Related papers: Fixation Maximization in the Positional Moran Proc…
The well-known Isothermal Theorem was introduced in a Nature Communications article in 2005 and has since contributed to the creation of the rich field of evolutionary graph theory. The theorem states under which conditions certain…
We consider a spatial (line) model for invasion of a population by a single mutant with a stochastically selectively neutral fitness landscape, independent from the fitness landscape for non-mutants. This model is similar to those…
In genetics the Moran model describes the neutral evolution of a bi-allelic gene in a population of haploid individuals subjected to mutations. We show in this paper that this model can be mapped into an influence dynamical process on…
We consider a generalized version of the birth-death (BD) and death-birth (DB) processes introduced by Kaveh, Komarova, and Kohandel (2015), in which two constant fitnesses, one for birth and the other for death, describe the selection…
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…
Many mathematical models of evolution assume that all individuals experience the same environment. Here, we study the Moran process in heterogeneous environments. The population is of finite size with two competing types, which are exposed…
Microbial dormancy is an evolutionary trait that has emerged independently at various positions across the tree of life. It describes the ability of a microorganism to switch to a metabolically inactive state that can withstand unfavorable…
Population structures can be crucial determinants of evolutionary processes. For the Moran process on graphs certain structures suppress selective pressure, while others amplify it (Lieberman et al. 2005 Nature 433 312-316). Evolutionary…
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…
We investigate the process of fixation of advantageous mutations in an asexual population. We assume that the effect of each beneficial mutation is exponentially distributed with mean value $\omega_{med}=1/\beta$. The model also considers…
We study the fixation probability of a mutant type when introduced into a resident population. As opposed to the usual assumption of constant pop- ulation size, we allow for stochastically varying population sizes. This is implemented by a…
Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of…
Tumors initiate when a population of proliferating cells accumulates a certain number and type of genetic and/or epigenetic alterations. The population dynamics of such sequential acquisition of (epi)genetic alterations has been the topic…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
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…
The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature…
In stochastic evolutionary dynamics, the replacement of an existing genotype or cultural trait by a newly introduced mutant is typically characterized by the quantities of fixation probability and fixation time. But in a structured…
We study the effect of the mutant's degree on the fixation probability, extinction and fixation times, in the Moran process on Erd\"{o}s-R\'{e}nyi and Barab\'{a}si-Albert graphs. We performed stochastic simulations and use mean-field type…
Cooperation is ubiquitous across all levels of biological systems ranging from microbial communities to human societies. It, however, seemingly contradicts the evolutionary theory, since cooperators are exploited by free-riders and thus are…
We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We…