SPECIATION AND EXTINCTION IN A SIMPLE-MODEL OF EVOLUTION

We introduce a simple model of macro-coevolution that allows the branc hing and termination of species lines and also incorporates external i nfluences to the ecosystem. The strength of the external influences an d the likelihood of speciation and extinction are defined from the fit ness landscapes by two parameters, delta g and delta s. Results from n umerical simulations show that the total number of species fluctuates about a natural system size N-infinity. We present a mean-field theory that predicts N-infinity(proportional to)(K-1)delta s/delta g(2), whe re K-1 is the system connectivity and delta s is small. This result co mpares well with the numerical simulations. For large delta s, we demo nstrate why this expression changes to N-infinity(proportional to)(K-1 )delta s(2)/delta g(2). We compare the model to the fossil record, and comment on the role of ecological niches in models of evolution.