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Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics.…
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…
We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
If rock beats scissors and scissors beat paper, one might assume that rock beats paper too. But this is not the case for intransitive relationships that make up the famous rock-paper-scissors game. However, the sole presence of paper might…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
Cooperation often depends on individuals avoiding exploitation and interacting preferentially with other cooperators. We explore how context-dependent migration influences the evolution of cooperation in spatially structured populations.…
Recent developments of eco-evolutionary models have shown that evolving feedbacks between behavioral strategies and the environment of game interactions, leading to changes in the underlying payoff matrix, can impact the underlying…
We discuss the long-run behavior of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash…
Understanding if and how mutants reach fixation in populations is an important question in evolutionary biology. We study the impact of population growth has on the success of mutants. To systematically understand the effects of growth we…
We introduce and study the spatial replicator equation with higher order interactions and both infinite (spatially homogeneous) populations and finite (spatially inhomogeneous) populations. We show that in the special case of three…
Predators may attack isolated or grouped prey in a cooperative, collective way. Whether a gregarious behavior is advantageous to each species depends on several conditions and game theory is a useful tool to deal with such a problem. We…
This paper investigates the long-term behavior of an interacting particle system of interest in the hot topic of evolutionary game theory. Each site of the $d$-dimensional integer lattice is occupied by a player who is characterized by one…
We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a L\'{e}vy dust, which allows…
We study the combined influence of selection and random fluctuations on the evolutionary dynamics of two-strategy ("cooperation" and "defection") games in populations comprising cooperation facilitators. The latter are individuals that…
We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for…
We introduce and study a stochastic model for the dynamics of colonial species, which reproduce through fission or fragmentation. The fission rate depends on the relative sizes of colonies in the population, and the growth rate of colonies…
To study later spatial evolutionary games based on the multitype contact process, we first focus in this paper on the conditions for survival/extinction in the presence of only one strategy, in which case our model consists of a variant of…
We present a set of numerical simulations of the dynamical evolution of compact planetary systems migrating in a protoplanetary disk whose inner edge is sculpted by the interaction with the stellar magnetic field, as described in Yu et al.…