Related papers: Absorption and fixation times for evolutionary pro…
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…
The Moran process, as studied by Lieberman, Hauert and Nowak, is a randomised algorithm modelling the spread of genetic mutations in populations. The algorithm runs on an underlying graph where individuals correspond to vertices. Initially,…
Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a…
Understanding how natural selection unfolds across space and time is a central problem in evolutionary biology. Classic models such as the Moran process capture stochastic birth-death dynamics in structured populations, while…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
Background: The accumulation of deleterious mutations of a population directly contributes to the fate as to how long the population would exist, a process often described as Muller's ratchet with the absorbing phenomenon. The key to…
This paper investigates the problem of dynamical sampling for graph signals influenced by a constant source term. We consider signals evolving over time according to a linear dynamical system on a graph, where both the initial state and the…
This paper considers a class of probabilistic cellular automata undergoing a phase transition with an absorbing state. Denoting by ${\mathcal{U}}(x)$ the neighbourhood of site $x$, the transition probability is $T(\eta_x = 1 |…
Whether or not cooperation is favored in evolutionary games on graphs depends on the population structure and spatial properties of the interaction network. Population structures can be expressed as configurations. Such configurations…
Complex spatial structure, with partially isolated subpopulations, and environment heterogeneity, such as gradients in nutrients, oxygen, and drugs, both shape the evolution of natural populations. We investigate the impact of environment…
We consider, through PDE methods, branching Brownian motion with drift and absorption. It is well know that there exists a critical drift which separates those processes which die out almost surely and those which survive with positive…
In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…
Moran or Wright-Fisher processes are probably the most well known model to study the evolution of a population under various effects. Our object of study will be the Simpson index which measures the level of diversity of the population, one…
In this paper we investigate geometric properties of graphs generated by a preferential attachment random graph model with edge-steps. More precisely, at each time $t\in\mathbb{N}$, with probability $p$ a new vertex is added to the graph (a…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
Over time, a population acquires neutral genetic substitutions as a consequence of random drift. A famous result in population genetics asserts that the rate, $K$, at which these substitutions accumulate in the population coincides with the…
A key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Population spatial structure can impact mutant fixation probabilities. We introduce a model for structured…
Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…
In this paper we consider a population process evolving on a dynamic random graph. The dynamic random graph is an Erd\H{o}s--R\'enyi graph that is resampled every time unit, independently of the previous ones, with `edge existence…
Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections…