Persistence of Transients in Spatially Structured Ecological Models

Simple discrete-time ecological models for a species with alternating reproduction and dispersal are shown to have complex transient dynamics. If the density dependence (nonlinearity) is strong enough, then the time required to reach the final dynamics is usually very long, approaching thousands of generations, and there are typically very sudden changes in the form of the dynamics. Apparent chaos can change to cycles or vice versa. These results are consistent with observed sudden changes in the form of the dynamics of a single species and imply that transient dynamics of ecological models may be more relevant than long-term behavior.

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

[2]  G. E. Hutchinson,et al.  The Balance of Nature and Human Impact: The paradox of the plankton , 2013 .

[3]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Yoh Iwasa,et al.  Demographic Theory for an Open Marine Population with Space-Limited Recruitment , 1985 .

[5]  Robert M. May,et al.  The Croonian Lecture, 1985 - When two and two do not make four: nonlinear phenomena in ecology , 1986, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[6]  M. Kot,et al.  Discrete-time growth-dispersal models , 1986 .

[7]  M. Hassell,et al.  The Dynamics of the Viburnum Whitefly (Aleurotrachelus jelinekii): A Case Study of Population Regulation , 1987 .

[8]  M. Hassell.  Detecting regulation in patchily distributed animal populations , 1987 .

[9]  Crutchfield,et al.  Are attractors relevant to turbulence? , 1988, Physical review letters.

[10]  J. Estes,et al.  The Ecology of Extinctions in Kelp Forest Communities , 1989 .

[11]  R. Vadas,et al.  Inference in Ecology: The Sea Urchin Phenomenon in the Northwestern Atlantic , 1990, The American Naturalist.

[12]  M. Tegner,et al.  Sea urchins, El Ninos, and the long term stability of Southern California kelp forest communities , 1991 .

[13]  S. Ruffo,et al.  Periodic orbits and long transients in coupled map lattices , 1991 .

[14]  A. Berryman.  Can economic forces cause ecological chaos ? The case of the northern California Dungeness crab fishery , 1991 .

[15]  Robert M. May,et al.  The spatial dynamics of host-parasitoid systems , 1992 .

[16]  Ricard V. Sole,et al.  Nonequilibrium dynamics in lattice ecosystems: Chaotic stability and dissipative structures. , 1992, Chaos.

[17]  K. Kaneko.  Overview of coupled map lattices. , 1992, Chaos.

[18]  S. Ellner,et al.  Chaos in Ecology: Is Mother Nature a Strange Attractor?* , 1993 .

[19]  Alan Hastings,et al.  Complex interactions between dispersal and dynamics: Lessons from coupled logistic equations , 1993 .

[20]  A. Weiss,et al.  Sequential interactions of the TCR with two distinct cytoplasmic tyrosine kinases. , 1994, Science.