Dynamics of Age-Structured and Spatially Structured Predator-Prey Interactions: Individual-Based Models and Population-Level Formulations

In this article, we investigate the spatial and temporal dynamics of predator and prey populations using an individual-based modeling approach. In our models, the individual is the fundamental unit, and the dynamics are governed by individual rules for growth, movement, reproduction, feeding, and mortality. We first establish the congruence between age-structured predator-prey population models and the corresponding individual-based population model under homogeneous spatial conditions. Given the agreement between the formalisms, we then use the individual-based model to investigate the dynamics of spatially structured predator-prey systems. In particular, we contrast the dynamics of predator-prey systems in which predators adopt either an "ambush" or a "cruising" strategy. We show that the stability of the spatially structured predator-prey system depends on the relative mobility of prey and predators and that prey mobility, in particular, has a strong effect on stability. Local density dependence in prey reproduction can quantitatively alter the asymmetrical influence of prey mobility on stability, but we show that the asymmetry exists when local density dependence is removed. We hypothesize that this asymmetrical response is due to prey "escape" in space caused by differences in rates of spread of prey and predator populations that arise because of fundamental differences between prey and predator reproduction.

[1]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[2]  明 大久保,et al.  Diffusion and ecological problems : mathematical models , 1980 .

[3]  H. W. Power.  The Foraging Behavior of Mountain Bluebirds: With Emphasis on Sexual Foraging Differences , 1980 .

[4]  The Foraging Behavior of Mountain Bluebirds: With Emphasis on Sexual Foraging Differences. American Ornithologists' Union, Washington, D.C. (1980), x, Ornith. Monogr. No. 28, +72. Price £8.50 , 1981 .

[5]  Peter Chesson,et al.  Models for Spatially Distributed Populations: The Effect of Within-Patch Variability , 1981 .

[6]  A. Hastings,et al.  Age structure in predator-prey systems. I. A general model and a specific example , 1982 .

[7]  J M Cushing,et al.  A predator prey model with age structure , 1982, Journal of mathematical biology.

[8]  William Gurney,et al.  The systematic formulation of tractable single-species models incorporating age structure , 1983 .

[9]  S. Pacala,et al.  Neighborhood Models of Plant Population Dynamics. I. Single-Species Models of Annuals , 1985, The American Naturalist.

[10]  T. Caraco,et al.  Risk‐Sensitivity: Foraging Mode in an Ambush Predator , 1986 .

[11]  O. Diekmann,et al.  The Dynamics of Physiologically Structured Populations , 1986 .

[12]  D. Padilla,et al.  Ecological neighborhoods: scaling environmental patterns , 1987 .

[13]  P. Bradley,et al.  Fluctuations in prey density: effects on the foraging tactics of scolopendrid centipedes , 1987, Animal Behaviour.

[14]  Raoul Kopelman,et al.  Fractal Reaction Kinetics , 1988, Science.

[15]  Robert W. Blake,et al.  Energetics of piscivorous predator-prey interactions , 1988 .

[16]  P. Hogeweg.  Cellular automata as a paradigm for ecological modeling , 1988 .

[17]  D. DeAngelis,et al.  New Computer Models Unify Ecological TheoryComputer simulations show that many ecological patterns can be explained by interactions among individual organisms , 1988 .

[18]  William Gurney,et al.  Structured population models: a tool for linking effects at individual and population level , 1989 .

[19]  Feeding Behavior of Free-Roaming Masticophis flagellum: An Efficient Ambush Predator , 1989 .

[20]  A. Cloarec.  Factors influencing the choice of predatory tactics in a water bug, Diplonychus indicus Venk. & Rao (Heteroptera: Belostomatidae) , 1990, Animal Behaviour.

[21]  Alan Hastings,et al.  Spatial heterogeneity and ecological models , 1990 .

[22]  Johan A. J. Metz,et al.  A size dependent predator-prey interaction: who pursues whom? , 1990 .

[23]  P. Kareiva.  Population dynamics in spatially complex environments: theory and data , 1990 .

[24]  Andrew D. Taylor.  Metapopulations, Dispersal, and Predator‐Prey Dynamics: An Overview , 1990 .

[25]  W. Gurney,et al.  THE PHYSIOLOGICAL ECOLOGY OF DAPHNIA: DEVELOPMENT OF A MODEL OF GROWTH AND REPRODUCTION' , 1990 .

[26]  William Gurney,et al.  The physiological ecology of Daphnia: a dynamic model of growth and reproduction , 1990 .

[27]  J. D. Reeve.  Stability, Variability, and Persistence in Host‐Parasitoid Systems , 1990 .

[28]  A. M. Turing,et al.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[29]  M. Gilpin,et al.  Metapopulation dynamics: a brief his-tory and conceptual domain , 1991 .

[30]  Michael P. Hassell,et al.  Spatial structure and chaos in insect population dynamics , 1991, Nature.

[31]  William G. Wilson,et al.  Mobility versus density-limited predator-prey dynamics on different spatial scales , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[32]  H. Stanley,et al.  Territory covered by N diffusing particles , 1992, Nature.

[33]  A. M. de Roos,et al.  The role of physiologically structured population models within a general individual-based modelling perspective , 1992 .

[34]  William Gurney,et al.  Individual-based models: combining testability and generality , 1992 .

[35]  Microscopic-based fluid flow invasion simulations , 1992 .

[36]  William Gurney,et al.  Two-patch metapopulation dynamics , 1993 .

[37]  W. Wilson,et al.  Spatial Instabilities within the Diffusive Lotka-Volterra System: Individual-Based Simulation Results , 1993 .