A model of macroevolution with a natural system size

We describe a simple model of evolution which incorporates the branching and extinction of species lines, and also includes abiotic influences. A first principles approach is taken in which the probability for speciation and extinction are defined purely in terms of the fitness landscapes of each species. Numerical simulations show that the total diversity fluctuates around a natural system size $N_{\rm nat}$ which only weakly depends upon the number of connections per species. This is in agreement with known data for real multispecies communities. The numerical results are confirmed by approximate mean field analysis.