Continuous versus discrete single species population models with adjustable reproductive strategies

We investigate population models with both continuous and discrete elements. Birth is assumed to occur at discrete instants of time whereas death and competition for resources and space occur continuously during the season. We compare the dynamics of such discrete-continuous hybrid models with the dynamics of purely discrete models where within-season mortality and competition are modelled directly as discrete events. We show that non-monotone discrete single-species maps cannot be derived from unstructured competition processes. This result is well known in the case of fixed reproductive strategies and our results extend this to the case of adjustable reproductive strategies. It is also shown that the most commonly used non-monotone discrete maps can be derived from structured competition processes.

[1]  S. Stearns,et al.  The Evolution of Life Histories , 1992 .

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

[3]  K. Cooke,et al.  One-dimensional linear and logistic harvesting models , 1986 .

[4]  AN ANALYSIS OF THE DATA FOR SOME EXPERIMENTS CARRIED OUT BY GAUSE WITH POPULATIONS OF THE PROTOZOA, PARAMECIUM AURELIA AND PARAMECIUM CAUDATUM , 1957 .

[5]  Mathematical analysis of a model for a plant-herbivore system , 1993 .

[6]  J. Maynard Smith,et al.  Mathematical Ideas in Biology , 1968 .

[7]  I. Hanski,et al.  A predator-prey model with optimal suppression of reproduction in the prey. , 1996, Mathematical biosciences.

[8]  P. Moran,et al.  Some remarks on animal population dynamics. , 1950, Biometrics.

[9]  S. Jørgensen.  Models in Ecology , 1975 .

[10]  R. Punnett,et al.  The Genetical Theory of Natural Selection , 1930, Nature.

[11]  I. Hanski.  Population biology of Eurasian shrews : towards a synthetis , 1989 .

[12]  Robert M. May,et al.  Models for single populations , 1981 .

[13]  F. David,et al.  On the Dynamics of Exploited Fish Populations , 1959, Fish & Fisheries Series.

[14]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[15]  R. May.  Ecosystem Patterns in Randomly Fluctuating Environments , 1974 .

[16]  Odo Diekmann,et al.  On evolutionarily stable life histories, optimization and the need to be specific about density dependence , 1995 .

[17]  R M May,et al.  Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos , 1974, Science.

[18]  T. W. Chaundy,et al.  THE CONVERGENCE OF SEQUENCES DEFINED BY QUADRATIC RECURRENCE-FORMULAE , 1936 .

[19]  R. May,et al.  Bifurcations and Dynamic Complexity in Simple Ecological Models , 1976, The American Naturalist.

[20]  S. Utida,et al.  Population Fluctuation, an Experimental and Theoretical Approach , 1957 .

[21]  Robert M. May,et al.  Patterns of Dynamical Behaviour in Single-Species Populations , 1976 .

[22]  A. Macfadyen,et al.  Animal Ecology: Aims and Methods , 1970 .

[23]  M. Williamson.  The analysis of discrete time cycles , 1974 .

[24]  C. Krebs.  Ecology: The Experimental Analysis of Distribution and Abundance , 1973 .

[25]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[26]  A. Hastings.  Evolution of Life Histories , 1997 .

[27]  P. Yodzis,et al.  Introduction to Theoretical Ecology , 1989 .

[28]  L. M. COOK,et al.  Oscillation in the Simple Logistic Growth Model , 1965, Nature.

[29]  R. Beverton,et al.  On the dynamics of exploited fish populations , 1993, Reviews in Fish Biology and Fisheries.

[30]  Robert M. May,et al.  On Relationships Among Various Types of Population Models , 1973, The American Naturalist.

[31]  O. Diekmann,et al.  On the formulation and analysis of general deterministic structured population models II. Nonlinear theory , 2000 .

[32]  C. Pennycuick,et al.  A computer model for simulating the growth of a population, or of two interacting populations. , 1968, Journal of theoretical biology.

[33]  M. Hassell,et al.  The dynamics of competition and predation , 1976 .

[34]  J. Beddington.  Age distribution and the stability of simple discrete time population models. , 1974, Journal of theoretical biology.

[35]  J. M. Smith.  The theory of games and the evolution of animal conflicts. , 1974, Journal of theoretical biology.

[36]  A. Nicholson.  An outline of the dynamics of animal populations. , 1954 .

[37]  W. Ricker.  Stock and Recruitment , 1954 .

[38]  J. G. Skellam.  Random dispersal in theoretical populations , 1951, Biometrika.

[39]  Michael P. Hassell,et al.  DENSITY-DEPENDENCE IN SINGLE-SPECIES POPULATIONS , 1975 .

[40]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[41]  伊藤 嘉昭,et al.  Animal Ecology, Aims and Methods, 2nd Ed., MACFADYEN, A.著, (1963), A5判, 344ページ, 2,520円, Pitman (London) 発行 , 1964 .