Related papers: Evolution of a Fluctuating Population in a Randoml…
The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…
Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…
Understanding under what conditions populations, whether they be plants, animals, or viral particles, persist is an issue of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations…
Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we…
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…
Evolution occurs in populations of reproducing individuals. In stochastic descriptions of evolutionary dynamics, such as the Moran process, individuals are chosen randomly for birth and for death. If the same type is chosen for both steps,…
We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end…
Two species with similar resource requirements respond in a characteristic way to variations in their habitat -- their abundances rise and fall in concert. We use this idea to learn how bacterial populations in the microbiota respond to…
This paper investigates the influence of environmental noise on the characteristic timescale of the dynamics of density-dependent populations. General results are obtained on the statistics of time spent in rarity and time spent in…
Recent theoretical studies have shown that demographic stochasticity can greatly increase the tendency of asexually reproducing phenotypically diverse organisms to spontaneously evolve into localised clusters, suggesting a simple mechanism…
An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
Time evolutions of number of cities, population of cities, world population, and size distribution of present languages are studied in terms of a new model, where population of each city increases by a random rate and decreases by a random…
The influence of migration on the stochastic dynamics of subdivided populations is still an open issue in various evolutionary models. We develop here a self-consistent mean-field-like method in order to determine the effects of migration…
We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…
We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We…
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…
The impact of environmental variability on population size growth rate in dynamic models is a recurrent issue in the theoretical ecology literature. In the scalar case, R. Lande pointed out that results are ambiguous depending on whether…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…