Related papers: Fixation probabilities in evolutionary dynamics un…
The Moran process is a classic stochastic process that models invasion dynamics on graphs. A single "mutant" (e.g., a new opinion, strain, social trait etc.) invades a population of residents spread over the nodes of a graph. The mutant…
We study the dynamics of a population subject to selective pressures, evolving either on RNA neutral networks or in toy fitness landscapes. We discuss the spread and the neutrality of the population in the steady state. Different limits…
Non-selective effects, like genetic drift, are an important factor in modern conceptions of evolution, and have been extensively studied for constant population sizes. Here, we consider non-selective evolution in the case of growing…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
A major aim of evolutionary biology is to explain the respective roles of adaptive versus non-adaptive changes in the evolution of complexity. While selection is certainly responsible for the spread and maintenance of complex phenotypes,…
Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that…
This paper is based on the complete classification of evolutionary scenarios for the Moran process with two strategies given by Taylor et al. (B. Math. Biol. 66(6): 1621--1644, 2004). Their classification is based on whether each strategy…
The characterization of plasticity, robustness, and evolvability, an important issue in biology, is studied in terms of phenotypic fluctuations. By numerically evolving gene regulatory networks, the proportionality between the phenotypic…
We study a family of selection-mutation models of a sexual population structured by a phenotypical trait. The main feature of these models is the asymmetric trait heredity or fecundity between the parents : we assume that each individual…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
The outcomes of evolution are determined by which mutations occur and fix. In rapidly adapting microbial populations, this process is particularly hard to predict because lineages with different beneficial mutations often spread…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can be found in stochastic game dynamical batch learning, and investigate fixation in learning…
We study the evolution of the probability density of an asexual, one locus population under natural selection and random evolution. This evolution is governed by a Fokker-Planck equation with degenerate coefficients on the boundaries,…
The multi-type Moran process is an evolutionary process on a connected graph $G$ in which each vertex has one of $k$ types and, in each step, a vertex $v$ is chosen to reproduce its type to one of its neighbours. The probability of a vertex…
Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are…
Population genetic studies have found evidence for dramatic population growth in recent human history. It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of…
We investigate the evolutionary dynamics of an age-structured population under weak frequency-dependent selection. It turns out that the weak selection is affected in a non-trivial way by the life-history trait. We can disentangle the…
The probability that the frequency of a particular trait will eventually become unity, the so-called fixation probability, is a central issue in the study of population evolution. Its computation, once we are given a stochastic finite…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…