An inhomogeneous stochastic rate process for evolution from states in an information geometric neighbourhood of uniform fitness

This study elaborates some examples of a simple evolutionary stochastic rate process where the population rate of change depends on the distribution of properties --- so different cohorts change at different rates. We investigate the effect on the evolution arising from parametrized perturbations of uniformity for the initial inhomogeneity. The information geometric neighbourhood system yields also solutions for a wide range of other initial inhomogeneity distributions, including approximations to truncated Gaussians of arbitrarily small variance and distributions with pronounced extreme values. It is found that, under quite considerable alterations in the shape and variance of the initial distribution of inhomogeneity in unfitness, the decline of the mean does change markedly with the variation in starting conditions, but the net population evolution seems surprisingly stable.

Keywords: Evolution, inhomogeneous rate process, information geometry, entropy, uniform distribution, log-gamma distribution.