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It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in…
Consider a branching process $\{Z_n\}_{n\ge 0}$ with immigration in varying environment. For $a\in\{0,1,2,...\},$ let $C=\{n\ge0:Z_n=a\}$ be the collection of times at which the population size of the process attains level $a.$ We give a…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
Populations exhibiting partial migration consist of two groups of individuals: Those that mi- grate between habitats, and those that remain fixed in a single habitat. We propose several discrete-time population models to investigate the…
A class of branching processes in varying environments is exhibited which become extinct almost surely even though the means M_n grow fast enough so that sum M_n^{-1} is finite. In fact, such a process is constructed for every offspring…
When four species compete stochastically in a cyclic way, the formation of two teams of mutually neutral partners is observed. In this paper we study through numerical simulations the extinction processes that can take place in this system…
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…
Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size $n$. A Markovian SIR (susceptible $\to$ infective $\to$ recovered) infectious disease,…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
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 $n\geq 0$.…
Understanding the mechanisms governing population extinctions is of key importance to many problems in ecology and evolution. Stochastic factors are known to play a central role in extinction, but the interactions between a population's…
We consider a birth and death process in which death is due to both `natural death' and to competition between individuals, modelled as a quadratic function of population size. The resulting `logistic branching process' has been proposed as…
The extinction and persistence of infective individuals are closely related to the random change of the environment. In this paper, via the random/stochastic SIRS models, we analyze qualitatively and quantitatively the impact caused by the…
We examine to what extent the tempo and mode of environmental fluctuations matter for the growth of structured populations. The models are switching, linear ordinary differential equations $x'(t)=A(\sigma(\omega t))x(t)$ where…
We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of $\mathbb {Z}^d$. In each of the four models studied, an individual in a local population can reproduce, die or…
Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given…
Given that extinction in a bisexual population is certain, we study a way to approximate the time when this extinction occurs. Our study is based on standard tools from Extreme Value Theory, which in practice are very easy to implement. We…
Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating…