Related papers: Bridging Wright-Fisher and Moran models
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…
We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we have computed the distributions of the total branch lengths of its sample genealogies.…
In both population genetics and forensic genetics it is important to know how haplotypes are distributed in a population. Simulation of population dynamics helps facilitating research on the distribution of haplotypes. In forensic genetics,…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
Migration between different habitats is ubiquitous among biological populations. In this Letter, we study a simple quasispecies model for evolution in two different habitats, with different fitness landscapes, coupled through one-way…
In this article, a biallelic reversible mutation model with linear and quadratic selection is analyzed. The approach reconnects to one proposed by Kimura ( Possibility of extensive neutral evolution under stabilizing selection with special…
If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as time progresses. The resulting "MRCA age"…
In large populations, multiple beneficial mutations may be simultaneously spreading. In asexual populations, these mutations must either arise on the same background or compete against each other. In sexual populations, recombination can…
We consider a Moran model with two allelic types, mutation and selection. In this work, we study the behaviour of the proportion of fit individuals when the size of the population tends to infinity, without any rescaling of parameters or…
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…
A framework for the mathematical modeling of evolution in group structured populations is introduced. The population is divided into a fixed large number of groups of fixed size. From generation to generation, new groups are formed that…
Widespread sharing of long, identical-by-descent (IBD) genetic segments is a hallmark of populations that have experienced recent genetic drift. Detection of these IBD segments has recently become feasible, enabling a wide range of…
A multi-type neutral Cannings population model with mutation and fixed subpopulation sizes is analyzed. Under appropriate conditions, as all subpopulation sizes tend to infinity, the ancestral process, properly time-scaled, converges to a…
The mean fixation time of a deleterious mutant allele is studied beyond the diffusion approximation. As in Kimura's classical work [M. Kimura, Proc. Natl. Acad. Sci. U.S.A. Vol.77, 522 (1980)], that was motivated by the problem of fixation…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
We study a class of Cannings models with population size $N$ having a mixed multinomial offspring distribution with random success probabilities $W_1,\ldots,W_N$ induced by independent and identically distributed positive random variables…
Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the…