In this paper we give a generalization of the doubly $\mathcal{D}$-homothetically warped metric introduced by Blair [4], and we study the construction of Kählerian structure on the product of two almost contact metric structures. It is shown that if one factor is $β$-Kenmotsu, the other is $β$-Kenmotsu or $α$-Sasakian, and if one factor is cosymplectic, the other is $α$-Sasakian, but the product of two $α$-Sasakian is never Kählerian. Several examples are discussed.

The purpose of this article is to study the look-down model with selection and mutation in the case of a population containing two types of individuals, where the population size $N$ is finite and fixed. We show (Theorem 3.6) that the proportion of one of the two types converges, as the population size $N$ tends to infinity, towards the Wright-Fisher diffusion with selection and mutation.