Populations under Periodically and Randomly Varying Growth Conditions

A large number of natural populations result from single generations that do not overlap, so that population growth occurs in discrete steps. The growth of a single species can then be described by an equation of the type (1) where we consider the time lapse between two generations as time unity. Examples of this type of poulation are many temperate zone arthropod species with one short-lived adult generation per year [15], bivoltine insects (i.e. insects having a summer and a winter generation [81) and cicadas with adults emerging every 13 years [13].

[1]  W M Schaffer,et al.  Can nonlinear dynamics elucidate mechanisms in ecology and epidemiology? , 1985, IMA journal of mathematics applied in medicine and biology.

[2]  Mark Kot,et al.  Do Strange Attractors Govern Ecological Systems , 1985 .

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

[4]  William M. Schaffer,et al.  Stretching and Folding in Lynx Fur Returns: Evidence for a Strange Attractor in Nature? , 1984, The American Naturalist.

[5]  Mark Kot,et al.  The effects of seasonality on discrete models of population growth , 1984 .

[6]  M. Kot,et al.  Nearly one dimensional dynamics in an epidemic. , 1985, Journal of theoretical biology.

[7]  Charles C. Elton,et al.  Voles, Mice and Lemmings: Problems in Population Dynamics , 1942 .

[8]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[9]  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 .

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

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

[12]  J. M. Cowley.  An Approximate Theory of Order in Alloys , 1950 .

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

[14]  Robert M. May,et al.  Theoretical Ecology: Principles and Applications , 1981 .

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

[16]  J. Davidson,et al.  Annual Trends in a natural Population of Thrips imaginis (Thysanoptera). , 1948 .

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

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