Speciation by local adaptation and isolation by distance in extended environments

Speciation is often associated with geographical barriers that limit gene flow. However, species can also emerge in parapatry, even in homogeneous environments, through spatially restricted mating and limited dispersal. When the environment is not homogeneous, natural selection contributes to differentiation by local adaptation and tends to facilitate speciation. To explore how isolation by distance and adaptation combine to determine species diversity, we propose a model regulated by these two components. The former is implemented via mating restrictions on spatial proximity and genetic similarity, whereas the latter is realized by an ecological phenotype subjected to adaptation by natural selection. We consider a scenario where the environment has two distinct optima, and compare the resulting diversity patterns and phenotypic distributions with those of a homogeneous environment, with a single ecological optimum. We show that the interplay between selection and isolation by distance affects not only species formation but also phenotypic distributions and the timing of diversification. Simulating individuals with either restrictive or permissive mating regimes, combined with strong or weak selection, we show that: (i) environmental selection can accelerate diversification but is not always necessary for reproductive isolation; (ii) bimodal phenotypic patterns can arise through different evolutionary pathways and are therefore not necessarily signatures of ecological speciation; and (iii) when selection is weak and mating is restrictive, parapatric speciation begins before pronounced ecological differentiation, while the phenotypic peaks can oscillate and fail to reach a stationary state.