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Evolutionary game dynamics are often studied in the context of different population structures. Here we propose a new population structure that is inspired by simple multicellular life forms. In our model, cells reproduce but can stay…

We study the large population limit of a multi-strategy discrete-time Moran process in the weak selection regime. We show that the replicator dynamics is interpreted as the large-population limit of the Moran process. This result is…

In this study we present an extension of the replicator equation with diffusion to multiplex graphs. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to…

To predict the behavior of a population game when time becomes very long, the process that characterizes the evolution of our game dynamics must be reversible. Known games satisfying this are 2 strategy games as well as potential games with…

Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…

We study evolutionary multi-player games in finite populations, subject to fluctuating environments. The population undergoes a birth-death process with absorbing states, and the environment follows a Markovian process, resulting in a…

Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…

Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…

In this review, we summarize recent developments in stochastic evolutionary game dynamics of finite populations.

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…

Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…

We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov, Moran process. We show that to $\mathcal O(1/N)$, the time-averaged fitness is lower for the finite…

The coevolutionary dynamics in finite populations currently is investigated in a wide range of disciplines, as chemical catalysis, biological evolution, social and economic systems. The dynamics of those systems can be formulated within the…

While generic competitive systems exhibit mixtures of hierarchy and cycles, real-world systems are predominantly hierarchical. We demonstrate and extend a mechanism for hierarchy; systems with similar agents approach perfect hierarchy in…

We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…

We study inhomogeneous host-pathogen dynamics to model the global amphibian population extinction in a lake basin system. The lake basin system is modeled as quenched disorder. In this model we show that once the pathogen arrives at the…

We consider an infinite-sized population where an infinite number of traits compete simultaneously. The replicator equation with a diffusive term describes time evolution of the probability distribution over the traits due to selection and…

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…

We consider a spatial multi-type branching model in which individuals migrate in geographic space according to random walks and reproduce according to a state-dependent branching mechanism which can be sub-, super- or critical depending on…

We consider evolutionary dynamics for population games in which players have a continuum of strategies at their disposal. Models in this setting amount to infinite-dimensional differential equations evolving on the manifold of probability…