Related papers: Fixation in large populations: a continuous view o…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
This work is a systematic study of discrete Markov chains that are used to describe the evolution of a two-types population. Motivated by results valid for the well-known Moran (M) and Wright-Fisher (WF) processes, we define a general class…
In population genetics, diffusions on the unit interval are often used to model the frequency path of an allele. In this setting we derive approximations for fixation probabilities, expected hitting times and the expected…
Understanding the evolutionary dynamics of reinforcement learning under multi-agent settings has long remained an open problem. While previous works primarily focus on 2-player games, we consider population games, which model the strategic…
Evolutionary models for populations of constant size are frequently studied using the Moran model, the Wright-Fisher model, or their diffusion limits. When evolution is neutral, a random genealogy given through Kingman's coalescent is used…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
In evolutionary dynamics, the probability that a mutation spreads through the whole population, having arisen in a single individual, is known as the fixation probability. In general, it is not possible to find the fixation probability…
Evolution strategies (ESs) are zeroth-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are…
In [12] we formulated an evolutionary game theory model as a dynamical system on the state space of finite signed Borel measures under the weak* topology. The focus of this paper is to extend the analysis to include the long-time behavior…
Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding…
While quite a few recent papers have explored game-resource feedback using the framework of evolutionary game theory, almost all the studies are confined to using time-continuous dynamical equations. Moreover, in such literature, the effect…
Emerging applications in engineering such as crowd-sourcing and (mis)information propagation involve a large population of heterogeneous users or agents in a complex network who strategically make dynamic decisions. In this work, we…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
The stage of evolution is the population of reproducing individuals. The structure of the population is know to affect the dynamics and outcome of evolutionary processes, but analytical results for generic random structures have been…
We are interested in the dynamics of a population structured by a phenotypic trait. Individuals reproduce sexually, which is represented by a non-linear integral operator. This operator is combined to a multiplicative operator representing…
Mating preferences of many biological species are not constant but season-dependent. Within the framework of evolutionary game theory this can be modeled with two finite opposite-sex populations playing against each other following the…
Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to…
Studying strategy update rules in the framework of evolutionary game theory, one can differentiate between imitation processes and aspiration-driven dynamics. In the former case, individuals imitate the strategy of a more successful peer.…
The study of the density evolution naturally arises in Mean Field Game theory for the estimation of the density of the large population dynamics. In this paper, we study the density evolution of McKean-Vlasov stochastic differential…
Different evolutionary models are known to make disparate predictions for the success of an invading mutant in some situations. For example, some evolutionary mechanics lead to amplification of selection in structured populations, while…