Entropy change due to selection in replicator and recombinator systems with randomly chosen interaction matrix values

Abstract

Selection can be described as a process of information accumulation21. The present work extends this for frequency-dependent selection. For recombination, it is shown that the total entropy change can be calculated by summing the contributions of the individual gene loci in this case as well. For more complex replicator systems with and without recombination with randomly selected interaction matrix values (defining the fitness landscape), a detailed investigation is made of how the number of replicators ("genotypes") surviving, the mean fitness, and the entropy change depend on the number of replicators initially present, on their initial frequencies, and on certain properties (symmetry: aij=aji versus aij=aji) of the interaction matrix. Survival of several to many replicators is the norm rather than the exception. The more survive, the smaller the entropy change due to selection, although this is no longer generally true for asymmetric interaction matrices. Cases deviating from the rule were studied, but their systematic classification is still lacking. Finally, how evolution alters replicator systems of greater complexity was analyzed. It is shown that different evolutionary algorithms can lead to an increase in mean fitness and/or an increase in the number of surviving replicators. In contrast to simple replicator systems, coexistence in more complex ones apparently results naturally as a consequence of selection and evolution. It results that the view that: "Evolution is based on a fierce competition between individuals and should therefore reward only selfish behavior"16 is merely an artifact that follows from the study of unrealistically simple systems.