An approach to modelling the dynamics of evolutionary self-organization

Abstract

We have simulated the dynamics of species evolution in a systems context on a parallel supercomputer. Population dynamics are represented as generalized Lotka-Volterra systems defined as points in a generalized phenotype or character space T . Populations which are closest in T compete most strongly for resources. A variety of systems with varying assumptions, resource distributions, and number of trophic levels were simulated. Starting with a random initial seed proceeding through a complex temporal sequence, most cases converged to essentially the same configuration. The final equilibrium state consisted of a gridwork of localized population clusters in T , representing individual species. The intercluster spacing was roughly equal to the standard deviation of the resource utilization function. Thus the systems self-organize to an array of niches which maximally fills the available volume of resource space while minimizing the overlap of resource utilization functions. The simulations were performed on a Connection Machine (a massively parallel supercomputer) which allowed up to 32 000 distinct points in character space to be modelled in parallel. Simulation allows a more realistic treatment of evolutionary dynamics and greater flexibility in experimental manipulation than previous analytical approaches. We experimented with temporal variations in the resource base. In most cases the niche structure was not affected; species prospered or declined as a function of local resource availability but the niche pattern remained invariant. However, in the case in which each species depends on only one or two resources, increasing randomness in the resource base resulted in a decrease in the number of species.