Related papers: Evolutionary Dynamics with Fluctuating Population …
Population dynamics deals with the collective phenomena of living organisms, and it has attracted much attention since it is expected to explain how not only living organisms but also human beings have been adapted to varying environments.…
It is well-known that interactions between species determine the population composition in an ecosystem. Conventional studies have focused on fixed population structures to reveal how interactions shape population compositions. However,…
We study effects of strategy-dependent time delays on equilibria of evolving populations. It is well known that time delays may cause oscillations in dynamical systems. Here we report a novel behavior. We show that microscopic models of…
Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…
We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large…
We propose a new evolutionary dynamics for population games with a discrete strategy set, inspired by the theory of optimal transport and Mean field games. The dynamics can be described as a Fokker-Planck equation on a discrete strategy…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…
The processes and mechanisms underlying the origin and maintenance of biological diversity have long been of central importance in ecology and evolution. The competitive exclusion principle states that the number of coexisting species is…
In this paper, we study analytically the statistics of the number of equilibria in pairwise social dilemma evolutionary games with mutation where a game's payoff entries are random variables. Using the replicator-mutator equations, we…
This paper is concerned with a diffusive Lotka-Volterra cooperative modelwith population flux by attractive transition. We study the time-global well-posedness and the large time behavior of solutions in a case where the habitat is a…
We study evolutionary game dynamics in a well-mixed populations of finite size, N. A well-mixed population means that any two individuals are equally likely to interact. In particular we consider the average abundances of two strategies, A…
Evolutionary games are a developing sub-field of game theory. This branch of game theory is used in the study of the adaptation of large, but finite, populations of agents to changes in the environment. It assumes that each agent has no…
We propose a model for evolutionary game dynamics with three strategies $A$, $B$ and $C$ in the framework of Moran process in finite populations. The model can be described as a stochastic process which can be numerically computed from a…
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…
Evolutionary transitions among ecological interactions are widely known, although their detailed dynamics remain absent for most population models. Adaptive dynamics has been used to illustrate how the parameters of population models might…
We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the…
In the past years, a remarkable mapping has been found between the dynamics of a population of M individuals undergoing random mutations and selection, and that of a single system in contact with a thermal bath with temperature 1/M. This…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial,…
The random Lotka-Volterra model is widely used to describe the dynamical and thermodynamic features of ecological communities. In this work, we consider random symmetric interactions between species and analyze the strongly competitive…