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Evolutionary game dynamics in finite populations provides a new framework to understand the selection of traits with frequency-dependent fitness. Recently, a simple but fundamental law of evolutionary dynamics, which we call {\sigma} law,…
Dormancy is a widespread adaptive strategy that enables populations to persist in fluctuating environments, yet how its benefits depend on the temporal structure of environmental variability remains unclear. We examine how dormancy…
In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…
We establish a theoretical framework to address evolutionary dynamics of spatial games under strong selection. As the selection intensity tends to infinity, strategy competition unfolds in the deterministic way of winners taking all. We…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
In the course of Darwinian evolution of a population, punctualism is an important phenomenon whereby long periods of genetic stasis alternate with short periods of rapid evolutionary change. This paper provides a mathematical interpretation…
We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur…
Microscopic strategy update rules play an important role in the evolutionary dynamics of cooperation among interacting agents on complex networks. Many previous related works only consider one \emph{fixed} rule, while in the real world,…
The usual Langevin approach to describe systems driven by noise fails to describe the long time behavior of systems with multiple attractors. The solution of the associated linear Fokker-Planck equation is always unique, even though it…
Condensation phenomena arise through a collective behaviour of particles. They are observed in both classical and quantum systems, ranging from the formation of traffic jams in mass transport models to the macroscopic occupation of the…
Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…
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…
Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The…
We consider a metapopulation made up of $K$ demes, each containing $N$ individuals bearing a heritable quantitative trait. Demes are connected by migration and undergo independent Moran processes with mutation and selection based on trait…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
We investigate evolutionary dynamics of two-strategy matrix games with zealots in finite populations. Zealots are assumed to take either strategy regardless of the fitness. When the strategy selected by the zealots is the same, the fixation…
We construct an individual-based metapopulation model of population genetics featuring migration, mutation, selection and genetic drift. In the case of a single `island', the model reduces to the Moran model. Using the diffusion…
Uncertainty, characterised by randomness and stochasticity, is ubiquitous in applications of evolutionary game theory across various fields, including biology, economics and social sciences. The uncertainty may arise from various sources…
Involution, a phenomenon of excessive competition with diminishing returns, has become a pressing socio-economic concern in contemporary China, prompting both academic inquiry and policy interventions. This paper proposes an evolutionary…