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

TL;DR

This paper models evolutionary dynamics using an inhomogeneous stochastic rate process influenced by initial distribution perturbations, revealing that population decline is sensitive to initial inhomogeneity shape but overall evolution remains stable.

Contribution

It introduces a stochastic rate process framework incorporating information geometric perturbations of initial distributions, extending understanding of population evolution under inhomogeneity.

Findings

Mean decline varies significantly with initial distribution shape and variance.

Population evolution remains surprisingly stable despite substantial initial inhomogeneity changes.

Solutions include approximations to truncated Gaussian distributions with small variance.

Abstract

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.