Search PubMed⌕ Search

Biomedical subjects

R M May

Publications and source records attributed to R M May.

At least 127 records · Page 7Linked to original sources
PubMed1976

Simple mathematical models with very complicated dynamics.

First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hiearchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.

Diffusion↗
PubMed1974

Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos.

Some of the simplest nonlinear difference equations describing the growth of biological populations with nonoverlapping generations can exhibit a remarkable spectrum of dynamical behavior, from stable equilibrium points, to stable cyclic oscillations between 2 population points, to stable cycles with 4, 8, 16, . . . points, through to a chaotic regime in which (depending on the initial population value) cycles of any period, or even totally aperiodic but boundedpopulation fluctuations, can occur. This rich dynamical structure is overlooked in conventional linearized analyses; its existence in such fully deterministic nonlinear difference equations is a fact of considerable mathematical and ecological interest.

Ecology↗
PubMed1972

Niche overlap as a function of environmental variability.

The relationship between environmental variability and niche overlap is studied for a class of model biological communities in which several species compete on a one-dimensional continuum of resources, e.g., food size. In a strictly unvarying (deterministic) environment, there is in general no limit to the degree of overlap, short of complete congruence. However, in a fluctuating (stochastic) environment, the average food sizes for species adjacent on the resource spectrum must differ by an amount roughly equal to the standard deviation in the food size taken by either individual species. This mathematical result emerges in a nonobvious yet robust way for environmental fluctuations whose variance relative to their mean ranges from around 0.01% to around 30%. In short, there is an effective limit to niche overlap in the real world, and this limit is insensitive to the degree of environmental fluctuation, unless it be very severe. Recent field work, particularly on bird guilds, seems in harmony with the model's conclusion.

Animals↗