UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Diffuse knapweed (Centaurea diffusa) : reproductive thresholds, population ecology and responses to the… Powell, Robert David 1988

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


831-UBC_1989_A1 P68.pdf [ 8.57MB ]
JSON: 831-1.0098219.json
JSON-LD: 831-1.0098219-ld.json
RDF/XML (Pretty): 831-1.0098219-rdf.xml
RDF/JSON: 831-1.0098219-rdf.json
Turtle: 831-1.0098219-turtle.txt
N-Triples: 831-1.0098219-rdf-ntriples.txt
Original Record: 831-1.0098219-source.json
Full Text

Full Text

Diffuse Knapweed (Centaurea diffusa): Reproductive Thresholds, Population Ecology and Responses to the Introduction of the Buprestid Beetle Sphenoptera jugoslavica. By Robert David Powell B.Sc, The University of British Columbia, 1975 M.Sc, Dalhousie University, 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR T H E DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Plant Science) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December 1988 © Robert David Powell, 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of PLANT SCIENCE The University of British Columbia Vancouver, Canada Date nFr.FMRFR ?Q, 1988 DE-6 (2/88) Abstract Diffuse knapweed (Centaurea diffusa), like other semelparous perennials, was found to have a minimum size requirement for flowering. This critical size conditions the plant's phenotypic response to variation in growth conditions. Experimentally crowded rosettes grew slowly, failed to reach the critical size and did not flower in the following season, whereas uncrowded rosettes grew rapidly, reached the critical size in a single year and flowered in the next. The proportion of plants that flowered and subsequently died in both field and experimental populations decreased with individual crowding. The effect of interference-related growth reduction was therefore to accentuate gaps in the population's spatial pattern. Interference-related mortality of seedlings and rosettes acted in the opposite direction. The three interference-related processes of recruitment, pre-reproductive and post-reproductive mortality determine the fine scale spatial pattern of the population, and its density. There is no theoretical basis for interpreting a shift toward regularity as evidence for interference. A model, proposed to explain the apparent ubiquity of critical size-dependent switching to reproductive development in semelparous perennials, shows that this adaptation maxi-mizes the intrinsic rate of increase of semelparous species subject to high juvenile mortality followed by low rosette mortality, seasonality, and extensive variability in rosette growth rates. The model suggests that biological control organisms might be chosen strategically to disrupt selection for the critical size. Age-structured field populations exhibit considerable spatial variation in density. To determine whether that variation could account for a significant proportion of the variability in rosette growth rates under field conditions, the growth rates of individual plants were observed and regressed against a series of 'crowding indices'. Two methods of delimiting a sample of neighbours for this purpose were compared. 'Circular sampling' defines neighbours as plants within a specified radius of a focal plant; 'polygonal sampling' defines neighbours as plants that share a boundary when the ground is partitioned into Dirichlet polygons. A simulation study of the sampling characteristics of the two methods in relation to the degree of aggregation in the population showed that polygon samples are statistically preferable i i in aggregated populations, but the two methods performed about equally, accounting for approximately 25% of the variance in the growth rates of rosettes in the field. The buprestid beetle Sphenoptera jugoslavica is the third insect established in Canada as a potential biological control for diffuse knapweed. The beetle population at the release site in British Columbia was monitored, and experiments were conducted to determine the beetle's effects on its host. S. jugoslavica reduces the survivorship of seedlings and rosettes, delays reproduction, and finally reduces seed output. Under favorable conditions the beetle can contribute to a significant reduction in knapweed population growth. Its effectiveness at the release site is limited by a phenological requirement for arrested plant growth during the oviposition period which leads to large fluctuations in the size of the beetle population, and only intermittent damage to the knapweed population. i i i Table of Contents Page Abstract i i Table of Contents iv List of Tables vii List of Figures viii Acknowledgements x Introduction 1 Ecological Theory and the Biological Control of Weeds 1 The Biological Control of Diffuse Knapweed in British Columbia 4 Organization of The Thesis 6 Chapter I. The Role of Spatial Pattern in the Population Biology of Diffuse Knapweed Centaurea diffusa 9 Abstract 9 Introduction 9 Materials and Methods 11 Diffuse Knapweed 11 The Study Site 11 Field Data Collection 12 Spatial Analysis 14 A Spacing Experiment 15 Results 16 The Fate of Rosettes in the Field in Relation to Size 16 The Spacing Experiment 16 Spatial Pattern in the Field 19 The Fate of Rosettes in Relation to Nearest Neighbour Distances 22 Discussion and Conclusions 26 Recruitment 26 Rosette Mortality 29 Pre-reproductive Mortality 29 Chapter II. Why Is Flowering in Semelparous Perennials Dependent Upon a Size Threshold? 30 Abstract 30 Introduction 30 Explanations for the Critical Size Threshold in Semelparous Perennials 31 Why Have Semelparous Perennials Evolved Critical Size Thresholds? 34 Methods 35 The Life History of Centaurea diffusa 35 The Model 36 The Intrinsic Rate of Increase 39 Results 40 Conditions Selecting for Pure Size Dependence 43 Selection for Other Phenotypic Responses: Patterns of Rosette Survivorship .. 44 The Fitness of Genotypes in Relation to Variability in Individual Growth Rates 47 iv Discussion and Conclusions 51 Intrinsic Rate as a Measure of Fitness 51 Adaptations of Semelparous Perennials 53 An Hypothesis to Explain Size Threshold Dependent Switching 54 Phenotypic Thresholds and Reaction Norms, and Seasonality 54 Approaches to Testing the Hypothesis 55 Chapter III. Circular Neighborhoods, Polygonal Neighborhoods, and The Growth of Centaurea diffusa in Relation to Individual Crowding 58 Abstract 58 Introduction 58 Methods 60 Simulation Methods 60 Field Materials and Methods 63 Descriptions of Crowding 64 I: Circular Crowding Indices 64 II: Polygonal Crowding Indices 66 The Size of the Focal Plant 67 Results: Simulation Experiment 67 Numbers of Neighbors 68 Angular Dispersion of Neighbors 68 Field Results 70 Discussion 74 Predictions of Plant Performance Based on Indices of Crowding 74 The Sample Must Permit the Detection of Gaps and Edges 74 The Distinction Between Adjacent and Once Removed Neighbors 76 Circular and Polygonal Indices in Population Dynamic Models 77 Crowding and Rosette Growth in Diffuse Knapweed 79 Chapter IV. The Effect of Sphenoptera jugoslavica Obenb. (Col. Buprestidae) on Its Host Plant Centaurea diffusa Lam. (Compositae) 80 Abstract 80 Introduction 80 Efforts to Control Diffuse Knapweed 80 Life History and Phenology of the Beetle in Relation to its Host 81 Oviposition 83 Methods 83 The Distribution of Beetle Eggs in the Field 83 Oviposition Preference Tests 83 The Effect of Temperature on Oviposition 84 Results 85 Oviposition in the Field 85 Oviposition Preferences 85 The Effect of Temperature on Oviposition 89 Discussion 90 Larval Feeding 91 Methods 93 The Effect of Sphenoptera Root Damage on Rosette Growth 93 The Effect of Plant Size on Larval Survival 93 The Effect of Sphenoptera Damage on Plant Size and Seed Production 94 v Mortality of Rosettes Caused by Larvae 94 Results 95 T i e Effect of Sphenoptera Root Damage on Rosette Growth 95 The Effect of Plant Size on Larval Survival 97 The Effect of Sphenoptera Damage on Plant Size and Seed Production 98 Mortality of Rosettes Caused by Larvae 100 Discussion 102 Adult Feeding 104 Methods, 104 Feeding Preference Tests 104 The Effect of Temperature on Adult Feeding Rate 105 Seedling Mortality in Response to Drought and Herbivory 105 Results 106 Adult Feeding Preference Tests 106 The Effect of Temperature on Adult Feeding Rate 106 Seedling Mortality in Response to Drought and Herbivory 106 Discussion 107 How Much Damage Can Adult Feeding on Foliage Do? 107 Discussion and Conclusions 108 Conclusion 114 Literature Cited 119 Appendix I: Conditions for Pure Size Dependence 131 Appendix II: Critical rm Values 132 Appendix III: Fitness of Genotypes in Relation to Variation in Individual Growth Rates 132 Appendix IV: Limits of Integration to Calculate the Fitness of Size Depen-dent and Age Size Dependent Types 133 vi List of Tables Chapter I Table I The Relative Growth Rates of Rosettes Subject to Varying Degrees of Crowding 19 Table II The Fates of Seedlings and Established Plants in Relation to the Nearest Estab-lished Plant 25 Chapter IV Table III Contingency Analysis of Beetle Egg Presence, Leaf Angle, and Number of Leaves for Five Sites in the White Lake Basin 88 Table IV Oviposition Preference Tests 89 Table V The Effect of Root Damage on Rosette Growth 96 Table V I Growth as a Function of Size and Root Damage 96 Table VII The Effect of Root Damage on the Bolting Size 97 Table VIII The Effect of Sphenoptera Attack on Plant Size and Seed Production 100 Table IX Effects of Larvae on Rosette Mortality 101 Table X Root Crown Diameters of Rosettes Killed by Larvae in Autumn Compared to Root Crown Diameters of Survivors 101 Table X I Adult Feeding Preference Tests 106 Table XI I Seedling Survival in Response to Drought and Herbivory 107 Table XIII Modelled Effects of Insects on Knapweed Rates of Increase I l l vi i List of Figures Chapter I Figure 1 The Allometric Relationship Between Root Crown Diameter and Rosette Dry Weight 13 Figure 2 The Fate of Rosettes in the Field in Relation to their Spring Root Crown Diameters 17 Figure 3 Growth Curves of Rosettes Subject to Varying Degrees of Crowding in the Spacing Experiment 18 Figure 4 The Fate of Rosettes Subject to Varying Degrees of Crowding in the Spacing Experiment 20 Figure 5 The Locations of Seedlings (a) and Established Plants (b) 21 Figure 6 Spatial Analysis of the Six Quadrats 23 Figure 7 Seedling, Rosette, and Flowering Plant Mortality in Relation to Nearest Estab-lished Plant Distance 27 Figure 8 The Effects of Recruitment, Pre-reproductive Mortality, and Post-reproductive Mortality on the Spatial Pattern of the Population 28 Chapter II Figure 9 Hirose's Graphical Argument for Size-Dependence 32 Figure 10 Seed Output vs Plant Weight in Diffuse Knapweed 37 Figure 11a The Functional Relationship Between Individual Growth Rate 7 and Population Growth Rate rm 42 Figure l i b Plant Weight as a Function of Individual Growth Rate and Time 42 Figure 12 Constraints on Selection for Pure Size-Dependence 45 Figure 13 The Effect of Greater Rosette Mortality 46 Figure 14 The Effect of Increasing Rosette Mortality After Four Years 48 Figure 15 The Phenotypic Threshold Curves of Some Genotypes Sample Discontiguous Segments of the Fitness Curves 50 Figure 16 The Relative Fitnesses of Genotypes Depend on the Distribution of Growth Rates 52 Figure 17 The Reaction Norm and Phenotypic Threshold of a Size-Dependent Genotype 56 Chapter III Figure 18 Simulated Spatial Patterns 62 Figure 19 The Effects of Neighborhood Sampling Method, and in the Circular Case, Sample Radius on the Number and Angular Dispersion of 'Neighbors' 69 Figure 20 The Number and Angular Dispersion of Neighbors in Circular and Polygonal Samples of the Knapweed Population 71 Figure 21 Variation in Root Crown Diameter Increment Explained by Regression on Size and Crowding 73 Figure 22 Circular and Polygonal Neighborhoods 75 Figure 23 Onion and Rosebud Neighborhoods 78 viii Chapter IV Figure 24 The Sizes and Shapes of Rosettes Available to Ovipositing Female Beetles Depend on Knapweed Density 86 Figure 25 The Distribution of Beetle Eggs With Respect to the Size and Shape of Knapweed Rosettes 87 Figure 26 The Proportion of Rosettes Bearing Beetle Eggs in Relation to Temperature and Rainfall 92 Figure 27 Beetle Survivorship and Root Damage as a Function of Rosette Size 99 Figure 28 The Proportion of Flowering Plants at White Lake With Damaged Roots Between 1977 and 1987 103 ix Acknowledgements In preparing this thesis I was fortunate to be part of a motley cohort of gifted ecology graduate students whose discussions, arguments and cooperative approach kept things lively. In particular I want to thank Brad Anholt, Alistair Blachford, Gayle Brown, Li Chao, Pete Cahoon, Helen Content, Judy Cooper, Horacio de la Cueva, Linda Edwards, Chris Foote, Chris Guppy, Aili Kaarik, Mrigesh Kshatriya, Werner Kurz, Ken Lertzman, Anne B. McGee, Peter Morrison, Grant Pogson, Don Robinson, Christoph Rohner, Jens Roland, Risa Smith, Paul Sneed, Andrew Trites, and Mike Wells. I was also helped by the friendship and encouragement I received from faculty members among whom I should like to particularly acknowledge Lee Gass, Buzz Holling, Peter Larkin and Don Ludwig, and by the support of Earl Jensen of the B.C. Ministry of Forests and Peter Harris of Agriculture Canada. I also thank my supervisory commmittee, Victor Runeckles, Peter Jolliffe, Mahesh Upadhyaya and Michael Pitt for their work on my behalf, and Roy Turkington, Bill Neill and Svata Louda for their useful suggestions. Jill Benzer, Rex Eng, Peter Morrison, Chris Risley, Mary Yates, and Susan Yates helped with the collection of data, including the drudgery of counting seedheads, fly galls and seeds. Danuta Dolecki and Teresa Patterson were simply good friends to talk to. Financial support was provided by a Hugo E. Meilicke Memorial Fellowship, a UBC Graduate Fellowship, and a B.C. Science Council GREAT award. I owe a special debt of gratitude to Judy Myers who supported my work generously with her time and advice, not to mention her research grant. Her enthusiam for the study of ecology and her friendship are the legacies I have gained. Finally, a share of the satisfaction in completing this project is due my wife Charlotte who bolstered me when things weren't going well and shared my exhilaration with quiet amusement when they were. x Introduction Ecological Theory and the Biological Control of Weeds Each time an exotic phytophagous insect is deliberately introduced to a naturalized population of its host plant there is an opportunity to learn how some types of insect her-bivory reduce the densities of plant populations, while others do not. Insect introductions can be treated as large scale experiments (Myers 1978), potentially addressing such basic ecological questions as what determines the dynamics of plant-herbivore systems (Myers 1980; Caughley and Lawton 1981), and what role herbivory plays in mediating interspecific competition in plant communities (Bentley and Whittaker 1967; Whittaker 1979; Burdon et al. 1981; Dirzo 1984). The practical success of any biological control of weeds pro-gram depends on introducing one or more agents capable of reducing plant densities, but in practice neither the accumulated experience with previous introductions (Julien 1982; Maw 1984), nor the nascent theory of plant-herbivore dynamics (Caughley and Lawton 1981, Edelstein-Keshet 1986) can reliably guide the selection of potential agents (Lawton 1985). Hokkanen and Pimentel (1984) suggested that new plant-herbivore associations should re-sult in control more often than coevolved associations. Their hypothesis, however, is not supported by the record of phytophagous insect introductions (e.g. Cullen 1978; Room et al. 1981; Goeden et al. 1985; Goeden and Kok 1986). Insects credited with reducing weed densities in successful biocontrol programs are taxonomically diverse, and attack their hosts in a variety of ways (Dodd 1959; Wilson 1960; Andres and Goeden 1971; Kok and Surles 1975). Insects that have failed to control their hosts are equally diverse, and more numerous (Julien 1982; Harris 1984a; Maw 1984). A n ambitious international effort to compile and analyse a database of over 600 individual biological control of weeds programs in the hope of discerning some common features of successful introductions (Moran 1985) has so far failed to provide new insight. Understanding of the dynamics of plant-herbivore systems has lagged far behind com-pared with predator-prey and host-parasite systems (e.g. Caughley and Lawton 1981; 1 Hassell 1981; May 1981). Reasons are not difficult to find. The diversity of phenomena embraced even under the more limited heading of 'plant-insect systems' is enormous (e.g. Crawley 1983; Strong et al. 1984) and data are surprisingly sparse (Caughley and Lawton 1981). Many of the insect-plant systems that have been intensively studied are crop-pest systems where human interventions in the form of planting and harvesting schedules, pes-ticide applications, and cultural practices etc., confine the system within agronomically desirable limits. Attention has naturally focused on the effect of insect populations on crop yields (e.g. Wang et al. 1977). Crop systems afford little opportunity to study how plant population size might respond to insect populations. In marked contrast to crop pests, the insects imported as biological control agents are generally poorly known. Consequently, considerable effort must be devoted to documenting the type and severity of damage inflicted by each new insect and how this is affected by environmental variation (e.g. Harris 1980b; Chapter IV of this thesis). Other limiting factors on weed population dynamics are generally not as well studied (cf. Shephard et al. in press). The compensatory responses of the plant population to insect damage are seldom identified and innumerated, and rarely quantified (cf. van der Meijden in press). Hence the relationship between the amount of insect damage and changes in the plant population size remains obscure (Myers et al. in prep). In the absence of real understanding of how plant populations respond to insect her-bivory, the theory of plant-insect population dynamics has developed by analogy with predator-prey systems, using elaborations of Lotka-Volterra models (e.g. May 1973; Caugh-ley and Lawton 1981; Crawley 1983), although the analogy is limited at best (Caughley and Lawton 1981; Edelstein-Keshet 1986). Among the numerous simplifying assumptions re-quired to reduce the description of interacting populations to a pair of ordinary differential equations (e.g. Pielou 1977) are at least two that plant population biologists should reject outright when one of the interacting populations is a plant species. To assume, in the tradition of classical population dynamics, that the insect population size responds to the plant population size (May 1973; Caughley and Lawton 1981) is questionable on two counts: First, many insects feed exclusively on specific plant parts, 'modules' such as seed heads, 2 and it is the population of these parts which best describes the resource available to them (Wang et al. 1977; White 1984). Because plants respond phenotypically to an increase in density by reducing the number of modules they produce (e.g. Harper 1961), the number of modules available to an insect population on an area basis can rise or fall with density depending on the shape of the plant's phenotypic response. For example, the number of knapweed seed heads available to the two tephritid flies Urophora affinis and U. quadri-fasciata (described below) first rises then falls with the density of the plant population (Myers and Powell unpub.). The second objection to assuming that the insect population size responds to the plant population size is that it implies that all members of the plant population are equally accessible and suitable as hosts. Considerable experimental evidence shows that this is not true. The population growth of many insects depends on what may be very broadly described as 'qualitative aspects' (sensu Edelstein-Keshet 1986) of the plant population. These include continuous qualitative variables such as nutrient content (Myers and Post 1981), levels of defensive chemicals (Rhoades and Cates 1976), and plant size (Myers et al. 1981), plus categorical variables such as plant stage. The beetle Sphenoptera jugoslavica (described below), for example, lays eggs on both rosettes and flowering plants of its host under some circumstances (Chapter IV). The proportion of developing larvae that survive to the adult stage within flowering plants is negligible; the proportion that survive within rosettes depends on the size of the plant. To assume that the growth rate of the plant population responds to its own density (May 1973; Caughley and Lawton 1981) is also problematic in view of recent findings in plant population biology. The relatively persistent spatial structure of plant populations implies that the survival and reproduction of individual plants is affected by fine scale variation in site quality, and a level of crowding that depends on a small number of nearby neighbors rather than the density of the population at large (e.g. Mack and Harper 1977; Weiner 1982; Silander and Pacala 1985 and refs. therein). This 'crowding dependence' could mean that the regulation of numbers in plant populations is a qualitatively distinct phenomenon from density dependence in populations with more transient spatial structure. The implications are only beginning to be explored in so-called neighborhood models (Antonovics and Levin 3 1980) of plant population dynamics (Holsinger and Roughgarden 1985; Pacala and Silander 1985; Pacala 1986). The growing understanding among plant population biologists of phenomena such as structural (modular) dynamics (e.g. Bazzaz and Harper 1977; White 1979; Harper and Bell 1979) and crowding dependence (e.g. Mack and Harper 1977; Weiner 1982; Mithen et al. 1984; Silander and Pacala 1985) is prompting a radical departure from the traditions of animal population theory (Harper 1980; Holsinger and Roughgarden 1985). The theory of plant population dynamics that will emerge from this research will be qualitatively distinct from previous population theory (Pacala and Silander 1985). The theoretical framework for understanding plant-insect systems wil l , I believe, be built on this more complete understanding of the mechanisms that determine the size and stablity of plant populations. The foregoing explains my motivation for devoting three of the four core chapters of a thesis entitled 'The Response of Diffuse Knapweed (Centaurea diffusa) to the Introduction of the Buprestid Beetle Sphenoptera jugoslavica' to aspects of the population biology of the weed, and only one to the effects of the beetle. The specific problems addressed in each of the four chapters are described following a brief introduction to the species of insects and the plant that are the subjects of this thesis. The Biological Control of Diffuse Knapweed in British Columbia Diffuse knapweed (Centaurea diffusa: Compositae) is a biennial to short lived mono-carpic perennial of Eurasian origin that has become a weed of the dry rangeland of western North America (Watson and Renney 1974; Harris and Cranston 1979; Maddox 1979). It has invaded over 80,000 ha of rangeland in British Columbia (Cranston pers. comm.), and a considerably larger area in the western United States. Maddox (1979) estimated that 800,000 ha in Montana alone were affected. Harris and Cranston (1979) estimated that 7.5 million ha in western Canada are vulnerable to invasion. C. diffusa's ability to invade grasslands even in good condition (Myers and Berube 1983), combined with its detrimental affect on forage yields (Cranston et al. 1983) have made it a serious threat to the cattle industry. 4 Temporary control of diffuse knapweed can be acnieved with the herbicide picloram (Renney and Hughes 1969), and recovery of forage production can be enhanced if seeding with crested wheatgrass (Agropyron cristatum) follows the application (Hubbard 1975). The cost of this treatment, however, is prohibitive for all but the most productive rangelands (Harris and Cranston 1979). There is also concern that picloram could contaminate ground water, because it is both persistent and highly water soluble (N .R .C .C . 1974). A biological control program for diffuse knapweed began with the introduction of two tephritid flies, Urophora affinis and U. quadrifasciata in the early 1970's (Harris 1980a; Harris and Myers 1984) and the buprestid beetle Sphenoptera jugoslavica in 1976 (Harris and Myers 1984). The two flies have spread throughout the knapweed population. Both species attack the developing seed heads of the flowering plants, reducing the number of seeds produced per seed head (Berube 1980; Harris 1980b; Roze 1981). They also cause the abortion of phenologically precedent buds, and reduce initiation of succedent buds (Morrison 1986). Although the two flies compete for the same resource (Berube 1980; Myers and Harris 1980), their combined damage is greater than the effect of either insect alone because their overlapping phenology of attack increases the proportion of seed heads attacked, and the number of fly galls per seed head (Myers and Harris 1980; Roze 1981; Morrison 1986). Estimates of the proportion of seeds destroyed by their combined damage range from 80% to 95% (Roze 1981; Harris 1980b; Morrison 1986). The buprestid beetle Sphenoptera jugoslavica was released in 1976 at two sites in south-ern British Columbia by Agriculture Canada. One population near Grand Forks failed to establish, but the second at the Dominion Radio Astrophysical Observatory site at White Lake, southwest of Penticton increased (Harris and Myers 1984). The White Lake site, described in Chapter I, was the only North American population of the beetle when the field work for this thesis began. The beetle has since been become established at a number of secondary release sites in B . C . (Muir pers. comm.) and the western U.S. (Rosenthal pers. comm.). Sphenoptera larvae develop in the tap root of knapweed rosettes, and it is this stage of the beetle's life which causes the greatest damage to its host. Zwolfer (1976), who 5 studied the beetle in Europe before its introduction to Canada, observed that attacked rosettes were retarded in their development, particularly on xeric sites with poor soil. He suggested that root feeding by the beetle might prolong the rosette stage, and facilitate secondary colonization by pathogens. Plants with damaged roots also produce fewer seeds than unattacked plants (Harris and Myers 1984; Powell 1984). Organization of This Thesis M y interest in the beetle and in diffuse knapweed was motivated not so much by a desire to research a practical and environmentally benign method of controlling knapweed as by the desire to gain a better understanding of why plant populations either persist or decline in response to introduced insects. I began with the premise that biological populations must possess compensatory responses if they are to persist. A first objective was therefore to identify the repertoire of responses of diffuse knapweed that could potentially maintain its population in the presence of insect damage. Chapter I examines the population biology of diffuse knapweed, emphasizing the role that spatial pattern plays in mediating changes in population size. Both recruitment and mortality are found to depend on the proximity of nearby neighbors. Like many other species formerly classified as biennial, diffuse knapweed is shown to flower in the year after it reaches a critical size threshold. The duration of the rosette stage, which is commonly several years under field conditions, is determined jointly by individual growth rates and the phenotypic response to switch to flowering after reaching a critical size. A spacing experiment confirms that faster growing plants exceed the critical size and flower in the following summer while slower growing plants persist as rosettes. The critical size and individual growth rate also indirectly determine seed output, because they determine how large plants are when they switch to flowering. The critical flowering size in diffuse knapweed plays a role in two of the potential com-pensatory responses identified in Chapter I: the higher rate of bolting and higher fecundity at low rosette densities. If we could understood why knapweed in particular and semel-parous perennials in general switch to reproductive development at a particular size rather than, say, a particular age it might be possible to strategically choose biological control 6 agents to disrupt selection for this phenotypic response. Chapter II follows up the empirical observations of size-dependence in diffuse knapweed with a theoretical exploration of the demographic conditions required for size-dependence in semelparous perennials. It is a well known result of life history theory that the tradeoff between decreasing survivorship and increasing fecundity can select for delayed reproduction (Cole 1954; Gadgil and Bossert 1970), but it is only recently that theorists (Hirose 1983; Stearns and Koella 1986) have at-tempted to understand how this tradeoff shapes both the age and size of first reproduction. The model proposed in this chapter suggests that size threshold-dependent flowering is a life history adaptation that can maximize the fitness of semelparous perennials subject to a particular suite of demographic constraints: high juvenile mortality followed by low adult mortality, an allometric or hyperbolic allometric fecundity-weight relation, and considerable variation in individual growth rates. The insects and other biocontrol agents we import to curb pest species can potentially do more than simply reduce plant growth rates, fecundities and survivorship; they can alter the selection regime in favor of a smaller critical size, or even shift selection away from size-dependence. The experimental manipulation of crowding in Chapter I demonstrated that the age of reproduction in diffuse knapweed is jointly determined by individual crowding, and the critical size threshold for bolting. In Chapter III I employ the method of regressing indi-vidual plant performance against an index of crowding in an attempt to explain variation in the growth rates of rosettes in the field. The method has proven to be a valuable tool in studying the role of spatial pattern in experimental annual populations and populations of even-aged perennials (Mack and Harper 1977; Weiner 1982). As expected, a smaller propor-tion of variation can be explained given the additional complication of an initial (unknown) age structure in the field population (e.g. Waller 1981). Numerous crowding indices have been proposed, based on two methods of delimiting samples of 'neighbors': 'circular sam-pling' and 'polygonal sampling' (Cormack 1979). The sampling characteristics of these two methods are compared using simulation, then indices of both kinds are regressed against rosette growth. 7 Chapter IV describes a series of experiments and observations designed to measure the effects of S. jugoslavica on the population of diffuse knapweed at the White Lake introduc-tion site. The beetle reduces the survivorship of seedlings and rosettes, delays flowering, and reduces seed output. Finally, Chapter IV is followed by a general discussion of the implications of this work. 8 Chapter I. The Role of Spatial Pattern in the Population Biology of Diffuse Knapweed, Centaurea diffusa. Abstract Diffuse knapweed, like other semelparous perennials, has a minimum size requirement for flowering. Interference among neighbouring rosettes reduces their growth rates and de-lays their flowering. The proportion of plants that flower, and subsequently die, is therefore positively correlated with the amount of available space. Post-reproductive mortality in this semelparous perennial increases aggregation in the plant population's spatial pattern, countering the regularizing effects of interference-related seedling and rosette mortality. Introduction The fine scale spatial patterns of terrestrial plant populations are generated by de-mographic events: by recruitment and mortality. The probability of either event at a particular microsite can be influenced by a potentially large number of physical variables, many of which are affected by the proximity of nearby plants. The spatial pattern of a plant population is therefore both a determinant and a consequent of the demographic events that govern local population size. This intermediary role in the population biology of plants has led to a kind of illogic in the interpretation of plant spatial patterns: interference is con-sidered more likely to occur in contagious populations (e.g. Anderson 1971), yet regularity is interpreted as evidence for interference (e.g. Woodell et al. 1969). Neither conclusion is necessarily valid. Even regular populations experience increased mortality at high densities (Yoda et al. 1963). The intensity as well as the grain of the pattern determine how crowded individual members of a population are. There are also numerous examples of populations where interference does not produce statistically regular patterns (Anderson 1971; Phillips and MacMahon 1981). The analysis of static spatial patterns in plant populations cannot resolve the ques-tion of whether the underlying pattern-generating mechanisms involve interference. Pielou (1960) has shown that a single mechanism can produce regular, random and contagious spa-tial patterns. Conversely, the same type of pattern can be produced by different mechanisms (Pielou 1977). The analysis of spatial patterns can however suggest how interference might 9 mediate plant population dynamics, and provide corroborative evidence for the effects of biological mechanisms identified by other means (Hill 1973). Recruitment in many semelparous perennials is exclusively by seed. H germination is less likely, or seedling survivorship is lower near established plants, seedlings will recruit in the interstices between established plants. The effect can be to fill in the holes, making the pattern of the overall population more regular, but if clumps of seedlings survive, this interference mechanism can make the overall pattern more contagious (Pielou 1960). The pre-reproductive mortality rates of established rosettes will most likely be greater for plants with nearby neighbours. Interference-related mortality should therefore tend to reduce aggregation in plant populations, and field observations indicating shifts toward regularity are normally interpreted as evidence for interference (McDonough 1965; Anderson et al. 1969; Malik et al. 1976). A n intriguing possibility implied by a recent discovery in the population biology of semelparous perennials is that interference interactions that cause a reduction in individual growth rates may act in the opposing direction, increasing aggregation. Werner (1975) dis-covered that the semelparous perennial Dipsacus fullonum flowered after achieving a critical minimum size. This result has subsequently been extended to many species (Oxley 1977; Thompson 1978; Baskin and Baskin 1979a, b; van der Meijden and van der Waals-Koi 1979; Gross 1981; Hirose and Kachi 1982; Kachi and Hirose 1983; de Jong et al. 1986; Klinkhamer et al. 1987). A t the same time it is now well established that growth rates of individual plants are related to available space (e.g. Mack and Harper 1977; Mithen et al. 1984). Faster growing uncrowded rosettes of semelparous perennials should therefore reach their critical size, flower and die sooner than slower growing crowded rosettes. On a statistical basis, the probability that a plant will flower and subsequently die should be positively correlated with available space, which will reinforce patchiness. If this mechanism operates as hypothesized, the spatial patterns of semelparous perennial populations are created by a dynamic balance between three processes: recruitment, which can either create greater regularity or contagion, the regularizing process of rosette (pre-reproductive) mortality, and the aggregating process of flowering plant (post-reproductive) mortality. There would then 10 be no theoretical basis for anticipating a net shift toward regularity in the spatial patterns of semelparous perennials as a consequence of interference. Each of the component processes must be studied to discern their effects. Materials and Methods Diffuse Knapweed Diffuse knapweed ( Centaurea diffusa) is a semelparous perennial of Eurasian origin that has become a serious range weed of the dry rangeland of western North America (Watson and Renney 1974; Harris and Cranston 1979; Maddox 1979). Its ability to invade grasslands even in good condition (Myers and Berube 1983) is likely due to a combination of traits: Like other 'biennials' (Salisbury 1942), it produces large numbers of seeds, particularly in disturbed areas. The rosettes are well adapted to dry conditions with deep tap roots that capture water inaccessable to the shallow fibrous-rooted grasses during the mid-summer drought. Diffuse knapweed thus has an extended growing season compared to its com-petitors. Grazing animals further tip the balance in favor of knapweed by preferentially consuming their grass competitors. There is also some evidence that C. diffusa produces allelopathic chemicals (Fletcher and Renney 1963; Muir and Majak 1983). The result is that C. diffusa forms virtual monocultures over large areas. The Study Site The White Lake Basin in southern British Columbia (49°19' 119°38') is within Kra-jina's (1965) Ponderosa Pine - Bunchgrass biogeoclimatic zone. Rainfall is less than 100 mm during the five months of May through September*, and mid-summer ground level temper-atures exceed 40° C. The perennial bunchgrass native to the area has largely been replaced by a variety of annual grasses, sagebrush (Artemisia spp.), and since the 1940's (Groh 1943) diffuse knapweed. The vegetation within the basin is a patchwork of communities as a result of both physical factors and range management. Prior to 1982, diffuse knapweed was by far the most abundant plant on the floor of the basin, except near a shallow saline lake where * Environment Canada data from nearby Okanagan Falls 11 halophytes dominate, and in a moist draw, where grasses dominate. In 1982, much of the basin was treated with the herbicide picloram; other parts have subsequently been burned. This study was conducted in a relatively homogeneous area, fenced from grazing and untreated with herbicide, on the site of the Dominion Radio Astrophysical Observatory. The knapweed population is a near-monoculture with spring rosette densities as high as 500 m~2. The mean densities (plants/0.5 m2) of seedlings, rosettes and flowering plants were respectively 44.08 (SD: 33.31), 41.99 (27.20) and 11.56 (6.36). Variation between transect stations at 25 m intervals along a 300 m transect was significant for seedlings (Kruskal-Wallace Hadj = 23.85; P = 0.021) and rosettes (Hadj = 23.26; P = 0.026), but not for flowering plants (Hadj = 19.69; P = 0.072). Field Data Collection The locations of all rosettes (n=1108) and seedlings (n=1831) in a 1.0 m by 6.0 m plot were recorded in early May using a mapping table and siting tube. The table consisted of a sliding 1.0 m 2 piece of 0.5 cm glass mounted on a 1.2 m by 7.0 m track surrounding the plot on the ground. The cylindrical plexiglass siting tube was 8 cm wide, 20 cm high with three sets of colored cross hairs at 2, 10, and 18 cm to avoid parallax, and had openings cut away on its lower sides to facilitate marking a location while siting. A sample of rosettes (n=971) and all seedlings were fitted with individual numbers. Rosettes were labelled by fastening slender plastic closures bearing numbered electrician's tags around their bases. The seedlings were marked with numbered toothpicks. The locations of the plants and their tag numbers were marked onto clear acetate sheets fastened to the mapping table. Overlapping acetate maps of the plant locations were digitized in segments and the map segments combined on the computer. The root crown diameters of the 971 labelled rosettes were measured with calipers. This measure of size was chosen because it is nondestructive and aUometricaily related to plant weight (Figure 1). Rosette diameter could not be used as a measure of size because diffuse knapweed rosettes lose much of their leaf area during the mid-summer drought. In mid-September I recorded the fate of each numbered rosette and seedling. Rosettes could die, persist or bolt. Seedlings could die or survive. The root crown diameters of surviving rosettes were remeasured. 12 F I G U R E 1 The Allometric Relationship Between Root Crown Diameter and Rosette Dry Weight. The data are from plants harvested in the spacing experiment. The regression is In Wt = 2.93 * In RCD + 2.87. Dashed lines indicate 95% confidence intervals. 13 Spatial Analysis The hypothesis of complete spatial randomness (henceforth CSR) was tested for both seedlings and established plants using Monte Carlo methods based on summary descriptions of the spatial point patterns of the plants (Diggle 1983). The two summary descriptions I used were the nearest-neighbour distances and the distances from points on a regular grid to the nearest plant. The two tests emphasize different aspects of potential deviations from random patterns. Nearest neighbour tests are more powerful than point to nearest plant tests against patterns that deviate toward regularity; point to nearest plant tests are more powerful against patterns that are more aggregated (Diggle 1983). For each summary description an empirical distribution function (EDF) describing the cumulative proportion of observed distances larger than a range of values was calculated and compared to the cumulative proportions expected i f plants were randomly distributed. For nearest neighbour distances, y;, the E D F was, G(y) = #(</,• < y)/n and for point-event distances, x,-, it was, F(x) = #(xi < x)/m where n is the number of plants and m is the number of grid points in a rectangular grid (Diggle 1983). A bivariate extention of nearest neighbour analysis (Diggle 1983) was used to determine whether the spatial patterns of germinating seedlings were independent of the established population. The statistic, Gij(y), is analogous to Gry) defined above, except that the nearest neighbour distances are between plants belonging to different categories, in this case seedlings and established plants. If the component patterns had been random, or alternatively, if the spatial point processes generating the component processes were known, the hypothesis that the patterns were independent could have been tested by comparing the distribution of nearest unlike neighbour distances with simulated expectations produced by independent realizations of the component processes (Diggle 1983). However, both 14 component patterns were nonrandom (see below) and the generating processes are unknown. I therefore employed the method proposed by Lotwick and Silverman (1983) to test whether the spatial pattern of the spring seedling population was independent of the spatial pattern of the established population. The method compares the distributions of nearest unlike neighbours in the data to simulated data in which one of the component patterns, the seedlings in this case, is subject to random toroidal shifts. The independence being tested is therefore conditional on the observed component patterns. No attempt was made to model the observed departures from expectation. The programs written to calculate these statistics and to produce the E D F graphs are available at the U . B . C . Biosciences Data Centre (Powell 1986). A Spacing Experiment A n experiment was conducted to determine if the spatial arrangement of individuals would affect the year in which they flowered. Spring germinated seedlings grown in seedling trays were thinned to one plant per 25 cm 2 cell and grown to the four leaf stage (seed leaves plus two). A subset of these, chosen to be as nearly uniform in size as possible, were planted out in 80 'wagonwheel' patterns in late June. Each wheel consisted of forty nine plants: one at the center plus six on each of eight replicate 'spokes' arranged at equal (45°) intervals. The distances between consecutive plants on the spokes doubled at each step away from the center beginning with 0.5 cm.; i.e. the interplant distances on the spokes were 0.5, 1.0, 2.0, 4.0, 8.0, and 16.0 cm. Thus plants near the center of each wheel were very crowded while those toward the periphery were uncrowded. The distance between adjacent wagonwheels was 50 cm. The plot was watered regularly for the first 6 weeks after planting to allow the seedlings to establish before the mid-summer drought. No further water was supplied for the remain-der of the experiment. Thirteen wheels chosen at random were harvested twice weekly from the beginning of the sixth week (July 26) to September 6. Leaf areas, root crown diame-ters, and dry weights of roots and shoots were recorded to obtain growth curves for the six crowding treatments. The remaining plants were left to overwinter. Their fate at the end of the following summer was recorded under three categories: 15 I died, II survived, but remained in the rosette stage, III flowered. Results The Fate of Rosettes in the Field in Relation to Size The fates of diffuse knapweed rosettes in the field, shown in Figure 2, were closely-related to their sizes. Pre-reproductive mortality rates (darkly shaded) were highest among the smaller rosettes, and declined with size. The proportion of individuals that switched from vegetative growth to flowering (unshaded) was very low for individuals smaller than 4 mm but increased abruptly thereafter, reaching greater than 90% over the next 2 mm. This pattern is very similar to the size-threshold dependence first observed by Werner (1975), and now known to be typical of semelparous perennials. The Spacing Experiment The treatments in the spacing experiment were successful in creating groups of rosettes with distinct growth rates and final sizes. Forty percent of seedlings in the most crowded treatment died. Figure 3 shows growth curves for dry weight vs time for the remaining five treatments fit by locally weighted least squares regression (Cleveland 1979). Notice that the less crowded, faster growing plants exceed the critical size identified in the field observations. Table I shows the relative growth rates of the five groups estimated from the linear regression of log dry weight on time. A n analysis of covariance of the slopes (e.g. Zar 1974) showed that they were unequal ( ^ 4 , 4 9 0 = 434.0, P < 0.001). The Student-Newman-Keuls multiple range test distinguished three sets of adjacent treatments (1 and 2 cm, 4 and 8 cm, and 8 and 16 cm), which are depicted as vertical bars in the right-hand column of Table I. 16 Died Remained a Rosette Flowered 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Root Crown Diameter (cm) FIGURE 2 The Fate of Rosettes in the Field in Relation to their spring Root Crown Diameters. Proportions were calculated for 2 cm distance classes. o cvi Days FIGURE 3 Growth Curves of Rosettes Subject to Varying Degrees of Crowding in the Spacing Experiment. The numbers labelling the curves refer to the distances between consecutive plants on wagonwheel spokes. Only five of the six treatments are shown because of the high mortality rate in the most crowded treatment. T A B L E I T h e Re la t i ve G r o w t h Rates o f Roset tes C r o w d i n g R . G . R . S . E . *0.05(2) d f P S . N . K . Trea tment 1 cm 0.0653 (0.0055) 11.89 96 < 0.001| 2 cm 0.0809 (0.0069) 11.70 95 < 0.001| 4 cm 0.1021 (0.0055) 18.59 100 < 0.001 | 8 cm 0.1159 (0.0049) 23.86 98 < 0.001 | | 16 cm 0.1289 (0.0052) 24.89 101 < 0.001 | Of the 67 wagonwheels left to overwinter, 3 were inadvertently destroyed before they could be scored, leaving 64 wheels x 8 plants/treatment/wheel or 512 plants/treatment. Figure 4 shows the fate of these plants. Rosette mortality, except in the most crowded treatment, was less than 7%. The proportion of surviving plants that flowered in their sec-ond year varied from 0% for the most crowded treatment to 97% for the least crowded. The space available to a plant in this experiment determined how fast it grew and consequently whether it grew large enough to flower in its second year. The data support the hypoth-esis that the proportion of plants that flower and subsequently die (i.e. post-reproductive mortality) increases with available space. Evidence that available space similarly limits the growth rates of plants in the field is found in the positive relationship ( r 2 = 0.116; P < 0.001) between the log of summed root crown diameters and log distances between mutual nearest neighbours (Pielou 1960). Spatial Pattern in the Field The high variance in quadrat densities reflects finer scaled patchiness in the spatial pattern of the population. Figure 5 shows the locations of adult and seedling plants in a 1 m x 6 m plot. Figure 5(c) is a density trace (Wegman 1972) of these data, showing an abrupt drop in adult densities with a correspondingly abrupt rise in seedling densities. The results of the two tests of CSR for each of the six contiguous quadrats are summa-rized in Figure 6(a,b) for seedlings, and in Figure 6(c,d) for mature plants. The horizontal 19 1.0 n 0.8 -| 0.6 H | £ 0.4 0.2 0.0 J 1 n500 400 1300 & J Q E 13 -1200 Z •100 0.5 1.0 2.0 4.0 8.0 16.0 Crowding Treatment Died Remained a Rosette Flowered F I G U R E 4 T h e Fa te o f Roset tes Subject to V a r y i n g Degrees o f C r o w d i n g i n the Spac ing E x p e r i m e n t . The numbers below the bars refer to the crowding treatments. a Seedlings F I G U R E 5 The Locations of Seedlings (a) and Established Plants (b). The density trace (Wegman 1972) shown in (c) confirms the visual impression of abrupt density changes. axes represent the cumulative proportions of the theoretical distributions of nearest neigh-bors distances, G(y), and grid point to nearest plant distances, F(x). Bars indicate regions where the EDF ' s were beyond the simulation envelopes. For each of the distance measures, the probability that the data lie beyond the simulation envelope at any point under the hypothesis of CSR is the inverse of the number of simulations plus one, in this case 0.05. Significant departures toward aggregation are shaded; departures towards regularity are unshaded. Tests based on both summary descriptions of the spatial pattern indicate a highly aggregated spatial pattern of seedlings. There are more small nearest neighbour distances (evidence of clumps), and more large point to plant distances (evidence of gaps) than expected. The overall pattern of established plants is also aggregated, although the pattern is less clear. The nearest neighbour test suggests a slight tendency toward regularity in quadrat 3, whereas the point to plant test finds no deviation in either direction. The point to plant test suggests both a deficit of small distances and an excess of large distances in quadrat 1, which suggests that rosettes tend to be regularly spaced within clumps. The results of the nearest neighbour test of independence between the population of established plants and seedlings are shown in Figure 6e. Deviations from random expec-tation observed in three of the six quadrats were toward regularity. Seedling to nearest rosette distances were greater than expected on the hypothesis that the two groups were independent, indicating some degree of repulsion between the groups. Seedlings of diffuse knapweed germinate into the interstices left by the parent population. The overall pattern is therefore one of clumps of seedlings interspersed between clumps of established plants. The Fate of Rosettes in Relation to Nearest Neighbour Distances Between May and mid-September 153 (19.3%) of the 971 marked rosettes bolted, flow-ered, and died, while 88 (11.1%) died as rosettes. A l l but 102 of the 1831 seedlings (94.4%) also died. Surviving seedlings tended to be further from seedling neighbours, although the difference was not signifcant (Mann-Whitney; P = 0.064). The two groups did have signif-icantly different nearest established plant distances (Mann-Whitney; P = 0.027). Seedling 22 Nearest Neighbour Distances, G(y) Grid Point to Plant Distances, F(x) aj M 5-n JZL 0.0 0.25 0.50 0.75 1.0 F I G U R E 6 Spatial Analysis of the Six Quadrats. Figures (a) and (b) show the results of nearest neighbour and grid point to nearest plant tests of C S R in the seedling population; (c) and (d) show the results for the established population. Figure (e) shows the results of a nearest unlike neighbour test of independence for the two groups. In each case the abscissa represents the cumulative proportion of distances. Bars indicate regions where the hypotheses are rejected. Shaded bars indicate deviation toward aggregation; unshaded bars indicate deviation toward regularity. 23 survivorship in relation to the nearest rosette distance was therefore tested by a contin-gency analysis of survivors and mortalities divided into five distance classes (Table II). The achieved probability level of 0.066 falls just short of the traditional criterion for significance. The fate of rosettes was definitely related to nearest neighbour distance (Kruskal-Wallace; P < 0.001), and the overall contingency analysis (Table II) rejected independence. The proportion of plants that died during the summer was higher in the lower distance classes, and of the survivors, the proportion that flowered was higher in the larger distance classes. Figure 7 shows the relationship between mortality in the seedling, rosette and flowering stages and the distance to the nearest established plant. Seedling and rosette mortality decline with neighbour distance, whereas post-reproductive mortality increases. Each of the processes individually, and combined affected the distribution of nearest neighbour distances. Figure 8 presents Tukey sum-difference graphs (Cleveland 1985) in which the abscissa is half the sum of corresponding percentiles of nearest neighbour distances for the two distributions being compared, and the ordinate is the difference between corresponding percentiles. (Only even percentiles are plotted.) Figure 8a, for example, compares the distribution of nearest neighbours among established plants in the spring with the same distribution plus the seedlings that survived the summer. Recruitment had little effect on the spatial pattern for the smallest 90% of distances. Beyond a mean percentile of about 6.0 cm the number of large nearest neighbor distances declined as recruiting seedlings filled gaps in the pattern of established plants. Rosette mortality (8b) opened spaces within clumps, increasing the smaller nearest neighbour distances in the range of 1.5 to 4.0 cm. Post-reproductive mortality (8c) widened existing gaps by increasing the larger nearest neighbour distances in the range of 4.0 to 8.0 cm. The two mortality processes were opposite in their effect on the spatial pattern, (pre-reproductive mortality increasing regularity, post-preproductive mortality increasing aggregation), yet together their effect was to increase nearest neighour distances throughout most of the range of values. Figure 8d shows the combined effect of all three processes. The linear rise of 10 - 12% up to about 7cm shows that the reduction in density (i.e. intensity) of the pattern did not affect the degree of 24 T A B L E II The Fates of Seedlings and Established Plants in Relation to the Distance to the Nearest Established Plant Distance to Nearest Distances Between Established Plant (cm) Groups Seedlings n 0-3 3-6 6-9 9-12 >12 Median P* Died 1729 398 609 421 209 90 5.29 0.027 Survived 102 12 40 26 17 7 5.83 Rosettes n 0-3 3-6 6-9 9-12 >12 Median Died 88 66 16 5 1 0 1.83 Survived 730 420 214 65 24 7 2.61 Flowered 153 52 74 17 6 4 3.93 * Mann-Whitney test; ** Kruskal-Wallace test. Log Likelihood (G) test of Independence df P Seedling Mortality vs Distance 8.81 4 0.066 Rosette Fate vs Distance 43.55 8 < 0.001 Died-(Survived, Flowered) vs Distance 14.40 4 0.006 (Died, Survived)-Flowered vs Distance 29.35 4 < 0.001 25 patchiness (grain) in that range. Larger nearest neighbour distances did not increase at a comparable rate. The overall effect was therefore a slight shift toward regularity. Discussion and Conclusions Semelparous perennials such as diffuse knapweed are useful subjects for the study of spatial pattern in relation to interference. Like longer lived perennials, many form natural monocultures in which established plants may influence the spatial pattern of recruits, but unlike longer lived perennials, the population turnover rate is conveniently rapid, allowing direct observation of large numbers of demographic events. Three processes, recruitment, pre-reproductive mortality and post-reproductive mortality determine the local spatial pat-tern and population size of diffuse knapweed. .Recruitment The contagious pattern of spring seedlings and the unexpectedly large number of large seedling-to-nearest-established plant distances showed that seedlings appear in the inter-stices between established rosettes. The biological mechanisms underlying this pattern are unknown. The prostrate leaves of rosettes could shelter the ground under them from the rain of seeds. Germination in diffuse knapweed is also strongly affected by the ratio of red to far red light associated with canopy shade (D. G. Nolan MSc. in prep), although Spears et al. (1980) found no evidence that experimental shading lowered emergence rates. The very high summer seedling mortality rate (94.4%) is largely due to desiccation (Schirman 1981). There is nevertheless a definite decline of four to five percent in mortality with distance from the nearest established plant. The small number of seedlings that survived the summer shifted the overall spatial pattern very slightly toward regularity in these data, but it would be premature to conclude that recruitment always acts that way. The major source of density independent seedling mortality is drought. It is quite possible that seedings establish in clusters at wetter sites and in wetter years. 26 co CO o CO I 1 1 i : i i • O 0 2 4 6 8 1012 14 Nearest Neighbour Distance 0 2 4 6 8 10 12 14 Nearest Neighbour Distance IB O > o => T5 O i _ CL CD O Q_ LO CO o m CvJ d m o LO O o 0 2 4 6 8 10 12 14 Nearest Neighbour Distance F I G U R E 7 Seedling, Rosette and Flowering Plant Mortality in Relation to Nearest Established Plant Distance. Distances are in centimeters. 27 Recruitment Rosette Mortality o in o O C CO o *-» w d b in < cp o 0 2 4 6 8 10 12 Nearest Neighbour Distance Post-reproductive Mortality CD O c CO +-» w b in d o d m d i q T I 0 2 4 6 8 10 12 Nearest Neighbour Distance All Three Processes <D O C e g to b d o d d 0 2 4 6 8 10 12 Nearest Neighbour Distance o c To Q d q d in d i q T— I 0 2 4 6 8 10 12 Nearest Neighbour Distance FIGURE 8 The Effects of Recruitment, Pre-reproductive Mortality, and Post-reproductive Mortality on the Spatial Pattern of the Population. Each graph is a modified Tukey Sum-Difference Graph comparing the distributions of near-est neighbours following recruitment or mortality with the prior distribution. The abscissa represents one half the sum of percentiles; the ordinate represents the 'after - before' change in percentile values, 'A Distance'. The distances are in centimeters. 28 Rosette Mortality Mortality among established rosettes of diffuse knapweed is concentrated in the summer months (Roze 1981; Powell and Myers 1988). It is more frequent among small rosettes and among rosettes with near neighbours. Each of these observations supports the conclusion that rosettes die as a result of interference. The most likely proximate mechanism is compe-tition for scarce water, but there is an additional complication. Almost all rosettes that died during the summer at the White Lake site bore evidence that larvae of the buprestid beetle Sphenoptera jugoslavica had attacked them (Powell and Myers 1988). The beetle does not ki l l the majority of the plants it attacks. It seems therefore that the damage caused by the larvae increases the susceptibility of rosettes to interference-related mortality. As expected, this process tended to make the spatial pattern of the population more regular. Post-reproductive Mortality Centaurea diffusa, like other semelparous perennials, flowers after reaching a critical rosette size. The age of reproduction thus depends on how fast the rosette grows. Crowding is one determinant of growth rates, and the spacing experiment showed that uncrowded plants grew large enough to switch to flowering, while crowded plants did not. In the field, plants with large nearest neighbour distances were more likely to flower and die. The effect of interference-related growth reduction in this semelparous perennial was to accentuate gaps, making the spatial pattern more aggregated. The net balance between recruitment and mortality that resulted in a smaller and slightly less aggregated population in this instance, might well shift under different environ-mental conditions to produce the opposite result. Indeed, since the knapweed population is presently quite aggregated, the combined effects of recruitment and mortality must at least sometimes generate greater contagion. The recruitment of clumps of seedlings within the gaps left by the parent population is one possibility that has already been discussed. Another is that the aggregating effect of post-reproductive mortality prevails when the op-posing process of interference related rosette mortality declines. This could happen in wet years i f drought stress is the proximate cause of death among competing rosettes. 29 Chapter II. Why is Flowering in Semelparous Perennial Plants Dependent Upon a Size Threshold? Abstract A model is proposed to explain the apparent ubiquity of critical size-dependent switch-ing to reproductive development in semelparous perennials. Size-dependent switching max-imizes the fitness of semelparous species subject to (1) high juvenile mortality, (2) extensive variation in individual growth rates, and (3) seasonality. The fairly restrictive conditions stipulated by the model provide a basis for experimentally evaluating its hypothesis. Introduction Werner (1975) discovered that the onset of flowering in the biennial teasel (Dipsacus fullonum) was more closely correlated with a plant's size than its age. Rosette plants that attained a critical size during one growing season bolted and flowered in the next, whereas rosettes smaller than the critical size did not. Critical size thresholds at which plants switch to reproductive development have subsequently been described for many species formerly classified as biennial (Digitalis purpurea, Oxley 1977; Pastinaca sativa, Thompson 1978, Baskin and Baskin 1979a; Grindelia lanceolata, Baskin and Baskin 1979b; Senecio jacobaea, van der Meijden and van der Waals-Kooi 1979; Oenothera biennis, Verbascum thapsus, Daucus carota, Tragopogon dubius, Gross 1981; Dontostemon dentatus, Erigeron strigosus, E. sumatrensis, Hirose and Kachi 1982; Oenothera erythrosepala, Kachi and Hirose 1983; Cynoglossum officiate, Jong et al. 1986; Cirsium vulgare, Klinkhamer et al. 1987; Centaurea diffusa, Chapter I). Since flowering in these species is more size-dependent than age-dependent, the term 'biennial' as it was previously applied is misleading (Harper 1977) and should be reserved to describe the two year life cycle phenotype displayed by these species under favourable conditions. Silver town (1984) has suggested that the phrase 'semelparous perennial' be used to describe what were once classified as biennials, although at least some of these species, including Senecio jacobaea (van der Meijden and van der Waals-Kooi 1979) and Centaurea diffusa (Powell unpub.), are occasionally polycarpic. The critical size for flowering in these species conditions their phenotypic responses to environmental variation. In conjunction with plant growth rate it determines the age at 30 which a plant will flower, and how large it will be at the time, which in turn determines the number of seeds produced. Since each of these life history variables strongly affects the rate of population increase, there must be strong natural selection for cueing the developmental switch to plant size or a correlated variable. Yet, other species of plants and animals, also presumably adapted, initiate reproduction at a particular age (e.g. Janzen 1976). Still oth-ers display more elaborate patterns in which the size of individuals that initiate reproduction changes with age (Lacey 1986, Stearns and Koella 1986). Why have semelparous perennials evolved critical size thresholds to control the initiation of reproductive development? Two conditions must be met for size-dependence to be adaptive. First, selection must favor delayed reproduction. Otherwise, the annual life history would be selected, and there would be no relationship between size and the onset of reproduction (e.g. Rathcke and Lacey 1985). Second, plant size or some strongly correlated variable must be a better cue for the appropriate time to reproduce than plant age. While the value of delayed reproduction has received a great deal of attention ever since Cole (1954) posed the problem (Harper 1967; Gadgil and Bossert 1970; Charnov and Schaffer 1973; Schaffer and Gadgil 1975; Hart 1977; Caswell and Werner 1978; van der Meijden and van der Waals-Kooi 1979; Klinkhamer and 'de Jong 1983; Hirose 1983), the question of why a single critical size should be selected rather than some more elaborate control has received relatively little comment, even among authors reporting empirical observations of size-dependence, and no satisfactory explanation has yet been proposed. Explanations for the Critical Size Threshold in Semelparous Perennials Hirose (1983) showed graphically that under some circumstances when deteriorating conditions result in lower age-specific fecundities, plants that continue to flower at the same size they did previously are more fit than those that continue to flower at the same age as before. Hirose's graphical argument is presented in Figure 9a. Note first that the ordinate is on a logarithmic scale; the abscissa, representing age x, is arithmetic. The graph shows an age-specific survivorship curve, lx, and two age-specific fertility curves, before and after environmental deterioration, mx and m* respectively. In semelparous species the net reproductive rate is determined by In R$ = In lx + In m,; the intrinsic rate of increase is 31 F I G U R E 9 Hirose's Graphical Argument For Size-Dependence. (a) The fitness of plants that flower at a consistent size (r*) is greater than the fitness of plants that flower at a consistent age (r*) when the age specific fertility declines from mx to m*. (b) A counter example in which the fertility curves mx and m* are unchanged, but survivorship declines at a greater rate than before. The fitness of plants that flower at a consistent size (r*) is lower than the fitness of plants that flower at a consistent age (r*). r = InRo/x. The net reproduction curves RQ and RQ therefore appear as the sums of survivorship and fertility curves, and the intrinsic rates are the slopes from the curves to the origin. The graph shows that the fitness of plants that flower at a constant size, r*(s), is greater than the fitness of plants that flower at a constant age, r*(a). As an explanation for the apparent ubiquity of size-dependence in semelparous perenni-als this argument has several flaws. First of all, it is equally true that if conditions improve, the relative advantages of the two strategies are reversed. It is hard to see how such a limited advantage would be selected unless conditions deteriorated more often than they improved. There is some merit to this idea. Most semelparous perennials opportunistically colonize disturbed sites and are subsequently forced out by competitors (e.g. Holt 1972). Successive cohorts of mullein, for example, consist of smaller individuals that reproduce at a greater age (Reinartz 1984), implying a lower age-specific fecundity. Nevertheless, the fertility curves must also increase each time a newly disturbed site is colonized. The ad-vantage of flowering at a constant size also depends on the shape of the Ro curve. Figure 9b shows an example in which flowering at the same age is a fitter response to the same deterioration in fertility. A more fundamental objection to Hirose's hypothesis is that it addresses the wrong question. The field observations are not that semelparous perennials reproduce at the same size, but rather that they switch to competency for flowering at the same size, which means that they actually flower over a range of sizes larger than a minimum. How large a plant grows beyond the critical minimum size in the year prior to flowering depends on its growth rate. It has been suggested that the accumulation of resources may determine the onset of flowering (Harper and Ogden 1970; Werner 1975; Rathcke and Lacey 1985, cf. Kachi and Hirose 1983) because seed production in semelparous plants is strongly correlated with plant size. Lacey (1986) notes that because the correlation between age and size weakens over time, size becomes a better predictor of accumulated resources. For this reason alone, she argues, the time of flowering should become increasingly size-dependent. The conditions under which Lacey's argument applies are limited because fitness is determined by both 33 fertility and survivorship. Potential gains in seed production that might accrue to a plant accumulating greater resources must be weighed against the chance that it will not survive to reproduce. Stearns and Koella (1986) have shown in a more general context that vari-ous forms of age-specific fertility and survivorship can select for a number of qualitatively distinct 'reaction norms' of age and size at maturity. The deteriorating correlation between age and size is therefore not a sufficient condition for the evolution of critical size thresholds. Finally, Lacey (1986) attributes an argument to Schaffer and Rosenzweig (1977) that environmental variance will favor size-dependence over age-dependence. What Schaffer and Rosenzweig actually said was that "...semelparous species living in fluctuating environ-ments should either be able to adjust the age at which they reproduce to environmental cues, or be capable of producing offspring preprogrammed to breed at different ages." Thus, although their conclusion does not preclude the more specific result, they did not address the issue of critical size. Why Have Semelparous Perennials Evolved Critical Size Thresholds? The 'principle of allocation' proposed by Richard Levins and Robert MacArthur (Cody 1966) states that natural selection will favor individuals that partition their resources so as to maximize their fitness. Since semelparous perennials partition resources into nonrepro-ductive and reproductive activities sequentially rather than simultaneously as iteroparous species do, their fitness will be maximized by devoting as much energy as possible to re-production once it has been initiated (e.g. Schaffer and Rosenzweig 1977). Hence the only adjustment these species can make to maximize their fitness is to ensure that they flower when the tradeoff between fecundity and survivorship is best. The principle of allocation suggests that semelparous perennials will evolve critical size thresholds to control the ini-tiation of reproductive development, because cueing this developmental switch to size or its correlate maximizes their fitness. On this assumption, I have constructed a life history model for the age and size of flowering in semelparous perennials. The content was guided by field observations and experiments on diffuse knapweed, Centaurea diffusa, but has been sufficiently generalized to include features that appear to be common to other semelparous 34 perennials in the literature. The model provides an explanation for the evolution of critical size thresholds that does not require a deterioration in age-specific fertility. Methods The Life History of Centaurea diffusa Diffuse knapweed, like other semelparous perennials, has two distinct morphological stages to perform the sequential functions of vegetative and reproductive development. The rosette stage produces and sequesters carbohydrates; the flowering stage converts the stored resources into seeds. Reproduction is size-dependent and usually semelparous, although a small fraction of the population flowers twice. A l l reproduction is by seeds. There are only four constraints to the population growth of diffuse knapweed, although the number of factors affecting the shape of the constraints may be large: I Survivorship: Knapweed seedlings on dry rangeland devote most of their early growth to extending their tap roots in a race against desiccation (Muller pers. comm.). Seedling mortality rates are commonly greater than 90% (Roze 1981; Chapter I). In contrast, the mortality rates of established rosettes are less than 5% per year. This is the Deevey type III survivorship pattern which appears to be common to many herba-ceous perennials (e.g. Sarukhan and Harper 1973; Baskin and Baskin 1979b). Deevey type II survivorship has also been reported in the literature (e.g Baskin and Baskin 1979a; Klemow and Raynal 1981). II Individual Growth Rates: The duration of the prereproductive (i.e. rosette) stage depends on plant growth rate because the switch to reproductive development depends on achieving a critical size (Chapter I). A broad range of growth rates caused by variation in individual crowding (e.g. Mack and Harper 1977) and microsite habitat differences (e.g. Tilman 1982) is characteristic of natural populations of herbaceous plants (Harper 1964). Experiments with C. diffusa in particular (Chapter I) have shown that spacing alone can account for instantaneous growth rates ranging from 0.065 to 0.129 g/g/day. 35 III Seed Output: The number of seeds a plant produces is an increasing function of its weight. Small plants invest a relatively high proportion of their resources to produce the stems and ancilliary reproductive structures which are prerequisite to the production of the first seed heads (Reinartz 1984; Silvertown 1986). The relative cost of adding further heads declines with size until seed output is an allometric function of plant weight. Figure 10 shows the relationship between seed output per plant and plant weight in a sample of 120 plants collected at White Lake, British Columbia. In the literature it is sometimes assumed that seed production is an allometric function of plant weight (e.g. Hirose 1983). IV Seasonality: Favorable growth conditions are discontinuous in seasonal environments. Since plants must synchronize the phenology of reproductive development with seasonal cues, the option of remaining vegetative or flowering is effectively limited to an annual event. The Model The growth of individual plants is sigmoidal within seasons if only because the growth rate increases with the onset of favorable growth conditions in the spring, and later declines with the onset of unfavorable conditions in the fall. The growth curve of a perennial over several seasons is an ascending series of sigmoids which can be approximated by a sigmoid when only the growth seasons are considered. Rosettes may approach an asymptotic size imposed by the morphological constraints of the rosette growth form and the physiological requirements of photosynthesis where the benefit, of adding a new leaf is balanced by its cost of production and the loss of photosynthesis of older leaves. This is rare. The vast majority of plants, whose growth rates are limited by competition or resource scarcity do not reach this ontogenetic asymptote. Thus growth is indeterminate for the majority, but not unlimited even for the fastest growing plants. If we assume logistic growth over several growing seasons the weight achieved at time t is, 36 Plant Weight (g) F I G U R E 10 Seed Output vs Plant Weight in Diffuse Knapweed. The fitted function is ln(seeds) = 0.81n(dryweight) + 5.55 - (l/(ln(dryweight) - 0.7)). where a is the asymptotic weight, /? = ("w^0); Wo is the initial weight, and 7 is a growth rate parameter. The time it takes a plant with size-dependent reproduction to reach a critical size, w, is therefore, 7 Rosette growth does not stop if the critical size is reached part way through a growing season; it continues until the autumn. The duration of the vegetative phase, say vu, is therefore the integer number of growing seasons needed to exceed the critical size, Vu = tj+i; tj < tu < t j + 1 ] tj = (0,1, . . . ) , (3) and the rosette's final weight is, The final rosette weight of a plant with age-dependent reproduction is just, w * - T T ^ - ( 5 ) where vr is the fixed duration of the prereproductive phase. The following spring the plant devotes its resources to the production of seeds. Seed output vs weight is linear for some species, and exponential for others (e.g. refs in Lacey 1986). The functional form is determined by plant architecture (Silvertown 1983). In C. diffusa small plants devote a relatively high proportion of resources to a flower stalk and branches. There is an asymptotic approach to an allometric limit as the relative cost of adding further seed heads declines. The function fit to the data in Figure 10 is, l n S = flrln(W)-re- 1 ; for l n W > C (6) an allometric function which decays hyperbolically toward a minimum weight, £. The simpler allometric fecundity-weight relation, lns = CTln(W) + e; for InW > ( (7) 38 which is often reported in the literature, was considered as an alternative to (6). Assuming that plants do not gain weight in the year of flowering, the number of seeds produced at time t + 1 by a plant with specific growth rate 7 can be calculated by substituting the expression for plant weight at time t, either (4) or (5), into the fecundity-weight relation, ('MTffr*) + ' - ' o r (6), where t = vw for a phenotype with critical size w, and t = vT for a phenotype with a fixed-duration vegetative stage. The assumption that plants do not gain weight in the year of flowering is not essential to the qualitative results of the model, and could be replaced in specific instances where there is evidence to the contrary. The Intrinsic Rate of Increase In a population with a stable age distribution the intrinsic rate of population growth can be determined by solving the equation, 00 ^2/lxmxe-rmX = 1 (9) x=l where lx is age-specific rosette survivorship, mx is age-specific fecundity, and rm is the intrinsic rate of increase (Andrewartha and Birch 1954). For semelparous plants (9) reduces to, lxmxe~v™x = 1 (10) which can be rewritten as, In lx + In mx rm = • (11) x The ruderal habit of most semelparous perennials precludes the establishment of stable age structure in the small populations that colonize disturbances. These populations are dominated by the colonizing cohort; subsequent recruitment is limited by competition (e.g. Holt 1972; Gross 1980). The intrinsic rate of increase cannot be calculated in the absence of a stable age distribution, but it is possible to calculate the related 'capacity for increase' rc = InRo/T (Laughlin 1965). Laughlin points out that rc is not only the approximate estimate for rm (Andrewartha and Birch 1954; Leslie 1966), but gives the actual rate of 39 increase for the first few generations arising from a cohort "...as, for example, when an empty piece of territory is colonized by immigrants". To see this recall that the net reproductive rate of a semelparous phenotype is Ro = lxmx, and that the generation time T is the age of reproduction, x, assuming there is no seed dormancy. Thus rc = rm for semelparous phenotypes without seed dormancy. If all plants in a population grew at a common rate 7 , their age specific fecundities would be equal to zero in the years prior to flowering, and equal to the per capita seed production in the year of flowering; i.e. mx = st+\ where t is the rosette duration. If these plants flowered in the year after achieving a critical size u, their intrinsic rate of increase would be, from (8) and (11), rm(j,u)=lnlv«+1+'»Sv"+1- (12) vu + 1 If, instead, they flowered after vT years as a rosette, their intrinsic rate would be, r m ( 7 , r ) = ^ ± i ± ^ ^ . (13) Equations (12) and (13) emphasize that evolved phenotypic responses have a role in deter-mining the ability of semelparous perennials to exploit their environment. We will shortly consider how variation in individual growth rates influences the relative rates of increase achieved by plants that initiate flowering according to different rules. But first we consider how patterns of age-specific survivorship determine selection for the age and size at which plants should initiate reproduction. Results Figure 11a shows an example of the functional relationship between the individual plant growth rate parameter ( 7 ) and the intrinsic rate of increase (rm). In this instance, survivorship and fecundity patterns were chosen to conform to the pattern described for semelparous perennials; seedling survivorship is 10%, subsequent rosette survivorship is 95%, and the fecundity-weight relation is (6) with parameters taken from the curve fit to the data in Figure 10. The labelled curves are for rosette durations of from one to seven 40 years. Thus the first curve describes the rate of increase of strictly biennial plants as a function of their growth rates, the second describes strictly triennial plants and so on. Each curve is a saturating function intersecting the abscissa at a critical value of 7 below which the intrinsic rate of increase is negative. Both the critical 7 values and the saturation values of r m decline with a delay in flowering, causing the curves to intersect. Consequently, no purely age-dependent genotype can achieve the maximum fitness possible over a broad range of individual growth rates. In this instance, for example, biennials are less fit than plants that further delay flowering over the entire range of individual growth rates shown on the graph, and plants that flower in their fourth year are less fit than plants that further delay flowering when 7 < 1.35, and lower than triennials when 7 > 1.95. Figure l i b shows the weights of plants (dotted curves) as a function of their growth rates and years spent as rosettes. The superimposed solid curves show the weights of plants that flower in the year that maximizes their fitness. (The growth rates with fitness maxima for n-year old rosettes in Figure 11a are mapped onto the corresponding weight curves.) For any growth rate 7 , a critical size smaller than the size a plant will reach in the year that maximizes fitness, but greater than the size it reached in the previous year will ensure flowering in the right year. Thus there is no optimal critical size for most specific growth rates, only a range of sizes which will have the same effect. This is because flowering is restricted by seasonality to a discrete set of times. The critical sizes that maximize fitness are shown as shaded areas under the solid curves. For example, a plant with 7 = 1.5 will reach its critical size during its third year, and flower at the most advantageous time if it has a critical size anywhere between about 20 and 50 g. The range of critical sizes constricts to an optimal size at each 7 value where consecutive annual fitness curves intersect. The optimal phenotypic response to a range of individual growth rates must therefore pass through this set of bottlenecks. In Figure 11, the intersections occur at almost the same size. A genotype that switches to flowering at a single critical size, shown here as a dashed line, will therefore be quite well adapted over a broad range of individual growth rates. The same qualitative pattern appears if the simpler allometric fecundity-weight relation (7) is substituted for (6). 41 F I G U R E 11a The Functional Relationship Between Individual Growth Rate 7 and Population Growth Rate r m . The numbers on each curve are the lengths of the rosette stage in years. In this example the fecundity-weight relation is (6) with a = 0.8, « = 5.55, and C, = 0.7. Juvenile survivorship is 10%; adult survivorship is 95% ( i.e. /„ = 0.10 * 0.95""'). 0 1 2 3 Individual Growth Rate F I G U R E l i b Plant Weight as a Function of Individual Growth Rate and Time. The dotted curves are the weights of rosettes after one to seven years. The superimposed solid curves show the weights of plants that flower at the age that maximizes their intrinsic population growth rates. The shaded area shows the range of critical sizes that maximizes the intrinsic rate for each individual growth rate 7. The horizontal dashed line shows a simple phenotypic response - to flower after reaching a single weight, regardless of age - that approximately maximizes fitness. Conditions Selecting for a Critical Size Threshold A single size threshold, independent of age, will be selected i f the intersections of consecutive annual fitness curves occur at a common critical size. Intersections are found at values of 7 where the intrinsic rate of increase achieved by a plant that delays flowering for a year exactly matches the rate it would have achieved had it not delayed, i.e. rm(jj,j + 1) = rm(lj,j), where j is the age at flowering, and 7^ is the individual growth rate where the intersection occurs. The condition for a single size threshold, independent of age, is that the weights of j year old plants have a common value a; at all intersections for all ages. For plants with an allometric fecundity-weight relation, for example, from (7) and (13), . . „, Inh +i + oInWj + e In / , + a lnu; + e , .. . . „ . rm(lj,J + l)= j + 1 = — 'j = rm(lj,j) forj = (2 ,3 , . . . , n), (14) where the weights of plants that delay flowering a full year after reaching the critical size are, W,= ° - and T j = ^ M S ) ( 1 5 )  3 1 + /3e-y>3 13 j - l y ' Equation (14) can be algebraically rearranged as a recursive equation defining survivorship in relation to the critical size and fecundity-weight relation, 7 + 1 e l n / i + i = ^ — ( l n Z j + crlnu) + - - crlnWj for j = ( 2 , 3 , . . . , n). (16) which has the solution, = 5 " " ' + ' g ( r 1 - 1 - ( * + !)] ( 1 T ) (see Appendix I). Since survivorship must be a nonincreasing fraction, this equation is subject to the condition that its discrete derivative is less than or equal to zero, which can be written (see Appendix I) as, •> l—o / v I—n ' ' + | < - ^ for 0 < / 2 < l (18) fc=2 '"' N fc=2 ' J When this inequality is met, the survivorship curve needed to select for any critical size u> can be calculated using equation (17); when the inequality is not met pure size-threshold dependence will not be selected for any survivorship curve. 43 Figure 12 shows how condition (18) limits selection for a purely age independent critical size to a condition of low juvenile survivorship. The abscissa is the critical size on a log scale; the ordinate is l o g 1 0 1%. The three solid curves show the constraints on pure size-dependence (18) up to ages three, four and five. Selection for a critical size is only possible when survivorship to the first possible age of reproduction (h) is beneath these curves. Notice that the condition becomes slightly more restrictive as the number of years increases. A lower fecundity-weight function (i.e. smaller e), extends the limit of second year survivivorship. If condition (18) is satisfied, a critical size threshold will only be selected if subsequent survivorship satisfies (17), which prescribes a nearly linear (actually slightly concave up-wards) decline in log survivorship. The rate of decline determines what size threshold will be selected. A large critical size is possible provided the decline is slow, but a faster decline selects for a reduced critical size. There is also a limit to the number of years in which pos-itive intrinsic rates can be achieved. The three dashed curves in Figure 12 show the limits for biennials, triennials and quadraennials. Below the straight line biennial curve, selection for a critical size produces negative intrinsic rates at all ages; above this line but below the next, biennials have positive rates, and beyond the next both biennials and triennials have positive rates, and so on. Notice that selection for a smaller critical size will reduce the number of years in which positive intrinsic rates can be attained by the plant. Selection for Other Phenotypic Responses; Patterns of Rosette Survivorship When conditions for a constant critical size are not met precisely, the size at which a plant should initiate reproductive development will depend on its age. Figure 13 shows the effect of accelerating mortality rates throughout the rosette stage. The size that maximizes the fitness of rosettes diminishes with age. Decelerating rosette mortality rates have the opposite effect; since older plants are more likely to survive, they can persist until they reach a larger size. In some semelparous perennials rosette mortality rates increase after a number years irrespective of plant size (Werner 1975; Werner and Caswell 1977; Gross 1981; Lee and Hamrick 1983). Figure 14 shows the ages and sizes of plants that maximize fitness for this 44 Critical Size ( U J ) F I G U R E 12 Constraints on Selection for Pure Size-Dependence. Selection for pure size-dependence is only possible when survivorship to the end of the second year is low. The three curves show the upper limit of I2 for size-dependence up to years 3, 4, and 5. (Parameters are as in Figure 11. The fecundity-weight relation is (7).) The dashed curves show the limits of positive intrinsic rates of increase. . 45 Individual Growth Rate Individual Growth Rate F I G U R E 13 The Effect of Greater Rosette Mortality. A higher rosette mortality rate limits the length of the rosette stage during which positive intrinsic rates are achieved. Plants must flower at successively smaller sizes in successive years to maximize fitness. (Parameters are as in Figure 11, except rosette survivorship of 75% per year.) pattern of rosette survivorship. In this example, the advantage of size-dependent reproduc-tion is limited to plants of 4 years and younger; five year old plants should flower whatever their size. This pattern of age and size dependence can be called age limited size-dependence to distinguish it from other forms of age-size dependence. The Fitness of Genotypes in Relation to Variability in Individual Growth Rates The relative fitnesses of genotypes with different phenotypic responses for age and size at flowering will depend on how well their phenotypes match the selection regime over the range of individual growth rates found in a particular environment. In Figure 11, for example, a purely size-dependent genotype with the right critical size will have a higher fitness than any purely age-dependent genotype if the range of individual growth rates in the environment spans one or more fitness curve intersections. Conversely, if all growth rates are within the range where a single flowering age maximizes fitness, reproduction at either the appropriate age or an appropriate size will maximize fitness. Notice also that a narrow range of growth rates is not sufficient to make age-dependence comparable to size-dependence if growth rates are not within the range where a single flowering age maximizes fitness. The fitness of a genotype subject to an environment that causes variation in individual growth rates can be calculated as follows. First, observe that the finite growth rate A of a population can be construed as the mean of individual per capita finite growth rates, say Aj, of the members of the population. The intrinsic rate of increase of a population can therefore be calculated as the log of the mean of the individual per capita finite rates, rm = ln(A,). (19) Now suppose that the distribution of individual growth rates (i.e. accumulation of biomass) is described by a probability density function / ( 7 ) . Consider first a genotype that always flowers at the same age j. Since its intrinsic rate rm is a strictly increasing asymptotic function of 7 , it follows that its finite rate, say 5 ( 7 , j) = A = er is likewise 47 Individual Growth Rate Individual Growth Rate F I G U R E 14 The Effect of Increasing Rosette Mortality After Four Years. Accelerating rosette mortality after four years limits the value of size-dependent reproduc-tion to plants growing fast enough to reach a critical size in four years or less. Slower growing plants should switch to flowering after their fourth year regardless of their size. (Parameters are as in Figure 11, except rosette survivorship decreases from 95% to 85% after four years.) strictly increasing. The probability density of the finite rate is therefore related to the probability density of individual growth rates by, / W ) = ^ / W A , i ) ) , (20) (e.g. Olkin et al. 1980) where h(X,j) is the inverse function of # ( 7 , j) and f(h(X,j)) = f(j). Combining equations (19) and (20) it follows that the intrinsic rate of an age-dependent genotype subject to variation in growth rates is, rm = In J°° Xf(X,j)dX = In J°° \d{h{^j))f(h(X,j))d\. (21) Size-dependent and age-size-dependent reproducers may reproduce over a number of years. Their intrinsic rates are therefore calculated on the segments of the fitness curves they sample, rm = l n £ [ K ' A / (A, j )dA = l n £ / * " ' Xd^j))f(h(X,j))d\. (22) For the allometric case see Appendix III. The limits of integration (Xij, A U J ) are determined by the intersections of the genotype's phenotypic threshold with the annual fitness curves (see Appendix IV) . A perfectly adapted genotype achieves the highest possible population growth rate over the range of individual growth rates it may encounter because the vector of 7 values where its phenotypic threshold curve intersects the size curves, say 7 P , corresponds exactly to the vector of 7 values where the fitness curves intersect, say 7 S . Less than perfectly adapted genotypes also sample contiguous segments of the fitness curves with respect to 7 , but not with respect to population growth. Consider the poorly adapted phenotypic threshold of the genotype depicted as a dashed line in Figure 15b. Since the vector of 7 values where its threshold curve intersects the size curves, 7 P , does not correspond to the vector of 7 values where the fitness curves intersect, 7 « , this genotype samples noncontiguous segments of the fitness curves with respect to the population growth rate. The segments may be discontinuous as in this case, or they may overlap. Equations (21) and (22) imply that the intensity of selection against poorly adapted genotypes will depend on the distribution of individual growth rates in the environment. 49 A B O O -Individual Growth Rate Individual Growth Rate FIGURE 15 The Phenotypic Threshold Curves of Some Genotypes Sample Discontiguous Segments of the Fitness Curves. The phenotypic threshold of the genotype depicted by the dashed line in (b) declines with age, but is poorly adapted to an environment that requires a smaller critical size throughout. (The values of 7 where the phenotypic threshold intersects the size curves, shown as vertical dotted lines, do not correspond to the 7 values where consecutive rm curves intersect, i.e. the lower ends of the solid lines). A genotype that responded to variation in inidvidual growth rates in this way delays reproduction too long. In (a) the shaded area above the abscissa is the distribution of growth rates. Note that this poorly adapted genotype samples contiguous segments of the curves with respect to 7, but not with respect to rm. The intrinsic rate of increase is lower than it could be in this environment. For example consider what would happen to the relative fitness of a size threshold depen-dent genotype with a critical size u following the introduction of a herbivore or pathogen that increased rosette mortality, shifting selection to a new smaller critical size OJ*. If the plant population were ruderal, the growth rates of successive cohorts after colonization might decline as in Figure 16a, causing the finite growth rates of both well adapted (A w . ) and poorly adapted (Au;) genotypes to decline (Figure 16a). A maladaptive phenotypic response to variation in individual growth rates is potentially most costly in the first few years of reproduction because the rates of increase are potentially greatest. The relative fitness ) of a poorly adapted genotype is therefore smallest under the most favorable conditions immediately following colonization. Discussion and Conclusions The Intrinsic Rate as a Measure of Fitness In this paper I have assumed that the intrinsic rate of increase is a useful measure of fitness. Giesel (1976) lists two additional definitions of fitness which may or may not coincide with the one I've chosen: 1/ The average rate of increase that a population can maintain given its probable existence in a variety of environments, or 2/ Its ability to persist in a variety or heterogeneity of environments. The two definitions are closely linked because populations must have an average rate of increase, f, greater than or equal to zero to avoid eventual extinction (Lewontin and Cohen 1969). Definition 2 can therefore be rephrased, 2a/ The ability of a population to maintain an average rate of increase greater than or equal to zero in a variety of environments. The distinction between the two definitions is then seen to be one of emphasis. The first stresses the overall average rate of increase given environmental heterogeneity, the second stresses the ability to maintain an average rate of increase greater than or equal to zero in a variety of environments. How closely these two definitions are allied with the definition 51 0 1 2 3 a b e d Individual Growth Rate F I G U R E 16 The Relative Fitnesses of Genotypes Depend on the Distribution of Growth Rates. (a) Curves a-e show how the distribution of individual growth rates might decline within a temporarily colonized patch. (The five curves are Weibull distributions.) (b) The population growth rates of both well adapted u>* and poorly adapted u genotypes decline as the mean growth rate drops, but the better adapted rate declines faster. Selection against poorly adapted genotypes is therefore greatest when growth conditions are most favourable. of fitness as the intrinsic rate of increase depends on the adaptations evolved to achieve a nonnegative average rate of increase. Species in general can evolve a high intrinsic rate of increase, a low variance in the actual rate of increase, or a combination of the two (e.g. Giesel 1976). Semelparous perennials however cannot avoid a high variance in their actual rates of increase because of the uncertainty associated with exploiting temporarily favorable disturbance habitats (e.g. van der Meijden and van der Waals-Koi 1979; Gross 1980). These species must therefore rely heavily on a high intrinsic rate of increase to boost their average rate of increase (Grime 1977). Thus their ability to persist depends on maintaining a high intrinsic rate, and the ability to persist in a variety of environments depends on their ability to maintain a high intrinsic rate in a variety of environments. Adaptations of Semelparous Perennials Hart (1977) showed that a biennial must produce at least twice as many seeds as an annual, and four times as many seeds as a polycarpic (iteroparous) perennial to achieve the same population growth rate. A semelparous perennial that delays reproduction beyond the second year must have an even higher seed output to compensate for the additional rosette mortality and longer generation time (e.g. van der Meijden and van der Waals-Koi 1979). Despite this apparent handicap, semelparous perennials are successful enough that many are significant agricultural pests (e.g Senecio jacobaea, Centaurea diffusa, Carduus nutans, Cynoglossum officinale). Semelparous perennials achieve a high seed production (Salisbury 1942, summarized in Hart 1977) by first allocating almost as much of their biomass (80%) to photosynthetic tissue as annual species (80-90%) during the rosette stage, and later allocating as much as 86% of plant weight to the shoot during the flowering stage (Struik 1965). Semelparous perennials also produce smaller seeds than either annuals or iteroparous perennials (Stevens 1932; Hart 1977). This pattern of resource allocation ensures that plant growth rates and the number of seeds produced as a function of weight, both components of age specific fecundity, are enhanced within the constraints imposed by limited resources and competition. The repertoire of life-history adaptations available to semelparous perennials to respond to environmentally determined variation in growth rates and survivorship is limited by 53 their morphology, (i.e. the initial size, the maximum rosette size, and the fecundity-weight relation), by their sequential allocation of resources to growth and reproduction, and by the seasonality of favorable growth conditions to a single option: the timing of reproduction. A l l evidence suggests that semelparous perennials cue the developmental switch to a critical size threshold, or some correlate. They are either size-dependent or age-limited size-dependent reproducers. A n Hypothesis to Explain Size-Threshold Dependent Switching The model presented here provides an explanation as to why semelparous perennials have evolved critical size thresholds to control the initiation of reproductive development. It shows that a specific application of the principle of allocation - the hypothesis that switching from vegetative to reproductive development at a single size maximizes fitness - is plausible because the demographic constraints that select for pure size dependence are broadly similar to those reported for semelparous perennials in the literature. The advantage of size-dependence under this hypothesis is not limited to environments with deteriorating growth conditions (cf. Hirose 1983), but does depend on specific survivorship patterns which can be used in designing experimental tests. Phenotypic Thresholds, Reaction Norms, and Seasonality The model is similar in spirit to a recently published general model of age and size at maturity proposed by Stearns and Koella (1986). They showed that the product of age-specific survivorship and fecundity curves over a range of growth rates defines a trajectory of age and size that maximizes fitness in the face of environmental heterogeneity. They called this trajectory the predicted 'reaction norm'. Since the age at maturity in their model was a continuous variable, the reaction norm was also a continuous function of age and size. For semelparous perennials, and many other organisms subject to the constraints of seasonality, the practicable ages to initiate reproductive development are constrained to integer intervals. Then, as we have seen, individuals over a sometimes broad range of sizes (e.g the solid lines on the size curves in Figures 11, 13, and 14) should initiate reproduction at a given age to maximize their fitness. The analogous discrete reaction norm consists of the means of the expected sizes at each age. 54 Stearns and Koella introduced the concept of reaction norms to life history theory in the hope that predictions of the age and size at maturity could be tested by employing existing data, or data that could be gathered within a single generation, thereby avoiding the need for selection experiments. The above model suggests the following caution, and extension to their approach. When organisms are subject to seasonal environments, selection may be for a phenotypic threshold rather than a reaction norm. The shape of the reaction norm is then an artifact of the the shape of the phenotypic threshold, and the growth rates of individuals that mature at each age. Consider for example Figure 17, which plots the expected sizes of mature plants at each age for the almost purely size threshold-dependent case shown in Figure 11. The reaction norm of data with this pattern declines with age because individuals that delay reproduction longer are slower growing, and therefore exceed the critical size by a smaller margin. The interpretation of selection for declining maturation size with age would be entirely spurious in this case. Equal weight should therefore be given to the alternate hypothesis that selection is for a minimum threshold size, unless either hypothesis can be discounted apriori. Approaches to Testing the Hypothesis The conditions under which size-threshold dependent flowering maximizes fitness (Fig-ure 12) are fairly restrictive. We can therefore test the hypothesis outlined in the model by predicting the form of rosette survivorship if the fecundity-weight relation and critical size are known. Although a more realistic treatment of individual growth curves than the simple logistic argument employed in the general model would be preferable in detailed studies of a single species, a provisional cross-species comparison is possible using equation 18 to predict the maximum second year survivorship expected for species, given their ap-proximate minimum and maximum sizes, their fecundity-weight relation and their critical size. A different approach is to predict the expected critical sizes (iterating equation 17) based on the fecundity-weight relation and survivorship. There is however one caveat. It is generally assumed in natural selection arguments of life historical evolution that there are no constraints to adaptation near local optima (e.g. Stearns and Koella 1986). The utility of this assumption is that it allows us to predict the phenotypic responses of populations to 55 o CxJ 3 S o Reaction Norm / . Critical Size Threshold Flowering Age (yrs.) F I G U R E 17 The Reaction Norm and Phenotypic Threshold of a Size-Dependent Genotype. The vertical bars show the range of sizes of plants that flower in the first seven years, for the example in Figure 11. Slower growing plants that de-lay bolting exceed the critical size by a smaller margin than faster growing plants that flower early. The reaction norm for the size of flowering individ-uals (upper dashed line) therefore declines with age though both selection, and the phenotypic response (lower dashed line) are for an age-independent critical size. 56 changing growth rates, survivorship and fecundity patterns. A potential pitfall arises when the importance of that qualification is forgotten. Concurrence between observations and our (qualified) predictions should not be taken as support for our theory in the absence of independent evidence that constraints do not limit the response to selection (post hoc, ergo proper hoc!). Discrepancies between observations and model predictions could either mean that the models are wrong, or that there are unanticipated constraints to local adaptation. In the present context we do not know what biochemical mechanisms might be involved in controlling the switch to competency for flowering even in the relatively simple case of pure size-dependence, although Thornley (1972) and Thornley and Cockshull (1980) have suggested how such a switch might work. Are these plants capable of evolving a genotype with a phenotypic response fitting a more complicated age-size dependent selection regime? At the moment we cannot rule out the possibility that the size threshold is merely an imperfect adaptation to selection for age-size dependence. Selection experiments based on life history model predictions are required to resolve the uncertainty. 57 III. Circular Neighborhoods, Polygonal Neighborhoods and The Growth of Centaurea diffusa Rosettes in Relation to Individual Crowding Abstract Neighborhood models of plant interference relate variation in plant survivorship, growth or seed output to variation in individual crowding. The measurement and description of crowding requires that for each focal individual a sample of nearby plants be selected and weighted in a summary description known as an 'index of crowding'. Two methods of sampling sets of neighbors have been described in the literature. 'Circular sampling' defines neighbors as plants within a specified radius of a focal plant; 'polygonal sampling' defines neighbors as plants that share a boundary when the ground is partitioned into Dirichlet polygons. The two methods define sets of neighbors that are not equally suitable as a basis for the description of individual crowding in plant populations. Polygonal sampling yields directionally unbiased samples of approximately constant size regardless of changes in population density or the degree of aggregation in the spatial pattern. A n important aspect of local spatial pattern, the size of gaps, is detected and the qualitative distinction between adjacent and once-removed neighbors is preserved. Circular sampling is sensitive to the choice of a sample radius in relation to the density and spatial pattern of the population. In patchy populations there may be no suitable tradeoff between a radius too small to detect the size of gaps, and one too large to exclude individuals with negligible effects on the focal individual. Crowding indices of varying complexity based on both methods of sampling were employed to explain variation in rosette growth in a natural population of Centaurea diffusa. Introduction The phenotypic responses of individual plants to local interference from neighbors determine the distributions of plant sizes and reproductive outputs (e.g Koyama and Ki ra 1956; Mack and Harper 1977; Weiner 1982). A theory of plant population dynamics must therefore include both a description of mechanisms that generate spatial patterns, and the demographic responses of plants to local variability in the intensity of interference (Holsinger and Roughgarden 1985; Pacala and Silander 1985). The neighborhood approach to the study of plant interference involves defining indices of crowding to summarize the local distribution of neighboring plants in a way that can be statistically related to a focal plant's performance. Crowding indices are thus analogous to the more familiar indices such as density and biomass per area; they are summary descriptions of the local distribution of individuals which can be related to morphological or demographic variation without necessarily invoking detailed ecophysiological explanations. Their advantage is that they 58 can predict individual variation in plant performance that summary descriptions on a greater spatial scale cannot. Neighborhood models (in agronomy: Mead 1966; Knight 1983, in forestry: Keister 1971; Bella 1971; Arney 1973; Hegyi 1974; Ek and Monserud 1974; Daniels 1976, and in plant ecology: Mack and Harper 1977; Waller 1981; Weiner 1982; Mithen et al. 1984; Silander and Pacala 1985) have been successful, accounting for as much as 60-70% of the variation in plant weight (Mack and Harper 1977; Mithen et al. 1984), and 70-86% of the variation in seed production (Weiner 1982; Silander and Pacala 1985). The neighborhood approach is not without problems, however. To create a neighbor-hood model it is first necessary to decide which of the nearby plants will be designated as the 'neighbors' of each individual. Then, a list of descriptive variables that could potentially affect the focal plant's performance is compiled. Some relevant variables are the number, distance, species, stage, age, size, and angular dispersion of neighbors. Finally, those vari-ables must be arranged in some functional form. The array of choices in this process has led to a proliferation of models, and some criticism of the apparently arbitrary judgements involved in their construction. Waller (1981) has suggested criteria for limiting the number of variables in neighborhood models, and Silander and Pacala (1985) have proposed a pro-cedure for choosing a functional form. But the most basic decision, the choice of a sampling method, has not been systematically considered. The two methods for sampling sets of neighbors that have been employed to date are polygonal or tessellation sampling, and circular or threshold sampling (Cormack 1979). Polygonal sampling (e.g. Mead 1966; Liddle et al. 1982; Mithen et al. 1984) partitions the ground into Dirichlet (also known as Theissen or Voronoi) polygons, formed by joining the perpendicular bisectors of line segments between nearby plants. Neighbors are denned as those plants which share a polygon side, or equivalently, are connected by the Delauney triangulation. Circular sampling (e.g. Mack and Harper 1977; Weiner 1982; Silander and Pacala 1985) defines the set of neighbors as all those individuals within a specified distance of a focal plant. These two sampling methods define incongruent sets of neighbors that are unlikely to be equally suitable as a basis for defining indices of crowding. The first 59 objective of this paper was to assess the sensitivity of the number and angular dispersion of neighbors in circular and polygonal samples to a range of spatial patterns, and discuss how the sampling method might bias an index of crowding. The second objective was to compare the ability of crowding indices based on both sampling methods to explain variation in rosette growth for a mapped population of the semelparous perennial, diffuse knapweed (Centaurea diffusa). Neighborhood models to date have dealt almost exclusively with annuals (e.g. Mack and Harper 1977; Weiner 1982; Silander and Pacala 1985) or even-aged populations of peren-nials (e.g. Weiner 1984) to avoid the added complication of an initial size structure in the plant population. These studies demonstrate the importance of local crowding in determin-ing the performance of individuals when other effects, notably the time of establishment and initial plant size are experimentally minimized. In annual populations, germination date strongly influences the relative performance of competing individuals (e.g. Ross and Harper 1972; Fowler 1984). In perennial populations with overlapping generations the size structure of the population should have an analogous effect. A plant's size at the beginning of a growth season should affect both its maximal growth rate and its sensitivity to inter-ference from neighbors. Two neighborhood studies of forest plantations (Alemdag 1978; Martin and Ek 1984) showed that tree size is an important determinant of stem diameter increment. Natural populations of semelparous perennials such as diffuse knapweed are size-structured except during the colonization of new territory because rosettes persist for several years. The neighborhood models described below therefore incorporate both initial plant size and crowding to predict rosette growth. Methods Simulation Methods I generated two dimensional spatial point patterns varying from underdispersed through random to overdispersed using an algorithm from Green (1979). Each pattern began with 25 random seed points. Subsequent random points were included or excluded according to 60 their distance from previously admitted points. Contagious patterns were created by ad-mitting points which would fall less than a specified threshold distance from any previously admitted point. Points less than one half of the specified distance from an existing point were admitted, points between one half the distance and the full distance were admitted with probability 0.5, and points beyond were excluded. Regular patterns were created by reversing the probabilities. Points which would fall less than one half the specified distance from a previously admitted point were not admitted, points between one half and the full distance were admitted with probability 0.5, and points beyond were admitted. In both cases the process continued until a total of 200 points, including the seed points, were ac-cepted for each pattern. Five replicate patterns (1000 points) of each type were simulated for each of five levels of dispersion. Figure 18 shows the range of dispersion used in the simulations. Spatial pattern type 1 is the most regular, type 3 is random, and type 5 is the most contagious. The numbers below each pattern are the threshold distances as a fraction of the linear dimension of the unit square. A sample of 500 points for each pattern type was obtained by randomly choosing 100 points from each of the five replicates, after first excluding points with polygons or circles touching a boundary. Three sets of neighbors were calculated for each point. 'Polygon neighbors' were defined as those points contiguous with respect to the Dirichlet tessellation of the plane, i.e. sharing a side of the focal point's polygon. There is only one set of polygon neighbors because the Dirichlet tessellation is unique (except under unusual circumstances). The contiguity list was generated using the computer program by Peucker et al. (1978). 'Circle neighbors' were defined as points within a specified radius of the central point. There are an infinite number of sets of circle neighbors with different radii, but just two sets were chosen to investigate the effect of the sample radius. The sample radii were 0.10 and 0.14 of the linear dimension of the unit square. The numbers of neighbors were recorded for each neighborhood sample, and circular variances (Mardia 1972) were calculated to measure their angular dispersion. 61 Spatial Pattern Type e s . t o a a a _ .« • « • « • • a • a a • " a a • a o • a • • a i a i a a a • a • ' . a « a a a , " a " " a . - a «•••_ a < a a a < " a a a ' • " , « « « • " - a . a a a a • " a "a a " a « " . « a a a a * • a « " a " . a " • a a a" a " <Ta^*, -" a « a « » - « j " " a " f "V V •» » • « " " « " - • • • a * _ a a a a a « « a I a" « «"_ a - a • a " <i a a a a ' , . « . . « « . « « « J • a" « " " " a > • a a a ,a a a ," a . a a a a -a- N . "« " « iPa • 1« a a "*• ""aa"*" » M a a a * a - a a" • a "a a*.*. a # * a" a MM a • •* - a*a • a a _ fi a _ a aa a a S a «a a • "I « * a a a a 41 * ^ « h JL-. « «_ # a • « ^ • *«".»•« **" aa ^ « aT a *" .* « « V a"* % a a 0.10 0.05 1.00 0.10 «a a a " a « *Mf a 0.05 F I G U R E 18 Simula ted Spa t ia l Pat terns . These five plots illustrate the range of dispersion used in the simulations. The parameters listed below each plot are threshold distances used to generate the spatial patterns. (See text for a full explanation.) Field Materials and Methods Diffuse knapweed (Centaurea diffusa) is a composite rangeland weed of Eurasian origin that displaces native vegetation in dry areas of western North America. Like other semel-parous perennials (Werner 1975), it switches to reproductive development after reaching a critical size. The age of reproduction is therefore determined by how fast the rosettes grow. This has been experimentally confirmed by measuring rosette growth rates and the subse-quent year's flowering rate in artificially planted populations subject to varying degrees of crowding (Powell 1988): Fast growing uncrowded rosettes exceeded the critical size in the first year, and flowered in their second year; slower growing crowded rosettes did not exceed the critical size, and did not flower in their second year. The knapweed population at White Lake, British Columbia (49°19' 119°38') is a near monoculture in which spring rosette densities range from 150 m~2 to 500 m~2. A l l rosettes in a 1.0 m by 6.0 m plot (n = 1108) were individually labelled by fastening slender plastic closures bearing numbered electrician's tags around their bases. Their locations were recorded using a mapping table and siting tube. The table consisted of a 1.0 m 2 piece of 0.5 cm glass mounted on a 1.2 m by 7.0 m track surrounding the plot on the ground. The cylindrical Plexiglass siting tube was 20 cm in height with three sets of colored cross hairs at 2, 10, and 18 cm, and had openings cut away on its lower sides to facilitate marking a location while siting. The locations of the plants and their tag numbers were marked onto clear acetate sheets fastened to the mapping table. Overlapping acetate maps of the plant locations were digitized in segments and the map segments combined on the computer. Rosette growth was observed by repeated measurements of the root crown diameter, a nondestructive measure of plant size related to plant weight. Rosette diameter, the usual nondestructive measure of size (e.g. Werner 1975), could not be used because knapweed rosettes loose much of their foliage during the midsummer drought. Root crown diameters were recorded by removing enough sand from the base of the plant to fit calipers immediately below the petioles of the lower leaves. Each root was measured at least twice to ensure accuracy. The measurements were made at the beginning of May and in mid September. 63 Finally, the size data were appended to the coordinate and labelling data from the maps. The circular and polygonal neighborhoods were then calculated from this data base. Lloyd's index of patchiness (Lloyd 1967), a density independent measure of pattern intensity (Pielou 1969), was calculated to locate the spatial pattern of the knapweed rosette population within the continuum of the simulated spatial patterns. Both simulated patterns and maps of the six contiguous meter squared quadrats were randomly sampled twenty times with square quadrats corresponding to 0.1 of the unit dimension. Descriptions of Crowding Crowding can be expressed as the sum of the effects of neighboring plants. Large or near neighbors can be expected to interfere more heavily than small or distant ones. Crowding is therefore expected to be proportional to the number or biomass of neighbors and inversely proportional to their distance from a focal plant. The angular locations of neighbors can also affect plant performance. Plants that are surrounded by neighbors grow slower than plants with neighbors on one side only, i.e. plants next to a gap (Ross and Harper 1972). Thus, crowding increases with the angular dispersion of neighbors, but there is also a relatively subtle interaction between angular location and neighbor distance. The expressions used to describe the effects of the numbers, sizes, distances, and angular locations of neighbors are operational definitions of hypotheses about which aspects of the local spatial pattern of biomass most affect the performance of individual plants. I: Circular Crowding Indices The circular indices examined were similar to those of Mack and Harper (1977) and Weiner (1982; 1984). Following Weiner, neighbors were grouped in three concentric annuli defined by radii in the ratio of 1:2:3. When the median distance to the area of the first annulus is set to one, the relative median distances to the second and third annuli are 2.24 and 3.61 respectively. The number of neighbors in each annulus was weighted either by the inverse of the median distance to the annulus, dk, 3 (1) 64 or by the inverse of the square of the median distance to the annulus, 3 W i = 2 = n i + °'2n2 + °-077n3 (2) k-i k (Weiner 1982) where nk is the number of neighbors in the /cth annulus. In addition to these 'number of neighbors' indices, analogous 'size' indices were calculated in which the sum of the root crown diameters of neighbors replaces their number in the numerator. These simple indices were also modified to include the effects of the angular locations of neighbors. Plants that are not surrounded by neighbors are less crowded because they can exploit adjacent gaps (Ross and Harper 1972). In the context of a circular crowding index, the presence of a gap is suggested (provided the sample radius is large enough to include the information) when, a) the angular dispersion of neighbors within annuli is low and, b) the mean angles (a^) of neighbors within annuli are similar, i.e., when most neighbors in both inner and outer annuli are to one side of the focal plant. I assumed, as did Mack and Harper (1977) and Waller (1981), that a circular variance (1 — r) of 0.75 or more indicates that a focal plant is effectively surrounded by neighbors. The variable, ou. = (1 — r')/0.75 where, r' — r if r > 0.25 and r' = 0.25 otherwise, ranging from 0.0 to 1.0, measures the extent to which neighbors within an annulus surround a focal plant. The simplest model is that crowding increases linearly with cr, e.g., W{ = 2~^ [1 — A ( l — Gk^n-k/dk where f\ is a constant describing the fractional reduction in the effect of neighbors in an annulus when they are minimally dispersed compared to when they are maximally dispersed. The difference between mean angles of the inner and outer annuli only has meaning provided that both mean angles are significant. If the mean angles of neighbors in the first two annuli combined (01,2), or the third annulus (03) was not significant (a : 0.05) by Rayleigh's test (Durand and Greenwood, 1958; see Zar 1974) the focal plant was considered to be surrounded by neighbors and no adjustment for the mean angles .was made. If, how-ever, both mean angles were significant, the focal plant was considered to be surrounded only to the extent that the mean angles of the neighbors in the annuli were opposite one another. 65 Mack and Harper (1977) discovered empirically that the effects of neighbors decreased pro-gressively as the mean angles were in opposite, adjacent, and the same quadrants. This is presumably because the size of a possible gap increases as the difference between the angles decreases. The scaled smallest difference between mean angles, 8 — arccos(cos(ai)2 — 0 3 ) ) / ^ ranges from 0.0 for coincident mean angles where the gap is potentially largest, to 1.0 for opposite mean angles. The simplest assumption is that crowding declines linearly as the mean angles converge, e.g., W, = [ 1 -A<1 -« ) ]£ [ ! -Ad-* ) ] « where, , = {\ ^ * < * (3) k=l K K and fa is the fractional reduction in the effect of neighbors when the mean angles coincide compared to when they are opposite. Each of the circular crowding indices was calculated for neighborhoods in which the first radius was 1.0, 2.0, 3.0, 4.0, and 5.0 cm. Values for the constants f\ and ji ranging from 0.1 to 0.9 were tried. II: Polygonal Crowding Indices Polygon crowding indices were constructed with sets of polygon neighbors obtained using the algorithm of Peuker et al. (1978). The simpler indices are like those described for their circular analogues except that summation is over all polygon neighbors rather than three annuli. The hyperbolic expressions 1/(1 + d) and 1/(1 + d?) were tested as an alternative distance weighting tol/d and 1/d2 because the variance of the latter expressions is very strongly affected by neighbor distances less than one. Since the angular dispersion of polygon neighbors is consistently high (see Simulation Experiments) the angular locations of neighbors should be relatively unimportant in polygon indices of crowding. Two methods of weighting the neighbors to reflect their share of the angular environment of a focal plant were nevertheless tested. The first was to bisect the angles formed between adjacent neighbors, attributing half to each neighbor. Another possibility takes into account not only the angles of adjacent neighbors but also their relative proximity to the central plant, by assigning to each neighbor the sum of the angles formed with the polygon vertices to either side. The difference in biological interpretation hinges on 66 whether near neighbors assume a disproportionate importance relative to adjacent neighbors which is not accounted for by their absolute angular proportions, distances and size. The 'bisected' angle weighting assumes that they do not; the 'vertex' angle weighting assumes that they do. Two methods of including the angular proportion were tried. In the first, the effect of the neighbor was weighted by its proportion of the circular environment of the focal plant, e.g., W i = E ? ^ (4) j=l 3 where ^ aj — 2TT , and aj is either the bisected or vertex angle of neighbor j. Alternately, the neighbor was weighted by the pie-shaped area determined by the neighbor distance and angular proportion, e.g., 3=1 J The Size Of The Focal Plant The indices of crowding denned above describe the distribution of competitive biomass surrounding an individual plant. Initial rosette size was included as a separate term in simple multiple regressions in which the dependent variable was the May to September increment in root crown diameter. Regressions were calculated for subsets of the data for which both polygonal and circular indices could be calculated. Results: Simulation Experiment Figure 19 shows how the numbers and angular dispersion of neighbors are influenced by the method chosen to sample them, and by the spatial pattern of the population. The numbers on the abscissa in each boxplot (Chambers et al. 1983) refer to the five types of spatial pattern illustrated in Figure 18. The top three boxplots (Figure 19 a,b,and c) show the distributions of numbers of neighbors; the lower three (Figure 19 d,e, and f) show the distributions of circular variances. Each box depicts the distribution of values in a sample 67 of 500 neighborhoods. The horizontal lines within the boxes are the medians, the box ends are the quartiles, and the 'whiskers' the range. Numbers of Neighbors Figures 19a and 19b show the numbers of 'neighbors' included in two sizes of circular samples over the range of spatial dispersion. The expected number of neighbors in circular samples of spatially random (type 3) populations is E(N) — irr2(N — 1), where JV is the number of individuals in a unit square. In particular, the expected numbers of neighbors in the two examples, with radii of 0.10 and 0.14, and with N = 200, are 6.25 and 12.25 respectively. The medians (which should equal the expected values for random populations) are in agreement with expectation. Increasing the circular sample area is formally equivalent to increasing the density in random populations. Note that the median number of circular neighbors increases not just with density (compare type 3 patterns in Figures 19a and 19b), but also with aggregation in spatial pattern. This is because circular samples of neighborhoods are centered on individuals, not on random points. Dispersion about the median, as seen in the interquartile range, increases dramatically with spatial aggregation. The number of individuals included in a neighborhood in the most aggregated (type 5) populations ranges from 1 to 34 for the smaller circles and from 1 to 47 for the larger circles. Polygon samples (Figure 19c), in contrast, have a constant median size, and a narrower range of values which is largely unaffected by spatial dispersion. (Very regular patterns have a smaller range of sample sizes.) The number of neighbors is never less than 3, because triangles are the simplest polygons, and never larger than 10. Angular Dispersion of Neighbors The angular dispersion of neighbors from both circular samples (Figure 19d and 19e) and polygonal samples (Figure 19f) decreases with spatial aggregation. Smaller circles (Figure 19d) have the lowest circular variances due in part to small sample sizes. A near doubling of the sample area increases the circular variances in samples of the most regular populations (compare type 1, Figures 19d and 19e), but has almost no effect in the most aggregated populations (compare type 5, Figures 19d and 19e). Increasing density (compare 68 Circles Polygons r=0.10 b r=0.14 CO o sz O) CD z CO E Z o O O PJ o tu o o 01 1 2 3 4 5 1 2 3 4 5 CD O c 03 \— c a > CO o O o d to o d a o a o d ID d o (VI d o * o 2 3 1 2 3 4 5 Spatial Pattern 1 2 3 4 9 Spatial Pattern F I G U R E 19 The effects of neighborhood sampling method, and in the circular case, sample radius on the number and angular dispersion of 'neighbors'. 69 pattern type 3, Figures 19d and 19e) also increases circular variance in circular samples. The circular variances of polygonal samples (Figure 19f) are large and narrowly dispersed relative to the circular variances of comparable circular samples. The decline in circular variance with spatial aggregation is much less pronounced. Field Results Estimates of Lloyd's index of patchiness and their standard errors for the five simulated spatial patterns from the most regular to the most clumped were 0.698 (0.030), 0.907 (0.115), 1.00 (0.167), 1.38 (0.293), and 3.99 (1.970). Estimates for the six quadrats in ascending order were 0.621 (0.124), 1.006 (0.071), 1.187 (0.465), 1.305 (0.216), 1.327 (0.516), 1.345 (0.410). The knapweed population was thus less patchy than the moderately clumped simulated pattern 4 in every case, although four of the six were more aggregated than a random pattern. The advantage of polygon samples suggested by the simulation experiment would therefore not apply to these data. The numbers of neighbors in the inner annuli and outer annulus of circular samples, and their circular variances are shown in Figure 20 with the corresponding numbers for the polygon samples. The ratio of the number of neighbors in the outer annulus to the number in the inner annuli was lower than expected for a random pattern ([7r(3r)2 — 7r(2r)2]/7r(2r)2) = 1.25 for the first three neighborhood sizes, indicating clumping at that scale. The number of neighbors in the circular samples ranged from x : 1.17, sd : 1.28 for — 1.0 to x : 23.39, sd : 12.82 for = 5.0. Even the largest circular neighborhoods (r^ = 5.0cm) sometimes contained only a single neighbor. Polygon sample sizes (x : 5.91, sd : 1.41) were intermediate in size between the second and third smallest circular neighborhoods. The median angular dispersion of circle neighbors rose over the range of sample sizes, whereas the angular dispersion of polygon neighbors was consistently high. A n unanticipated consequence of the increase in angular dispersion of circle neighbors with neighborhood size was that a correction for the difference between mean angles (equa-tion 5) was rarely necessary for these data. Recall that such a correction requires that both the mean angles in the inner annuli and outer annulus be significant. The proportion of 70 Annulus Annulus 1,2 1.2 CO o JQ O) CD Z CD J O E 3 z to o CO ID CM O ru ID to o -1 2 3 4 5 1 2 3 4 5 Sample Rad ius M (cm) CD O c CO co > « 3 o O CO d CO d ru d o d 1 2 3 4 5 » f n 1 till 1 2 3 Sample Rad ius r1 4 5 (cm) F I G U R E 20 The Number and Angular Dispersion of Neighbors in Circular and Polygonal Samples of the Knapweed Population. The boxplots show the numbers and angular dispersion of neighbors in the first and second annuli (labelled 1,2) and the third annulus (3) for circular samples with inner radii ranging from 1 cm to 5 cm, and for the corresponding polygon samples (P). neighborhoods with one or both mean angles insignificant rose almost as quickly as the pro-portion of neighborhoods with neighbors in both the inner annuli and outer annulus. The correction for angular dispersion within annuli was potentially of greatest value where the variance in dispersion was the greatest, i.e. the second and third smallest neighborhoods. This pattern was observed, but the correction proved to be of no value in improving the regressions, both lowering the R2 and increasing bias as measured by Mallow's Cp statistic relative to the uncorrected models. The angular weightings in the polygon indices were similarly unhelpful. The indices most successful in predicting the growth of knapweed rosettes were among the simplest. Figure 21 shows the coefficients of determination for the multiple regressions on size and crowding and the proportion of the explained variation attributed to crowding. The numbers in the far left column are the inner radii of the circular samples. The second column identifies the indices as follows: The circular indices were C I ; the number of circular neighbors YJnt, C2; t n e combined sizes of the circular neighbors YJsjk, C3; the number of circular neighbors weighed by their median annular distances a n d C4; the combined sizes of circular neighbors weighted by their median annular distances Y_) Sk/dk-The polygon indices were P I ; the sum of the inverse of neighbor distances ^2[l/(l + dj)] and P2; the summed sizes of neighbors weighted by their mean distance n YJ sy/YJ dj = YJ Sj/dj. N N is the nearest neighbor distance. The next two columns show the proportion of variation explained (-R2) and proportion of explained variation attributed to the crowding indices when the number of polygon neigh-borhoods is limited to the set of plants for which circular indices can be calculated. Polygon indices are coded as diamonds; circular indices are coded as dots. The R2 values for the two polygon indices (max: 22.8%) declined as the circular sample radius increased, reflecting the smaller number of neighborhoods. The R2 values for the circular indices (max: 22.1%) at first increased, because circular indices based on the smaller circular neighborhoods per-formed poorly: The proportion of explained variation attributed to crowding was calculated as the ratio of the standard partial regression coefficient for the crowding index over the sum of standard partial regression coefficients for size and crowding: [b'c/(b'c + b's)]. The two 72 r1 Coefficient of Determination Prop, of Explained Variation Attributed to Crowding P1 P2 5.00 4.00 3.00 2.00 1.00 —tt T 1 1 0.40 0.50 0.60 0.70 T 0.10 0.15 0.20 FIGURE 21 Variation in Root Crown Diameter Increment Ex-plained by Regression on Size and Crowding. The proportion of variation explained by multiple regression R2 of size in-crement on size and crowding is shown on the left; the fraction of explained variation attributed to a crowding index (b'c)/(b'c +b'a) is shown on the right. Values are shown for each of seven indices, for sample sizes limited by the circular sample radii ranging from ri of 1.0 to 5.0 cm. The seven indices are, PI: £ ( 1 / ( 1 + ^)), P2: nJ^Sj/Y^dj, CI: £ n f c , C 2 : £ 5 f c , C 3 : £ n f c / d f c , C4: £ s f c / d f c , NN: min(dj). • 73 polygon indices accounted for 60.1 to 66.8% of the variation explained by the regressions. The circular indices did poorly when the neighborhood size was small, but improved as the sample radius grew, accounting for 46.7 to 66.3% variation explained by the regressions. Indices based on the summed size of neighbors, C2 and C4, were marginally better than indices based on the number of neighbors. Discussion Predictions of Plant Performance Based on Indices of Crowding It is unlikely that incongruent circular and polygonal samples will be equally suitable as a basis for interference models in light of their distinct statistical properties. The value of either method ultimately depends on the proportion of variation in plant performance that can be explained by specific models, but some generic predictions can be made by comparing how well the two types of samples fulfill a number of qualitative requirements of neighbor samples identified in previous work. The polygon method does well some things which the circle method does poorly. The Sample Must Permit the Detection of Gaps and Edges The consistently high angular dispersion of polygon neighbors reflects the fact that they always surround the focal individual. Circle neighbors may not, and if they don't, the neighbor distances in the circular sample contain no information about the size of an adjacent gap, a crucial aspect of the local interference environment. Figure 22 illustrates this difference. The gap adjacent to the focal individual in Figures 22a and 22c grows larger in Figures 22b and 22d when two plants near the gap die, or are removed. The circular samples of neighbors, Figures 22a and 22b, do not respond to the change in the size of the adjacent space while the polygon samples, Figures 22c and 22d do. In effect, the circle method fails to see the adjacent open space. The polygon method on the other hand 'detects' the open space because it includes information about neighbors on all sides. Ross and Harper (1972) demonstrated that the size of such gaps strongly affects the growth of seedlings whether the seedlings are near the edge or the center of the openings. The problem created by low 74 Circular Samples * b N N * * K M M • \ * M N * * M M N Polygonal Samples F I G U R E 22 Circular and Polygonal Neighborhoods. The sets of neighbors selected by the two methods are distinct. One important difference is that/circle neighbors do not surround a focal individual on the edge of a gap, and therefore have a low circular variance, whereas polygon neighbors do surround a focal individual and have a high circular variance. Polygon neighbor distances measure the size of gaps. Figures a and b show how the set of circle neigh-bor distances does not reflect the larger gap created when two nearby individuals die. Figures c and d show how the polygon neighbor distances respond to the same change. 75 angular dispersion of neighbors in circular samples cannot be rectified through recourse to any correction because the information required to make such a correction, i.e. the size of the opening, is not available. Circle samples with neighbors on all sides can be obtained provided the sample radius is large enough to substantially include gaps. But increasing the radius also increases the number and variance in number of neighbors (Figures 19a and 19b). Even the modest radius of 0.14 (Figure 19b), which is not large enough to include gaps common in type 5 patterns, leads to samples of more than thirty 'neighbors' for one quarter of all the individuals in type 5 populations. A high proportion of these 'neighbors' are unlikely to have a substantial effect on the focal individual because they stand behind a number of intervening neighbors. Thus there is no guarantee of a suitable tradeoff between a radius too small to detect the extent of open spaces, and one too large to exclude individuals with negligible effects on the focal individual. The Distinction Between Adjacent and Once-Removed Neighbors The neighbors defined by the polygon method are in some sense the nearest plants on all sides, which seems to be a natural definition of neighbors. By contrast, the set of neighbors defined by the circle method lumps together individuals directly adjacent to the focal plant and individuals which stand behind intervening neighbors. Hozumi et al. (1955) and Yoda et al. (1957) have shown that the effects of those two groups are qualitatively different, apparently because 'adjacent neighbors' compete directly, while 'once-removed' neighbors affect each other indirectly through intervening plants. The method of subdividing circular samples into groups of neighbors within concentric annuli (Mack and Harper 1977; Waller 1981; Weiner 1982) goes some distance in accommodating this distinction, but inevitably introduces error because no one set of annuli can separate adjacent from once-removed neighbors in all instances. Figure 23 shows how a set of annuli in such an 'onion' sampling scheme separates the two classes in one case (Figure 23a) and fails to separate them in another (Figure 6b). Polygon samples, on the other hand, have been criticized because they exclude plants beyond a set of adjacent neighbors (Cormack 1979; Silander and Pacala 1985). But there is no intrinsic reason why polygonal samples should not be elaborated to 76 include the effects of once-removed neighbors. Figures 23c and 23d show 'rosebud' samples of concentric polygons. Each set of neighbors beyond the first is found by excluding the inner ones. This method provides an operational definition of adjacent and once-removed neighbors. The degree to which any circular sampling scheme meets the requirements discussed above depends on the choice of a radius. Whether this choice is made in an arbitrary fashion (Mack and Harper 1977; Weiner 1982) or by minimizing the residual sum of squares in a particular model application (Silander and Pacala 1985), indices of crowding based on circular samples depend on a construction which is in no sense intrinsic to the data, and are therefore prone to the familiar problems associated with quadrat size. Elaborations such as concentric annuli and quadrants (Mack and Harper 1977; Waller 1981) compound the number of decisions involved in sampling, and presumably the potential for error as well. In contrast, the neighbors included in polygonal (and rosebud) samples are determined by the spatial pattern of individuals surrounding the focal individual. Circular and Polygonal Indices in Population Dynamic Models A n index of crowding for individual-based population dynamic models (Pacala and Silander 1985; Holsinger and Roughgarden 1985) must be robust to changes in population density and spatial pattern. Circular samples appear to be a poor candidate as a basis for such a description because the information they contain about gaps, the extent to which adjacent and once-removed neighbors can be distinguished, and the number of extraneous individuals designated as neighbors are sensitive to changes in both density and aggregation. Thus, a sample radius chosen to minimize the residual sum of squares (Silander and Pacala 1985) at one time may perform poorly at a later date when the density or patchiness of the population has changed. Polygon samples appear to be a better candidate as a basis for a description of crowding because they respond to important aspects of the local spatial pattern, particularly the size of gaps, and because groups of neighbors which may have qualitatively different effects can be distinguished regardless of the spatial pattern of the population. 77 "Onion" Samples (Concentric Circles) "Rosebud" Samples (Concentric Polygons) F I G U R E 23 Onion and Rosebud Neighborhoods. More elaborate samples of concentric circles, 'onions', or concentric polygons, 'rose-buds', address the need to treat adjacent and once-removed neighbors separately. Figures a and b show that a set of concentric circles which divides adjacent from once-removed neighbors in one circumstance lumps them together in another. Con-centric polygons, in contrast, are defined as sets of nearest neighbors, next nearest neighbors, and so on. Figures c and d show polygons defining the first three sets of polygon neighbors. Only the nearest polygon neighbors are shown as dots. 78 Crowding and Rosette Growth in Diffuse Knapweed Circular crowding indices based on large samples of neighbors and polygonal indices did about equally well in predicting the increment in root crown diameter in the diffuse knapweed. The regressions show that crowding and initial size account for between a fifth and a quarter of the variance in rosette growth rate, and that crowding is roughly twice as important as initial size. As Silander and Pacala (1985) have stressed, the proportion of variation explained by crowding should not be interpreted as a generalized measure of the importance of neighborhood interactions, because the R2 depends on the variance of the crowding index within the population sampled. This variance, within the relatively dense stand sampled, is naturally lower than it would have been if the area of the natural population sampled had spanned the range of possible plant densities by including patch boundaries. However, the purpose was to discover how much of the variation in rosette growth within a dense natural stand was due to the effects of crowding. The relatively low proportion of explained variation implies that some variables not included in this analysis, e.g. plant age, microsite variability and herbivory, will be required to predict the growth rates of diffuse knapweed in natural stands. 79 Chapter IV. The Effect ot Sphenoptera jugoslavica Obenb. (Col. Buprestidae) on Its Host Plant Centaurea diffusa Lam. (Compositae) Abstract The buprestid beetle Sphenoptera jugoslavica is the third insect established in Canada as a potential biological control for diffuse knapweed, Centaurea diffusa. The beetle pop-ulation at the release site in British Columbia was monitored, and experiments were con-ducted to determine the beetle's effects on its host. S. jugoslavica reduces the survivorship of seedlings and rosettes, delays reproduction, and finally reduces seed output. Under favor-able conditions the beetle can contribute to a significant reduction in knapweed population growth. Its effectiveness at the release site is limited by a phenological requirement for arrested plant growth during the oviposition period which leads to large fluctuations in the size of the beetle population, and only intermittent damage to the knapweed population. Introduction Efforts to Control Diffuse Knapweed Diffuse knapweed, Centaurea diffusa, is an invasive composite rangeland weed that has displaced forage grasses over a large area in western Canada (Watson and Renney 1974) and the U.S .A . (Maddox 1979). A biological control is being sought because the alternative methods of cultural and chemical control (with picloram) are both prohibitively expensive, and the herbicide option is environmentally unacceptable on the scale that would be required to control the weed (Harris and Cranston 1979). Two European tephritid flies, Urophora affinis and U. quadrifasciata were introduced to Canada in the early 1970's (Harris 1980a; Harris and Myers 1984), and have spread throughout the knapweed population. Both species attack the developing seed heads of the flowering plants. They cause the abortion of phenologically precedent buds, reduce initiation of succedent buds, and reduce the number of seeds per seed head (Morrison 1986). Their combined effect is greater than the effect of either insect alone because their overlapping phenology of attack increases both the proportion of seedheads attacked, and the number of fly galls per seed head (Myers and Harris 1980; Roze 1981; Morrison 1986). Estimates of the proportion of seeds destroyed by their combined damage range from 80% to 95% (Roze 1981; Harris 1980b; Morrison 1986). 80 Recruitment of diffuse knapweed is limited by very high density-independent seedling mortality (Roze 1981; Schirman 1981; Berube and Myers 1982; Chapter I). The mortality rate of established rosettes however is very low (Roze 1981; Berube and Myers 1982; Chap-ter I). Knapweed population densities should therefore be closely related to the level of recruitment, and Myers and Berube (1983) observed that the densities of seedlings and ma-ture plants were proportional over a broad range of densities. Unfortunately, the significant reduction in seed output caused by the two flies has not produced the desired reduction in knapweed densities (Harris and Myers 1984). The root-feeding buprestid beetle Sphenoptera jugoslavica was introduced to Canada in 1976. One population near Grand Forks, British Columbia failed to become established, but a second at White Lake south of Penticton, B . C . expanded from 188 adults to sev-eral million (Harris and Myers 1984). The beetle has subsequently become established at several secondary release sites in B . C . (Muir pers. comm.), and the western United States (Rosenthal pers. comm.). Zwolfer (1976), who studied the beetle's potential value as a biocontrol agent, observed that Sphenoptera-attacked rosettes in Europe were retarded in their development, particu-larly on xeric sites with poor soil. He suggested that root feeding by the beetle might prolong the rosette stage and facilitate secondary colonization by microorganisms which destroy the roots. Harris and Myers (1984) observed that flowering plants with beetle-damaged roots produced fewer seeds than undamaged plants. This paper describes experiments and obser-vations conducted between 1982 and 1985 to determine the effect of S. jugoslavica on the knapweed population at White Lake, B . C . Life History and Phenology of the Beetle in Relation to its Host Diffuse knapweed is a generally semelparous perennial in which the initiation of flower-ing depends on achieving a critical size (Chapter I). Crowded plants in the near monoculture populations common in the invaded areas of western North America persist in the rosette stage for several years before growing large enough to flower. Very few plants (2% at White Lake) survive the winter after flowering. 81 The beetle's life history has been described by Zwolfer (1976): Adult females lay their eggs between the appressed petioles of knapweed rosette leaves in mid to late summer. Larvae hatch within two weeks, and after their first molt, enter the petioles. Successful penetration by the second instar depends on a period of arrested rosette growth. The eggs and early instar larvae can be crushed or dislodged if the rosette grows. The larvae mine down into the tap root, where they feed during the fall and spring. Only one Sphenoptera larva survives in a rosette root. Supernumary larvae are presumably cannibalized as they are in other mining Coleoptera. In late May or early June the beetle pupates. Adults emerge by chewing their way out of the root, and feed on the leaves of seedlings, rosettes, and flowering plants. Newly emerged females must feed to complete maturation of their ova. The dates of pupation and emergence at White Lake are within the range Zwolfer described for southern European populations of the beetle. In 1983, for example, pupae were first seen on June 1, and about 75% of the population had pupated in a sample collected sixteen days later. Some larvae, however, persisted into late July. The delayed pupation of a proportion of the beetle population likely reflects the heavily skewed distribution of larval weights in the early spring. Very small larvae presumably need much of the summer to complete their growth, and therefore lag behind. The pupal stage is brief. Field collected prepupae, placed in glass vials of moist peat moss, completed their pupation to ecdysis development in 9 days at 20° C. Adults appeared in the roots by mid June, about two weeks after the first pupae, but did not begin to emerge until the first week of July. Most adults emerged within three weeks. The emergence of the adult beetles coincides approximately with the appearance of the first knapweed flowers. Oviposition begins within a week of emergence and lasts ap-proximately one month. The state of the knapweed population during this critical period depends on weather conditions. In dry years the basal (rosette type) leaves of bolted plants are senescent, rosette growth is arrested by the lack of water, and only a small fraction of the seedlings that germinated in the spring survive. In wetter years flowering plants retain their basal leaves well into the oviposition period. Seedlings and rosettes continue to grow. 82 The flowering plants are producing seed when the second instar larvae penetrate the petioles of rosette leaves between mid August and mid September. Thus larvae that attack already flowering plants are too small to retard the growth or reduce the seed production of their host plant. Only larvae that develop in rosettes in the years prior to flowering can cause significant damage. Oviposition Sphenoptera's attack on diffuse knapweed begins when a female places one or more eggs between the petioles of the leaves of a rosette plant or the basal leaves of a flowering plant. The type of plant the female chooses is important. Eggs laid on the small plants which will die even without Sphenoptera feeding are wasted. They neither damage the plant population nor contribute to the beetle population. Similarly, eggs laid on plants that are already flowering will fail to develop because most of these plants die in the winter after setting seed. Early instar larvae cause negligible damage to these plants. It is among those plants large enough to survive, but too small to flower in the current year, that the beetle can potentially complete its development and damage its host. The potential of the beetle to control knapweed depends in the first instance on the number and distribution of eggs on these rosettes. Methods The Distribution of Beetle Eggs in the Field In late August 1982 rosettes were collected at five sites in the White Lake basin by clearing 10 cm squared quadrats of all rosettes until approximately 200 rosettes were ob-tained for each site. I recorded the number of leaves, the angle of the outermost leaves (measured against a protractor), the root crown diameters, and numbers of Sphenoptera eggs and larvae on all rosettes. The density of rosettes was measured for three 50 cm squared quadrats at each location. Less extensive samples were taken in the three following years to compare the densities of beetle eggs between years. Oviposition Preference Tests One female and one male beetle were placed midway between two knapweed rosettes 20 cm apart in screened insectary cages 40 cm x 30 cm x 25 cm in height. The roots of the 83 plants descended into distilled water below the cage floors. I recorded the numbers of eggs laid on the two plants after 24 hours. Five sets of plants were tested to determine whether female beetles actively select the plants most frequently attacked in the field. I Leaf Angle: 20° vs 80° from horizontal. Plants having the same number and length of leaves were paired; angles of the leaves were experimentally altered. II Leaf Number: One plant had twice as many leaves as the other. Pairs of plants were matched for leaf length and angle. A l l pairs had leaf angles of either 40° or 60° from horizontal. III Small Erect Plants vs Large Erect Plants: Plants typical of those apparently avoided in the field, i.e. with three or four leaves at 80° from horizontal, were paired with larger erect plants. The larger plants had eight to ten longer leaves, and the same leaf angle as the smaller plants. IV Flowering Plants Wi th Live Basal Leaves vs Rosettes: Plants were matched with respect to leaf number and angle. V Basal Leaf Senescence: Flowering plants with senescent basal leaves were paired with flowering plants with live basal leaves. Both groups of plants were collected along a moisture gradient at White Lake. The Effect of Temperature on Oviposition Five female and five male beetles were placed in each of sixty leaf cages. The cages consisted of standard 15 mm x 100 mm petri dishes fitted with wire mesh windows for ventillation, and stood on edge. The petioles of the leaves inside the cages descended through small apertures in the cages into jars of distilled water. The leaf cages were divided among four temperature controlled cabinets at 15°, 20°, 25°, and 30° C. I recorded the number of eggs produced and the number and sex of any dead beetles every third day between July 8 and August 8. The leaf material was changed at each check. A t the end of the experiment the treatments for surviving beetles from the highest and lowest temperatures were reversed. 84 Results Oviposition in the Field The sizes and shapes of rosettes that were available to ovipositing females at the five sampling sites within the White Lake basin are shown in Figure 24. Higher density stands consist almost entirely of erect (leaf angle > 75°) rosettes with few leaves, while lower density stands include more prostrate and larger rosettes. Although these samples were collected up to one km apart, density gradients as great or greater than the difference between sites 1 and 5 occur on a scale of a few meters within sites (Chapter I). The beetles, which have been observed to fly at least tens of meters, can therefore move between patches. Figure 25 shows the distribution of beetle eggs with respect to plant size and shape. The shaded areas represent the numbers of rosettes bearing one or more eggs, and the connected dots are the corresponding proportions. At sites with higher plant densities, the proportion of plants with eggs increases with the number of rosette leaves and decreases with leaf angle. This pattern erodes with decreasing density until, at the lowest density site, there is no discernable relationship. Table III summarizes the density data and 3-way log likelihood (G) test of independence (Sokal and Rohlf 1969) for the five sites. The significant association between leaf angle and leaf number reflects the fact that small rosettes tend to be erect even at low plant densities (Figure 24). The association between the presence of eggs and leaf angle could reflect a preference based on number of leaves or vice versa but there may be no active selection of oviposition sites by females (see below). The association could be due to more frequent encounters with larger, flatter plants. The proportion of plants with eggs was lower at sites with higher plant densities (Table III). Oviposition Preferences Beetles in cages showed no preference for prostrate (20°) over erect (80°) plants, and no preference for larger over smaller plants. However, when small erect plants were paired with larger erect plants, the beetles strongly preferred the larger plants. Rosettes and flowering plants with living basal leaves were equally acceptable, but flowering plants with senescent basal leaves received few eggs. These results are summarized in Table IV. 85 s 0 6 0 -4 0 20 c < s o 60 -4 0 -2 0 03 CD 80 -60 -4 0 2 0 2 4 6 Number of L e a v e s F I G U R E 24 The Sizes and Shapes of Rosettes Available to Ovipositing Female Beetles Depend on Knapweed Density. The data are presented as contour plots of the sizes and shapes of rosettes at the five sampling sites. The abscissa is the number of leaves (a measure of plant size); the ordinate is leaf angle (a measure of plant shape). The outer contour encloses the data. Subsequent consecutive contours indicate interpolated frequencies in multiples of three. The more common types (with frequencies greater than 6) are darkly shaded. Densities are listed in Table III, and range from high density at site 1 to low density at site 5. S6 •o o X) CO H OT v> O) O) 0) <D CD c i w o DC X) E 3 2 N 3 5 7 0 11 1] IB umber of L e a v e s ^ A 10 28 40 68 70 as L e a f AngIe w.o 1.0 v.o 1.0 •0.0 1.0 w.o 1.0 F I G U R E 25 The Distribution of Beetle Eggs with Respect to the Size and Shape of Knapweed Rosettes. The histograms show numbers of plants with neither eggs nor larvae (unshaded) and plants with one or more eggs or larvae (shaded). The connected dots are the corresponding pro-portions of plants with beetle eggs or larvae. Densities are listed in Table III, and range from high density at site l td low density at site 5. 87 T A B L E III Contingency Analysis of Beetle Egg Presence, Leaf Angle, and Number of Leaves for Five Sites in the White Lake Basin Site Rosettes per .5m 2 58.0 54.7 39.0 30.3 21.7 (Standard Deviation) (23.4) (18.7) (9.1) (5.0) (4.9) Proportion of Rosettes: In The Highest Angle Class 0.26 0.19 0.00 0.01 0.01 Bearing Eggs 0.31 0.24 0.49 0.40 0.36 Number of Plants in Sample 190 216 214 189 208 3-way G Test of Independence: (Sokal and Rohlf 1969) Hypothesis: Significance Level* Independence of: Leaf Angle x Leaf Number *** *** *** *** *** Beetle Eggs x Leaf Angle *** * * ** n.s. Beetle Eggs x Leaf Number *** n.s. ** * n.s. Interaction n.s. n.s. n.s. n.s. n.s. Three Way Independence *** *** *** *** t n.s.: Not Significant *: < 0.05 **: < 0.01 ***: < 0.001 *** 88 T A B L E IV Oviposition Preference Tests Experiment Treatments Pooled # of Eggs G P 1/ Leaf Angle 20° 26 0.624 n.s. 80° 32 2/ Leaf Number Large (8-16 leaves) 28 1.522 n.s (60°) Small (4-8 leaves) 38 3/ Leaf Number Large (8-12 leaves) 38 17.414 < 0.001 (80°) Small (4-8 leaves) 10 4/ Rosettes vs Rosettes 61 0.311 n.s. Basal Leaves Flowering Plants 55 5/ Basal Leaf Green 107 109.448 < 0.001 Senescence Senescent 7 The Effect of Temperature on Oviposition The mean number of eggs per female per day was estimated as number of eggs pro-duced in the interval, Bx, divided by the number of females alive at x, Nx, divided by the length of the interval (x - x') in days. As preliminary data analysis revealed no trend in oviposition rates over time at any temperature, the data from the ten intervals were com-bined to estimate the oviposition rate at each temperature. A total of only 12 eggs were produced in 4425 female days at the two lower temperatures. The mean ovipositions rates in eggs/female/day were 0.002 (SD=0.018) at 15° and 0.004 (SD=0.019) at 20°. The rate increased with temperature, to 0.631 (SD=0.618) at 25° and 2.606 (SD=2.188) at 30°. The outliers in the data show that the rate can be much higher than these figures. Five females in one cage averaged more than 5.5 eggs/female/day, and individual females laid up to 16 eggs/day at higher daytime temperatures in the insectary. 89 The rate of oviposition responded quickly to reversing the temperature treatments. Beetles from the 30° treatment stopped laying eggs less than six hours after being placed in the 15° incubator. Beetles from the 15° treatment, which had produced virtually no eggs in a month, produced eggs within 12 hours at 30°. Discussion The oviposition preference tests suggest that females will place eggs on any rosette or flowering plant with green basal leaves, but that few eggs are placed on the small, erect plants most common in denser populations. The deficit of eggs on these plants probably does not indicate a true preference for larger plants. Rather, I suggest, the narrow petioles of small plants pose mechanical difficulties for ovipositing females: During oviposition a female must push her abdomen into the axil formed between petioles. Larger petioles are U-shaped in cross section and 3-6 mm in width. As a female pushes her abdomen (3-4 mm in width) downward, the sides of the petiole guide her into the axil. The slender petioles of smaller plants (1-2 mm in width), too narrow to contain the female's abdomen, act in the opposite way, forcing the female out to one side. If this explanation is correct, the females express no active preference for any type of plant. That few eggs are spent on small plants is fortunate, particularly in years of low egg production, because such plants are too small to support a developing beetle (see The Effect of Plant Size on Larval Survival below). The beetle's acceptance of bolted plants with live basal leaves means that a considerable fraction (about a quarter) of eggs are wasted in wet years for that part of the oviposition period when bolted plants retain their basal leaves. Larvae cannot overwinter in these plants because the plants die shortly after flowering. The number of eggs placed on suitable rosettes will be diminished in cold, wet summers both because the beetles produce fewer eggs at low temperatures, and because more of these eggs are wasted on unsuitable flowering plants. If eggs were laid on plants at random at a rate of 0 eggs/female/day, the proportion of plants bearing at least one egg would be p = 1 — e~etf where f is the ratio of adult females to plants. A t White Lake f varied from a low of 0.014 (1/69) in 1984 to a high of 0.167 (1/6) in 1985. Unless beetles concentrate through immigration, it is doubtful that 90 f could ever be much greater than 1/6 because a proportion of plants are too small to support overwintering larvae even in low density sites and because half of the survivors are males. Even with good overwinter survival after a favorable summer (f = 0.167) the beetles need 8 days at 30° C or 24 days at 25° C to saturate 95% of the plant population with eggs. Ground temperatures during poor summers are low enough to limit the number of plants attacked. Conversely, ground level temperatures higher than 30° C may contribute to a more rapid saturation of the host population if oviposition rates are still greater at higher temperatures. The small population of females surviving the poor summer of 1983 saturated the plant population with eggs under favorable conditions the following year. Figure 26 shows that beetles place eggs on all knapweed rosettes during favorable summers, but on only a fraction of rosettes in cool, wet years. Rainfall in July and August of 1982 and 1983 was exceptionally high compared to historical weather data at three times the mean value. The beetle's requirement for fairly high temperatures for oviposition will limit its usefulness as a biocontrol to areas with reliable summer drought. Larval Feeding Sphenoptera larvae feed on the cortex of the root during the autumn and spring. How much damage is done to the vascular tissue of the root, and the extent to which the beetle induces gall formation in its host is currently under investigation (Shorthouse pers. comm.). Larval consumption of the root cortex can kil l small rosettes, and leave survivors vulnerable to secondary colonization by pathogens. The depletion of the cortex, which can be entire, destroys the plant's major carbohydrate reserve, stalls subsequent growth and reduces the eventual production of seeds. Thus larval feeding reduces knapweed survivorship, delays its reproduction, and reduces its fecundity. Since flowering in diffuse knapweed is size-dependent, the duration of the rosette stage and hence the number of years that a plant can be attacked by the beetle, depends on its growth rate. Fast-growing plants are biennial; they can be attacked only once. These plants can escape attack in years when the beetles fail to saturate the plant population with eggs. The majority of plants in crowded monocultures such as the population at White Lake take 91 1.0p to D) LU c o o Q . O t o 1.0c 0 10 20 30 40 50 60 Days With Maximum Temperature > 3 0 ° 6 > 2 5 ° C O o LU c o o a o 20 40 60 Rainfall (mm) 80 100 F I G U R E 26 The Proportion of Rosettes Bearing Beetle Eggs in Relation to Temperature and Rainfall. The first graph plots the proportion of knapweed rosettes with eggs vs the number of days in the July-August oviposition period with maximum temperatures >= 25° C (hexagons), and >= 30° C (circles). The second graph shows the same proportion vs rainfall for the two months. Beetles laid eggs on all rosettes in the hot, dry summers of 1984 and 1985. The two years of 1982 and 1983, when beetles failed to attack all rosettes, were exceptionally cold and wet compared to historical weather data. several years to reach the flowering stage (1987a). Since the beetles lay eggs on all plants in good years, the majority of these slower-growing plants are attacked repeatedly. Not all plants that are attacked are damaged, however because not all rosettes are equally suitable as hosts. The success of the attack can be evaluated both in terms of its effectiveness in damaging the plant and in terms of successful completion of the beetle's life cycle. Methods The Effect of Sphenoptera Root Damage on Rosette Growth Data on the distribution of root damage and its effect on the annual increment in rosette size were gathered as part of an effort to determine the effect of crowding on rosette growth rates (Chapter III). The root crown diameters of 971 rosettes were measured in early May and those that survived the summer were remeasured in late September to obtain a growth estimate. The roots of these plants were examined and assigned to one of four categories; I Not Attacked: The root showed no evidence of larval penetration. II Aborted Attack: The root showed evidence of larval penetration, but insignificant damage. III Previously Damaged: The root was damaged by the beetle. IV Live Larvae: Current occupancy by early instar larvae obscured the previous history of attack despite the relatively small size of the insect. These plants were damaged only for the latter part of the summer. The Effect of Plant Size on Larval Survival The observed distribution of larval damage to knapweed roots could be influenced by, I Oviposition preference: We have seen that smaller plants may escape attack when egg production is low, II Host size-dependent larval mortality, and III The correlation between size and age: Most larger plants are also older plants that have been attacked repeatedly, and thus are more likely to be damaged. It is possible to separate the effect of plant size on larval mortality from the other two causes by studying the distribution of damage among previously undamaged plants in years when all plants bear eggs. A random sample of 200 rosettes taken in late August, 1984 93 contained no plants without Sphenoptera eggs or first instar larvae. To determine the effect of plant size on egg and larval survivorship a second larger random sample (n=763) was collected in early May 1985 prior to bolting of the plants and pupation of the insects. The roots of these plants were examined and assigned to one of four categories; I No evidence of root penetration or damage by Sphenoptera: The lack of any damage indicates egg or early instar mortality before penetration of the root. II Evidence of post-penetration larval mortality: The roots contained evidence of damage caused by Sphenoptera including frass and sometimes the dead larva. III Previous damage: The roots showed evidence of Sphenoptera damage from previous years, but no fresh frass or dead larva. IV Live larvae A third sample (n=200) was collected in July of 1985 after the majority of adults had emerged. The roots of these plants were assigned to one of the first four categories, or to, V Pupal Mortality: The root contained a dead pupa. V I Pre-emergence Adult Mortality: The root contained a dead adult. VII Live Adult . VIII Emerged Adult . The Effect of Sphenoptera Damage on Plant Size and Seed Production Random samples of flowering plants were collected in late summer in 1983 and 1984. In 1983 I recorded the plant dry weights, and the numbers of developed and undeveloped seed heads, seeds, and Urophora larvae for each plant. A developed seed head was operationally defined as any seed head containing either seeds or Urophora larvae. In 1984 I recorded the contents of each seed head to obtain variance estimates for seeds and fly larvae per seed head in addition to the whole plant variables. Mortality of Rosettes Caused by Larvae In late August or September a proportion of rosettes within a fairly narrow size range die while smaller and larger rosettes remain alive. The cortex of the roots of these plants has been almost completely consumed by well developed beetle larvae. In 1984 and 1985 we collected samples of these plants, which are easily distinguished from other dead rosettes 94 by their relatively abundant, but chlorotic leaves. To estimate the proportion of the rosette population affected, I recorded their numbers in quadrat samples. Summer and winter mortality rates were estimated by censusing marked populations of rosettes. .Results The Effect of Sphenoptera Root Damage on Rosette Growth To compare the sizes of damaged and undamaged plants I combined the categories 'not attacked' and 'aborted attack' as 'undamaged' plants, and the categories 'previous attack' and 'larva present' as 'damaged plants'. In the sample of plants that survived the summer (n = 927) half of the plants that bolted (89/179) were damaged. The root crown diameters among damaged flowering plants (x — 0.532, SD = 0.12, n = 89) were not significantly different (Mann-Whitney U : P = 0.377) from undamaged flowering plants (x = 0.535, SD = 0.15, n = 90). Root crown diameters among damaged rosettes were normally distributed with a mean of 0.335 cm (SD — 0.09, n = 293). Undamaged rosettes were significantly skewed with a mean of 0.263 cm (SD = 0.08, n — 455). The size distributions of the two groups of rosettes were statistically distinct (Mann-Whitney U : P < 0.0001). Small rosettes were less often beetle-damaged. The effect of root damage on rosette growth rates is shown in Table V . Annual in-crements in root crown diameter are quite variable in all four categories of root damage. Plants that are previously damaged might be expected to grow at a slower rate than un-damaged plants ('not attacked' and 'aborted attack') and plants currently containing larvae because the majority of these were not previously attacked and the larvae they contain in September are still small. Overall, however, there is no clear difference between previously damaged plants and the rest. The mean relative growth rates of previously damaged plants are noticeably lower, but this is at least in part a reflection of their larger average size. A n interesting pattern is revealed when the annual increments are compared within size classes (Table VI) . Previously damaged plants grow more slowly than undamaged plants of the same size, except in the largest size class where the rates are comparable. A l l that is known about previously damaged plants is that their roots were damaged by Sphenoptera at least one year prior to the year in which they are observed, and that they were not subsequently 95 occupied. It is therefore not possible to discern between two plausible explanations for the relative differences in annual increment of damaged and undamaged plants related to size, I The larger rosettes are older plants which were damaged when small, and have recov-ered, and II The larger plants were damaged recently, but are not as severely affected as are the smaller plants. Measurements of annual increments of damaged plants of known history will be required to settle this point. T A B L E V The Effect of Root Damage on Rosette Growth Damage Category Initial Size Increment Mean r.g.r. n X S.D. x S.D. X S.D. Not Attacked 300 0.263 (0.068) 0.040 (0.034) 0.139 (0.106) Larva Present 553 0.300 (0.085) 0.053 (0.042) 0.156 (0.107) Aborted Attack 155 0.322 (0.086) 0.058 (0.040) 0.168 (0.109) Previously Damaged 26 0.390 (0.106) 0.045 (0.054) 0.100 (0.105) T A B L E V I Growth as a Function of Size and Root Damage Size Class (cm) Mean Increment % Mann P Previously Reduction Whitney Undamaged Damaged 0.0 to 0.2 0.034 0.020 41.2 — — 0.21 to 0.3 0.041 0.017 58.5 129527 < 0.05 0.31 to 0.4 0.063 0.039 38.1 38451 < 0.05 0.41 — 0.077 0.067 13.0 5880 n.s. 96 Another important question is whether knapweed alters its critical size of flowering when damaged. To test the hypothesis I calculated expected frequencies of rosettes and bolted plants based on the observed size of 0.45 cm at the midpoint of the transition from rosettes to flowering plants (Chapter I). The results shown in Table VII reject the hypothesis; critical size is apparently not affected by root damage. T A B L E VII The Effect of Root Damage on the Bolting Size Damage Category Rosettes Flowering Plants Gt P Not Attacked Observed 300 49 0.398 n.s. Expected 304 45 Larva Present Observed 554 100 2.461 n.s. Expected 539 115 Aborted Attack Observed 155 41 0.030 n.s. Expected 154 42 Previously Damaged Observed 33 26 0.069 n.s. Expected 34 25 f Log Likelihood Ratio Test (Sokal and Rohlf 1969) The Effect of Plant Size on Larval Survival Previously damaged plants made up 14.2% of the total. The actual percentage may be somewhat higher because current larval occupancy can obscure evidence of a previous attack. The fairly low percentage of previously damaged plants is likely due to the very poor oviposition in the cool summer of 1983. The predominance of large plants among previously damaged plants could indicate oviposition preference for larger plants, plant size-dependent larval survival, or merely a correlation between age and size, since, to be previously damaged, a rosette would have to be at least three years old (i.e. seedling in 82, rosette (attacked) 83, rosette (not damaged again) 84, observed 85). Among plants which showed no evidence of previous damage, 38.3% escaped dam-age, 30.9% were damaged by larvae which did not survive, and an equal number (30.8%) 97 were damaged by surviving larvae. The size distributions of the three groups were dis-tinct (Kruskal-Wallace /J a dj(2) = 106.8, P < 0.001). Undamaged plants were smaller (x = 0.365cm) than damaged plants without larvae (x = 0.425cm), which in turn were smaller than damaged plants with live larvae (x = 0.489cm). Figure 27 plots the observed propor-tions of the three groups in each size class. Closed circles are the proportions of damaged plants with surviving larvae; open circles are the proportions of damaged plants. Curves were drawn by non-linear smoothing (Tukey 1977). Egg, or first and second larval instar mortality (unshaded region) can occur at all plant sizes, but is much more frequent in smaller plants. The proportion of plants damaged (shaded region) rises from near zero for plants with 0.2 cm root crown diameters to about 80% at 0.6 cm, while the proportion of plants bearing live larvae (darkly shaded region) rises to about 45%. Pupal and pre-emergence adult mortality was rare. Only 2 dead pupa and no dead adults were found in the sample of 200 plants in the late summer compared with 57 roots with evidence of emerged adults and 3 roots still containing live adults. Thus more than 95% of beetles which pupate emerge as adults. The Effect of Sphenoptera Damage On Plant Size and Seed Production Since the distributions of root crown diameters in flowering plants with and with-out 5p/ieno»£era-damaged roots are comparable, and damaged flowering plants are neither more nor less crowded than undamaged plants, any differences between damaged and un-damaged plants can be attributed to the effects of larval feeding. Table VIII summarizes the effects. The upper part of the table, which deals with whole plant variables, shows that root-damaged plants weighed less, initiated fewer seed heads, developed fewer seed heads, and produced fewer seeds per plant than undamaged plants with comparable root crown diameters. The reduction in seed heads per plant agrees well with data for 1979 and 1980 (Harris and Myers 1984). Sphenoptera-damaged plants produced 58.76% fewer seeds than undamaged plants in 1983, and 38.16% fewer in 1984. The developed seed heads of damaged and undamaged plants contained similar numbers of seeds, on average slightly less than five, and similar numbers of larvae of both Urophora species. 98 o Root Crown Diameter (mm) F I G U R E 27 Beetle Survivorship and Root Damage as a Function of Rosette Size. The shaded region indicates the proportion of attacked plants that are dam-aged by Sphenoptera. The darkly shaded region indicates the proportion of plants in which the beetle survives to maturity. 99 T A B L E VIII The Effect of Sphenoptera Attack On Plant Size And Seed Production Damaged Undamaged mean (SD) mean (SD) t (d.f.)t P Whole Plant Variables: 1983 n=34 n=29 Weight (g) 1.98 (1.30) 3.14 (1.75) 2.95 (51) < 0.01 Total Seed Heads 54.79 (45.08) 91.00 (55.58) 2.81 (53) < 0.01 Developed Seed Heads 23.50 (16.17) 42.86 (22.58) 3.85 (49) < 0.01 Seeds 43.94 (40.88) 106.55 (113.89) 2.81 (34) < 0.01 1984 n=38 n=61 Total Seed Heads 28.79 (17.79) 48.15 (35.36) 3.60 (93) < 0.01 Developed Seed Heads 17.11 (10.14) 27.67 (19.55) 3.53 (94) < 0.01 Seeds 75.42 (62.48) 132.71 (117.43) 3.16 (95) < 0.01 Seed Head Contents: 1984 n=668 n=1728 Seeds 4.67 (5.33) 4.95 (4.26) 1.21 (1013) n.s. U. quadrifasciata 0.199 (0.523) 0.197 (0.512) 0.07 (1189) n.s. U. affinis 0.725 (1.164) 0.665 (1.023) 1.15 (1087) n.s. * Degrees of freedom have been reduced to compensate for unequal variances (Zar 1974). Mortality of Rosettes Caused by Larvae Table IX summarizes the observations on rosette mortality. Summer mortality (April to September) was the greatest, and of the roots which could be unambiguously assigned, almost all were beetle-damaged. Very few rosettes died during the winter. Rosettes within a narrow range of root crown diameters were killed by beetle larvae in late September (Table X ) . 100 T A B L E IX Effects of Larvae on Rosette Mortality Season Year Proportion Proportion of Rosettes of Dying Rosettes Dying Damaged* Autumn 1984 0.020 (11/538) 1.000 (50/50)* 1985 0.053 (26/477) 1.000 (50/50) Winter 1982- 1983 0.004 (1/250) N . A . 1983- 1984 0.000 (0/250) N . A . 1984- 1985 0.012 (3/250) N . A . Summer 1984 0.116 (58/500) 0.913 (21/23) 1985 0.159 (176/1108) 0.946 (87/92) T A B L E X Root Crown Diameters of Rosettes Killed By Larvae in Autumn Compared to Root Crown Diameters of Survivors Year Mortalities Survivors x (S.D.) n x (S.D.) n 1984 0.271 (0.030) 50 0.329 (0.089) 50 1985 0.275 (0.030) 50 0.385 (0.123) 50 ' The sample size is smaller than the total number of deaths in some cases because only-deaths which could be unambiguously assigned to the Sphenoptera-damaged or undamaged categories were included. The roots of some marked plants which died in winter and summer were too decayed to assign them with any confidence. * Estimates based on samples of apparently affected (chlorotic) rosettes. 101 Discussion The pattern of beetle damage with respect to plant size is apparently attributable to several factors. Rosette growth rates observed in dense near-monoculture populations (Chapter III) extend the duration of the vegetative phase to several years. Thus older, larger plants are more likely to have been damaged. Larger plants are also disproportionately attacked in years of low egg production. The observed plant size-dependent larval survival reinforces the same pattern; the probabilities of penetrating the root, and surviving to maturity both increase with the size of the rosette host. The proportion of plants that are damaged prior to flowering at White Lake has risen since the beetles introduction in 1976 and may have plateaued at about 6 0 % (Figure 28) . Thus the significant reduction in seed output due to the beetle is diminished because many plants escape damage during years of low beetle population. The beetle may therefore be more valuable as a biocontrol at sites with more consistent summer droughts than White Lake. The rosettes that are killed directly by larval damage are apparently large enough to permit the development of large larvae, but too small to sustain them when they grow large in the late summer. Rosettes, restricted by drought, may be unable to produce sufficient gall tissue to prevent the beetle from entirely consuming the cortex. Then both insect and host perish. Direct mortality of rosettes as a consequence of larval depletion of the root cortex was not observed prior to 1984. One explanation is that I overlooked the phenomenon. Another explanation is that this type of mortality occurs only in years when late summer temperatures promote rapid larval growth. In cooler years, such as 1983 , larvae are much smaller in September, and therefore must complete most of their growth the following spring when growing rosettes can presumably produce enough gall tissue to feed the beetle. The majority of rosette mortality occurs during the summer when competitive interactions between neighboring plants may be involved. The fact that the majority of rosettes dying at this time are beetle-damaged suggests that these plants may succumb in part because they are damaged. 102 1976 1980 1984 1988 Year F I G U R E 28 The Proportion of Flowering Plants at White Lake with Beetle-Damaged Roots Between 1977 and 1987. (Data from 1977-1981, and 1986-1987, J .H . Myers unpub.). The proportion of flowering plants damaged by the beetle has grown since its introduction. Notable setbacks followed the wet, cool summers of 1982, and 1983. 103 Adult Feeding Adult beetles feed on knapweed seedlings, rosettes, and flowering plants throughout the summer months. Zwolfer (1976), noting that the feeding marks left by adults on the margins of rosette leaves were only 2 to 5 mm in length and 1 to 2 mm in depth, concluded that adult feeding must have an insignificant effect on rosettes. But could adult feeding increase seedling mortality during the summer drought when a large proportion of seedlings succumb even without the added stress of herbivory (Schirman 1981; Roze 1981)? If so, it may be partly responsible for the observed shortfall in knapweed recruitment at White Lake (Chapter I). In July, when the adult beetles begin to feed on leaves, 85% of the spring cohort of seedlings have already died. The survivors typically have two slender erect leaves with a combined leaf area of slightly less than 1 cm 2 ; the seed leaves are senescent. A t White Lake, with July seedling densities slightly less than 20 per m 2 , the total seedling leaf area is therefore less than 20 c m 2 / m 2 , an area which could be consumed by a low density beetle population feeding at a very modest rate. But seedlings account for an insignificant proportion of the available leaf area: Rosettes and flowering plants at White Lake have a mid July leaf area index (LAI) of 8,700 to 15,000 c m 2 / m 2 , depending both on local density and annual precipitation. If seedlings are not actively preferred by beetles, or disproportionately attacked for some other reason, the proportion of seedlings suffering significant feeding damage will be small, and the effect of adult feeding on seedling mortality will be insignificant. I therefore observed the defoliation rates and leaf preferences of adult beetles in laboratory experiments, and the mortality rates of seedlings in response to drought and defoliation by Sphenoptera adults. Methods Feeding Preference Tests Adult beetles in petri dish cages were presented with the tips of rosette and seedling leaves sandwiched between microscope slides to expose identical leaf areas and perimeters. A single beetle was placed in each cage for 8 hours at 30° C. Leaf areas were then measured 104 and scored as 'preferred' or 'unpreferred' according to their relative sizes. Three tests were conducted, using 40 beetles in each case: I Leaf Condition: The slightly chlorotic outer leaves of mature rosettes were paired with adjacent nonchlorotic leaves from the same plant. II Leaf Age: Recently expanded rosette leaves were paired with older leaves from the same plant. I l l Seedling vs Rosette Leaves: The first mature leaves of seedlings were paired with recently expanded rosette leaves. The Effect of Temperature on Adult Feeding Rate Leaf area loss was measured over 48 hours by repeated leaf area measurements with a L I - C O R LI-3000 leaf area meter. Flat rosette leaves, chosen to minimize leaf area mea-surement error, were placed in petri dish cages. Each cage contained three leaves with a combined initial leaf area of approximately 20 c m 2 . Petioles were placed in a water bath 24 hours prior to the experiment to fully engorge the leaf tissue. This pretreatment was necessary to avoid leaf area gain in the controls. Ten adult beetles were placed in each of twenty cages divided among four temperature treatments; 15°, 20°, 25°, and 30° C. A n equal number of cages with knapweed leaves, but no beetles, served as controls. Seedling Mortality in Response to Drought and Herbivory Knapweed seeds were sown and germinated in sixteen 1 m 2 quadrats arranged in a 4 x 4 grid with 1.5 m alleys between quadrats. As the seedlings began to produce mature leaves, they were thinned to 300 seedlings/m 2. Each quadrat was assigned to one of four treatments consisting of supplementary water (+/—) and herbivory by adult beetles (+/—) arranged in a latin square. Watered quadrats received approximately 5 litres every other day. Unwatered quadrats received only 0.3 mm of rainfall, which fell on the 12th day of the experiment. Eight beetles were placed in each of the -f-beetle treatments. After one month the numbers of surviving seedlings were counted. 105 Results Adult Feeding Preferences Table X I shows the results of the feeding preference trials. There is no evidence of a preference for seedlings over rosettes, or for newly opened leaves over mature leaves. Chlorotic leaves, however, are avoided. T A B L E X I Adult Feeding Preference Tests Experiment Treatments Frequencies G P 1 / Leaf Age Newer 18 0.40 n.s. Older 22 2/ Leaf Condition Chlorotic 2 39.57 < 0.001 Non-chlorotic 38 3/ Leaf Type Seedling 24 1.61 n.s. Rosette 16 Tie Effect of Temperature on Adult Feeding Rate The feeding rates expressed as cm2/adult/day were 2.24 (SD=0.58) at 15°, 2.05 (SD=0.78) at 20°, 8.19 (SD=1.48) at 25° and 16.82 (SD=0.62) at 30°, the highest temper-ature in this experiment. Seedling Mortality in Response to Drought and Herbivory A n analysis of variance for the seedling mortality experiment is presented in Table XII . Treatments were not affected by their spatial arrangement in the latin square, so the precau-tion of the arrangement was unnecessary. Orthogonal comparisons of treatments show the obvious overwhelming importance of precipitation in determining seedling mortality. The remaining two comparisons show that beetle feeding has no significant effect on seedling mortality when water is plentiful, but does have a significant affect when water is scarce. 106 TABLE XII Seedling Survival in Response to Drought and Herbivory N=300 Precipitation Present Precipitation Absent Beetles Present 275.25 (8.66) 42.50 (3.70) Beetles Absent 273.00 (11.05) 58.50 (6.95) Entries are the means and standard deviations of the numbers of surviving seedlings. Analysis of Variance Source of Variation df SS MS F P Rows 3 309.56 34.42 0.87 n.s Columns 3 229.26 76.42 1.92 n.s. Treatments 3 200554.70 66851.57 1685.62 n.s E20(+/-) 1 200032.60 200032.60 5043.69 < 0.05 H20 + (Beetle + /-•) 1 10.13 10.13 0.26 n.s. H20 - (Beetle + /-0 1 512.00 512.00 12.91 < 0.05 Error 6 237.94 39.66 Total 15 201331.40 Discussion How much damage can adult feeding on foliage do? Leaves growing at a leaf area-specific rate g — (1/L * dL/dt) consumed by beetles at a rate ft = (1/6 * dL/dt) have a net leaf area-specific growth rate of / = g — (b/L)h assuming there is no compensatory growth. The ratio b/L can be calculated as the product of the number of beetles per plant and the inverse of mean leaf area per plant (or as the product of beetle density and the inverse of the leaf area index, Watson 1947). Barring immigration, the number of adult beetles per plant cannot be greater than one, because only one beetle can develop in each rosette root, and will generally be less because some rosettes are too 107 small to support a developing larva. Following years of low egg production or high larval mortality, the number of adult beetles per plant is considerably less than one. It ranged from 0.029 to 0.366 at White Lake between 1982 and 1985. The mean leaf area per plant in early July, when the adult beetle population is at its peak, varied from 44.7 (SD=29.8) to 57.8 (SD=27.7). Thus, when rosettes stop growing under drought conditions (g=0), adult feeding at the observed rates can reduce leaf area by as little as 0.8% or as much as 13.7% per day at 30° C. Even at the most modest rate the beetles could completely defoliate the seedling population, which typically accounts for a fraction of 1% of the total leaf area, in less than one day, if seedling leaves were taken before rosette leaves. Unfortunately, there is no evidence that Sphenoptera adults actively select seedling leaves when both seedling and rosette leaves are presented, and no evidence for any behavior which might concentrate adults near seedlings, leading to higher than expected seedling defoliation in the absence of an active preference. Sphenoptera adults typically consume less than 0.25 cm 2 of any leaf before moving away. Seedlings can sustain much greater damage without mortality, unless they are otherwise stressed. Discussion and Conclusions The several effects of Sphenoptera jugoslavica observed by Zwolfer (1976), Harris and Myers (1984), and the current study make it unlike the two other insect herbivores imported to control diffuse knapweed in Canada because the gall flies alter only one of three variables which determine the rate of knapweed population growth (i.e. seed output), whereas the beetle reduces the survivorship of seedlings and small rosettes, delays flowering, and reduces seed output. Reduction in seed output has often been reported as a measure of the impact of insect herbivores because it is straightforward to measure and, for species such as the two Urophoras, it is also the most important measure of damage. Unfortunately knowing the magnitude of seed reduction does not allow us to predict a herbivore's effect on its host's population dynamics (Myers et al. in prep.) For that purpose, which is the sensible goal .of a biological control study, we require a demographic model of the plant population. The need is all the more apparent when herbivory affects a plant's survivorship, reproductive 108 schedule and seed output; the magnitude of these effects can only be compared when they are expressed in the common currency of population growth rates. A simple and general demographic model for that purpose can be constructed because both the reproductive and mortality schedules of diffuse knapweed are highly size-dependent (Chapter I). In semelparous perennials in general and diffuse knapweed in particular the proportion of plants that flower at any age, fx, is determined by the proportion of rosettes that exceed a critical size in the previous year (Chapter I, Chapter II). Thus the duration of the prere-productive rosette stage depends on how fast a rosette grows. Naturally, growth rates will vary between individuals, between sites, and between years. A t White Lake the distribution of annual size increments was adequately described by the fairly flexible gamma distribution (Powell unpub. obs.). Since the time, t, required to reach a critical size is roughly the ratio of that size to the annual increment, it is reasonable to assume that the distribution of t can also be described by a gamma distribution. The proportion flowering at age x is then, fx = P{x - 1 < t < x} = Ir([x]9) - Ir([x - 1]0); x = (1 ,2 , . . . , n) where Ir is the incomplete gamma function with parameters 0 and r, and n is an age greater than the maximum lifespan. The distribution of flowering times strongly affects both age specific fertility and survival rates. Age specific fertility is mx = sxfx, where sx is the number of seeds produced by a flowering plant aged x. In semelparous perennials sx should decline slightly with age because faster growing plants can overshoot the critical size by a greater margin (Chapter III). This effect is most dramatic among the fast growing survivors released from competition by herbicide application (Myers and Powell unpub.) but in undisturbed populations the large year to year variation in seed output correlated with rainfall (Morrison 1986) overwhelms the expected differences. The simplest provisional assumption is therefore that seed output is not affected by age, ie. mx = sfx. Mortality can be divided into pre- and postreproductive components. Prereproduc-tive mortality in knapweed is concave (Deevey type III). A t White Lake seed mortality of about 90% followed by seedling mortality of 85% combine for a first year mortality rate 109 of approximately 5 0 — 0.985, while subsequent rosette mortality was less than 0.20 per year, and declined to less than 0.01 for larger rosettes (Chapter I). A t the observed mean growth rate this corresponds to an approximate halving of the mortality rate per year, ie qx = 0.2(0.5a;-1). Only about 2% of flowering plants survive the winter, and of these about half produce a small number of seeds. If we assume for simplicity that all plants that flower die immediately afterward then the proportion of plants dying as a result of reproduction is fx. The number of individuals surviving to age x is then the number alive at the beginning of the forgoing interval multiplied by the probability of neither dying without reproducing nor flowering; lx - k - i ( l - 9x-i)(l - fx-i)',x = ( l ,2 , . . . ,n) . The age specific survival and fertility rates can then be combined with Euler's equation to calculate rates of population increase reflecting changes in the plant population's demo-graphic parameters due to biocontrol agents. Table XIII summarizes the anticipated effects of U. affinis, U. quadrifasciata and S. jugoslavica and shows how these effects are mediated by the duration of the rosette stage. It should be emphasized that because the fx curves have been assumed rather than measured, the entries in the table are not meant to reflect the particular population at White Lake. The calculated rates are, however, of the appropriate magnitude because the parameters used to calculate them span the range which we know from observation and experiment to be realistic. Furthermore, the relative magnitudes of the rates are quite robust to the assumption of a nonstandard gamma distribution parameter 9; the differences are less than those expected between years as a consequence of seasonal differences in growth conditions. Prior to the establishment of the two tephritid flies, Watson and Renney (1974) mea-sured a mean seed output of 925 for diffuse knapweed under range conditions. Assuming present survivorship patterns and modest plant growth rates (J = 3) a population could triple annually, and even under poor conditions (t = 5) could nearly double. The estimated twelve fold increase under good conditions is likely conservative; Watson and Renney's es-timate of seed production for plants grown on irrigated plots was greater than 18,000. It is not surprising that diffuse knapweed is an invasive weed in the absence of insect herbivores. 110 T A B L E XIII Modelled Effects of Insects on Knapweed Rates of Increase Insect Species Effect Assumptions Mean Time to Critical Size (Years i = 1 i = 3 0 t = 5 None — s = 925* go = 0.980 qx = O^O.l - 1 ) 11.80 2.96 1.76 U. affinis and U. quadrifasciata Reduced Seed Output s = 124.3* 1.69 1.12 1.05 Urophora spp. and S. jugloslavica 0.40 0.60 Proportion Damaged by Sphenoptera 0.80 0.40 0.60 0.80 0.40 0.60 0.80 Reduced Seed Output s = 60.6* 1.37 1.22 1.06 1.02 0.97 0.92 0.99 0.97 0.94 Rosette Mortality qx = 0.2(0.2*"1) q, = O^O.S*"1) 1.37 1.37 1.22 1.22 1.06 1.06 1.01 0.99 0.97 0.95 0.92 0.90 0.99 0.97 0.97 0.95 0.94 0.92 Seedling Mortality go = 0.985 go = 0.990 1.07 0.78 0.95 0.70 0.84 0.63 0.93 0.82 0.88 0.78 0.84 0.75 0.94 0.87 0.91 0.85 0.89 0.82 Flowering Delay 30% 40% 1.07 0.97 0.96 0.87 0.86 0.78 0.94 0.91 0.90 0.87 0.86 0.84 0.95 0.93 0.92 0.91 0.90 0.88 * Seed production per plant (Watson and Renney 1974). * Weighted mean seed output for Sphenoptera undamaged flowering plants in 1984 and 1985 (Table VIII). * Weighted mean seed output for Sphenoptera damaged flowering plants in 1984 and 1985 (Table VIII). The current mean seed output of plants which are attacked only by the tephritid flies, s = 124.3, is a reduction of more than 86%. Nevertheless, the calculated finite rates are greater than unity, and thus sufficient to maintain knapweed population densities, which agrees with the empirical evidence (Harris and Myers 1984). The mean seed output of plants which are also damaged by the beetle, s = 60.6, represents a further 50% drop, but not all plants are damaged. The proportion of flowering plants damaged at White Lake has grown steadily since the beetle's introduction to a present level of about 60% (Figure 28). While the further reduction in seed output caused by the beetle leads to some estimated finite rates slightly less than unity, the margin of uncertainty in these tentative calculations warrants caution. The 1983 mean seed output of s = 43.9 (Table VIII) would suggest a population decline; the 1984 mean 5 = 75.4 would suggest an increase. Furthermore, a decline of a few percent would be difficult to detect against the background of year to year variation in growth conditions and seed output. I conclude that the beetle's reduction of seed output alone will not reduce knapweed densities. Rosette mortality is largely due to beetle root damage (Table IX) but, only a small fraction of rosettes die annually. Increasing the annual decrement in the rosette mortal-ity rate to 50% to reflect beetle inflicted rosette mortality has a minimal impact on the calculated finite rates, particularly for fast-growing populations where biennials dominate. Seedling mortality, on the other hand, has a large effect. The estimated q0 at White Lake is approximately 1.0 — (0.10)(0.15) = 0.985, where the multiplied terms are the pro-portion of seeds that result in spring seedlings and the proportion of seedlings surviving. If beetles are responsible for 25% of seedling mortality, as they were in the seedling mor-tality experiment (Table XII), the pre-beetle q0 would be 1.0 - (.10)(0.20) = 0.98, which we have assumed. Since it is not clear that the results of this experiment will hold under field conditions, it is worth recalculating the finite rates for the fly species alone assuming that the beetle is not responsible for any seedling mortality (i.e. qo = 0.985). The rates corresponding to t — 1,2, and 3 respectively are 1.30, 1.00 and 0.99. So the conclusion that the flies alone should not reduce plant density is not affected. The entries in the table assume low rosette mortality (qx — 0.2(0.1 a : _ 1)) and are therefore conservatively high. Still , 112 the model predicts an approximate 10% annual reduction in density when qo = 0.985. A change of this magnitude should be detectable. The delay in flowering implied by the smaller size increments of damaged rosettes (Table VI) and an unchanged size threshold for flowering (Table VII) will also reduce population growth rates. Unfortunately, the length of this delay is presently unknown. To measure it will require a means of detecting root damage in in situ rosettes. The entries in the table were calculated by adjusting the parameter 9 on the provisional assumption that the delay is roughly proportional to the observed reductions in growth rates (Table VI) . To be conservative, neither seedling nor rosette mortality increases are included in the estimated rates (i.e. q0 = 0.980; qs = 0 .2 (0 . l x _ 1 ) ) . On the basis of these rough calculations we can tentatively conclude that the three bio-control insects have reduced the finite rate of increase of diffuse knapweed to the breakeven point or slightly beyond, but that no dramatic reduction in knapweed density can be an-ticipated. A t best, we can expect an annual reduction of about 10%, although this may decrease with compensatory density dependent responses of the plant population which are not included in these calculations. Among the compensatory responses I anticipate are lower seedling mortality rates, faster rosette growth rates leading to earlier flowering, and greater fecundity (Myers and Powell unpub.; Chapter I). The knapweed population at White Lake appears to be declining at about the expected rate as seedling recruitment fails to keep pace with pre- and post-reproductive mortality (Chapter I), but with the limited number of years of seedling recruitment data, the possibility that present densities will be maintained by occasional years of exceptional recruitment cannot be ruled out. 113 Conclusion In the introduction to this thesis I expressed the opinion that a greater understanding of the mechanisms that determine the size and stability of plant populations is required before we can understand why some biocontrol insects reduce plant densities while others do not. This assertion is based on two observations: firstly, that some plant populations sustain very high levels of insect damage with little or no decline in their densitites (Myers et al. in prep), and secondly, that plant populations that are depressed by phytophagous insects may recover (Lawton 1985). Our inability to predict either the level of host depression or the stability of the interactions between insect and plant populations based on the level of insect damage is due to our lack of understanding of how plant populations compensate. The large populations of the two flies Urophora affinis and U. quadrifasciata reduce diffuse knapweed seed production by 80% to 95% (Harris 1980b; Rose 1981; Morrison 1986). The beetle Sphenoptera jugoslavica further reduces seed production by 40% to 65% in the plants it attacks. It also reduces rosette growth rates which prolongs the rosette stage, and it kills some seedlings and rosettes. Despite large fluctuations in the size of the beetle population due to its vulnerability to weather conditions during oviposition and early larval development (Zwolfer 1976), the proportion of flowering plants that are damaged by the beetle has grown steadily toward its present range of between 70% and 90%. There is ample evidence that the three biological control insects have inflicted considerable damage. Nevertheless, there is no clear indication of a decline in knapweed densities at the White Lake release site (Myers et al. in prep.). A controversial question that current plant-herbivore theory cannot adequately address is whether insects that damage their hosts without reducing their densities are likely to contribute to the eventual control of their hosts. Harris (1984b) believes they are. He has argued that the practice of rating the success of individual agents according to their impact on the densities of their hosts (e.g. Laing and Hamai 1976) is misleading because insects that cause significant damage, but do not reduce plant density, may reduce density in concert with future introductions. Evidence for a cumulative effect of damage caused 114 by two or more insects is abundant (e.g. Myers and Harris 1980); evidence that two or more insects are needed to reduce plant population density is harder to find (Myers 1985; cf. McEvoy et al. in press). Harris (1984b) has suggested that the cumulative damage caused by successive insect introductions pushes a weed population toward a threshold level of consumption of its annual production which cannot be sustained. His analogy with grazing pressure models clearly applies where insect damage can be summarized as a fractional reduction of a single variable measuring plant productivity (e.g. number of plant parts, biomass, or leaf area). The damage threshold for yield vs defoliation in many crops (e.g. Guene and Minnick 1967) is a good example. In other cases, the effects of damage inflicted by insects cannot be condensed into a measure of annual productivity. The effects of insect feeding may depend as much on the phenology of attack, and the quality of plant tissue destroyed, as on its quantity. Sackston (1959) showed, for example, that removing the older 50% of sunflower leaves reduced seed production by 14% whereas removing the younger 50% reduced seed output by 52%. Insects that damage critical vascular tissue, or expose their hosts to subsequent attack by pathogens (Robinson 1962) have effects out of proportion to the amount of tissue damaged. A n alternative approach is to measure the effects of insect herbivory on recruitment and mortality rates that determine a plant population's growth rate. This 'phytocentric' perspective emphasizes that weed populations are not passive victims of insect attack. Their flexible life histories have evolved to compensate for less than optimal conditions, including insect damage (Harper 1977). From the perspective of the plant, the number of species of herbivores is irrelevant. What matters is the type and severity of damage, where it is sustained, and when. Thus the problem of controlling weeds is not so much one of matching insect agents with plants as of matching damage with stages of the plant's life history where it is least able to compensate. The compensatory density-dependent responses of diffuse knapweed are, I increased seedling survival rate II increased rosette survival rate 115 III increased rosette growth rate, which results in IV a higher proportion of established plants flowering, and V a higher number of seeds per plant. S. jugoslavica adults eat seedling leaves, but the rate of consumption is apparently too low in relation to the rate of seedling growth to limit seedling recruitment. Larval damage is found in the majority of dying rosettes, but the fact that most of the dead rosettes are unexpectedly close to other established plants suggests that beetle damage weakens those rosettes already stressed by interference. As density declines, and nearest neighbour distances increase, the proportion of rosettes that succumb in this manner will also decline from its present low level. The beetle will not therefore be effective in countering a compensatory increase in rosette survival. The three remaining compensatory responses of diffuse knapweed increase the seed production per area by advancing the age of reproduction and increasing the seed production per plant. In the initial stages of a decline from high plant densities, the compensatory increase in plant growth rates should make a greater fraction of the rosette population large enough to be vulnerable to Sphenoptera attack. The effects of larval damage, slower rosette growth rates, delayed flowering and reduced seed production, should directly counter the compensatory responses of the plant population. At still lower densities, however, the majority of plants will grow quickly enough to flower as biennials. The proportion of plants that are successfully attacked under these circumstances is lower because the rosettes of biennials are only vulnerable for one year, and because the rate of pre-penetration larval mortality is greater on these fast growing rosettes (Myers and Powell in prep.). Thus Sphenoptera cannot curtail the increased growth rates, advanced reproduction and higher seed production of knapweed at lower densities. The tephritid flies have no effect on seedling and rosette survival rates, rosette growth rates or the proportion of plants that flower. Their only effect is on seed production. Since the proportion of seeds destroyed by the flies does not increase with plant size, their damage does not impede compensatory seed production. 116 Implications for the Biological Control of Semelparous Perennials The limited repertoire of compensatory responses of diffuse knapweed is likely shared with other semelparous perennials, but not with annuals and iteroparous perennials since the age of flowering in those groups is not mediated by a critical size (Lacey 1986). Is it possible then to develop a generic prescription for the biological control of semelparous perennials? M y answer to this question has several parts. The mathematics of population growth show that a negative rm will occur when In lxmx is negative. Two ways of forcing a decline in plant density are therefore to reduce survivor-ship and to reduce fecundity. We know, however, that seedling survival, rosette survival and growth, the proportion of plants flowering, and the number of seeds produced per flowering plant increase as density declines. We must therefore anticipate that density will decline to a lower equilibrium in the presence of insect damage, unless that damage also increases at lower plant densities. The high seed output of diffuse knapweed in particular (Watson and Renney 1974; My-ers and Powell in prep) and semelparous perennials in general (Salisbury 1942) is apparently an adaptation to cope with the considerable uncertainty of the ruderal habit (Grime 1977; Gross 1981). When an exotic semelparous perennial succeeds in dominating a native flora, it produces considerably more seed than is required to maintain its population. The first three biocontrol agents have reduced the seed production diffuse knapweed by 95%, but the reduction in 'nonredundant' seeds (Rose 1981) has been small. Depleting this large buffer may nevertheless be an important step toward controlling a semelparous perennial because it will presumably limit the possibility that greater mortality caused by future introductions will be balanced by greater recruitment. A third method of forcing a decline in a semelparous population is implicit in the denominator of Euler's equation. If a semelparous plant reproduces too early or too late it will fail to achieve the highest possible intrinsic rate. The result can be a negative intrinsic rate of increase in an environment where a positive rate is possible. The model in Chapter II shows that semelparous perennials maximize their intrinsic rates by flowering after reaching a critical size. It also suggests a potential method of disrupting selection for 117 that critical size. A n insect that killed a higher proportion of older, larger rosettes would cause an accelerating age-specific mortality rate, which would lead to selection for a declining threshold size with age. The weevil Cyphocleonus achates, slated for introduction to diffuse knapweed (Peter Harris pers. comm.) may be such an insect. It is not known whether the as yet unidentified biochemical mechanism that controls the switch to reproductive development in these species could produce the more complex phenotypic behaviour that increasing age-specific mortality would demand. It would be interesting to measure the flowering ages of plants before and after such an introduction. It is not presently possible to prescribe a generic solution for the biological control of semelparous perennials, even though successes are known. In contrast to the modest progress toward the control of diffuse knapweed achieved by the two flies and the beetle, a single insect, the seed weevil Rhinocyllus conicus, dramatically reduced the density of its host Carduus nutans (Kok and Surles 1975). In both cases the imported insects reduced seed production, but in the latter case competing plant species apparently contributed toward control by occupying the space as it was vacated by the thistle (Kok and Surles 1975; Laing and Heels 1978). Recruiting thistle seedlings therefore faced crowded conditions even as the population declined. Diffuse knapweed's resilience in the face of considerable insect damage must be attributed in part to the virtual absence of competition from other species which might limit compensation for insect damage. 118 Literature Cited Alemdag, I.S. 1978. Evaluation of some competition indexes for the prediction of diameter increment in planted white spruce. Canadian Forestry Service, Forest Management Institute, Information Rep. FMR-X-108 39 pp. Anderson, D . J . 1971. Pattern in desert perennials. J . Ecol. 59: 555-560. Anderson, D.J . , S.W.L. Jacobs and A . R . Malik 1969. Studies on structure in plant communities. V I : The significance of pattern evaluation in some Australian dry land vegetation types. Aust. J . Bot. 17: 315-322. Andres, L . A . and R . D . Goeden 1971. The biological control of weeds by introduced natural enemies. Biological Control. Huffaker, C B . (ed.). Plenum Press, London, pp. 143-164. Andrewartha, H . G . and L . C . Birch 1954. The Distribution and Abundance of Animals. Univ. of Chicago Press, Chicago. Antonovics, J . and D . A . Levin 1980. The ecological and genetic consequences of density-dependent regulation in plants. Ann . Rev. Ecol. Syst. 11: 411-452. Arney, J .D. 1973. Tables for quantifying competitive stress on individual trees. Can. For. Serv. Pac. Forest Res. Cent. Inf. Rep. BC-X-78, 10 pp. Baskin, J . M . and C .C . Baskin 1979a. Studies on the autecology and population biology of the weedy semelparous perennial, Pastinaca sativa. J . Ecol. 67: 601-610. Baskin, J . M . and C .C . Baskin 1979b. Studies on the autecology and population biology of the monocarpic perennial Grindelia lanceolata. A m . Mid i . Nat. 102: 290-299. Bazzaz, F . A . and J .L. Harper 1977. Demographic analysis of the growth of Linum usitatissimum. New Phytol. 78: 193-208. Bella, J .E . 1971. A new competition model for individual trees. For. Sci. 17: 364-372. Bender, C M . and S.A. Orszag 1978. Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hil l , N . Y . , 593 pp. Bentley, S. and J .B . Whittaker 1967. Effects of grazing by a chrysomelid beetle, Gas-trophysa viridula, on competition between Rumex obtusifolius and Rumex crispus. J . Ecol. 67: 79-90. Berube, D .E . 1980. Interspecific competition between Urophora affinis and U. quadri-fasciata (Diptera: Tephritidae) for ovipositional sites on diffuse knapweed Centau-rea diffusa (Compositae). Z. ang. Ent. 90: 299-306. 119 Berube, D . E . and J .H . Myers 1982. Suppression of knapweed invasion by crested wheatgrass in the dry interior of British Columbia. J . Range. Manage. 35: 459-461. Burdon, J.J . , R . H . Groves and J . M . Cullen 1981. The impact of biological control on the distribution and abundance of Chondrilla juncea in South-eastern Australia. J . Appl . Ecol. 18: 957-966. Caswell, H . and P .A . Werner 1978. Transient behavior and life history analysis of teasel (Dipsacus sylvestris Huds.). Ecology 59: 53-66. Caughley, G . and J .H . Lawton 1981. Plant-herbivore systems In Theoretical Ecology, Principles and Applications. (2nd Ed.), R. May (ed.) Blackwell, Oxford pp. 132-166. Chambers, J . M . , W.S. Cleveland, B . Kleiner, and P .A. Tukey 1983. Graphical Methods for Data Analysis. Wadsworth International Group, Belmont, California. Charnov, E . L . and W . M . Schaffer 1973. Life-history consequences of natural selection: Cole's result revisited. Amer. Nat. 107: 791-793. Cleveland, W.S. 1979. Robust locally weighted regression and smoothed scatterplots. J . Amer. Stat. Assoc. 74: 829-836. Cleveland, W.S. 1985. The Elements of Graphing Data. Wadsworth, Monterey. 323 pp. Cody, M . L . 1966. A general theory of clutch size. Evolution 20: 174-184. Cole, L . C . 1954. The population consequences of life history phenomena. Quart. Rev. Biol . 29: 103-137. Cormack, R . M . 1979. Spatial aspects of competition between individuals, pp 151-212 in Spatial and Temporal Analysis in Ecology, R . M . Cormack and J . K . Ord (eds.), Statistical Ecology Series vol 8, International Publishing Co-op. Cranston, R. Personal communication. Cranston, R.S., A . H . Bawtree, and G.R. Keay 1983. Knapweed in British Columbia. A description of the problem, efforts to contain its spread and the economics of control. B . C . M i n . of Agric. and Food. 18 pp. Crawley, M . J . 1983. Herbivory: The Dynamics of Animal-Plant Interactions. Studies in Ecology 10. Univ. California Press, Berkeley. Cullen, J . M . 1978. Evaluating the success of the programme for the biological control of Condrilla juncea L . Proc. IV. Int. Symp. Biol . Contr. Weeds, Aug 30 - Sept 2 1976, Gainesville, U .S .A. Freeman, T . E . (ed.). pp 117-121. 120 Daniels, R . F . 1976. Simple competition indices and their correlation with annual Loblolly pine tree growth. For. Sci. 22: 454-456. Diggle, P . J . 1983. Statistical Analysis of Spatial Point Patterns. Academic Press, London. 148 pp. Dirzo, R. 1984. Herbivory: a phytocentric overview, pp 141-165 in Perspectives on Plant Population Ecology. R. Dirzo and J . Sarukhan (eds.), Sinauer Assoc., Sun-derland, Mass. 478 pp. Dodd, A . P . 1959. The biological control of prickly pear in Australia, pp. 565-577 in Biogeography and Ecology in Australia. Dr. W . Junk Publ. , The Hague, Nether-lands. Durand, D. , and J .A. Greenwood 1958. Modifications of the Rayleigh test for unifor-mity in analysis of two-dimensional orientation data. J . Geol. 66: 229-238. Edelstein-Keshet, L . 1986. Mathematical theory for plant-herbivore systems. J . Math. Biol . 24: 25-58. Ek, A . R . and R . A . Monserud 1974. F O R E S T : a computer model for simulating the growth and reproduction of mixed species stands. Univ. Wis. Sch. Nat. Resource Res. Rep. R2635, 13 pp. Fletcher, R . A . and A . J . Renney 1963. A growth inhibitor found in Centaurea spp. Can. J . PL Sci. 43: 475-481 Fowler, N . L . 1984. The role of germination date, spatial arrangement, and neighbour-hood effects in competitive interations in Linum. J . Ecol. 72: 307-318 Gadgil, M . D . and W . H . Bossert 1970. Life historical consequences of natural selection. Amer. Nat. 104: 1-24. Giesel, J .T. 1976. Reproductive strategies as adaptations to life in temporally hetero-geneous environments. Ann. Rev. Ecol. Syst. 7: 57-79. Goeden, R . D . and L . T . Kok 1986. Comments on a proposed "new" approach for selecting agents for the biological control of weeds. Can. Ent. 118: 51-58. Goeden, R .D. , D . W . Ricker, and B . A . Hawkins 1985. Ethological and genetic dif-ferences among three biotypes of Rhinocyllus conicus (Coleoptera: Curculionidae) introduced into North America for the biological control of Asteraceous thistles. Proc. V I . Int. Symp. Biol . Contr. Weeds., Vancouver, Aug. 19-25, 1984, Delfosse, E.S. (ed.). pp 191-190. Green, R. 1979. Sampling Design and Statistical Methods for Environmental Biologists. Wiley 257 pp. Grime, J.P. 1977. Evidence for the existence of three primary strategies in plants and its relevance to ecological and evolutionary theory. Amer. Nat. I l l : 1169-1194. 121 Groh, H . 1943. Canadian weed survey. 2nd Annual Report of the Canadian Depart-ment of Agriculture, 74 pp. Gross, K . L . 1980. Colonization by Verbascum thapsus (Mullein) of an old field in Michigan: experiments on the effects of vegetation. J . Ecol. 68: 919-927. Gross, K . L . 1981. Predictions of fate from rosette size in four "biennial" plant species: Verbascum thapsus, Oenothera biennis, Daucus carota, and Tragopogon dubius Oe-cologia48: 209-213. Guene, G . L . and D.R. Minnick 1967. Snap bean yields following simulated insect defoliation. Proc. Fla . State Hortic. Soc. 80: 132-143. Harper, J .L . 1961. Approaches to the study of plant competition, in Mechanisms in Biological Competition. F . L . Milthorpe (ed.) Symp. Soc. Exp. Biol . 15: 1-39. Harper, J .L . 1964. The individual in the population. J . Ecol. 52 (suppl.): 149-158. Harper, J .L . 1967. A Darwinian approach to plant ecology. J . Ecol. 55: 247-270. Harper, J .L . 1977. The Population Biology of Plants. Academic Press, London, N . Y . Harper, J .L . 1980. Plant demography and ecological theory. Oikos 35: 244-253. Harper, J .L . and A . D . Bell 1979. The population dynamics of growth form in organisms with modular contruction. Population Dynamics, 20th Symp. Brit . Ecol. Soc. pp 29-52. Harper, J .L . and J . Ogden 1970. The reproductive strategy of higher plants I: The concept of strategy with special reference to Senecio vulgaris L . J . Ecol. 58: 681-689. Harris, P. 1980a. Establishment of Urophora affinis Frfld. and U. quadrifasciata (Meig.) (Diptera:Tephritidae) in Canada for the biological control of diffuse and spotted knapweed. Z. ang. Ent. 89: 504-514. Harris, P. 1980b. Effects of Urophora affinis Frfld. and U. quadrifasciata (Meig.) (Diptera: Tephritidae) on Centaurea diffusa Lam. and C. maculosa Lam. (Com-positae). Z. ang. Ent. 89: 190-201. Harris, P. 1984a. Status of introductions and main indigenous organisms attacking weeds targeted for biological control: Canada 1984. A g . Can., Regina. 13 pp. Harris, P. 1984b. Current approaches to the biological control of weeds. Biological Control Programmes Against Insects and Weeds in Canada 1969-1980. Kelleher, J.S. and Hulme, M . A . (eds.). Commonwealth Agricultural Bureaux, pp 95-103. Harris, P. and R. Cranston 1979. A n economic evaluation of control measures for diffuse and spotted knapweed in western Canada. Can. J . PI. Sci. 59: 375-382. 122 Harris, P. and J .H . Myers 1984. Centaurea diffusa Lam. and C. maculosa Lam. s. lat., diffuse and spotted knapweed (compositae). Biological Control Programmes Against Insects and Weeds in Canada 1969-1980., J.S. Kelleher and M . A . Hulme (eds.), Commonwealth Agricultural Bureaux, pp.127-138. Hart, R. 1977. Why are biennials so few? Amer. Nat. I l l : 792-799. Hassell, M . P . 1981. Arthropod predator-prey systems pp 105-131 in Theoretical Ecol-ogy: Principle and Applications. 2nd ed., R . M . May (ed.). Hegyi, F . 1974. A simulation model for managing jack pine stands, pp 74-90 in Growth Models for Tree and Stand Simulation, Royal College of Forestry, Stockholm, Swe-den. Hi l l , M . O . 1973. The intensity of spatial pattern in plant communities. J . Ecol. 61: 225-236. Hirose, T . 1983. A graphical analysis of life history evolution in biennial plants. Bot. Mag. Tokyo 96: 37-47. Hirose, T. and N . Kachi 1982. Critical plant size for flowering in biennials with special reference to their distribution in a sand dune system. Oecologia 55: 281-284. Hokkanen, H . and D . Pimentel 1984. New approaches for selecting biological control agents. Can. Ent. 116: 1109-1121. Holsinger, K . E . and J . Roughgarden 1985. A model for the dynamics of an annual plant population. Theor. Pop. Biol . 28: 288-313. Holt, B .R . 1972. Effect of arrival time on recruitment, mortality, and reproduction in successional plant populations. Ecology 53: 668-673. Hozumi, K . , H . Koyama and T. K i r a 1955. Intraspecific competition among higher plants. IV . A preliminary account on the interaction between adjacent individuals. J . Biol . Osaka City Univ. 6: 121-130. Hubbard, W . A . 1975. Increased range forage production by reseeding and chemical control of knapweed. J . Range Manage. 28: 406-407. Janzen, D . H . 1976. Why bamboos wait so long to flower. Ann . Rev. Ecol. Syst. 7: 347-391. de Jong, T . J . , P .G .L . Klinkhamer and A . H . Prins 1986. Flowering behaviour of the monocarpic perennial Cynoglossum officinale L . New Phytologist 103: 219-229. Julien, M . H . 1982. Biological Control of Weeds. Commonw. Inst. Biol . Contr. Commonwealth Agricultural Bureaux, London, 108 pp. Kachi, N . and T. Hirose 1983. Bolting induction in Oenothera erythrosepala Borbas in relation to rosette size, vernalization, and photoperiod. Oecologia 60: 6-9. 123 Keister, T . D . 1971. A measure of the intraspecific competition experienced by an individual tree in a planted stand. La State Univ. Stn. Bul l . 447. 109 pp. Klemow, K . M and D . J . Raynal 1981. Population ecology of Melilotus alba in a lime-stone quarry. J . Ecol. 69: 33-44. Klinkhamer, P .G .L . and T . J . de Jong 1983. Is it profitable for biennials to live longer than two years? Ecol. Modelling 20: 223-232. Klinkhamer, P .G .L . , T . J . de Jong and E . Meelis 1987. Delay of flowering in the 'bien-nial ' Cirsium vulgare: size effects and devernalization. Oikos 49: 303-308. Knight, R. 1983. Some factors causing variation in the yield of individual plants of wheat. Aust. J . Agric. Res. 34: 219-228. Kok, L . T . and W . W . Surles 1975. Successful biocontrol of musk thistle by an introduced weevil Rhinocyllus conicus. Envir. Ent. 4: 1025-1027. Koyama, H . and T. K i r a 1956. Intraspecific competition among higher plants VIII: frequency distribution of individual plant weight as affected by interaction between plants. J . Inst. Polytechnics, Osaka City Univ., series D 7: 73-94. Krajina, V . J . 1965. Biogeoclimatic zones and biogeocoenoses of British Columbia, pp 1-17 in Ecology of Western North America (Vol. 1), V . J . Krajina (ed.). Lacey, E .P . 1986. Onset of reproduction in plants: size- versus age-dependency. Rec. Trends Ecol. Evol . 1: 72-75. Laing, J .E . and J . Hamai 1976. Biological control of insect pests and weeds by imported parasites, predators and pathogens. The Theory and Practice of Biological Control. Huffaker, C B . and Messenger, P.S. (eds.)., Academic Press, pp 685-743. Laing, J .E . and P.R. Heels 1978. Establishment of an introduced weevil, Rhinocyllus conicus (Coleoptera: Curculionidae) for the biological control of nodding thistle, Carduus nutans (Compositae) in southern Ontario. Proc. Ent. Soc. Ont. 109: 3-8. Laughlin, R. 1965. Capacity for increase: a useful population statistic. J . Anim. Ecol. 34: 77-91. Lawton, J .H . 1985. Ecological theory and choice of biological control agents. Proc. V I . Int. Symp. Biol . Contr. Weeds, Vancouver, Canada, Aug 19-25, Delfosse, E.S. (ed.) pp 13-26. Lee, J . M . and J .L. Hamrick 1983. Demography of two natural populations of musk thistle (Carduus nutans). J . Ecol. 71: 923-936. Leslie, P . H . 1966. The intrinsic rate of increase and the overlap of successive generations in a population of guillemots (Uria aalge Pont.). J . Anim. Ecol. 35: 291-301 124 Lewontin, R . C . and D . Cohen 1969. On population growth in a randomly varying environment. Proc. Natl. Acad. Sci. 62: 1056-1060. Liddle, M . J . , C.S.J . Budd and M . J . Hutchings 1982. Population dynamics and neigh-bourhood effects in established swards of Festuca rubra. Oikos 38: 52-59. Llyod, M . 1967. Mean crowding. J . Anim. Ecol. 36: 1-30. Lotwick, H .W. and B . W . Silverman 1982. Methods for analysing spatial processes of several types of points. J . Roy. Stat. Soc. B 44: 406-413. Mack, R . N . and J .L . Harper 1977. Interference in dune annuals: spatial pattern and neighborhood effects. J . Ecol. 65: 345-363. Maddox, D . M . 1979. The knapweeds: their economics and biological control in the western states, U.S .A. Rangelands 1: 139-143. Malik, A . R . , D . J . Anderson and P .J . Myerscough 1976. Studies on structure in plant communities. VII : Field and experimental analysis of Atriplex vesicaria populations from the Riverine Plain of New South Wales. Aust. J . Bot. 24: 265-280. Mardia, K . V . 1972. Statistics of Directional Data. Academic Press, New York, 357 pp. Mart in, G . L . and A . R . Ek. 1984. A comparison of competition measures and growth models for predicting plantation red pine diameter and height growth. For. Sci. 30: 731-743. Maw, M . G . 1984. Biological control of weeds (1984) - an update of Julien's world catalogue of agents and their targets. A g . Can., Regina. May, R . M . 1973. Stability and Complexity in Model Ecosystems. Princeton Mono-graphs 6, Princeton Univ. Press., 235 pp. May, R . M . 1981. Models for two interacting populations, pp 78-104 in Theoretical Ecology: Principles and Applications. 2nd ed., R . M . May (ed.). McDonough, W . T . 1965. Pattern changes associated with the decline of a species in a desert habitat. Vegietatio 13: 97-101. McEvoy, P .B. , C.S. Cox, R.R. James and N . T . Rudd 1989. (in press) Ecological mecha-nisms underlying successful biological weed control: field experiments with ragwort Senecio jacobaea. Proc. VII . Int. Symp. Biol . Contr. Weeds, March 6-11, 1988, Rome, Italy. Delfosse, E.S. (ed.). Mead, R. 1966. A relationship between individual plant-spacing and yield. Ann . Bot. 30: 301-309. van der Meijden, E . 1989. (in press) Defense and regrowth: alternative strategies in the struggle against herbivores. Proc. VII . Int. Symp. Biol . Contr. Weeds, March 6-11, 1988, Rome, Italy. Delfosse, E.S. (ed.). 125 van der Meijden, E . and R . E . van der Waals-Kooi 1979. The population biology of Senecio jacobaea in a sand dune system I: reproductive strategy and the biennial habit. J . Ecol. 67: 131-153. Mithen, R., J .L . Harper and J . Weiner 1984. Growth and mortality of individual plants as a function of "available area". Oecologia 62: 57-60. Moran, V . C . 1985. The Silwood international project on the biological control of weeds. Proc. V I . Int. Symp. Biol . Contr. Weeds, Aug. 19-25, 1984, Vancouver, Canada. Delfosse, E.S. (ed.), pp 65-68. Morrison, P.D.S. 1986. Host plant variation and population limitation of two intro-duced insects. Ph. D . thesis, University of British Columbia. Muir , A . , Personal communication. Muir , A . D . and W . Majak 1983. Allelopathic potential of diffuse knapweed Centaurea diffusa extracts. Can. J . PL Sci. 63: 989-996. Muller, H . Personal Communication. Myers, J .H . 1978. Biocontrol introductions as grandiose field experiments: adaptations of the cinnabar moth to new surroundings. Proc. IV Int. Symp. Biol . Contr. Weeds, Aug. 30-Sept. 2, 1976, Gainesville, U .S .A. Freeman, T . E . (ed.)., pp 181-188. Myers, J .H . 1980. Is the insect or the plant the driving force in the cinnabar moth -tansy ragwort system? Oecologia 47: 16-21. Myers, J .H . 1985. How many insect species are necessary for successful biological control? Proc. V I Int. Symp. Biol . Contr. Weeds, Aug. 19-25, 1984, Vancouver, Canada. Delfosse, E.S. (ed.). pp 77-82. Myers, J .H . and D. Berube 1983. Diffuse knapweed invasion into rangeland in the dry interior of British Columbia. Can. J . PL Sci. 63: 981-987. Myers, J .H . and P. Harris 1980. Distribution of Urophora galls in flower heads of diffuse and spotted knapweed in British Columbia. J . Appl . Ecol. 17: 359-367. Myers, J .H . , J . Monro and N . Murray 1981. Egg clumping, host plant selection and population regulation in Cactoblastus cactorum (Lepidoptera). Oecologia 51: 7-13. Myers, J .H . and B . J . Post 1981. Plant nitrogen and fluctuations of insect populations: a test of the cinnabar moth - tansy ragwort system. Oecologia 48: 151-156. Myers, J .H . and R .D . Powell. Unpublished data on competitive release effects of her-bicide (picloram) application. Myers, J .H . , C . Risley, R . D . Powell and R. Eng (in prep.) Seed production may not be a good measure of the impact of insect herbivores on plant population dynamics. 126 Nolan, D . (in prep.). Masters Thesis, University of British Columbia. N . R . C . C . 1974. Picloram: the effects of its use as a herbicide on environmental quality. National Research Council of Canada. Pub. no. 13684. Olkin, I., L . J . Gleser, and C. Derman 1980. Probability Models and Applications. MacMil lan, N . Y . 576 pp. Oxley, E . R . H . 1977. The population dynamics of the foxglove, Digitalis purpurea L . Unpublished, (summarized in) J .L . Harper, Population Biology of Plants. Aca-demic Press 892 pp. Pacala, S.W. 1986. Neighbourhood models of plant population dynamics. Multi-species models of annuals. Theor. Popul. Biol . 29: 262-292. Pacala, S.W. and J .A. Silander Jr. 1985. Neighborhood models of plant population dynamics. 1. Single-species models of annuals. Amer. Nat. 125: 385-411. Peucker, T . K . , R . J . Fowler, J .J . Little, and D . M . Mark 1978. The triangulated irregular network. Proc. of D T M Symposium, Amer. Soc. Photogrammetry, Falls Church, Va . pp 516-540. Phillips, D . L . and J .A. MacMahon 1981. Competition and spacing patterns in desert shrubs. J . Ecol. 69: 97-115. Pielou, E . C . 1960. A single mechanism to account for regular, random and aggregated populations. J . Ecol. 48: 575-584. Pielou, E . C . 1969. A n Introduction to Mathematical Ecology. Wiley Interscience, N . Y . Pielou, E . C . 1977. Mathematical Ecology. Wiley, Toronto. 385 pp. Powell, R . D . 1984. Some preliminary results concerning the beetle Sphenoptera ju-goslavica as a biological control for diffuse knapweed. Proc. Knapweed Symp. Apr i l 3-4 1984, Great Falls, Montana, pp 45-52. Powell, R . D . and J .H . Myers 1988. The effect of Sphenoptera jugoslavica Obenb. (Col., Buprestidae) on its host plant Centaurea diffusa Lam. (Compositae). J . Appl . Ent. 106: 25-45. Rathcke, B . and E.P. Lacey 1985. Phenological patterns in terrestrial plants. Ann. Rev. Ecol. Syst. 16: 179-214. Reinartz, J . A . 1984. Life history variation of common mullein Verbascum thapsus III: differences among sequential cohorts. J . Ecol. 72: 927-936. Renney, A . J . and E . C . Hughes 1969. Control of knapweed (Centaurea spp.) in British Columbia with Tordon herbicide. Down to Earth 24: 6-8. 127 Rh.oad.es, D .F . and R . G . Cates 1976. Toward a general theory of plant antiherbivore chemistry. Rec. Adv. Phytochem. 10: 168-213. Robinson, R . C . 1962. Blue stain fungi in lodgepole pine (Pinus contorta Dougl. var. latifolia Engelm.) infested by the mountain pine beetle (Dendroctonus monticolae Hopk.). Can. J . Bot. 40: 609-614. Room, P . M . , K . L . S . Harley, I.W. Forno and D .P .A . Sands 1981. Successful biological control of the floating weed Salvinia. Nature 294: 78-80. Rosenthal, S., Personal communication. Ross, M . A . and J .L . Harper 1972. Occupation of biological space during seedling establishment. J . Ecol. 60: 77-88. Roze, L . D . 1981. The biological control of Centaurea diffusa Lam. and C. macu-losa Lam. by Urophdra affinis Frauenfeld and U. quadrifasciata Meigen (Diptera: Tephritidae). MSc. Thesis, University of British Columbia, Vancouver. 208 pp. Sackston, W . E . 1959. Effects of artificial defoliation on sunflowers. Can. J . PI. Sci. 39: 108-118. Salisbury, E . J . 1942. The reproductive capacity of plants. Bell , London. Sarukhan, J . and J .L. Harper 1973. Studies on plant demography: Ranunculus repens L . , R. bulbosus L . and R. acris L . I. Population flux and survivorship. J . Ecol. 61: 675-716. Schaffer, W . M . and M . D . Gadgil 1975. Selection for optimal life histories in plants, in M . L . Cody and J . M . Diamond (eds.) Ecology and Evolution of Communities, pp 142-157. Harvard Univ. Press. Schaffer, W . M . and M . L . Rosenzweig 1977. Selection for optimal life histories. II. multiple equilibria and the evolution of alternative reproductive strategies. Ecology 58: 60-72. Schirman, R. 1981. Seed production and spring seedling establishment of diffuse and spotted knapweed. J . Range Manage. 34: 45-47. Shepherd, A . W . , J-P Aeschlimann, J . M . Cullen, J-L Sagliocco and J . Vitou 1989. (in press) The importance of insect biocontrol agents relative to other limiting factors on weed population dynamics: a case study of Carduus nutans L . Proc. VII . Int. Symp. Biol . Contr. Weeds, March 6-11, 1988, Rome, Italy. Delfosse, E.S. (ed.). Shorthouse, J . , Personal communication. Silander, J .A . Jr. and S.W. Pacala 1985. Neighborhood predictors of plant perfor-mance. Oecologia 66: 256-263. 128 Silvertown, J . 1983. Why are biennials sometimes not so few? Amer. Nat. 121: 448-353. Silvertown, J . 1984. Death of the elusive biennial. Nature 310: 271. Silvertown, J . 1986. Biennials: a reply to Kelly. Amer. Nat. 127: 721-724. Sokal, R .R . and F . J . Rohlf 1969. Biometry: The Principles and Practice of Statistics in Biological Research. W . H . Freeman and Co., San Francisco U.S .A. Spears, B . M . , S.T. Rose and W.S. Belles 1980. The effects of canopy cover, seedling depth, and soil moisture on the emergence of Centaurea maculosa and C. diffusa. Weed Res. 20: 87-90. Stearns, S.C. and J .C . Koella 1986. The evolution of phenotypic plasticity in life-history traits: predictions of reaction norms for age and size at maturity. Evolution 40: 893-913. Stevens, O.A. 1932. The number and weight of seeds produced by weeds. Amer. J . Bot. 19: 784-794. Strong, D.R. , J .H . Lawton and T . R . E . Southwood 1984. Insects on Plants: Community Patterns and Mechanisms. Blackwell Scientific Pubs., 313 pp. Struik, G . J . 1965. Growth patterns of some native annual and perennial herbs in southern Wisconsin. Ecology 46: 401-420. Thompson, J .N . 1978. Within-patch structure and dynamics in Pastinaca sativa and resource availability to a specialized herbivore. Ecology 59: 443-448. Thornley, J . H . M . 1972. A model of a biochemical switch, and its application to flower initiation. Ann. Bot. 36: 861-871. Thornley, J . H . M . and K . E . Cockshull 1980. A catastrophe model for the switch from vegetative to reproductive growth in the shoot apex. Ann . Bot. 46: 333-341. Tilman, D . 1982. Resource Competition and Community Structure. Princeton U . Press, Princeton, New Jersey. Tukey, J .W. 1977. Exploratory Data Analysis. Addison-Wesley, Reading Mass. U.S .A. Waller, D . M . 1981. Neighborhood competition in several violet populations. Oecologia 51: 116-122. Wang, Y . , A . P . Gutierrez, G . Oster and R. Daxl 1977. A population model for plant growth and development: coupling cotton-herbivore interaction. Can. Ent. 109: 1359-1374. Watson, A . K . and A . J . Renney 1974. The biology of Canadian weeds. 6. Centaurea diffusa and C. maculosa. Can. J . PL Sci. 54: 687-701. 129 Watson, D . J . 1947. Comparative physiological studies on the growth of field crops. I. Variation in net assimilation rate and leaf area between species and varieties, and within and between years. Ann . Bot 11: 41-76. Wegman, E . J . 1972. Nonparametric probability density estimation I. A summary of available methods. Technometrics 14:533-546. Weiner, J . 1982. A neighborhood model of annual plant interference. Ecology 63: 1237-1241. Weiner, J . 1984. Neighbourhood interference amongst Pinus rigida individuals. J . Ecol. 72: 183-195. Werner, P .A . 1975. Predictions of fate from rosette size in teasel (Dipsacus fullonum L.) Oecologia 20: 197-201. Werner, P .A . and H . Caswell 1977. Population growth rates and age versus stage-distribution models for teasel (Dipsacus sylvestris Huds.). Ecology 58: 1103-1111. White, J . 1979. The plant as metapopulation. Ann . Rev. Ecol. Syst. 10: 109-145. White, J . 1984. Plant metamerism, pp 15-47 in Perspectives on Plant Population Ecology. R. Dirzo and J . Sarukhan (eds.), Sinauer Assoc., Sunderland, Mass. 478 pp. Whittaker, J .B . 1979. Invertebrate grazing: competition and plant dynamics in Popu-lation Dynamics., R . M . Anderson, B . D . Turner, and L . R . Taylor (eds.), Blackwell, Oxford pp. 207-222. Wilson 1960. A review of the biological control of insects and weeds in Australia and Australian New Guinea. Commonw. Inst. Biol . Contr. Tech. Comm. # 1, 102 pp. Woodell, S.R.J. , H . A . Mooney and A . J . Hi l l 1969. The behaviour of Larrea divaricata (creosote bush) in response to rainfall in California. J . Ecol. 57: 37-44. Yoda, K . , T. K i r a and K . Hozumi 1957. Intraspecific competition among higher plants I X . Further analysis of the competitive interaction between adjacent individuals. J . Inst. Polytech. Osaka City Univ. 8: 161-178. Yoda, K . , T . Ki ra , H . Ogawa and K . Hozumi 1963. Self thinning in overcrowded pure stands under cultivated and natural conditions. J . Biol . Osaka City Univ. 14: 107-129. Zar, J .H . 1974. Biostatistical Analysis. Prentice Hall , Englewood Cliffs, N . J . 620 pp. Zwolfer, H . 1976. Investigations of Sphenoptera (Chilostetha) jugoslavica Obenb. (Col. Buprestidae), a possible biocontrol agent of the weed Centaurea diffusa Lam. (Com-positae) in Canada. Z. ang. Ent. 80: 170-190. 130 Appendix I: Conditions for Pure Size Dependence The equation l n / i + 1 = ^ y^(ln/j + cTlna;) + -. - alnWj for j = ( 2 , 3 , . . . , n ) is a first order linear inhomogeneous difference equation and therefore has the general so-lution (constrained by the minimum one year rosette duration prior to flowering) of i - i l n / i = II P ( m ) m=2 i - i / q(k) + l n / 2 , i > 3 where, p(m) = and q(k) = — a In Wk m k (e.g. Bender and Orszag 1978). Substituting p(m) and q(k) into the above equation we obtain, 3 In/,- = n  3 2 Jk=2 \ 2 / which simplifies to, l n ^ = 2 l n / 2 + J g l * JkTT)) The discrete derivative of D l n / j is D l n / j = l n / J + i — Inlj (op cit). Letting r(k) stand for the expression in parentheses we have, j . j — i D In = 3 - ± - In l2 + (j + 1) £ - £ In Z2 - j J3 r(fc) 2 l n / : ~2~ In/ fc=2 i fc=2 fc=2 fc=2 fc=2 i - i i i - i 2 + J 53 r(fc)+j'r0")+53 r(*o ~- j 53 r(*) k=2 k-2 k=2 Ink + jr(j) + 53 r(k) fc=2 The condition that D In L < 0 can then be written, MJ)+53 r(fc) - _ l n / 2 k=2 which is equivalent to, J k=2 k=2 + | < - ( ^ ) for 0 < / 2 < l 131 Appendix II: Critical rm Values For populations with an allometric weight-fecundity relation from equation 14, 3 + The critical value rm = 0 is therefore found where log survivorship and log seed output are of equal magnitude, but opposite sign, l n / j + 1 = -(alnWj + e). Substituting equation 17 for the left side we have, fc=2 V which can be rearranged to solve for ln/2 for all values of u, l n / 2 = - ( - ) 3 alnWj.r + e + j ^ i %  k=2 Appendix III: Fitness of Genotypes in Relation to Variation in Individual Growth Rates The function A = g(j,j) in our model is, exponentiating (14), Rearranging and substituting for Wj-\ from (1) we have, a A^ which can be solved for 7 . The inverse function is, 7 = fc(^)=--L_ln(i a 1/<T J±L ) - 1 The derivative of the inverse function with respect to the finite rate is, I / O -d(h(X,j)) j "XT aX l / < 7 1/a 132 The probability density of the finite rate is then, f(XJ) = 3-1 3 aX a -f(h(x,j)), and the finite rate for the population as a whole is the mean of the p.d.f. of A, from equation In general, the integral expression must be solved numerically. Appendix IV: Limits of Integration to Calculate the Fitness of Size-dependent and Age-size-dependent Types The lower limits of integration are determined by the threshold itself. If wj is a vector of intersections of the phenotypic threshold with the size curves, we have, for the purely allometric case (substituting wj into the left half of equation (15) and exponentiating), To obtain the upper limits we must know the weights of plants growing at rates -yp that delay flowering for a full year. Since, 22, for j=l ,2, . . . ,n-2; for j = n-1. 7pi — 3 the weights are, W u ( j + i ) - a 1 + /3e-Tpi(j'+1) and the upper limits of integration are "(i+D - 1 ( / i + 1 W u V e ) 1 / ( i + 1 ) > for j = 2,3,. . . , n - l . 133 


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items