arXiv subjects

Helene Leman

Publications and source records attributed to Helene Leman.

4 recordsLinked to original sources

arXiv2017

A stochastic model for reproductive isolation under asymmetrical mating preferences

More and more evidence shows that mating preference is a mechanism that may lead to a reproductive isolation event. In this paper, a haploid population living on two patches linked by migration is considered. Individuals are ecologically and demographically neutral on the space and differ only on a trait, $a$ or $A$, affecting both mating success and migration rate. The special feature of this paper is to assume that the strengths of the mating preference and the migration depend on the trait carried. Indeed, patterns of mating preferences are generally asymmetrical between the subspecies of a population. I prove that mating preference interacting with frequency-dependent migration behavior can lead to a reproductive isolation. Then, I describe the time before reproductive isolation occurs. To reach this result, I use an original method to study the limiting dynamical system, analyzing first the system without migration and adding migration with a perturbation method. Finally, I study how the time before reproductive isolation is influenced by the parameters of migration and of mating preferences, highlighting that large migration rates tend to favor types with weak mating preferences.

q-bio.PE↗

arXiv2017

Looking for the right mate in diploid species: how dominance relationships affect population differentiation in sexual trait?

Divergence between populations for a given trait can be driven by natural or sexual selection, interacting with migration behaviour. Mating preference for different phenotypes can lead to the emergence and persistence of differentiated populations. Dominance between alleles encoding for divergent phenotypes can interfere in such processes. Using a diploid model of trait determining both mating success and migration rate, we explored differentiation between two connected populations, assuming either co-dominance or strict dominance between alleles. The model assumes that individuals prefer mating with partners displaying the same phenotype and therefore tend to move to the other population when their own phenotype is rare. We show that the emergence of differentiated populations in this diploid model is limited as compared to results obtained with the same model assuming haploidy. When assuming co-dominance, differentiation arises only when migration is limited as compared to preference. Such differentiation is less dependent on migration when assuming strict dominance between haplotypes. Dominant alleles frequently invade populations because their phenotype is more frequently expressed, resulting in higher mating success and rapid decrease in migration. However, depending on the initial distribution of alleles, this advantage associated with dominance (i.e. Haldane's sieve) may lead to fixation of the dominant allele throughout both populations. Depending on the initial distribution of heterozygotes, persistence of polymorphisms within populations can also occur because heterozygotes displaying the predominant phenotype benefit from mating preferences. Altogether, our results highlight that heterozygotes' behaviour has a strong impact on population differentiation and stress out the need of diploid models of differentiation and speciation driven by natural and sexual selection.

q-bio.PE↗

arXiv2015

Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence

We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves also a birth rate, a density-dependent logistic death rate and a probability of mutation at each birth event. We study the convergence of the microscopic process when the population size grows to $+\infty$ and the mutation probability decreases to $0$. We prove a convergence towards a jump process that jumps in the infinite dimensional space of the stable spatial distributions. The proof requires specific studies of the microscopic model. First, we examine the large deviation principle around the deterministic large population limit of the microscopic process. Then, we find a lower bound on the exit time of a neighborhood of a stationary spatial distribution. Finally, we study the extinction time of the branching diffusion processes that approximate small size populations.

math.PR↗

arXiv2014

Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation

The electrostatic potential in the neighborhood of a biomolecule can be computed thanks to the non-linear divergence-form elliptic Poisson-Boltzmann PDE. Dedicated Monte-Carlo methods have been developed to solve its linearized version (see e.g.Bossy et al 2009, Mascagni & Simonov 2004}). These algorithms combine walk on spheres techniques and appropriate replacements at the boundary of the molecule. In the first part of this article we compare recent replacement methods for this linearized equation on real size biomolecules, that also require efficient computational geometry algorithms. We compare our results with the deterministic solver APBS. In the second part, we prove a new probabilistic interpretation of the nonlinear Poisson-Boltzmann PDE. A Monte Carlo algorithm is also derived and tested on a simple test case.

math.NA↗