arXiv subjects

Alejandro H. Wences

Publications and source records attributed to Alejandro H. Wences.

3 recordsLinked to original sources

arXiv2025

Genealogical transition in the noisy $N$-Branching Random Walk. How stronger selection may promote genetic diversity

We consider an extension of the noisy $N$-Branching Random Walk that models the evolution of a population subject to natural selection. We show the existence of a critical value for the noise which separates the limiting genealogical structure into two regimes, which we respectively call the semi-pulled and the fully-pulled regimes. In the fully-pulled regime, the genealogy converges to a discrete time Poisson-Dirichlet coalescent. In the semi-pulled regime, the genealogy converges to the Bolthausen-Sznitman coalescent. We discuss some interesting biological consequences of this result. In particular, our model predicts a non-monotone relation between the selection strength and the effective population size.

q-bio.PE↗

arXiv2024

Exchangeable coalescents beyond the Cannings class

We propose a general framework for the study of the genealogy of neutral discrete-time populations. We remove the standard assumption of exchangeability of offspring distributions appearing in Cannings' models, and replace it by a less restrictive condition of non-heritability of reproductive success. We provide a general criterion for the weak convergence of their genealogies to $Ξ$-coalescents, and apply it to a simple parametrization of our scenario (which, under mild conditions, we also prove to essentially include the general case). We provide examples for such populations, including models with highly-asymmetric offspring distributions and populations undergoing random but recurrent bottlenecks. Finally we study the limit genealogy of a new exponential model which, as previously shown for related models and in spite of its built in (fitness) inheritance mechanism, can be brought into our setting.

math.PR↗

arXiv2019

Site Frequency Spectrum of the Bolthausen-Sznitman Coalescent

We derive explicit formulas for the two first moments of he site frequency spectrum $(SFS_{n,b})_{1\leq b\leq n-1}$ of the Bolthausen-Sznitman coalescent along with some precise and efficient approximations, even for small sample sizes $n$. These results provide new $L_2$-asymptotics for some values of $b=o(n)$. We also study the length of internal branches carrying $b>n/2$ individuals. In this case we obtain the distribution function and a convergence in law. Our results rely on the random recursive tree construction of the Bolthausen-Sznitman coalescent.

math.PR↗