Related papers: A dynamical phase transition in a model for evolut…
We study the effect of migration between coupled populations, or patches, on the stability properties of multistrain disease dynamics. The epidemic model used in this work displays a Hopf bifurcation to oscillations in a single well mixed…
This survey focuses on the most important aspects of the mathematical theory of population genetic models of selection and migration between discrete niches. Such models are most appropriate if the dispersal distance is short compared to…
We introduce an asymmetric noisy voter model to study the joint effect of immigration and a competition-dispersal tradeoff in the dynamics of two species competing for space in regular lattices. Individuals of one species can invade a…
This paper proposes a stochastic block model with dynamics where the population grows using preferential attachment. Nodes with higher weighted degree are more likely to recruit new nodes, and nodes always recruit nodes from their own…
The purpose of this roadmap article is to draw attention to a paradigm shift in our understanding of evolution towards a perspective of ecological-evolutionary feedback, highlighted through two recent highly simplified examples of rapid…
Cellular differentiation and evolution are stochastic processes that can involve multiple types (or states) of particles moving on a complex, high-dimensional state-space or "fitness" landscape. Cells of each specific type can thus be…
The dynamics of the model of agents with limited confidence introduced by Hegselmann and Krause exhibits multiple well-separated regimes characterised by the number of distinct clusters in the stationary state. We present indications that…
We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two adjacent populations: each population undergoes linear diffusion and logistic growth, and the boundary between…
We consider an asexual population evolving on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local optima. We track the most populated genotype as it changes when the population jumps from…
We consider adaptive change of diet of a predator population that switches its feeding between two prey populations. We develop a novel 1 fast--3 slow dynamical system to describe the dynamics of the three populations amidst continuous but…
We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the…
We consider the Derrida-Higgs (DH) statistical model of species formation in the case where the population is geographically distributed in discrete locations, and mating only takes place within one location. Keeping the rate of migration…
Many biological populations exhibit diversity in their strategy for survival and reproduction in a given environment, and microbes are an example. We explore the fate of different strategies under sustained environmental change by…
Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium…
Migration's impact spans various social dimensions, including demography, sustainability, politics, economy and gender disparities. Yet, the decision-making process behind migrants choosing their destination remains elusive. Existing models…
In this paper we consider two continuous-mass population models as analogues of logistic branching random walks, one is supported on a finite trait space and the other one is supported on an infinite trait space. For the first model with…
We suggest a natural approach that leads to a modification of classical quasispecies models and incorporates the possibility of population extinction in addition to growth. The resulting modified models are called open. Their essential…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…
Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we…
This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance).…