Sexual and natural selection in a continuous time model

We call sexual selection the selection attributable only to the mating system, to distinguish it from other forms of selection (i.e. viability or fertility) which we call natural selection. We introduce a new continuous time model of sexual selection and we explore its relationship with natural selection. This model is an extension of the model proposed by Hoppensteadt [Hoppensteadt, F., 1977. Mathematical Theories of Populations: Demographics, Genetics and Epidemics. SIAM] and considers the three genotypes determined by two alleles in a locus, each with its own mortality and fertility rates, and the respective mating preferences.