SSStttooonnnyyy BBBrrrooooookkk UUUnnniiivvveeerrrsssiiitttyyy The official electronic file of this thesis or dissertation is maintained by the University Libraries on behalf of The Graduate School at Stony Brook University. ©©© AAAllllll RRRiiiggghhhtttsss RRReeessseeerrrvvveeeddd bbbyyy AAAuuuttthhhooorrr... Predation and its Consequences: Insights into the Modeling of Interference A Dissertation Presented by Christopher Jon Jensen to The Graduate School in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Ecology and Evolution Stony Brook University May 2007 Stony Brook University The Graduate School Christopher Jon Jensen We, the dissertation committee for the above candidate for the Doctor of Philosophy degree, hereby recommend acceptance of this dissertation. Lev R. Ginzburg, Dissertation Advisor Professor, Department of Ecology and Evolution, Stony Brook University Jessica Gurevitch, Chairperson of Defense Professor, Department of Ecology and Evolution, Stony Brook University Stephan B. Munch Assistant Professor, Marine Sciences Research Center, Stony Brook University Leo S. Luckinbill Associate Professor of Biological Sciences, College of Liberal Arts and Sciences, Wayne State University This dissertation is accepted by the Graduate School Lawrence B. Martin, Dean of the Graduate School ii Abstract of the Dissertation Predation and its Consequences: Insights into the Modeling of Interference by Christopher Jon Jensen Doctor of Philosophy in Ecology and Evolution Stony Brook University 2007 Ecological theory depicts predators and their prey as instantaneously interacting particles, a way of looking at predation with a historical footing in chemical kinetics. A series of recent models that consider mutual interference between predators to be an important factor in determining consumption rate and therefore predator-prey dynamics have challenged this view of predation. In this dissertation I investigate the importance of interference and design experiments to contrast between competing models of predator-prey interaction. After laying out the history of this theoretical controversy and the data that accompanies it, I establish the importance of using appropriately simple models in light of limited ecological data. I then present a rationale for questioning traditional theory. In order to provide a full understanding of the competing models, I present a detailed exploration of their stability space and equilibriums based on numerical simulations. These explorations establish that models of predation can be contrasted across two biological parameters: the prey growth rate (r) and the prey carrying capacity (K). I discuss their meaning and show that they can be effectively manipulated in the laboratory. I argue that the time scale of predation rates is not universal and show that the degree of predator interference detected depends on the time scale on which predation is measured. Based on the experimental and theoretical insights of my work, I conclude with a novel predator-prey model designed to bridge the gap between historically competing representations of predation. iii In honor of my father Robert Jensen a man of intense intellectual curiosity who would have wanted to share in the joy and accomplishment of my own Table of Contents Abstract ……………………………………………………………..……… iii Dedication ……………………………………………………………..…… iv Table of Contents ……………………………………………………..….. v List of Illustrations ……………………………………………………….....viii Acknowledgements …………………………………………..…………… x I. Introduction to the Dissertation: Gause, Luckinbill, Veilleux and What to Do .……………...………… 1 Introduction ………………………………………………..…………. 2 Critical empirical outcomes in the Paramecium-Didinium system …………………….……….. 3 Competing functional responses …………………………..………. 6 Understanding the unresolved controversy ………….…...… 7 Meaningful contrasts: how the two models differ in qualitative terms ……………………………….……... 9 Simple quantitative differences: getting beyond trajectory fitting ………………………………. 11 Competing views of Gause, Luckinbill, and Veilleux …………….. 11 What to Do Analytically ……………………………………………... 13 What to Do Empirically ……………………………………………… 14 Salt Revisited …………………………………..….…………… 14 The Paradox of Enrichment Reversed ………..….…………. 14 Reversing The Paradox of Enrichment ……………………… 15 Why Use a Laboratory Microcosm? …………………………. 16 Conclusion ………………………...…………………………………. 16 Tables ………………………………………………………………… 17 Figures ………………………………………………………………... 19 Literature Cited ………………………………………………………. 20 II. Paradoxes or theoretical failures? The jury is still out. …………... 24 Introduction …………………………………………………………... 25 The paradox of enrichment ………………………………………… 25 The enrichment response …………………………………………... 29 Origins of the paradox: how the field got this far astray ………… 32 The fallacy of instantism ……………………………………… 33 Literalism in using mathematical constructs ………………... 34 Intuition, evidence, and math ………………………………… 35 The potential hazards of blind faith ……….……………………….. 36 Acknowledgements …………………………………………………. 36 Figures ………………………………………………………………... 37 Literature Cited ………………………………………………………. 39 III. The Interdependence of r and K ………………………………………. 44 v Introduction …………………………………………………………... 45 Methods ………………………………………………………………. 48 Results ………………………………………………………………... 49 Discussion ……………………………………………………………. 50 Conclusion …………………………………………………………… 51 Acknowledgements …………………………………………………. 51 Tables ………………………………………………………………… 52 Figures ………………………………………………………………... 55 Literature Cited ………………………………………………………. 58 IV. The Consequences of Functional Response Choice: Differences in Stability and Equilibrium ……………………………... 59 Introduction …………………………………………………………... 60 Methods ………………………………………………………………. 62 Results ………………………………………………………………... 64 Discussion ……………………………………………………………. 66 Conclusion …………………………………………………………… 71 Acknowledgements …………………………………………………. 71 Tables ………………………………………………………………… 72 Figures ………………………………………………………………... 74 Literature Cited ………………………………………………………. 82 V. A Direct, Experimental Test of Resource vs. Consumer Dependence: Comment. ……………………………… 84 Literature Cited ………………………………………………………. 89 VI. Direct measurements of functional response over varying time intervals in the Paramecium-Didinium system ……………………...91 Introduction …………………………………………………………... 92 Methods ………………………………………………………………. 93 Results ………………………………………………………………... 95 Discussion ……………………………………………………………. 95 Acknowledgements …………………………………………………. 97 Tables ………………………………………………………………… 98 Figures ………………………………………………………………... 102 Literature Cited ………………………………………………………. 103 Appendices ………………………………………………………………… 104 Appendix A. The non-deterministic explanation of dual extinction and predator extinction ..………………………………... 104 Appendix B. More on the difference in qualitative outcomes between the prey- and ratio-dependent limit myths ……………... 106 Appendix C. Understanding capture efficiency in the Hassell-Varley-Holling models ……………………………………... 111 vi Appendix D. Coding and parameterization of simulations in Mathematica ……………..…………………………………………... 112 Appendix E. Modeling prey depletion in the Beddington-DeAngelis functional response …………………….… 116 vii List of Illustrations Chapter 1 Table 1. Alternative Forms of the Functional Response ………………. 17 Table 2. Comparison of prey- and ratio-dependent outcomes based on decreases in fundamental parameters ……………………….17 Table 3. The results of Veilleux (1979) ………………………………….. 18 Figure 1. Expected and actual outcomes of Gause’s experiment with Didinium and Paramecium ……………………………………………….. 19 Chapter 2 Figure 1. The enrichment response ……………………………………... 37 Figure 2. Theoretical paradoxes and their resolution by comparison with data ……………………………………………………… 38 Chapter 3 Table 1. Effect of enforced mortality on final abundances of replicate treatments …………………………………………………….. 52 Table 2. 2-way ANOVA of the Aggregated Last 4 Days of Abundances ……………………………………………… 53 Table 3. Actual Versus Predicted Abundances Under Enforced Mortality Treatment …………………………………….. 53 Table 4. Estimation of the intraspecific competition constant (γ) for both enforced mortality treatments…………………….. 54 Figure 1. Logistic Growth Under The Verhulst and Pearl-Reed Equations …………………………………………………..… 55 Figure 2. Effect of Enforced Mortality on Paramecium Growth ………. 56 Figure 3. Boxplots for the Last 4 Days of Growth by Enforced Mortality Treatment …………………………………………….. 57 Chapter 4 Table 1. State variables and parameters employed in these simulations ………………………………………………………. 72 Table 2. Rates for asynchronous discrete event simulations ……..…. 73 Figure 1. Flow diagram for asynchronous discrete event simulations ………………………………………………………….. 74 Figure 2. Color guide for understanding replicate outcomes in stochastic simulations ………………………………………………….. 75 Figure 3. Stability properties of Beddington-DeAngelis versus Hassell-Varley-Holling models ………………………………...… 76 Figure 4. Effect of initial conditions on the stability properties of the Hassell-Varley-Holling model ……………………………………... 78 Figure 5. Effect of enforced proportional prey mortality on the Hassell-Varley-Holling and Beddington-DeAngelis models ………...… 79 viii Figure 6. Large-scale equilibrial response to enrichment in the Hassell-Varley-Holling and Beddington-DeAngelis models ………...… 80 Chapter 6 Table 1. Average consumption rates per hour for varying numbers of predators and consumption intervals ..……………………. 98 Table 2. Total average consumption per interval for varying numbers of predators and consumption intervals …………………..…. 98 Table 3. Analysis of Variance for