Related papers: Fixation probabilities for multi-allele Moran dyna…
We study the combined influence of selection and random fluctuations on the evolutionary dynamics of two-strategy ("cooperation" and "defection") games in populations comprising cooperation facilitators. The latter are individuals that…
We analyze the dynamics of evolutionary games in which fitness is defined as an affine function of the expected payoff and a constant contribution. The resulting inhomogeneous replicator equation has an homogeneous equivalent with modified…
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain…
Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank…
We use the Fokker Planck equation as a starting point for studying the orientational probability distribution of an Active Brownian Particle (ABP) in $(d+1)$ dimensions. This Fokker Planck equation admits an exact solution in series form…
We study fixation in large, but finite, populations with two types, and dynamics governed by birth-death processes. By considering a restricted class of such processes, we derive a continuous approximation for the probability of fixation…
A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on behaviour of locusts. It exhibits nontrivial…
In the last years, tens of thousands gene expression profiles for cells of several organisms have been monitored. Gene expression is a complex transcriptional process where mRNA molecules are translated into proteins, which control most of…
The growing probabilities of additional offspring with the beneficial reversal allele for various population sizes, $N$, sequence lengths, $L$, selective advantages, $s$, fitness parameters, $k$, and measuring parameters, $C$, were…
We apply the averaging method to a coupled system consisting of two evolution equations which has a slow component driven by fractional Brownian motion (FBM) with the Hurst parameter $H_1> \frac12$ and a fast component driven by additive…
While generic competitive systems exhibit mixtures of hierarchy and cycles, real-world systems are predominantly hierarchical. We demonstrate and extend a mechanism for hierarchy; systems with similar agents approach perfect hierarchy in…
When a population inhabits an inhomogeneous environment, the fitness value of traits can vary with the position in the environment. Gene flow caused by random mating can nevertheless prevent that a sexually reproducing population splits…
The minimum-effort coordination game, having potentially important implications in both evolutionary biology and sociology, draws recently more attention for the fact that human behavior in this social dilemma is often inconsistent with the…
A fundamental problem in the fields of population genetics, evolution, and community ecology, is the fate of a single mutant, or invader, introduced in a finite population of wild types. For a fixed-size community of $N$ individuals, with…
We present insights and empirical results from an extensive numerical study of the evolutionary dynamics of the iterated prisoner's dilemma. Fixation probabilities for Moran processes are obtained for all pairs of 164 different strategies…
We consider two population models subject to the evolutionary forces of selection and mutation, the Moran model and the $\Lambda$-Wright-Fisher model. In such models the block counting process traces back the number of potential ancestors…
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…
Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a…
We study competition between two biological species advected by a compressible velocity field. Individuals are treated as discrete Lagrangian particles that reproduce or die in a density-dependent fashion. In the absence of a velocity field…
For a beneficial allele which enters a large unstructured population and eventually goes to fixation, it is known that the time to fixation is approximately $2\log(\alpha)/\alpha$ for a large selection coefficient $\alpha$. For a population…