2013/06/02 by Baruch Meerson, Otso Ovaskainen · 17 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Biology #Demography #Diffusion and Search Dynamics #Distribution (mathematics) #Dynamics (music) #Ecology #Econometrics #Extinction (optical mineralogy) #Geography #Immigration #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Occupancy #Physics #Population #Population size #Simple (philosophy) #Sociology #Statistical physics #Statistics #Stochastic modelling #Stochastic processes and statistical mechanics #cond-mat.stat-mech #q-bio.PE
paper · pdf · doi:10.1103/physreve.88.012124
published in Physical Review E 88(1), 012124 (American Physical Society) · 7 pages, 3 figures
arxiv created 2013/06/02 · openalex publication_date 2013/07/19 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
How high should be the rate of immigration into a stochastic population in order to significantly reduce the probability of observing the population become extinct? Is there any relation between the population size distributions with and without immigration? Under what conditions can one justify the simple patch occupancy models, which ignore the population distribution and its dynamics in a patch, and treat a patch simply as either occupied or empty? We answer these questions by exactly solving a simple stochastic model obtained by adding a steady immigration to a variant of the Verhulst model: a prototypical model of an isolated stochastic population.