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Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been…
Phenotype-switching with and without sensing environment is a ubiquitous strategy of organisms to survive in fluctuating environment. Fitness of a population of organisms with phenotype-switching may be constrained and restricted by hidden…
How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under…
Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when…
Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the…
In this paper, we wish to investigate the dynamics of information transfer in evolutionary dynamics. We use information theoretic tools to track how much information an evolving population has obtained and managed to retain about different…
Convergence of discrete-time Markov chains with two timescales is a powerful tool to study stochastic evolutionary games in subdivided populations. Focusing on linear games within demes, convergence to a diffusion process for the strategy…
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…
Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense…
In binary decision-making, individuals often choose either the rare or the common action. In the framework of evolutionary game theory, the best-response update rule can be used to model this dichotomy. Those who prefer the common action…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash…
A new approach to understanding evolution [Val09], namely viewing it through the lens of computation, has already started yielding new insights, e.g., natural selection under sexual reproduction can be interpreted as the Multiplicative…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
Finite-size fluctuations arising in the dynamics of competing populations may have dramatic influence on their fate. As an example, in this article, we investigate a model of three species which dominate each other in a cyclic manner.…
We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling…
We study the evolution of asexual microorganisms with small mutation rate in fluctuating environments, and develop techniques that allow us to expand the formal solution of the evolution equations to first order in the mutation rate. Our…
Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that…