Complex dynamics in multispecies communities

Communities of living organisms have potentially very complex population dynamics. Two components of complexity are considered, the dimensionality of the attractor underlying the persistent dynamics, and the presence of chaos. The dimensionality of real biological communities is unknown while there is great controversy about the presence of chaos in population dynamics. The evidence for chaos, and changes in the popularity of chaos among empirical biologists, is reviewed. Two new techniques developed in the physical sciences, attractor reconstruction and the estimation of the correlation dimension, are described and examples of their use in biology discussed. Although these techniques offer exciting new prospects for investigating community dynamics, there are some major problems in using them in biology. These problems include the length of biological time series, the ubiquity of noise, transient behaviour, Drawinian evolution and problems in interpretation. These problems are discussed and it is concluded that the best prospects of applying these techniques are using data collected in laboratory microcosms.

[1]  A A Berryman,et al.  Are ecological systems chaotic - And if not, why not? , 1989, Trends in ecology & evolution.

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

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

[4]  A. Howell.  Theories of Distribution‐‐A Critique , 1924 .

[5]  W. Hamilton.  Sex versus non-sex versus parasite , 1980 .

[6]  W. Gurney,et al.  Parameter evolution in a laboratory insect population , 1988 .

[7]  Michael E. Gilpin,et al.  Chaos, Asymmetric Growth and Group Selection for Dynamical Stability , 1980 .

[8]  R. May,et al.  Population biology of infectious diseases: Part II , 1979, Nature.

[9]  M. Hassell,et al.  The dynamics of age-structured host-parasitoid interactions , 1988 .

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

[11]  G Sugihara,et al.  Applications of fractals in ecology. , 1990, Trends in ecology & evolution.

[12]  S. P. Blythe,et al.  Nicholson's blowflies revisited , 1980, Nature.

[13]  Jm Colebrook,et al.  Continuous plankton records - zooplankton and environment, northeast atlantic and north-sea, 1948-1975 , 1978 .

[14]  Stephen H. Levine,et al.  Competitive Interactions in Ecosystems , 1976, The American Naturalist.

[15]  R. May,et al.  The Dynamics of Host-Parasitoid-Pathogen Interactions , 1990, The American Naturalist.

[16]  W. Schaffer.  Order and Chaos in Ecological Systems , 1985 .

[17]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[18]  T. Prout,et al.  Competition Among Immatures Affects Their Adult Fertility: Population Dynamics , 1985, The American Naturalist.

[19]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[20]  Michael E. Gilpin,et al.  Spiral Chaos in a Predator-Prey Model , 1979, The American Naturalist.

[21]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

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

[23]  W. Schaffer.  ECOLOGICAL ABSTRACTION: THE CONSEQUENCES OF REDUCED DIMENSIONALITY IN ECOLOGICAL MODELS' , 1981 .

[24]  C. Elton,et al.  The Ten-Year Cycle in Numbers of the Lynx in Canada , 1942 .

[25]  R M Nisbet,et al.  Population dynamics in a periodically varying environment. , 1976, Journal of theoretical biology.

[26]  Peter Kareiva,et al.  5. Renewing the Dialogue between Theory and Experiments in Population Ecology , 1989 .

[27]  P. Grassberger,et al.  14. Estimating the fractal dimensions and entropies of strange attractors , 1986 .

[28]  G. Nicolis,et al.  Is there a climatic attractor? , 1984, Nature.

[29]  P. Grassberger.  Do climatic attractors exist? , 1986, Nature.

[30]  S. Blythe,et al.  Biological Attractors, Transients, and Evolution , 1988 .

[31]  Robert M. May,et al.  NONLINEAR PHENOMENA IN ECOLOGY AND EPIDEMIOLOGY * , 1980 .

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

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

[34]  G. Oster,et al.  Models for Age‐Specific Interactions in a Periodic Environment , 1974 .

[35]  J. Readshaw,et al.  A Model of Nicholson's Blowfly Cycles and its Relevance to Predation Theory , 1980 .

[36]  R. Levins.  Evolution in Changing Environments , 1968 .

[37]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[38]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

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

[40]  F. Ayala,et al.  Dynamics of Single‐Species Population Growth: Stability or Chaos? , 1981 .

[41]  W M Schaffer,et al.  Chaos in ecological systems: The coals that Newcastle forgot. , 1986, Trends in ecology & evolution.