Adaptation of a population to a changing environment in the light of quasi-stationarity

DOI10.1017/APR.2023.28arXiv1903.10165MaRDI QIDQ6119938

Aurélien Velleret

Publication date: 20 February 2024

Published in: Advances in Applied Probability (Search for Journal in Brave)

Abstract: We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion modeling population size. As the individual features in the population become further away from the optimal ones, the growth rate declines, making population extinction more likely. Assuming that the environment changes deterministically and steadily in a constant direction, we obtain the existence and uniqueness of the quasi-stationary distribution, the associated survival capacity and the Q-process. Our approach also provides several exponential convergence results (in total variation for the measures). From this synthetic information, we can characterize the efficiency of internal adaptation (i.e. population turnover from mutant invasions). When the latter is lacking, there is still stability, but because of the high level of population extinction. Therefore, such a characterization must be based on specific features of this quasi-ergodic regime.

Full work available at URL: https://arxiv.org/abs/1903.10165

zbMATH Keywords

evolutionjump processesquasi-stationary distributionecologyMarkov process in continuous time and continuous spacemobile optimum

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Population dynamics (general) (92D25) Ecology (92D40) Random measures (60G57)

Cites Work

• Title not available (Why is that?)
• Title not available (Why is that?)
• The branching process with logistic growth
• Quasi-stationary distributions and diffusion models in population dynamics
• Phenotypic lag and population extinction in the moving-optimum model: insights from a small-jumps limit
• Quasi-stationary distributions and population processes
• Small jumps asymptotic of the moving optimum Poissonian SDE
• Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes
• More on the long time stability of Feynman-Kac semigroups
• Unique quasi-stationary distribution, with a possibly stabilizing extinction
• Erratum: ``Practical criteria for \(R\)-positive recurrence of unbounded semigroups
• On an irreducibility type condition for the ergodicity of nonconservative semigroups
• On time scales and quasi-stationary distributions for multitype birth-and-death processes
• Quasi-stationary distributions for discrete-state models
• On the uniqueness of solutions of stochastic differential equations
• Exponential convergence to quasi-stationary distribution and \(Q\)-process
• Probabilistic Models of Population Evolution
• Quasi-Stationary Distributions
• Uniform convergence of penalized time-inhomogeneous Markov processes
• Criteria for Exponential Convergence to Quasi-Stationary Distributions and Applications to Multi-Dimensional Diffusions
• On the large-time behaviour of the solution of a stochastic differential equation driven by a Poisson point process
• On the predictable representation property of martingales associated with Lévy processes
• Stochastic Models for Structured Populations
• An Introduction to the Theory of Point Processes
• A non‐conservative Harris ergodic theorem

Related Items (1)

Exponential quasi-ergodicity for processes with discontinuous trajectories

This page was built for publication: Adaptation of a population to a changing environment in the light of quasi-stationarity

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6119938)