arXiv subjects

Leonardo Videla

Publications and source records attributed to Leonardo Videla.

3 recordsLinked to original sources

arXiv2025

Age-structured stochastic populations under dynamic harvesters' behavior: well-posedness, asymptotic stability and numerically-amenable approximations

In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of coupled stochastic differential equations. This limit process is complemented with socio-ecological and environmental factors. For the resulting system we establish well-posedness, positivity, and the non-attainability of extinction boundaries, together with its long-term behavior and numerical approximation, relying on ad-hoc arguments to handle the super-linear growth and non-Lipschitz coefficients. Finally, we illustrate some of our findings with numerical experiments.

math.PR↗

arXiv2024

Wright--Fisher kernels: from linear to non-linear dynamics, ergodicity and McKean--Vlasov scaling limits

We study the evolution of a pathogen with two allelic types infecting a population of hosts, where within-host type frequencies evolve in discrete time. Our framework is built on a two-parameter family of transition kernels on [0,1], which describe one-step updates of type frequencies. In the absence of host interaction, the single-host type-frequency process admits, for a broad class of parameters, a moment dual with a branching-coalescing structure reminiscent of the Ancestral Selection Graph. Under suitable parameter and time scalings, it converges to a Wright--Fisher diffusion with drift. To incorporate interactions among hosts, we introduce a mean-field mechanism whereby within-host dynamics depend on the empirical type distribution across the population. We prove uniform-in-time propagation of chaos, comparing the dynamics in a typical host with a corresponding non-linear Markov chain. Under appropriate scaling, this non-linear chain converges to a McKean--Vlasov Wright--Fisher diffusion. As an illustration, we analyse a model where mutation rates depend on the current type distribution across hosts and establish uniform-in-time propagation of chaos together with ergodicity of the limiting McKean--Vlasov equation.

math.PR↗

arXiv2023

Persistence and neutrality in interacting replicator dynamics

We study the large-time behavior of an ensemble of entities obeying replicator-like stochastic dynamics with mean-field interactions as a model for a primordial ecology. We prove the propagation-of-chaos property and establish conditions for the strong persistence of the $N$-replicator system and the existence of invariant distributions for a class of associated McKean-Vlasov dynamics. In particular, our results show that, unlike typical models of neutral ecology, fitness equivalence does not need to be assumed but emerges as a condition for the persistence of the system. Further, neutrality is associated with a unique Dirichlet invariant probability measure. We illustrate our findings with some simple case studies, provide numerical results, and discuss our conclusions in the light of Neutral Theory in ecology.

math.PR↗