Entropy Rates of the Multidimensional Moran Processes and Generalizations

Abstract: The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The entropy rate is shown to behave intuitively with respect to evolutionary parameters such as monotonicity with respect to mutation probability (for the neutral landscape), relative fitness, and strength of selection. Strict upper bounds, depending only on the number of replicating types, for the entropy rate are given and the neutral fitness landscape attains the maximum in the large population limit. Various additional limits are computed including small mutation, weak and strong selection, and large population holding the other parameters constant, revealing the individual contributions and dependences of each evolutionary parameter on the long-run outcomes of the processes.