Related papers: Fixation probability in Moran-like Processes on gr…
We consider the modified Moran process on graphs to study the spread of genetic and cultural mutations on structured populations. An initial mutant arises either spontaneously (aka \emph{uniform initialization}), or during reproduction (aka…
This work studies the generalized Moran process, as introduced by Lieberman et al. [Nature, 433:312-316, 2005]. We introduce the parameterized notions of selective amplifiers and selective suppressors of evolution, i.e. of networks (graphs)…
In this paper, we study the absorption and fixation times for evolutionary processes on graphs, under different updating rules. While in Moran process a single neighbour is randomly chosen to be replaced, in proliferation processes other…
Broom and Rycht\'{a}\v{r} [Proc. R. Soc. A (2008) 464, 2609--2627] found an exact solution for the fixation probabilities of the Moran process for a structured population, in which the interaction structure among individuals is given by the…
Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are…
We consider the classic Moran process modeling the spread of genetic mutations, as extended to structured populations by Lieberman et al.\ (Nature, 2005). In this process, individuals are the vertices of a connected graph $G$. Initially,…
The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of…
We study evolutionary dynamics on graphs in which each step consists of one birth and one death, also known as the Moran processes. There are two types of individuals: residents with fitness $1$ and mutants with fitness $r$. Two standard…
Finite and infinite population models are frequently used in population dynamics. However, their interrelationship is rarely discussed. In this work, we examine the limits of large populations of the Moran process (a finite-population…
The Moran process is one of an basic mathematical structure in the evolutionary game theory. In this work, we introduce the formulation of the path integral approach for evolutionary game theory based on the Moran process. We derive the…
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…
The causal compatibility question asks whether a given causal structure graph -- possibly involving latent variables -- constitutes a genuinely plausible causal explanation for a given probability distribution over the graph's observed…
We reconsider the Moran model in continuous time with population size $N$, two allelic types, and selection. We introduce a new particle representation, which we call the labelled Moran model, and which has the same distribution of type…
There is evidence that taking the time average of the work performed by a thermally isolated system effectively "transforms" the adiabatic process into an isothermal one. This approach allows inherent quantities of adiabatic processes to be…
The Moran process models the spread of mutations in populations on graphs. We investigate the absorption time of the process, which is the time taken for a mutation introduced at a randomly chosen vertex to either spread to the whole…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
The celebrated van der Waals model describes simple fluids in the thermodynamic limit and predicts the existence of a critical point associated to the gas-liquid phase transition. However the behaviour of critical isotherms according to the…
The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with…
The Moran process is a classic stochastic process that models the rise and takeover of novel traits in network-structured populations. In biological terms, a set of mutants, each with fitness $m\in(0,\infty)$ invade a population of…