Information and (co)variances in discrete evolutionary genetics involving solely selection

The purpose of this paper is twofold. First, we introduce the general formalism of evolutionary genetics dynamics involving fitnesses, under both the deterministic and stochastic setups, and chiefly in discrete time. In the process, we particularize it to a one-parameter model where only a selection parameter is unknown. Then and in a parallel manner, we discuss the problems of estimation of the selection parameter on the basis of a single-generation frequency distribution shift under both deterministic and stochastic evolutionary dynamics. In the stochastics, we consider both the celebrated Wright–Fisher and Moran models