Related papers: Minimizing the population extinction risk by migra…
Sexually reproducing populations with small number of individuals may go extinct by stochastic fluctuations in sex determination, causing all their members to become male or female in a generation. In this work we calculate the time to…
We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
The stability of ecosystems as well as the relation between topology and dynamics on multilayer networks are important questions that are usually discussed in separate communities. Here, we combine these two topics by investigating the…
The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…
The survival of natural populations may be greatly affected by environmental conditions that vary in space and time. We look at a population residing in two locations (patches) coupled by migration, in which the local conditions fluctuate…
Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V.…
Many species are unsustainable at small population densities (Allee Effect), i.e., below a threshold named Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to…
One of the critical measures to control infectious diseases is a lockdown. Once past the lockdown stage in many parts of the world, the crucial question now concerns the effects of relaxing the lockdown and finding the best ways to…
In this paper we afford a quantitative analysis of the sustainability of current world population growth in relation to the parallel deforestation process adopting a statistical point of view. We consider a simplified model based on a…
Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently…
We consider three regions with different public health conditions. In the absence of migration among these regions, the first two have good health conditions and the disease free state is stable; for the third region, on the other hand, the…
Life is on the razor's edge as resulting from competitive birth and death random forces. We illustrate this aphorism in the context of three Markov chain population models where systematic random immigration events promoting growth are…
The way diseases spread through schools, epidemics through countries, and viruses through the Internet is crucial in determining their risk. Although each of these threats has its own characteristics, its underlying network determines the…
We introduce a population model to test the hypothesis that even a single migrant per generation may rescue a dying population. Let $(c_k)$ be a sequence of real numbers in $(0,1)$. Let $X_n$ be a size of the population at time $n\geq 0$.…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
This paper is a follow-up to a previous work where we considered populations with time-varying growth rates living in patches and irreducible migration matrix between the patches. Each population, when isolated, would become extinct.…
In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the…
Comprehensive models of stochastic, clonally reproducing populations are defined in terms of general branching processes, allowing birth during maternal life, as for higher organisms, or by splitting, as in cell division. The populations…
Genetic fitness optimization using small populations or small population updates across generations generally suffers from randomly diverging evolutions. We propose a notion of highly probable fitness optimization through feasible…