Related papers: Discreteness Effects in Population Dynamics
Environmental variability greatly influences the eco-evolutionary dynamics of a population, i.e. it affects how its size and composition evolve. Here, we study a well-mixed population of finite and fluctuating size whose growth is limited…
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes…
This paper analyzes a stochastic logistic difference equation under the assumption that the population distribution follows a normal distribution. Our focus is on the mathematical relationship between the average growth rate and a newly…
We consider a hierarchically structured population in which the amount of resources an individual has access to is affected by individuals that are larger, and that the intake of resources by an individual only affects directly the growth…
Understanding the evolutionary dynamics of reinforcement learning under multi-agent settings has long remained an open problem. While previous works primarily focus on 2-player games, we consider population games, which model the strategic…
Establishing a quantitative connection between the population growth rate and the generation times of single cells is a prerequisite for understanding evolutionary dynamics of microbes. However, existing theories fail to account for the…
In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyze how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes…
Our theoretical understanding of crossover is limited by our ability to analyze how population diversity evolves. In this study, we provide one of the first rigorous analyses of population diversity and optimization time in a setting where…
We investigate the exploration of rugged fitness landscapes by spatially structured populations with demes on the nodes of a graph, connected by migrations. In the rare migration regime, we find that finite structures can adapt more…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
We propose a mathematical model for collective sensing in a population growing in a stochastically varying environment. In the population, individuals use an information channel for sensing the environment, and two channels for signal…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial…
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.…
While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven,…
Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference…
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…
Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in carrying capacity on the fate of a…
Different evolutionary models are known to make disparate predictions for the success of an invading mutant in some situations. For example, some evolutionary mechanics lead to amplification of selection in structured populations, while…
We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many…