A stochastic model for speciation by mating preferences

Abstract

Abstract. Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the population size. Our results rely on a fine study of the stochastic process and of its deterministic limit in large population, which is given by a system of coupled nonlinear differential equations. Besides, we propose several generalisations of our model, and prove that our findings are robust for those generalisations.

Crossing a fitness valley as a metastable transition in a stochastic population model

“…Contrarily to the population genetics approach, individual-based models of adaptive dynamics take into account varying population sizes as well as stochasticity, which is necessary if we aim at better understanding of phenomena involving small populations, such as mutational meltdown [21], invasion of a mutant population [14], evolutionary suicide and rescue [1], population extinction time [18,20], or recovery phenomena [4,8].…”

Well-posedness of Hamilton–Jacobi equations in population dynamics and applications to large deviations

“…A much studied question is the dynamics of the population in the large population scaling limit. Typical results include laws of large numbers to a solution of a firstorder differential equation or weak convergence of the process to a solution of a stochastic differential equation as in [3,6,22] and [13,Chapter 11]. Additional work is required for the estimation of the exit time from a domain: time spent before extinction, time for the propagation of a disease among a population, time for a mutation to establish itself in a population.…”

A Stochastic Model for Reproductive Isolation Under Asymmetrical Mating Preferences

“…For example, the initial divergence in traits may be the result of natural selection in order to decrease hybridization and then be subjected to mating preference [34], producing speciation by reinforcement [19]. Other studies illustrate the direct and promoting role of assortative mating, using numerical simulations [27,32,41], or theoretical results [36,10].…”

“…Then, studying both models, I established the main result of the paper, which ensures that the mechanism of mating preference combined with a negative type-dependent migration is sufficient to entail reproductive isolation and which gives the time needed before reproductive isolation. Here, unlike [10], the time is written with both mating preference parameters and both migration parameters, related to both alleles. I finally conducted an extensive study on the influence of migration and preference parameters on this time showing that large migration rates can favor types with a weak mating preference.…”

“…In particular, global results on the dynamical system are established such that the dynamics of almost all trajectories can be predicted. To do so, I developed an original method based on a perturbation theory of the migration parameters, which fully differs from the method used by [10]. The asset of this method is that it can easily be adapted to other dynamical systems.…”