We introduce a simple model of macro-coevolution that allows the branching and termination of species lines and also incorporates external influences to the ecosystem. The strength of the external influences and the likelihood of speciation and extinction are defined from the fitness landscapes by two parameters, δg and δs. Results from numerical simulations show that the total number of species fluctuates about a natural system size ${\mathrm{N}}_{\mathrm{\infty }}$. We present a mean-field theory that predicts ${\mathrm{N}}_{\mathrm{\infty }}$∝(K-1)δs/δ${\mathrm{g}}^2$, where K-1 is the system connectivity and δs is small. This result compares well with the numerical simulations. For large δs, we demonstrate why this expression changes to ${\mathrm{N}}_{\mathrm{\infty }}$∝(K-1)δ${\mathrm{s}}^2$/δ${\mathrm{g}}^2$. We compare the model to the fossil record, and comment on the role of ecological niches in models of evolution.

DOI:https://doi.org/10.1103/PhysRevE.55.3312