Complex dynamics in multispecies communities

Abstract

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 comm unity 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, Darwinian 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.

Disappearing refuges in time and space: how environmental change threatens species coexistence

“…In field studies, it is a challenging task to identify communities that rely (fully or partly) on this coexistence mechanism because the mechanism of density regulation is particularly difficult to estimate from field data (Godfray et al 1990;Morris 1990). However, species that exert density regulation in early life stages (and thus are most probable to overcompensate, Sinclair 1989) and live in highly diverse communities with apparently limited number of resources may depend critically on this mechanism.…”

Controlling Chaos in Ecology: From Deterministic to Individual-based Models

“…Complex dynamical patterns are an inherent part of both real and model ecosystems and have been a matter of extensive studies in recent years [Hassell et al (1976); Godfray and Blythe (1990); Tilman and Wedin (1991); Bascompte and Solé (1995) and references therein]. Chaos is a particularly relevant example of 0092-8240/99/061187 + 21 $30.00/0 c 1999 Society for Mathematical Biology these patterns and it can be obtained even from very simple nonlinear models as a result of intrinsic nonlinearities (May, 1974(May, , 1976May and Oster, 1976;Schaffer and Kot, 1986).…”

Intraseasonal predictability of natural phytoplankton population dynamics

“…Takens's theorem (Takens, 1981 ) suggests that it is possible to reconstruct the dynamical attractor of a system with time lags of a variable of interest. This concept has been historically applied in ecology to understand the population dynamics of species in complex biological systems (Godfray & Blythe, 1990 ; Schaffer, 1984 ), including the prediction of coastal phytoplankton dynamics (McGowan et al, 2017 ).…”