Related papers: An alternative delayed population growth differenc…
We study a generalised model of population growth in which the state variable is population growth rate instead of population size. Stochastic parametric perturbations, modelling phenotypic variability, lead to a Langevin system with two…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits are vertically inherited unless a mutation occurs, and…
We introduce, and formally establish, a variant of the Hawkes-fed birth-death process -- the delayed Hawkes birth-death process -- in which the conditional intensity does not increase at arrivals but at departures from the system. In a…
Habitat destruction threatens the viability of many populations, but its full consequences can take considerable time to unfold. Much of the discourse surrounding extinction debts--the number of species that persist transiently following…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…
We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death…
Ecological and evolutionary processes show various population dynamics depending on internal interactions and environmental changes. While crucial in predicting biological processes, discovering general relations for such nonlinear dynamics…
The Hassell model has been widely used as a general discrete-time population dynamics model that describes both contest and scramble intraspecific competition through a tunable exponent. Since the two types of competition generally lead to…
The rates at which individuals memorize and forget environmental information strongly influence their movement paths and long-term space use. To understand how these cognitive time scales shape population-level patterns, we propose and…
Compartment models with delay terms are widely used across a range of disciplines. The motivation to include delay terms varies across different contexts. In epidemiological and pharmacokinetic models, the delays are often used to represent…
Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 50's with the KiSS (after Kierstead, Slobodkin…
The time evolution of the Partridge-Barton model in the presence of the pleiotropic constraint and deleterious somatic mutations is exactly solved for arbitrary fecundity in the context of a matricial formalism. Analytical expressions for…
We study the posterior contraction behavior of the latent population structure that arises in admixture models as the amount of data increases. We adopt the geometric view of admixture models - alternatively known as topic models - as a…
In this paper, we study Hegselmann-Krause models with a time-variable time delay. Under appropriate assumptions, we show the exponential asymptotic consensus when the time delay satisfies a suitable smallness assumption. Our main strategies…
Non-selective effects, like genetic drift, are an important factor in modern conceptions of evolution, and have been extensively studied for constant population sizes. Here, we consider non-selective evolution in the case of growing…
We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the…
We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new…