state of the cells. 47 10. Prey selection curves for adult female Pseudocalanus sp. under three alternative prey selection models. 49 11. Phytoplankton biomass spectrum (Day 51) with opportunistic feeding by Pseudocalanus sp. SI 12. Time series of biomass of bacteria and flagellates in well phased and poorly phased predator-prey systems. 56 13. Classical and contemporary views of the planktonic food web. 58 14. Phytoplankton biomass spectra (Day 21) under alternative models of extracellular metabolism. 61 15. Phytoplankton biomass spectra (Day 60) with conventional (nightime) and reverse (daytime) vertical migration of Pseudocalanus sp. 70 16. Time series of biomass of Calanus sp. under deterministic (Monod) and stochastic predation models. 73  - vii -  Acknowledgements I thank my research supervisor, Dr. T.R. Parsons, for encouragement, support and advice throughout the course of this study. I thank also Drs. W.W. Hsieh and W . E . Neill for continued assistance and support. Advice, references, and technical support were also generously provided by Ms. N. Butler, Dr. P J . Harrison, Mr. P. Clifford, Mr. D. Jones, Dr. D. Schluter, Mr. M . St. John, Dr. F.J.R. Taylor, Mr. D. Webb, and Ms. L. Wooton; I thank them all for their assistance.  -11 Introduction  Allometry, or dependence on body size, is an important concept in ecological modelling. Fenchel (1974) observed that, within broad functional groups (unicells, poikilotherms, homiotherms) rates of growth, reproduction, and respiration are closely related to body size, irrespective of the particular species involved (see also Piatt, 1985). While there are some important differences among taxa that can not be related to body size (Banse, 1976; Frost, 1980), as a simplifying assumption it is a highly useful one, because it can be related to both the taxonomic composition and the dynamics of the community. This contrasts with traditional "qualitative" approaches - species composition, food webs, diversity - which are purely static and not adaptable to simulation and prediction, and to the traditional "quantitative" approach of systems analysis modelling (SAM), which ignores taxonomy altogether, creating what Steele and Frost (1977, p. 486) describe as the "aura of unreality" about an "ecology without species".  The only planktonic ecosystem simulation models to incorporate this concept are the SIZES model of Steele and Frost (1977), and its descendent, the SELECT model (Frost, 1982). The expressed objective of these modelling efforts was to simulate the internal structure of each trophic level, extending ecosystem modelling beyond the "common practice" of defining the food web "in terms of biomass, organic matter, or energy in various very general trophic categories such as herbivores or primary carnivores "(Steele and Frost, 1977, p. 486).  The SELECT model (Frost, 1982) forms the basis for this study. A critique of the model itself is developed, and the model is modified to embrace a number of  -2-  important facts and concepts of importance in contemporary plankton ecology that were originally omitted. As with all simulation models, the necessary simplifications involve ignoring variations in important parameters that occur among taxa, or even among races and populations of a single species. In addition, uncertainty about the true values of the parameters always exists. For example, Gargas et al. (1979, p. 119) cast the measurement of primary production as a Heisenberg problem, suggesting that "all methods will disturb the equilibrium of the system" and that therefore "it is not possible to recommend a method which would accurately estimate the real daily primary production". Statistical techniques can quantify, but not eliminate, the imprecision present infieldand laboratory measurements, and can not detect inaccuracy flowing from the method used. Rigler (1982) discusses the difficulty of making predictions by using theory to extrapolatefromsuch measurements; he concludes that some things are unpredictable even in principle.  The planktonic environment presents particular challenges in this respect. Firstly, water motion makes measurements over long time periods on particular water masses nearly impossible, and continuously alters the water mass being observed. Secondly, organisms whose interactions are ecologically important can have very different scales of aggregation and mobility (cf. Legendre and Demers, 1984), and no single spatial scale is appropriate for all of the relevant components of the community.  To a large extent these difficulties can be overcome, and modelling still has a useful contribution to make to ecology. Sensitivity analysis (section 3.1) can determine how robust the model is with respect to uncertainty about parameter values. Section 3.2  -3-  presents a new method of assessing the significance of species' or populations' deviations from parameter values based on allometric assumptions. It is important, however, to recognize that the results of these analyses are a property of the model itself and not of the natural system it represents (see Skellam, 1971 for the definitive discussion of this concept) and will not necessarily identify deeper flaws in the model's structure (cf. Silvert, 1981).  Leaving aside the inevitable uncertainties about the natural world that contemporary ecologists recognize, our knowledge of those things that can, in principle, be understood is still far from complete. A great deal of new information about the planktonic food web has emerged in recent years, and much of it is not included in the original SELECT model.  Firstly, there is the question of how and on what copepods feed. The new information about these animals amounts to a minor revolution. The old view of copepods as passive filter feeders has been laid to rest, and the jury is still out on what will replace it. They seem to have several different feeding modes. One is a sort of pseudo-filtering that involves remote detection of preferred food particles by chemoreception whereupon a parcel of water is captured between the second maxillae, which are then drawn together, forcing the water out between the setules, which retain the food particles (Koehl and Strickler, 1981). Raptorial feeding on larger particles such as nauplii has also been observed (Landry, 1981). They also appear to be able to 'taste' particles to determine their quality as food (Poulet and Marsot, 1978).  Our view of what copepods eat has also been questioned and broadened. Landry (1981) has demonstrated that Calanus pacificus, generally considered a herbivore,  -4-  will feed on nauplii, including its own. Feeding on ciliated protozoa has frequently been observed (Berk et al., 1977; Robertson, 1983; Sheldon et al., 1986). Poulet (1983) has suggested that, as well as living particles, copepods will feed on detritus and faeces. The evidence for this is inconclusive, however. Paffenhoffer and Van Sant (1985) have demonstrated that Eucalanus pileatus will feed on these but will preferentially select living cells.  The food web is becoming more complex at all levels. Evolving concepts of the base of the food chain resemble those of the atomic nucleus: each time someone has trumpeted the discovery of the "fundamental particle", a smaller and more fundamental one has been found. The phytoplankton - copepod - fish food chain has become a scientific dinosaur, superceded by a web of ever-increasing complexity.  A large fraction of primary production is now known to pass through the "microbial loop" (Azam et al., 1983) before being passed up the food chain. This involves loss of phytoplankton production as dissolved organic matter (DOM), which is utilized by bacteria (Larsson and Hagstrom, 1979), which are consumed by phagotrophic flagellates, which are in turn consumed by ciliates, sarcodinians, and perhaps the smaller copepods. To complicate matters further, bacteria share the smallest size range (< 1 jim) with very small phototrophic cells (Piatt et al., 1983), and 'phototrophic* phytoplankton have been observed to feed phagotrophically on bacteria (Bird and Kalff, 1986) and perhaps on smaller phytoplankton as well. So even before the 'second' trophic level (herbivorous copepods) is reached, a web of great complexity exists.  -5-  Much of this new information has been incorporated into the variants of the SELECT model described below. Other variants incorporate representations of the temporal and spatial structure of the ecosystem that modellers have traditionally ignored.  Diel variations in photosynthesis, grazing, and predation on copepods are incorporated by replacing a single 24 h time step with a sinusoidal variation (Pepita and Makarova, 1969) over 24 h based on a time step of 3 h. Patchiness of populations in space is incorporated by including a stochastic (carnivore) predation function (Steele and Henderson, 1981) that represents the quasi-random variations in local abundance of predators that result from the different scales of aggregation and mobility of predator and prey (Smith, 1978; Legendre and Demers, 1984).  2 Methods and Materials 2.1 Computer Simulation  The computer simulation is a technique for "calculating, for particular values of the coefficients, the consequences of the assumptions derived" from a conceptual model of the system (Steele and Frost, 1977, p. 511). The advantage of simulation modelling is that various alternative scenarios can be explored in a relatively short time and at little expense. The logistical difficulties of carrying out experimental manipulations of entire ecosystems (cf. Grice and Reeve, 1982) make this an attractive option. The disadvantage is that several alternative models or combinations of coefficients may give similar or identical results and the data to choose the 'correct' model may be unavailable (Silvert, 1981; 1985). However, simulation modelling can narrow the range of a priori possibilities sufficiently to  -6-  reduce the ultimate cost of field research. Examples of simulation models from the marine plankton include Winter et al. (1975), Jamart et al. (1977; 1979), Steele and Frost (1977), Evans et al. (1977), Steele and Henderson (1981), Frost (1982), Peterson and Festa (1984), Evans and Parslow (1985), and Parsons and Kessler (1986; 1987).  Simulation models are most successful when there is strong and directional change in the principal inputs. The plankton community in early spring is such a system. A system in a quasi-equilibrium state, such as the plankton in summer, is less amenable to simulation and prediction. In the absence of directional change the predictions of simulation models are unreliable and become more so as the run length increases.  22 The SELECT Model  The SELECT model was developed by Frost (1982) and originally presented to the Second USA/USSR Syposium on the Biological Aspects of Pollutant Effects on Marine Organisms. The basic form of the model is the same as the SIZES model of Steele and Frost (1977) but several important modifications were made.  SIZES simulates the development of a planktonic community in a temperate ocean following the formation of a seasonal thermocline in the spring (Sverdrup, 1953). A phytoplankton bloom is followed by the development of breeding populations of two copepods, Calanus sp. and  Pseudocalanus sp.,fromthe overwintering  adult  populations. Because the half saturation constants for nutrient uptake are proportional to the size of the cell (Eppley et al., 1969; Parsons and Takahashi,  -7-  1973), depletion of nutrients following the bloom results in a second, smaller bloom of much smaller cells. These events are discussed in more detail in 3.1.0 below.  Because the equations governing growth and reproduction of copepods in SIZES resulted in severe "numerical dispersion" (a small but finite fraction passing at an unrealistically rapid rate through the successive life stages; cf. Evans et al., 1977) they were replaced with a multiple cohort reproduction scheme whereby "each day's reproductive products are followed as a cohort until all members of the cohort die" (Frost, 1982). The maximum specific growth rate was a single constant in SIZES, while in SELECT each copepod genus (Calanus and Pseudocalanus) has its own characteristic value of this parameter (Frost, 1982; see also Frost, 1980). The function used to describe carnivore predation on herbivorous zooplankton in SIZES was replaced with a much simpler Monod (1942) function of the form G = G  max' /( z ) z  K  + z  where G = predation rate, G  m a x  = maximum predation rate,  Z= prey (herbivore) abundance,and K = Zat which G=G z  max  /2.  The main events in the simulation are described in section 3.1.0 and depicted in Figure 2. A list of the coefficients in the model and their base values is given in Table I. The FORTRAN source code for the model is given in Appendix A. Several conventions followed in the ensuing discussion require clarification. Because the model assumes that nitrogen is the limiting nutrient at all times (phosphorous is not included in the model at all) and does not distinguish between the different forms of inorganic nitrogen, "nutrients" refers to any or all of these, and the terms "nutrients" and "nitrogen" are equivalent. The two copepods are referred to only by  -8genus names, and no distinction among species is made. In most cases the length of the r u n is 60 days.  -9Table  I  - List  of  Input V a r i a b l e s  f o r t h e SELECT M o d e l  A  0 .02  B  0 .1  C  2 .5  (Maximum p h o t o s y n t h e t i c r a t e  DD  1 .134  (Half-saturation  (Constants  f o r equation determining  attenuation coefficient) (d~^))  f o r N uptake)  R  10 .0  (Initial  RO  10 .0  (Deep w a t e r n u t r i e n t c o n e .  GC  0 .1  (Predation constant  RM  0 .02  (Mixing r a t e  D(l)  2 .0  (Diameter o f s m a l l e s t  V  0 .1  (Sinking  CHMAX  0 .033  (Maximum c h l o r o p h y l l / c a r b o n r a t i o )  EUPH RESP H Zl  40 .0 0 .36 100000 .0 0 .0  n u t r i e n t cone.  (uM)) (uM))  f o r Calanus)  (d~*)) cells  rate)  (Euphotic  zone d e p t h (m))  (Constant  (a) i n r e s p i r a t i o n e q u a t i o n )  (1/2-sat.  f o r p r e d a t i o n on C a l a n u s )  ( T h r e s h o l d f o r p r e d a t i o n on z o o p l a n k t o n )  DMAX  10 .0  DMIN  2 .0  EE  0 .00015  (Constant  ZB  0 .1  (Zooplankton b a s a l metabolic  ITIME  60 .0  (um))  (Constants  d e t e r m i n i n g shape  of grazing  curve)  determing a s s i m i l a t i o n  rate)  rate)  (Length o f r u n (days))  F  0 .4  (Calanus  GZ  0 •0  (Predation constant  F2  0 .2  (Pseudocalanus  HP  200000 .0  GP  0 .1  (1/2-sat.  maximum g r o w t h r a t e  (d~^))  (not used))  maximum g r o w t h r a t e  (d~*))  f o r p r e d a t i o n on P s e u d o c a l a n u s )  (Predation constant  f o r Pseudocalanus)  -10-  2.3 Sensitivity Analysis  Sensitivity analysis is the analysis of a mathematical or computer model to determine the robustness of its output with respect to uncertainty about the values of its input variables. There are two basic types of sensitivity analysis. Theoretical sensitivity analysis consists of computing "sensitivity coefficients" which express the extent to which changes in the values of input parameters may shift the solution of the system out of its region of stability in the phase plane or space (Tomovic, 1963). It is used primarily in engineering applications. Ecologists primarily employ empirical sensitivity analysis. This consists of running a series of simulations, or numerical experiments, in order to determine directly the effect of changing the value of a given input variable (cf. Jamart et al., 1979).In most ecological models there will be signifant biological events or phenomena in the output that transcend the individual parameter values and persist through small changes in these values, although the values of the output variables may change. To facilitate interpretation of the output it is desirable to vary only one parameter at a time, or a logical combination of two or three that can be expected to act in concert (see section 3.1.4).  Ideally, a parameter should be variable within a narrow range of the (empirically determined or theoretically derived) base value. Small changes should not affect the model's output, but with greater deviations the ability of the model to produce the identical result should fall off rapidly. Violation of either of these criteria should call the integrity of the model into question: in the former case, which shall be called Type I, because the results are strongly dependent upon the chosen parameter values being extremely accurate (which is rare in ecology), and in the latter (Type II), because some input variables have no discernable effect on the output,  -11-  suggesting that the model is more complex than it needs to be (Silvert, 1981). This is illustrated visually in Figure 1. Although the figure suggests that increasing and decreasing a parameter value have symmetrical effects, this is rarely the case.  Figure 1 - Schematic diagram of parameter sensitivity  T Y P E II  0  +  2.4 Similarity Index  When discussing the similarity of the output of two alternative models or two sets of parameter values, some objective criterion is needed. Statistical techniques are not appropriate because the two alternative outcomes are purely deterministic, or, even if the model has a stochastic component, nothing analogous to a random sampling process takes place (D. Schluter, pers. comm.).  The similarity index (Whittaker and Fairbanks, 1958) has been used for a variety of applications, including comparing net catches of zooplankton (Whittaker and Fairbanks, 1958) and measuring "niche overlap" of sympatric species (Hurlburt, 1978). The similarity index is calculated as  -12-  Sj =1.0-0.52j|Pij-P | k  ik  where PJJ and P^ are the proportions of the /th species in the ;th and kxh samples.  In sections 3.2 and 3.3.3 below this has been applied to comparing the size spectra of phytoplankton and the stage distributions of copepods from two model runs. In these cases PJJ and P^ represent the fraction of the total biomass occurring in the ith size class (range) or life stage, while j and k represent the two model runs being compared.  2.5 Random Number Generator  Stochastic models are becoming more prevalent in ecology (e.g. Steele and Henderson, 1981; 1984; Colwell and Winkler, 1984) and require some means of generating random or pseudorandom numbers. Pseudorandom numbers are generally used. Pseudorandom numbers are numbers generated by a deterministic program that approximate random values. The various types of pseudorandom number generators are discussed by Kalos and Whitlock (1986). The criteria for a good pseudorandom number generator are uniformity (all values over the desired interval should have an equal probabilty of being chosen) and completeness (there should not be any "black holes", values which, by some quirk of the generating function, are never chosen).  The pseudorandom number generator used here is UNIRAN (Marse and Roberts, 1983); it is a REAL FUNCTION in the FORTRAN language. This is a public domain subprogram available on UBC MTS.  -133 Results and Discussion  3.1 Sensitivity Analysis  3.1.0 Introduction  As discussed in 2.3 above, sensitivity analysis in ecology consists of conducting numerical experiments with the values of input variables in order to determine the robustness of the output with respect to the assumed values, with robustness defined as the persistence of important biological events in the model ecosystem. In the SELECT model two important trends can be observed:  a) an initial bloom of large cells, presumed to be diatoms, occurs in the first 40 days, after which nitrate concentration declines, the phytoplankton size spectrum becomes bimodal, and a second bloom of much smaller cells, presumed to be largely flagellates, occurs (Figure 2a); and  b) chlorophyll a concentration reaches a peak during the initial diatom bloom, followed by biomass peaks of both copepod species, with Calanus contributing approximately two thirds of the total biomass (Figure 2b).  Table II shows the results of a series of numerical experiments with the various input parameters in terms of their effects on these events. These are discussed at length below (sections 3.1.1 to 3.1.11).  -14-  Figure 2 - Development of the plankton community over 100 days as described by the S E L E C T model.  -15T a b l e I I - ( f o l l o w i n g pages) R e s u l t s o f n u m e r i c a l experiments w i t h v a l u e s o f input parameters i n t h e standard SELECT m o d e l . DXX i n d i c a t e s t h a t t h e e v e n t o c c u r r e d on t h e X X t h d a y o f t h e s i m u l a t i o n , numbers i n p a r e n t h e s e s i n d i c a t e v a l u e s o f t h e s p e c i f i e d q u a n t i t y on t h a t d a y . D a t e s i n t h e BIMODAL SPECTRUM c o l u m n i n d i c a t e t h e d a y t h a t t h e b i m o d a l biomass spectrum f i r s t appeared. * i n d i c a t e s t h a t t h i s c o n d i t i o n i s t r a n s i e n t a n d one mode d i s a p p e a r s a l m o s t i m m e d i a t e l y . "NO" c o p e p o d maximum i n d i c a t e s t h a t t h e r e i s no o b v i o u s b i o m a s s p e a k a n d g e n e r a l l y means t h a t a v i a b l e b r e e d i n g p o p u l a t i o n f a i l e d t o d e v e l o p . T h e v a r i a b l e names CHMAX a n d RESP h a v e b e e n a b b r e v i a t e d t o CHM a n d RSP respectively.  PUN DESCRIPTION  CHLOROPHYLL MAXIMUM  CHLOROPHYLL MINIMUM  8IMODAL SPECTRUM  CALANUS MAXIMUM  PSEUDOCRLANUS MAXIMUM  STANDARD  018(7.97)  041(3.25)  038  035(2011)  032(857)  ATTENUATION COEFFICIENT A=0.014, B=0.07  017(12.0(0  036(3.15)  NO  D34(3508)  036(1628)  A=0.026, 0=0.13  D29(6.30)  065(3.51)  NO  056(2120)  NO  MAXIMUM PHOTOSYNTHETIC RATE C=2.0  026(6.44)  D6K3.41)  NO  D54(2309  NO  C=2.2S  020(7.00)  035(3.17)  NO  049(2312)  NO  C=2.75  018(9.26)  037(2.74)  D34  034(2677)  D33(1375)  C=3.0  018(10.59)  D38(2.37>  037  D36(3623)  D36(1527)  EUPHOTIC ZONE DEPTH EUPH=20.0  012(14.83)  NO  NO  024(1464)  026(1078)  EUPH=30.0  017(11.28)  033(2.35)  D32  032(2895)  032(1398)  HALF-SATURATION FOR N UPTAKE 00=0.567  020(9.27)  046(0.57)  NO  046(2971)  038(487)  DD=0.7938  018(8.53)  048(2.74)  D51  042(25B6>  D39(724)  00=0.9072  018(8.31)  D45(2.93>  D45  D39(2372)  036(773)  00=1.3608  018(7.69)  039(3.31)  036  033(1823)  030(932)  D0=1.4742  018(7.59)  036(3.30)  D36  D33(1762)  030(973)  00=2.268  019(7.18)  D36(2.80)  035  D32(1882)  D32U044)  D1B(8.40)  040(2.16)  D36  033(2260)  032(961)  R0=7.0, RM=0.014 018(8.11)  D42(2.63)  036  033(1951)  D30(968)  R0=13.0, RM=0.026 018(7.89)  048(3.51)  D48  D45(2529)  D39(755)  R0=15.0, RM=0.03 018(7.85)  042(6.09)  NO  D48(2S94)  039(666)  R0=20.0, RM=0.04 022(8.04)  D30(7.89>  NO  048(2555)  NO  MIXING RATE R0=5.0, RM=0.01  SINKING RATE V=0.055  019(8.50)  D47(2.71)  D46  044(2893)  038(678)  V=0.22  D19(7.68>  D36O.07)  D37  D33(1983)  D32(949)  CHLOROPHYLL/CRRBON RATIO CHH=0.017  018(6.90)  D37(1.64)  NO  035(3330)  D3605B9)  CHM=0.066  042(11.7)  NO  NO  068(1141)  NO  RESPIRRTION RATE OF PHYTOPLRNKTON RSP=0.18  020(12.95)  035(4.81)  032M  D360562)  038(1661)  RSP=0.28  018(9.77)  D36(2.8B)  D33  033(2737)  033(1625)  RSP=0.324  018(8.71)  036(3.22)  033  033(2226)  030(1200)  RSP=0.378  D18C7.69)  D45O.02)  051  D39(2148)  D36(695)  RSP=0.396  018(7.48)  048(2.83)  NO  045(2546)  039(508)  RSP=0.44  021(7.20)  NO  NO  051(2846)  NO  ZOOPLRNKTON ASSIMILATION EFFICIENCY EE=8.0E-5  022(9.08)  D50O.94)  NO  D46(2571)  D45(300)  EE=1.2E-4  D18(8.24)  045(339)  D54  039(2119)  D36(707)  EE=1.3E-4  018(8.14)  042(3.34)  045  039(2050)  033(760)  EE=1.4E-4  018(8.05)  042(3.29)  042  D36(203S)  033(814)  EE=1.7E-4  D1B(7.83)  039(3.17)  033  D33(19B5)  030(934)  EE=1.8E-4  018(7.78)  039(3.12)  D33  033(2003)  030(971)  EE=3.0E-4  018(7.50)  035(2.28)  030  D32(2568)  D30(1138)  ZOOPLRNKTON BRSRL METRBOLIC RATE ZB=0.05  019(8.02)  040(2.66)  037  036(2773)  034(1136)  ZB=0.08  018(7.91)  042(3.10)  036  036(2110)  D33(1004)  ZB=0.12  D1B(7.91>  042(3.10)  D36  D36(2U0)  033(1004)  ZB=0.15  018(8.13)  042(3.41)  048  D39(1982)  033(521)  ZB=0.20  D20(8.52)  045(3.38)  D52  041(2340)  039(249)  SIZE SELECTION OF CELLS DMAX=7.0  022(8.60)  NO  D4B(2971>  NO  0MRX=8.0  018(8.14)  054(2.74)  048(2826)  NO  DMAX=9.0  D18(8.00)  048(2.81)  D42(2513)  039(647)  0MRX=9.5  018(7.97)  042(3.07)  D39(2180)  D33(751)  DnRX=13.0  019(8.30)  D37(2.8B)  D34(2368)  033(1200)  DMr1X=15.0  018(8.23)  036(2.79)  D33(2180)  033(1542)  OMIN=1.0  D23(9.05)  NO  051(2702)  NO  DMIN=1.5  018(8.25)  051(3.14)  048(2654)  D39(499)  0MIN=1.75  018(8.08)  045(3.03)  D42(2282)  039(713)  0MIN=2.5  018(7.85)  036(3.10)  033(1953)  030(1118)  OMN=3.0  018(7.92)  D36(2.61)  032(2445)  D32(1177)  DMHX=B.0,DMIN=1.5 027(8.69)  NO  051(2343)  NO  0MAX=13, 0MIN=3  036(2.32)  D33(2334)  D18(7.94)  033(1551)  CARNIVORE PREDATION GC=0.05  018(7.80)  048(3.29)  D5K2665)  GC=0.075  018(7.89)  045(3.44)  D33(2178)  NO  GC=0.12  018(8.02)  045(2.88)  D39(1903>  027(697)  GC=0.15  018(8.09)  054(3.16)  D48(1658)  039(1068)  GC=0.2  021(8.27)  NO  048(1111)  039(1226)  GP=0.05  D18(7.60)  051(2.88)  045(1636)  D39(1385)  GP=0.15  021(8.24)  042(2.90)  D39O063)  027(1156)  HC=5.0E4  018(8.04)  042(2.97)  039(1928)  036(451)  HC=1.5E5  018(7.92)  D42(3.38)  D36(2031)  D36(1031)  HP=1.0E5  018(8.09)  042(3.14)  D36(2272)  D30(774)  HP=3.0E5  018(7.89)  042(3.33)  036(1852)  033(794) 030(886)  -193.1.1 Attenuation Coefficient (k ) and Maximum Photosynthetic Rate (C, or P e  m a x  )  These two parameters may be treated as one. Each appears only once, in the equation determing phytoplankton growth rates. They are linearly and inversely related, so that the effect of doubling P  m a x  is the same as that of halving k . The e  model is very sensitive to this parameter, particularily if P increased. A decrease of only 10% of P  m a x  m a x  is decreased or k  e  will remove important biological events,  such as the evolution of a bimodal size spectrum in the phytoplankton and of a biomass peak of Pseudocalanus, from the simulation (see Table II). An increase of up to 17% makes some quantitative changes in the results but does not disrupt the overall pattern of community development.  The model's sensitivity to these parameters can largely be explained by its assumption of a homogeneous mixed layer (Steele and Frost, 1977, p. 491). In the real ocean phytoplankton are not homogeneously distributed in the mixed layer . A spring phytoplankton bloom will exhibit vertical structure including a chlorophyll maximum and a photosynthesis maximum, generally not at the same depth (Jamart et al.,1977; 1979; Herman et al., 1981). Changes in the extinction coefficient can alter the depth of maximum biomass or photosynthesis without altering the integrated values of these variables over the entire euphotic zone.  Nor would changes in the depth of the chlorophyll and production maxima affect the density of food available to herbivores. Because they can migrate vertically copepods can exploit these concentrations of food at whatever depth they occur. Were the phytoplankton actually distributed homogeneously throughout the euphotic zone, their concentration would be universally too low to support viable herbivore populations (T.R. Parsons, pers. comm.). Thus the drastic repercussions  -20-  that changes in the extinction coefficient have for the herbivores in the model are unlikely to materialize in the real world. 3.1.2 Euphotic Zone Depth (z ) e  A serious weakness of this model is its sensitivity to an arbitrary constant mixed layer depth. The photosynthetic rate is proportional to l/z , based on the e  assumption that as the depth of the mixed layer is increased the average light intensity in the euphotic zone will decrease. This is predicated on the assumption of a homogeneous mixed layer. As with the sensitivity to k and P e  m a x  it can be  rationalized by recalling that the vertical structure of the phytoplankton prevents the repercussions for the rest of the community of changes in these parameters from being realized in the real ocean. Still, it represents a serious weakness of the model.  Coastal oceanic communities may have a mixed layer of 20 to 30 m depth, but in the SELECT model these values will cause depletion of the available nitrate in a very short period of time, because phytoplankton growth is inversely related to the mixed layer depth. In order to properly simulate the desired biological events a value of 40 m must be chosen, as it is in all of the simulations carried out.  3.13 Half-saturation Constant for Nitrogen Uptake (k ) g  kg is given as DD*D(I), where D(I) is the equivalent spherical diameter of the cell, so that smaller cells will be better able to grow at low ambient concentrations of nitrate and/or ammonium. The model is not particularily sensitive to changes in DD; it can be increased or decreased by as much as 30% without affecting the main events in the simulation (see Table II).  -21The chief effect of decreasing DD is to delay the emergence of a bimodal phytoplankton size spectrum, because it allows larger cells to take up nutrients effficiently at low concentrations. Decreasing DD tends to favour Calanus, which feed on larger cells than Pseudocalanus, which are favoured when DD is increased.  3.1.4 Mixing Rate  The rate of mixing across the thermocline, RM, is varied in concert* with the nutrient concentration below the thermocline, RO. The net effect is to alter the rate of nutrient input into the euphotic zone. Sensitivity to this parameter is weak: the primary phytoplankton bloom is driven by nutrients already present in the euphotic zone at the formation of a seasonal thermocline, rather than upwelled nitrogen. This model is not intended to represent a strong upwelling region such as the Peru or Benguela currents.  Interestingly, a decrease in the mixing rate, even in concert with a decrease in the deep water nutrient concentration, actually increases the peak biomass of phytoplankton at the primary bloom (Table II). At this point the nutrient concentration is high and decreased rnixing of phytoplankton cells out of the euphotic zone overrides the effect of decreased nutrient input. This may reflect an erroneous model of interface mixing, which assumes symmetry of upward and downward mixing. The validity of this assumption depends on the unspecified spatial boundaries of the model. There can be local upwelling but ultimately the system must be closed by an equal mass of downwelled water. If the boundaries of the model are not the land boundaries of the basin (which they should not be, as the * "In concert" means that both are increased, or both decreased.  -22-  model is designed for an open water environment in a coastal sea too large to be homogeneous in space) the assumption of symmetrical mixing is probably wrong. However, since it is still necessary to close the system, this is an inevitable artificiality in a model that eschews spatial structure.  The chlorophyll minimum shows decreased biomass, indicating that at this point (days 40-43) upwelled nutrients are of some importance to the phytoplankton.  RO and RM can be increased or decreased by (each) up to 30% without affecting the overall pattern of community development. Increases of 50% or more will prevent nutrient depletion and the emergence of a bimodal phytoplankton size spectrum, and starvation of juvenile copepods occurs because of the absence of prey cells of appropriate size.  3.1.5 Sinking Rate (V)  Sensitivity to this parameter is very limited. The base rate can be halved or doubled without greatly affecting the pattern of community development. Quantitative effects do occur, with greater sinking rates tending to favour the smaller cells.  -233.1.6 Maximum Chlorophyll/Carbon Ratio (CHMAX)  The chlorophyll concentration in the euphotic zone is  CHL= 2jCHMAX*P(J)*[N]/(k +[N]), s  where P(J) = carbon content of phytoplankton size class J, [N] = nutrient concentration, and kg=half-saturation constant.  CHL in turn determines the attenuation coefficient k =A*CHL+B. The effects of e  CHMAX on the simulation are virtually identical to those of A and B (section 3.1.1).  3.1.7 Respiration Rate  The weight-specific respiration rate of phytoplankton is given as a*D -1/3 , where D is the equivalent spherical diameter of the cell. Sensitivity to the value of the exponent was not tested (but see Steele and Frost, 1977, p. 496). The following discussion refers to the coefficient a (RESP) only. Sensitivity to this parameter is pronounced but asymmetrical. Decreases of up to 50% do not affect the qualitative features of community development but cause fairly substantial increases in the biomass of both phytoplankton and zooplankton. Increasing a causes a strong and lasting dominance of the phytoplankton community by the largest cells. The other size-dependent parameters in the phytoplankton submodel are the sinking rate and the half-saturation constant; both tend to favour  -24the smaller cells. The respiration rate, which balances this out by favouring the larger cells, is quantitatively more significant. Increasing a by more than 10% prevents the lower mode in the phytoplankton size spectrum from emerging within 60 days, and has a strong negative impact on the Pseudocalanus population (but see 3.3.4 below).  3.1.8 Zooplankton Assimilation Efficiency  A constant, EE, determines the assimilation efficiency of feeding zooplankton. The model assumes that zooplankton can alter their their feeding rate according to the food concentration in a way that will maximize the rate of growth F up to some maximum F  m a x  (Steele and Frost, 1977, p. 505). Increasing EE decreases the  concentration of prey cells required for F to reach F  m a x  , and vice versa.  The model's output is quite sensitive to the value of EE, but again the effect is not symmetrical. Increases of up to 100% do not affect the main features of the simulation. Increasing EE causes heavy grazing near the center of the phytoplankton size spectrum, probably due to increased zooplankton abundance, advancing the evolution of a bimodal spectrum, and tends to favour Pseudocalanus, which is more subject to food limitation than Calanus (but see 3.3.4 below).  Decreasing EE puts Pseudocalanus at a strong disadvantage; even a decrease of 6.7% (EE=0.00014) causes noticeable starvation of Pseudocalanus juveniles. Because decreasing EE increases the food requirements of these nauplii, it also causes heavy grazing on the smallest cells and delays the emergence of a bimodal phytoplankton size spectrum.  -25The model's sensitivity to decreases in EE is due to two assumptions that are probably erroneous. Firstly, the assumption of a homogeneous euphotic zone eschews vertical structure as discussed in 3.1.1 above and overestimates the impact on copepod populations of changes in the average phytoplankton cell concentration. Decreasing EE negatively impacts Pseudocalanus by increasing the concentration of cells they require, whereas in the real ocean the concentration available to a vertically migrating animal in the production maximum is much greater than the average concentrations depicted in the model (see 3.1.1 above). Secondly, food limitation resultsfromlow concentrations of the small cells on which Pseudocalanus are assumed to depend, whereas in fact they are capable of feeding efficiently on larger cells than the model allows (Poulet and Chanut, 1975; Harris, 1982; see 3.3.4 below).  3.1.9 Zooplankton Basal Metabolic Rate (ZB)  The primary effects of changes in this parameter are felt by the zooplankton; effects on the phytoplankton depend on changes in the mortality rates of juvenile zooplankters. Increases or decreases of up 50% do not affect the main features of the simulation. Increasing ZB slows naupliar development and decreases peak biomasses of zooplankton.  - 2 6 -  3.1.10 Size Selection of Cells  Two parameters, D M I N and D M A X , determine the shape of the curve that represents grazing efficiencies on different sizes of cells, according to the equation  S =EXP(-ln X/DMIN), where 2  e  X = (DJ/DMAX)*W /3 1  where DJ=diameter of cell, and W=mass of copepod. The shape of this curve is more or less a parabola, although asymetric (steeper on the left hand side: see Figure 3). D M A X can roughly be be defined as the mode of the curve, or the value of D J at which S is maximized, and D M I N as the variance, or breadth, of the curve. In e  empirical terms, D M A X determines the size of cells that are most efficiently captured and D M L N the range of sizes that can be captured efficiently.  -27-  SE  0 ~i—r—i—i—i—i  i  i  i  i  i  i  i  i  i  i i —  0 K> 20 30 40 50 60 70 80 90 100110 120130140150160170  D  Figure 3 - Shape of selection curve (for adult female Pseudocalanus).  Increases in either parameter, or both, do not greatly affect the results. Increases of up to 50% can be accomodated without affecting the main features of the simulation. Increasing either parameter tends to favour Pseudocalanus.  Decreasing DMAX by even 10% causes heavy predation by the larger copepods (CV and adult Calanus) on the smaller cells. This prevents the emergence of a bimodal phytoplankton size spectrum and inhibits the development of a viable Pseudocalanus population. Decreasing DMIN prevents Pseudocalanus from feeding efficiently on larger cells (which are the most numerous at the critical stage) and strongly impacts the development of the population. A decrease of 25% causes starvation of juvenile Pseudocalanus. DMAX can be decreased by 5% and DMIN by 12.5% without affecting the main features of the simulation.  -28-  The assumption that DMAX and DMIN are the same for both copepod species is probably erroneous (see section 3.3.4). The true values for Pseudocalanus are considerably greater than those used here.  3.1.11 Carnivore Predation  Carnivore predation on copepods is described by an Monod (1942) function Predation Rate = G*N/(H+N), where G is the maximum predation rate (d"*), N is the number of copepods, and H is a half-saturation constant.  GC and HC, and GP and HP, are the values of G and H for Calanus and Pseudocalanus, respectively.  Changes in H do not have much impact. Increases or decreases of up to 50% of HC or HP cause only quantitative changes in the output.  The model is more sensitive to GC than GP, since Calanus are more abundant than Pseudocalanus and have a greater impact on the phytoplankton community. Changes of ±20-25% can be sustained with only quantitative changes in the output. Greater decreases prevent the Pseudocalanus populationfromdeveloping due to interspecific competition. Greater increases dramatically alter the pattern of phytoplankton community development because Pseudocalanus become the major herbivores. Changes of+.50% of GP can be sustained although Pseudocalanus biomass increases or decreases proportionately.  -2932 Deviation from Mass-Dependence  In the submodel of phytoplankton growth, nutrient uptake, sinking, and respiration are all dependent on the size of the cell, expressed as equivalent spherical diameter (ESD). A fourth parameter, the maximum photosynthetic rate, is assumed constant for all phytoplankton. Noise about these relationships can be simulated with an equation of the form  X(J)=X (J)*(1-MAXDEV+2*MAXDEV*RV), where 0  X(J) = value of variable (with noise) for phytoplankton size  '  class J, XQ(J)=base value from size dependent or constant relationship, MAXDEV=maximum deviation from base value, as a proportion of X Q , and RV=a random value in the interval (0,1) (see 2.5 above).  This creates a uniform distribution of random values X on the interval (X (1-MAXDEV),X (1 +MAXDEV)). The input variables (X) that correspond to 0  0  the four parameters named above are DD, V, RESP, and C, respectively.  Model runs simulating noise about these four parameters were carried out for several values of MAXDEV. In each case the similarity index (section 2.4) was calculated for each day's output to estimate the similarity of the phytoplankton size spectrum and the copepod stage distribution to those in the basic model. Because random number generators sometimes produce clusters of very high or very low  -30-  values that giveriseto anomalous results, several runs were done in each case. The minimum similarity indices for these runs are given in Table III.  -31T a b l e I I I - Minimum s i m i l a r i t y i n d i c e s f o r b i o m a s s s p e c t r a o f p h y t o p l a n k t o n (P) a n d s t a g e d i s t r i b u t i o n s o f C a l a n u s (CAL) a n d P s e u d o c a l a n u s (PSEUDO). VARIABLE  MAXDEV  P  CAL  PSEUDO  DD  0.2  0.838  0.892  0.881  0.916  0.926  0.852  0.933*  0.873  0.770  0.775  0.888  0.816  0.895  0.874  0.840  0.850  0.891  0.879  0.3  0.5  V  0.2  0.4  C  0.2  0.3  RESP  0.2  0.4  c * *  RESP**  0.3  0.3  0.789  0.890  0.758  0.545  0.797  0.851  0.950  0.896  0.856  0.944  0.928  0.880  0.896  0.886  0.902  0.942  0.911  0.857  0.930  0.890  0.830  0.855  0.878  0.794  0.518*  0.740*  0.778  0.467*  0.478*  0.823  0.398*  0.072*  0.488*  0.262*  0.044*  0.468*  0.152*  0.443*  0.600  0.213*  0.052*  0.371*  0.701*  0.766  0.695  0.652*  0.777*  0.792*  0.657*  0.586*  0.549*  0.387*  0.063*  0.540*  0.281*  0.172*  0.157*  0.460*  0.267*  0.395*  0.843  0.807  0.791  0.870*  0.760  0.836  0.923*  0.889*  0.915  0.928*  0.878*  0.867  * Low v a l u e o c c u r r e d on l a s t d a y ( 6 0 ) o f s i m u l a t i o n . ** Random d e v i a t i o n n o t c o n s t a n t t h r o u g h o u t ( s e e t e x t ) .  -32The results basically conform to what was observed in the basic sensitivity analysis: the model is far more sensitive to changes in C and RESP than DD or V. In the two former cases, the similarity indices decrease rapidly towards the end of the simulation (note the number of asterisks), and the phytoplankton size spectra look rather unnatural and implausible (Figure 4b).  This leaves the question of whether the deviations are themselves constant throughout the simulation, that is, whether noise about the hypothesized values of these parameters occurs only among the size classes (species) and not within the classes over time. The last four rows of Table III show the results of runs where C and RESP for all size classes are given new random values each day. Not surprisingly, the rather unnatural-looking spectral shapes that appeared when a constant deviation was assumed disappear (Figure 4c), and the similarity indices are much greater. This is perhaps a more realistic representation of 'noise' in a community with an 'average' P  m a x  of 2.5, or there may be an element of each (i.e.  species' rates change over time but by less than their base rates deviate from the assumed constant value).  33  Figure 4 - Biomass spectra at day 50 for A) basic model B) C±30% with constant deviation C) Q+30% with new random deviations each day. In this and all subsequent figures D on the horizontal axis is the equivalent spherical diameter of the phytoplankton cell in micrometres.  MG C  MGC  3  4  LOG(2)D  5  8  -34-  -35-  33 Phytoplankton and Copepods - Alternative Models  33.1 Photosynthetic Rates of Diatoms and Flagellates  The SELECT model proposes a maximum photosynthetic rate, C (P )> which is max  constant for all phytoplankters. Realized rates vary among different-sized cells according to size-dependent models of respiration and nutrient uptake. The maximum photosynthetic rate is not, however, actually the same for all taxa. Parsons et al. (1978) suggest that diatoms (Bacillariophyceae) generally have a higher P  m a x  than do flagellated forms (Dinophyceae, Chrysophyceae, others).  Because the SELECT model is extremely sensitive to this parameter (sections 3.1.1, 3.2), such variations may significantly affect its predictions.  In this model two values of C are used: 2.1 for 'flagellates' and 2.8 for 'diatoms'. 20 u,m ESD is taken to be the cutoff point between the two groups (T.R. Parsons, pers. comm.).  The resulting size spectrum is quite different from that produced by the basic model. All of the 'flagellate' size classes remain rare throughout the simulation, while the 'diatom' size classes are abundant throughout. The use of an arbitrary cutoff point across which a significant change in the value of C occurs results in a rather implausible spectrum shape that drops off precipitously at 20 \xm (Figure 5).  This is a necessary artificiality that would not occur in the real world because the division of the size spectrum would not produce a precise division by taxa: some diatoms are smaller than 20 itm and many dinoflagellates are larger. It may also be  -36that the difference between the maximum photosynthetic rates of the two groups is less than the 4/3 ratio used here. Figure 5 - Biomass spectra at day 50 for A) standard SELECT and B) higher photosynthetic rate for diatoms than flagellates.  25  MGC -i  LOG(2)D  -373.32 Vertical Migration of Dinoflagellates  Some dinoflagellate species have half-saturation constants for nutrient uptake (k ) §  that are much greater than those of other, sirnilarily sized cells (Eppley et al., 1969). Unable to compete for nutrients at low ambient concentrations, these organisms survive by migrating downward at night into the nutrient-rich waters about the thermocline  (ibid.).  Two size classes of phytoplankton were designated a 'species' possessing this adaptation, and were exemptedfromnutrient limitation by setting RFA=0.95 (RFA= [N]/(k +[N]); see Table IV), regardless of the ambient nutrient s  concentration.  A significant increase in the number of cells in these classes over that in the basic model appears after 45 days, at which time the ambient concentration of nitrate/ammonia is 2.51 jiM (Figure 6). After this point a spike in the spectrum remains throughout the simulation and grows to rather absurd proportions.  -38Figure 6 - B i o m a s s spectra at day 60 for A ) standard S E L E C T and B ) dinoflagellate vertical migration.  MGC  MGC  LOG(2)D  -39If organisms with this adaptation could potentially come to dominate the community, but generally do not, there must be some cost associated with it, either metabolic or through increased predation. That copepods will prey preferentially on cells with internal nutrient pools of greater than ambient concentration is confirmed by Butler et al. (1988, in press): this scenario is discussed separately below. A metabolic cost expressed as a lower P  m a x  for those size classes designated as  migrators can certainly prevent these classes from becoming the dominant 'species' present. A decrease of only 10% significantly overcompensates for the advantage derived from migration: these size classes are much less abundant than in the basic model. A decrease of 5% overcompensates for the first 60 days but is inadequate thereafter, as the nutrient concentration is very low.  T a b l e IV - V a l u e s o f RFA-[N]/(k +[NJ). C e l l s i z e i n c r e a s e s t o p t o bottom, n u t r i e n t c o n c e n t r a t i o n i n c r e a s e s l e f t t o right. B  0.31 0.26 0.22 0.16 0.15 0.12 0.11 0.08 0.06 0.05 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0.01 0.01 0.01 [N]=0.0  0.47 0.41 0.36 0.31 0.26 0.22 0.18 0.15 0.12 0.09 0.08 0.06 0.05 0.04 0.03 0.03 0.02 0.02 0.01 0.01  0.57 0.51 0.45 0.39 0.34 0.29 0.25 0.21 0.17 0.14 0.12 0.09 0.07 0.06 0.05 0.04 0.03 0.03 0.02 0.02  0.64 0.58 0.53 0.47 0.41 0.36 0.31 0.26 0.22 0.18 0.15 0.12 0.09 0.08 0.06 0.05 0.04 0.03 0.03 0.02  0.69 0.64 0.58 0.52 0.47 0.41 0.36 0.31 0.26 0.22 0.18 0.15 0.12 0.09 0.08 0.06 0.05 0.04 0.03 0.03  0.73 0.68 0.62 0.57 0.51 0.45 0.39 0.34 0.29 0.25 0.21 0.17 0.14 0.11 0.09 0.00 0.06 0.05 0.04 0.03  0.76 0.71 0.66 0.61 0.56 0.49 0.44 0.38 0.33 0.28 0.23 0.19 0.16 0.13 0.11 0.09 0.07 0.06 0.05 0.04  0.78 0.74 0.69 0.64 0.58 0.53 0.47 0.41 0.36 0.31 0.26 0.22 0.18 0.15 0.12 0.11 0.08 0.06 0.05 0.04  0.81 0.76 0.71 0.66 0.61 0.56 0.49 0.44 0.38 0.33 0.28 0.24 0.21 0.16 0.14 0.12 0.09 0.07 0.06 0.05  0.83 0(1) 0.7G 0.74 0.69 0.64 0.58 0.52 0.47 0.41 0.36 0.31 0.26 0.23 0.16 0.15 0.13 0. 11 0.06 0.06 0.05 0(20)  ©  [N]=10.0  1  -413.33  Chemosensory G r a z i n g  The SELECT model is based on assumptions about copepod feeding that are largely obsolete, representing copepods as passive filter feeders selecting cells according to the spacing of the setules (Steele and Frost, 1977, p. 500). While the spacing of the setules appears to affect cell size selection even in non-filtering modes (Boyd, 1976; Koehl and Strickler, 1981), it is unlikely that particle selection by copepods is a purely mechanical process: there is a chemosensory component as well (Poulet and Marsot, 1978; Koehl and Strickler, 1981; Butler et al., 1988, in press).  Because the SELECT model depicts strong top-down control of the phytoplankton community by grazers (Steele and Frost, 1977; Steele and Gamble, 1982), changes in grazing pressure can significantly alter the composition of the phytoplankton community. As in 3.3.2 above, these effects are examined by designating two size categories to be a 'species', to which an alternative grazing model is applied.  333.1  Toxicity  When this 'species' is given a refuge from predation by, for example, toxic metabolites, it can come to dominate the system rapidly. In this model the rate of consumption by grazers is reduced to one tenth of what it would be under the passive filtering model.  Figure 7 shows size spectra for phytoplankton in the standard model and the "predation refuge" model. A phytoplankton species that is unpalatable to grazers will dominate a community in which the standing crop is controlled by grazing.  -42-  Producing toxic metabolites must have some metabolic cost, if such organisms are not numerically dominant most of the time (in which case secondary production would cease). Because grazer control is strong in the S E L E C T model, a significant metabolic cost, expressed as a reduced P  m a x  , must be imposed on the species  possessing the predation refuge in order to maintain their biomass at reasonable levels. A P  m a x  of 1.75 (70% of that of other species) compensates for the predation  refuge for the first 60 days of the simulation but is inadequate thereafter. In the context of the S E L E C T model this is a highly significant reduction (see sections 3.1.1 and 3.2).  -43Figure 7 - Biomass spectra at day 30 for A) standard SELECT and B) the "predation refuge" model.  -44-  3332 Nutritional State of Cells  It has been demonstrated that copepods will feed preferentially on phytoplankton cells grown in nutrient-rich media (Butler et al., 1988, in press). In the SELECT model, the rate of grazing can be adjusted for the nutritional state of the prey cells by multiplying the selection function S by RFAV3 (RFA as in 3.3.2, see Table IV). e  The 1/3 power is used so that the range of values approximates the 3:1 ratio of grazing rates observed by Butler et al.  (ibid).  When this simple modification is introduced alone, it has the predictable effect of increasing the average size of the phytoplankton. There is a slight decrease in the biomass of the smaller cells (low kg - high RFA - heavy grazing) and an increase in that of the larger ones (high kg - low RFA - weak grazing). The size spectrum is bimodal after day 40 as in the standard simulation, but the lower (flagellate) mode is weaker (Figure 8).  -45Figure 8 - Biomass spectra at day 60 for A) standard SELECT and B) grazer response •RFAV3. MG C 25 T  25  MGC T  0  1  2  3  4  5  LOG(2)D  6  7  6  -46-  It could be hypothesized that such a grazer response could compensate for variations in growth rate created by variations in kg among species or strains. This hypothesis was tested by running the model of stochastic variations in DD among size classes of phytoplankton (section 3.2) to a maximum of ±50% of the base values with the modified grazer response to see whether it would 'smooth out' the irregularities in the spectrum. The answer is basically negative. The irregularities in the spectrum do not disappear and the 'smoothing' effect is marginal to nonexistent (Figure 9). The similarity indices (comparison to standard simulation) are very slightly lower (mean difference 0.005) to day 50, after which they are higher, probably due to the weakness of the flagellate peak under the modified grazer response.  47  Figure 9 - Biomass spectra at day 50 for A) DD+50% and B) DD + 50% with grazer response  MGC  MGC  -4833.4 Size Selection of Cells by Pseudocalanus  The assumption that size selection of prey cells by several species of copepods can be described by a single function scaled to the weight of the animal is of doubtful validity (Harris, 1982; see also Frost, 1980). Two studies in particular suggest an alternative formulation for Pseudocalanus.  Poulet and Chanut (1975) observed that Pseudocalanus minutus feeds opportunistically on a wide range of particle sizes. Their data show negligible differences between the size spectra of cells captured and those available. A later experiment (Poulet, 1978) showed similar results for several other species, Oithona similis,Acartia clausi, Temora longicomis, and Eurytemora herdmani. Harris (1982)  demonstrated that Calanus do, on average, capture larger cells than Pseudocalanus, but that the difference is not as great as that predicted by the SELECT model. Both of these reults can be incorporated into the model by altering the values of DMAX and DMIN for Pseudocalanus.  Opportunistic feeding can be represented by setting DMAX=20.0 and DMIN = 10.0 in order to make the selection curve broad and flat (the POULET model, Figure 10b). Setting DMAX=10.0, with DMIN=2.0 as in the basic model (the HARRIS model) reduces the ratio of the cell diameters at the modes of the grazing curves (the size of cells most efficiently grazed) for adult Calanus and Pseudocalanus from about 2 to the 1.2 observed by Harris (1982), but does not broaden the range of cell sizes captured by Pseudocalanus (Figure 10c). The POULET model predictably benefits Pseudocalanus at the expense of Calanus (Table V). This model has rather drastic effects on the phytoplankton community. After day 33, when the Pseudocalanus population reaches its biomass peak, the  -49-  diatom community is rapidly decimated. Initially it retains its unimodal shape but the biomass drops off rapidly. A second (flagellate) mode emerges after day 45 but is very weak. On the whole the spectrum is much more nearly flat than in the standard SELECT model (Figure 11). Figure 10 - Selection curves for adult female Pseudocalanus for A) standard grazing model B) POULET grazing model C) HARRIS grazing model. SE 1 -i 0 H—I—i—I—i—i—i—i—i—i—i—r—i—|—T—i—i— 0 10 20 30 40 50 60 70 80 90 100 I K ) 120130 U0150160170 0  -50-  -51Figure 11 - Biomass spectra at day 51 for A) standard SELECT and B) POULET grazing submodel.  MGC  MGC  -52-  The phytoplankton fare somewhat better under the HARRIS model. The emergence of a bimodal size spectrum is advanced somewhat because Pseudocalanus grazing is shifted from the smaller cells towards the centre of the spectrum. Pseudocalanus biomass is greater than in standard SELECT but less than in POULET (Table V).  CALANUS  PSEUDOCALANUS  STANDARD  2071  847  HARRIS  1845  1464  POULET  1788  1997  T a b l e V - P e a k c o p e p o d b i o m a s s (mgC/m^) u n d e r  alternative  s e l e c t i o n models f o r Pseudocalanus.  In general the HARRIS model is preferable. The POULET model may be applicable in certain environments. Poulet's (1978) experiment was conducted with animals taken from Bedford Basin, Nova Scotia. Bedford Basin is a highly eutrophic environment (L. Wooton, pers. comm.), so the decimation of the phytoplankton community observed here would be unlikely to occur. Opportunistic feeding on a wide range of particle sizes may be an adaptation peculiar to this population of P. minutus, for two reasons. Firstly, in a highly eutrophic environment such as Bedford  Basin, nutrient depletion and the emergence of a phytoplankton community dominated by small cells would be an infrequent and unpredictable occurence, so that specialization on such cells would clearly be a losing strategy. Secondly, this population does not have to compete with a population of large Calanus of the parificus/finmarchicus group. These conditions appear to be conducive to the evolution of an opportunistic feeding strategy, and the fact that this is shared by the  -53other four species present suggests a site-specific adaptation. In the open ocean, the POULET model is inconsistent with the observed shape of the phytoplankton biomass spectrum during the spring bloom (Gamble, 1978: see Figure 11).  Saanich Inlet, British Columbia, where Harris' (1982) experiment was conducted, is much more representative of the type of environment upon which the SELECT model is based. Surface heating produces a stable thermocline that will permit nutrient depletion (Harrison et al., 1983). Calanus are present and a clear separation of niches by particle size is apparent.  33.5 Copepod Carnivory Landry (1981) observed that Calanus pacificus will feed on nauplii and other animal foods in the 100-200 u,m ESD size range. The LANDRY model permits a 'switching' response whereby adult and CV Calanus may feed raptorially on such particles (including the largest phytoplankton cells, NLTJ nauplii of Calanus, and Nil, NIV, and NV nauplii of Pseudocalanus) rather than by sieving particles according to the S grazing function, if it is energetically advantageous to do so. Under the e  conditions simulated, it is never advantageous to excercise this option, even with some fairly optimistic assumptions about its energetic yield. No animals ever did, and the results are identical to those of standard SELECT. This behaviour may be advantageous at certain times of the year when phytoplankton food is not available, but does not appear to be important in the springtime.  -543.4 Protozooplankton and the "microbial loop"  3.4.0 Introduction Protozooplankton is the term coined by Sieburth et al. (1978) to describe heterotrophic unicellular organisms other than bacteria. These include heterotrophic microflagellates (Fenchel, 1982a-c), Tintinnids and other ciliated forms (Heinbokel, 1978; Sherr et al., 1986), sarcodinians, or amoeboid forms, including Radiolaria and Foraminifera (Sieburth, 1979; Anderson, 1986), and heterotrophic dinoflagellates (Smetacek, 1981; Gaines and Elbrachter, 1987). Until recently the dominant view of the planktonic food web was that the phytoplankton-copepod food chain represented in the SELECT model was responsible for virtually all of the transfer of energy from primary producers up the food chain. More recently, the quantitative importance of bacteria and protozooplankton has been recognized (Sorokin, 1977; Williams, 1981; Azam et al., 1983; Laval-Peuto et al., 1986). Omission of this segment of the community is a major flaw of the SELECT model (B.W. Frost, pers. comm.). The following section discusses the introduction of the protozooplankton community into the model. The FORTRAN source code for these models is given in Appendix B.  In order to include the protozooplankton it is necessary to include bacteria, the primary food source for heterotrophic microflagellates (Fenchel, 1982c; 1985; Sherr et al., 1983), and extracellular metabolism of the phytoplankton, the primary source of substrate for free-living bacteria (Larsson and Hagstrom, 1979; Azam et al., 1983; Linley et al. 1983).  -55-  3.4.1 Some definitions  In the following discussion, certain functional groups have been defined according to their role in the food web. "Flagellates" or "microflagellates" refers to small monad-like forms that prey primarily on bacteria (Fenchel, 1982a-c; Sherr et al., 1983) and excludes the dinoflagellates. "Phytoflagellates" are those flagellates (as defined above) that contain chlorophyll and are assumed to be at least partly autotrophic (Estep et al., 1986). "Microzooplankton" includes the sarcodinians and those ciliated forms that prey primarily on flagellates (Sheldon et al., 1986) but excludes those ciliates that are primarily bacterivores (Sherr et al., 1986), as these do not exist in significant numbers in the open sea (Fenchel, 1980a-c).  3.42 Protozooplankton Growth Rates Growth and respiration rates of protozooplankton are based on the allometric equation R=aW , a  where R is the rate function (e.g. growth rate), W is the mass of the cell, and a and a are constants (Fenchel, 1974; Piatt, 1985). This can also be formulated as a weightspecific rate R  =  a  W  a - l  Respiration rates are given by Steele and Frost's (1977, p.496) formulation for nonvacuolated cells. This corresponds to a value of a of 0.667. (Gross) growth rates are given this same value of a so that one value is used for both terms. Growth rate data for copepods (Ikeda, 1974), as well as Tmtinnids (Heinbokel, 1978) conform closely to this relationships can also be set at 0.75, as advocated by Fenchel (1974), with only minor effects on the model's output.  -56Different values of a are used for flagellates (a^) and microzooplankton (a^. afW*" gives rates in the size range of the microzooplankton that are much lower a  than those observed in the literature (e.g. Heinbokel, 1978). Microzooplankton thus have growth rates much higher than would an hypothetical flagellate of similar size. Trophic Phasing in the Microbial Food Chain  When different values of a are used, it immediately becomes apparent that higher growth rates do not result in higher biomass. Models where growth rates are lowest tend to have the greatest biomass of protozoplankton.  This can be explained by the trophic phasing of predator and prey (Parsons, 1988). Low flagellate growth rates result in poor phasing between growth of prey (bacteria) and predator (flagellates) that allows a large standing crop of prey to accumulate, which gives rise to a similar increase in predator biomass shortly afterward (Figure 12b). The same effect is apparent at the next step of the food chain, where flagellates are prey for microzooplankton. When growth rates of both flagellates and microzooplankton are low, biomass of all three groups remains high throughout the simulation. Figure 12 - Time series of biomass of bacteria (solid) and flagellates (dots) in A) poorly phased system (low a^) and B) well phased system (high af).  -573.4 J Pathways of Energy Flow and Succession  Recognition of the importance of the protozooplankton and the "microbial loop" has radically altered perceptions of the planktonic food web (Williams, 1981), producing a much more complex set of interactions than was previously recognized (Figure 13). Not only have a number of new actors been introduced to the web, but new links between existing ones have been established. For example, some species of unicellular algae may feed phagotrophically on bacteria (Bird and Kalff, 1986).  Inclusion of these new players and alternative pathways in the SELECT model confounds the picture of phytoplankton succession it depicts. In many cases the shift from a diatom to a flagellate dominated community does not occur. While this does in fact occur in nature (Gamble, 1978), it does not appear to occur simply because of nutrient competition as Steele and Frost (1977) believed. The picture of succession, like that of the food web, is becoming more complex, and its exact form can not be deduced at this time.  -58-  Figure 13- A) Old and B) recent views of the lower levels of the planktonic food web.  PHYTOPLANKTON  I  COPEPODS  B  DOC  I  BACTERIA  DOC BACTERIA  PHYTOPLANKTON HETEROTROPHIC COPEPODS  FLAGELLATES  MICROZOOPLANKTON  -59-  3.4.4 Extracellular Metabolism  It has long been believed that excretion of metabolites by phytoplankton is the result of photosynthetic production in excess of nitrogen available for protein synthesis (the "overflow" hypothesis: Vaccaro et al., 1968; Joiris et al., 1982; Azam et al., 1983). This has recently been disputed by Bjornsen (1988), who observed that amino acids are among the low molecular weight (LMW) organic compounds excreted. He proposed that extracellular metabolism is not related to ambient nutrient concentration but rather represents simple diffusion of LMW compounds across cell membranes that are permeable to molecules of this size (the "passive diffusion" hypothesis).  Two corollaries follow from this: extracellular metabolism should be related to phytoplankton biomass rather than production, and the smaller cells should have relatively greater losses due to their greater surface-to-volume ratio (Bjornsen, 1988). Both of these have empirical support. Fuhrman et al. (1980, p. 201) state that in their study of the Southern California Bight "bacterioplankton growth rate was evidently influenced more by the standing stock of phytoplankton than by the primary production". Paerl and MacKenzie (1977) observed that the nanoplankton have much greater excretion losses during the hours of darkness than the netplankton.  The feeding behaviour of copepods also provides clues. Feeding is induced at least partially by the dissolved compounds released by food particles (Poulet and Marsot, 1978). Amino acids appear to be important among these (Poulet and Ouellet, 1982), and it is difficult to see how copepods could feed preferentially on nutrientsaturated cells (Butler et al., 1988, in press) if their excretion function was inhibited.  -60While it is necessary to include phytoplankton excretion in the expanded model in order to provide a substrate for bacterial production, closure of this term (i.e. accounting for dissolved organic carbon (DOC) gained as lost phytoplankton production or biomass) has serious consequences for the phytoplankton community.  When the nutrient concentration-dependent excretion rates depicted in Joiris et al. (1982) are used, the phytoplankton biomass spectrum is nearly flat in the early stages of the simulation (Figure 14b), and the initial diatom bloom does not develop until much later. The early chlorophyll peak disappears and the time series of chlorophyll becomes similarity flat. The copepod populations fail to develop due to a paucity of food cells at the critical stage: the diatom bloom comes too late, after the overwintering adults are mostly dead (as in the match-mismatch hypothesis of Cushing (1975)).  When a form of Bjornsen's (1988) "passive diffusion" hypothesis is used the major events in the simulation are intact, except that a breeding population of Pseudocalanus fails to develop. Because this excretion model is biased against the smaller cells, the small cells that juvenile Pseudocalanus are assumed to depend upon for food are scarce. This can be rectified by using the HARRIS model of Pseudocalanus grazing (section 33.4). On the whole this model is preferred, because the other, with its flat biomass spectrum and time series, is quite implausible. The passive diffusion model has been used throughout the remainder of the simulations, although in many cases other runs with a nutrient dependent DOC input were carried out, with similar results.  -61Figure 14 - Biomass spectra at the height of the bloom (day 21) under A) standard SELECT (no excretion) B) "overflow" excretion model C) "passive diffusion" excretion model. MG C 30 ~\  oH——i  0  1  1  2  1  3  1  4  1  5  LOG(2)D  MGC 30 T  1  6  1  1  7  8  -6230  MC C  25-  C  2015105-  0 0  2  3  4  5  6  7  8  L0G(2)D  3.4.5 Protozooplankton Herbivory  In addition to the bacteria -flagellate- microzooplankton food chain described above, microzooplankton may graze on small phytoplankton, providing an intermediate link between phytoplankton and copepods in oligotrophic systems dominated by very small cells (Parsons and Lalli, 1988). In addition, Goldman and Caron (1985) have shown that microflagellates will prey upon small phytoplankton as well as bacteria.  Inclusion of these pathways in the SELECT model results in the decimation of the smallest classes of phytoplankton and prevents the development of a phytoflageUate-dominated community after 60-70 days as in the basic model. While to some extent this effect is delayed in any case by excretion losses (3.4.4 above), including these additional forms of predation virtually wipes out the phytoflagellate community. Microzooplankton and heterotrophic flagellates persist, however, and this scenario is generally consistent with a post-bloom ecosystem dominated by heterotrophs (Sorokin, 1977).  -63-  3.4.6 Phytoflagellate Bacterivory Facultative heterotrophy of 'phyto'plankton has been observed on many occasions. Some diatom species can grow saprotrophically on dissolved sugars such as glucose and galactose (White, 1974a,b). More recently, phagotrophic feeding on bacteria has been observed (Bird and Kalff, 1986). Estep et al. (1986) have suggested that among the microflagellates the distinction between heterotrophic and phototrophic forms is essentially an arbitrary one: the presence of chlorophyll does not necesssarily indicate that a strain or species of monad is not partially or even primarily heterotrophic. Phagotrophy is known among chlorophyll-containing dinoflagellates as well, but may represent a source of concentrated vitamins rather than a carbon source (Gaines and Elbrachter, 1987).  Two models were used to describe phytoflagellate bacterivory: a "switching" model and a "simultaneous heterotrophy and autotrophy" model. In the switching model the potential energy gain from each nutritional mode was calculated for each day, and the cell utilized whichever was most advantageous for that day. In the simultaneous model the energy derived from bacterivory is simply added to that derived from photosynthesis. The real situation probably lies somewhere in between, i.e. the two modes can operate simultaneously but there is some loss of photosynthetic capacity involved. Lacking verification or quantification of this effect, the two models offer two estimates, one conservative, one perhaps overoptimistic, of the energy that can be derived from phagotrophy.  The result of these models is rapid decimation of the bacteria in the absence of protozooplankton predation on the phytoflagellates. When this latter effect is  -64included, however, bacterivory, under either model, does not prevent the decimation of the phytoflagellates by protozoan predation. The 'heterotrophic' flagellates are not similarily decimated. If the distinction between autotrophic and heterotrophicflagellatesis indeed an arbitrary one (Estep et al.,1986) this result may indicate that the observed shift from a diatom to a flagellate-dominated 'phyto'plankton community as nutrients are depleted in late spring (Parsons et al., 1978; Gamble, 1978) is accompanied by a shift from photosynthesis to phagotrophy as the primary energy source for these organisms.  Another factor that must be considered is the possible presence of very small (picoplankton) autotrophic cells (Piatt et al., 1983). These would provide an additional food source for phagotrophicflagellatesthat was not present in these models.  3.4.7 Nutrient Regeneration  Recent evidence has shown that microflagellates, not bacteria, are the primary remineralizers of organic nitrogen in the marine pelagial (Goldman and Caron, 1985; Goldman et al., 1985). Regeneration efficiencies are high: up to 50% of the nitrogen content of prey cells may be released as ammonia, although this percentage will decrease if the prey cells are nutrient-stressed (Goldman and Caron, 1985).  It might appear that this efficient regeneration of inorganic nitrogen is responsible for the inhibition of the shift to aflagellate-dominatedcommunity in the expanded model, but this is not the case. This shift does not occur when the maximum  -65-  regeneration efficiency is reduced to 25%, or even when regeneration is eliminated altogether. 3.4.8 Seasonal Succession  The modelling excercises described above complicate the picture of plankton succession simulated by the SELECT model. Under several alternative models, large diatoms remain the dominant component of the phytoplankton into the late spring and early summer.  Sorokin (1977, p. 107) described a "heterotrophic phase" of plankton succession in the Sea of Japan, following the spring phytoplankton bloom, where "heterotrophic metabolism and production predominate". He hypothesized that low water temperatures inhibited the growth of heterotrophic organisms in early spring, and that in late spring they were utilizing "mostly energy from organic matter accumulated during the previous spring phytoplankton bloom".  A simulation model incorporating this idea, with an Arrhenius temperature function (Eppley, 1972) regulating the growth rate of protozooplankton and a gradually increasing water temperature, lends some support to this. It is the only scenario where protozooplankton are truly dominant in terms of biomass at the end of the 60 day period.  The main drawback of this model is that phasing effects ( above) result in very high biomass of protozooplankton in early spring when, according to Sorokin (1977), they should be virtually absent.  -66-  3.5 Temporal Structure and Vertical Migration  The SELECT model calculates the rates of primary production, grazing, nutrient consumption, and other ecosystem parameters on the basis of a 24 hour time step. Like most simulation models, it ignores the variations in these that occur within each 24 hour period.  Photosynthesis of phytoplankton undergoes a distinct diel cycle induced by both endogenous and exogenous factors (Sournia, 1974; Harding et al., 1982a,b; Legendre et al., 1988). Grazing rates also undergo such a cycle (Duval and Geen, 1976; Mackas and Bohrer, 1976). Predation rates on vertically migrating herbivores must also undergo such a cycle since visual predators feed largely in the surface layer where light is sufficient for prey capture (Stich and Lampert, 1981; 1984; Gliwicz, 1986; Vuorinen, 1987). Pseudocalanus may undergo an unusual "reverse migration" (at the surface in the daytime, migrating downward at night) in order to escape nonvisual (invertebrate) predators (Ohman et al., 1983) which themselves undertake the conventional downward migration during daylight to escape visual (fish) predators (e.g. Pearre, 1973, on Sagitta elegans).  All of these effects can be built into the model by multiplying the relevant coefficients (the photosynthetic rate, the grazing rates of Calanus and Pseudocalanus, and the predation rates GC and GP) by a sinusoidal term P=l + sin[(2<rrT+<t>)/24], where T=time of day (h, 0 =24:00), and <b=initial phase (h). A time step of 3 h is used. Values of <J> are given in Table VI.  P dt = 2TT, so that  the total values over 24 h are the same as if constant values are used (P= 1).  -67T a b l e V I - I n i t i a l p h a s e (h) f o r p a r a m e t e r s t h a t u n d e r g o d i e l v a r i a t i o n . Values f o r Pseudocalanus are f o r t h e reverse m i g r a t i o n m o d e l . P r e d a t i o n on P s e u d o c a l a n u s i s on a c y c l e o f 12 h . Photosynthesis Calanus: Grazing Basal metabolism Predation Pseudocalanus: Grazing Basal metabolism Predation  -6.0 +6.0 +6.0 +6.0 -6.0 -6.0 -3.0  The effects of changing water temperature on migrating copepods (McLaren, 1963; 1974) is included but is unlikely to have much effect. Sensitivity analysis has demonstrated that the metabolic rate of zooplankton (ZB) does not have much effect on the model's output (3.1.9 above). Its major effect is to increase naupliar development time. The results of Ohman et al. (1983) and Vuorinen (1987) show that the effect of migration on development time is marginal. MacLaren's (1963; 1974) hypothesis that temperature effects are a major force behind the evolution of vertical migration has been quite thoroughly discredited (Stich and Lampert, 1981; 1984; Gliwicz, 1986; Vuorinen, 1987).  Two alternative models were tested, one where Pseudocalanus undergo the same conventional migration as Calanus, and one incorporating the "reverse migration" observed by Ohman et al. (1983). The FORTRAN source code for these is given in Appendix C.  The results of these excercises corifirm the observation of Pepita and Makarova (1969) that diel changes in grazing increase the net phytoplankton production. The peak chlorophyll concentration is greater in all cases than in the temporally  -68unstructured model (Table VLT). Secondary production also increases: peak biomass of both species increases. Calanus in particular benefit. The "reverse migration" model does not alter this pattern but may overestimate predation on Pseudocalanus (see below).  When photosynthesis and grazing are out of phase, the time sequence of events slows down. The initial chlorophyll peak comes later and lasts longer because grazing of new production is not instantaneous. The biomass peaks of the two copepods are delayed because high rates of primary production are sustained longer.  The size structure of the phytoplankton is also affected. The biomass spectrum remains unimodal and dominated by large cells throughout the simulation (Figure 15a), probably due to sustained production of juvenile copepods that graze heavily on the smaller cells. This occurs despite the fact that nutrients are depleted much more rapidly than in the standard model (Table VII).  The "reverse migration" model may overestimate the rate of predation on Pseudocalanus. Predator and prey migrations are a half cycle out of phase, so they will encounter each other largely during the migration. Both populations will be relatively diffuse in the water column during migration (Evans, 1977) and no data exist to accurately estimate their densities or encounter rates. Because densities should be lower than if both populations were concentrated in the surface layer, GP=0.1 may be too high.  The 3 h time step used in this model benefits Calanus at the expense of Pseudocalanus (Table VJJ), probably because its higher growth rate (Frost, 1980;  -69-  1982) allows it to more rapidly exploit available phytoplankton production. Out of phase grazing exacerbates this effect. To determine whether this can be rectified by biologically plausible modifications, the predation rate was reduced (GP=0.07) and the HARRIS grazing model (3.3.4 above) was applied. The results show spectacular gains for Pseudocalanus (Table VII), indicating that the low biomass predicted by the previous models should not be taken too literally.  This modification also affects the size structure of the phytoplankton. Because the HARRIS model concentrates Pseudocalanus grazing near the centre of the size spectrum, the biomass spectrum becomes bimodal by day 48 and by day 60 the flagellate mode is much stronger than the diatom mode. This represents a complete reversal of the pattern observed in the first two models (Figure 15), and may be an important factor in explaining the shift to a flagellate-dominated community in summer. STD VM RM RM+  CHL(MAX) 7.35 8.82 8.88 8.46  CAL(MAX) 2194 2699 2698 1881  PSE(MAX) 713 749 741 2226  [N](D60) 1.67 0.81 0.80 2.44  T a b l e V I I - Peak c o n c e n t r a t i o n o f c h l o r o p h y l l (CHL), peak biomass o f Calanus (CAL) and Pseudocalanus (PSE), and c o n c e n t r a t i o n o f n u t r i e n t s a t day 60 ( [ N ] ) . STD = standard s i m u l a t i o n w i t h 3 h time step, VM = standard v e r t i c a l m i g r a t i o n model f o r both copepod s p e c i e s , RM = r e v e r s e m i g r a t i o n o f Pseudocalanus, RM+ = r e v e r s e m i g r a t i o n w i t h reduced p r e d a t i o n and HARRIS g r a z i n g model.  -70Figure 15 - Biomass spectra at day 60 for A) regular migration of both Calanus and Pseudocalanus and B) reverse migration of Pseudocalanus.  MG C  MG C  -71-  3.6 Spatial structure - the stochastic predation model  A primary assumption of the SELECT model is homogeneity in space. Steele and Frost (1977) chose to emphasize the details of the biological interactions in the plankton community and ignore the spatial variabilty of the ecosystem. Because plankton (and nekton) are in fact distributed in patches, an important component of the dynamics of the community may be overlooked.  Because the scale and intensity of patchiness increases moving up the food chain (cf. Mackas and Boyd, 1979), patchiness is best incorporated as a predation term, or "top down" effect (Carpenter et al. 1985; McQueen et al., 1986).  Vertical migration through a changing current field is believed to be the main cause of day to day variations in local abundance of zooplankton (Wroblewski, 1977; Evans, 1977; Steele and Henderson, 1981). Predators must thus search a whole new configuration of patches each day. This results in quasi-random fluctuations in the number of predators encountered by an 'average' zooplankter each day (Steele and Henderson, 1981). A stochastic predation function representing this effect was used by Steele and Henderson (ibid.). This had the effect of keeping the biomass of phytoplankton and zooplankton within a much narrower range than was the case with a constant number of predators, which tends to drive the system to extremes due to the absence of a phase lag between prey and predator (Parsons, 1988). This is observed in enclosures, where top predators captured at enclosure can not escape, so that their initial density governs the system thereafter (Steele and Gamble, 1982).  Such a function, when introduced into the SELECT model, has a similar result. The copepod populations peak at about the same time as in the standard model, but are  -72-  not rapidly driven to a low level afterward as in the standard model. This applies particularily to Calanus, as the decline of the Pseudocalanus population is driven largely by factors other than predation (starvation of nauplii, competition from Calanus). Calanus biomass remains in the 2000-2500 mgC/m^ range, fluctuating somewhat erratically with the changing intensity of predation (Figure 16). The pattern of development of the phytoplankton community is not affected. Steele and Frost (1977) emphasize that the effects of carnivore predation flow down the food chain, affecting phytoplankton as well as herbivores. Steele and Gamble (1982) demonstrated this experimentally in enclosures. However, as stated above, these enclosures represent extreme situations. McQueen et al. (1986) have demonstrated that the effect of "top down" factors weakens going down the food chain, and that of "bottom up" (nutrient) factors weakens going up.  The significance of this result is that it iUurninates the weakness of the Monod (1942) predation model in spatially structured communities. In the Monod model the predators resemble a cat fishing in a tropical fish shop. The prey have no way of escaping and the predator's response to increasing prey density is cumulative: the search need not begin anew each day. But real communities do not behave like this, particularily in the plankton where the prey take refuge in deep water each day (Stich and Lampert, 1981; 1984; Gliwicz, 1986; Vuorinen, 1987). The classic experiment of Huffaker (1958) suggests that such a community would be highly unstable.  -73-  Figure 16 - Biomass of Calanus over 60 days under A) standard SELECT B) stochastic predation function.  BtOMASS (MG C/W*2)  2500-T 200015001000500-  o H—i i i i—i—i—i—i i i—i—i—i—i i  i—i—rn—I  0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 5154 57 60 DAY  BtOMASS (MC C/M**2) 2500 ~r 200015001000500-  o -t~-i—i—i—i—i—i i i i—i—i—i i i—i—i—i—r—T—I 0 3 6 9 12 15 18 21 24 27 303336 39 42 45 48 5154 57 60 DAY  -744 Conclusions The following conclusions may be drawn from this study. The first four involve the SELECT model itself. The remainder deal with conclusions drawn from these modelling excercises about the planktonic ecosystem and models of it in general.  1. The absence of the details of vertical structure makes the model very sensitive to small changes in the values of k , P e  m a x  , the chlorophyll-to-carbon ratio, and an  arbitrary constant mixed layer depth. This is not in itself a fatal flaw, as it does not really interfere with the primary objective of the original excercise, which was to model the internal structure of each trophic level in terms of organism size. But Steele and Frost (1977, p. 486) assert that a primary motive behind this effort was "the need to compare theory and observation". Because population structure is less variable in space than biomass, this approach is preferable to biomass-based models from this perspective. But in practice, the model's requirement that k and e  especially z fall within a very narrow range precludes the flexibility required to e  carry out this mandate.  2. Despite recent suggestions that the importance of interspecific competition in stracturing communities has been vastly overstated by many ecologists (Lewin, 1983), numerical experiments with the copepod prey selection curves (sections 3.1.10 and 3.4.4) and predation rates on copepods (section 3.1.11) indicate that competition between Calanus and Pseudocalanus is a real and important factor in this model community. Harris' (1982) results (contrast to Poulet, 1978: see section 3.3.4) suggest that this exists in the real world as well.  -75-  3. The success of the HARRIS grazing model in rectifying the poor showing of Pseudocalanus in several otherwise plausible results indicates that the assumption of a single mass-dependent selection function for both copepods is in error. This has already been established experimentally (Harris, 1982). This further suggests that the ratio of Calanus to Pseudocalanus biomass predicted by the model is too high (see Table V).  4. The bulk of the sensitivity analysis results indicate that most of the input variables satisfy the criterion of having perceptible but not overwhelming effects on the simulation. This model can not be said to suffer from the "Meadows syndrome" of being burdened with a plethora of superfluous inputs with no apparent effect on the output.  5. One of the main conclusions drawn by Steele and Frost (1977, p. 486) was that "the larger herbivores, such as Calanus ... depend on their coexistence with the smaller copepod species which control the smaller phytoplankton" and that "stress on the system, if it adversely affects the smaller herbivores, can lead to the breakdown of the Calanus-diatom component". But experience with the HARRIS grazing model in section 3.5 suggests just the opposite: strong Pseudocalanus grazing induces a strong shift in phytoplankton biomass towards the smaller cells (Figure 15). Their conclusion needs to be reappraised in light of the observations that Pseudocalanus do not graze primarily on the smallest phytoplankton, and that protozoa, not copepods, are the major grazers of these small cells in oligotrophic waters (Parsons and Lalli, 1988). This conclusion was based on the assumption that the succession of phytoplankters from a diatom to a flagellate dominated community is driven by nutrient competition. This assumption appears to be incorrect (see (8) below).  -76-  6. The sensitivity of the model to changes in the light attenuation rate (3.1.1) and the results of the "vertical migration" (3.5) and "stochastic predation" (3.6) models indicate that vertical, temporal and (horizontal) spatial structure are all important components of the ecosystem that can not safely be overlooked by modellers. While omitting these factors for purposes of simplicity may be necessary to achieve other objectives, defining these clearly is imperative. Pursuing simplicity as an end in itself, while generally a laudable goal (Silvert, 1981), risks rendering the whole excercise irrelevant if it excludes critical inputs. The "vertical-horizontal coupling" discussed by Evans (1977) and Evans et al. (1977) appears to be a promising approach.  As oceanographers begin to perceive the lower levels of the food web in their full complexity detailed models of the microbial community will be developed. While this component of the community can be viewed on smaller spatial scales and may be less structured in space than the metazoan community (although this latter point is far from certain: see Goldman, 1984), at the very least the variability of predation by metazoans that range over much greater distances should be included as a stochastic predation term.  7. The devastating consequences of the nutrient-dependent excretion rates given by Joiris et al. (1982) for the phytoplankton community and the apparent success of the alternative model of Bjornsen (1988) suggests that the nature of this whole process be examined closely. Presumably there is some validity to the observations that gave rise to the "overflow" model. Extensive research will be required to determine exactly what is going on, and it may be years before the process of excretion is really understood.  -77These results indicate that excretion is an extremely important component of community metabolism that can not safely be omitted from planktonic ecosystem models. This requires that priority be given to the research that will make it possible to model this process realistically.  8. There are a variety of scenarios where the shift from a diatom to a flagellate dominated phytoplankton community fails to materialize. Yet this does occur in nature (Gamble, 1978). It does not, however, appear to occur for the reasons presently accepted. That this process is driven by nutrient depletion is an a priori assumption of the SELECT model: the model demonstrates only the plausibilty of the assumption, it can not prove it to be correct. Because succession fails to occur in a number of alternative models, at nutrient concentrations that are not appreciably greater than those in the basic model, the validity of this assumption must be questioned.  The primary reasons for continued diatom dominance are the "passive diffusion" excretion model's greater loss rates for the smaller cells, and predation on those cells by protozooplankton (note that these models do not include a generally greater photosynthetic rate for diatoms (Parsons et al., 1978), which also produces this result). There are two possible explanations that could reconcile these results with the observation that temperate waters are generally dominated by small, flagellated phytoplankters in late spring and summer.  Firstly, the possibilty of 'death', or lysis, of the diatoms needs to be considered. Lysis is at present a poorly understood process, but is believed to be induced by bacteria (P J . Harrison, pers. comm.). It is not known whether it plays a regular role in the  -  7  8  -  process of seasonal succession. The bacteria responsible might be induced to multiply by increasing water temperature as in Sorokin's (1977) hypothesis. The death of a winter diatom bloom by self-shading due to a paucity of consumers capable of exploiting it has been observed by Rodriguez et al. (1987). The general scenario is correct but some other mechanism is required for spring blooms.  Secondly, the whole idea of chlorophyll-containing microflagellates as autotrophic organisms needs to be reappraised and extensive research into their actual nutritional mode carried out. 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