Related papers: The Moran process on 2-chromatic graphs
The long-term growth rate of populations in varying environments quantifies the evolutionary value of processing the information that biological individuals inherit from their ancestors and acquire from their environment. Previous models…
We study fixation probabilities for the Moran stochastic process for the evolution of a population with three or more types of individuals and frequency-dependent fitnesses. Contrarily to the case of populations with two types of…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
In this paper, we introduce a class of graphs which we call average hereditary graphs. Many graphs that occur in the usual graph theory applications belong to this class of graphs. Many popular types of graphs fall under this class, such as…
Weak and strong coloring numbers are generalizations of the degeneracy of a graph, where for each natural number $k$, we seek a vertex ordering such every vertex can (weakly respectively strongly) reach in $k$ steps only few vertices with…
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…
In classical evolutionary theory, genetic variation provides the source of heritable phenotypic variation on which natural selection acts. Against this classical view, several theories have emphasized that developmental variability and…
In this work, we study the color discrepancy of spanning trees in random graphs. We show that for the Erd\H{o}s-R\'enyi random graph $G(n,p)$ with $p$ above the connectivity threshold, the following holds with high probability: in every…
We study the evolution of the population genealogy in the classic neutral Moran Model of finite size and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise…
We consider the dynamics imposed by natural selection on the populations of two competing, sexually reproducing, haploid species. In this setting, the fitness of any genome varies over time due to the changing population mix of the…
A connected graph can be associated with two distinct evolution algebras. In the first case, the structural matrix is the adjacency matrix of the graph itself. In the second case, the structural matrix is the transition probabilities matrix…
Environmental variability greatly influences the eco-evolutionary dynamics of a population, i.e. it affects how its size and composition evolve. Here, we study a well-mixed population of finite and fluctuating size whose growth is limited…
We consider a single genetic locus which carries two alleles, labelled P and Q. This locus experiences selection and mutation. It is linked to a second neutral locus with recombination rate r. If r=0, this reduces to the study of a single…
We study a complementarity game as a systematic tool for the investigation of the interplay between individual optimization and population effects and for the comparison of different strategy and learning schemes. The game randomly pairs…
This article deals with the emergence of a specific mating preference pattern called homogamy in a population. Individuals are characterized by their genotype at two haploid loci, and the population dynamics is modelled by a non-linear…
We consider a population of N individuals, whose dynamics through time is represented by a biparental Moran model with two types: an advantaged type and a disadvantaged type. The advantage is due to a mutation, transmitted in a Mendelian…
Understanding the statistical dynamics of growth and inequality is a fundamental challenge to ecology and society. Recent analyses of wealth and income dynamics in contemporary societies show that economic inequality is very dynamic and…
Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We…
The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The…
Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two…