Fixation probabilities of mutant genes with artificial selection

Fixation Probabilities and Times

Within a population, any allele must ultimately persist or be lost. If, sometime in the future, all members of the population are descendants of the allele, then that allele is said to have fixed within the population. If, sometime in the future, no members of the population are descendants of the allele, then that allele is said to have been lost. Using mathematical models, the probability of ...

The Moran model with selection: fixation probabilities, ancestral lines, and an alternative particle representation.

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 frequencies as the original Moran model, provided the initial values are chosen appropriately. In the new model, individuals are labelled 1,2,…,N; neutral resampl...

Fixation probabilities for simple digraphs

The problem of finding birth–death fixation probabilities for configurations of normal andmutants on an N-vertex graph is formulated in terms of a Markov process on the 2N-dimensional state space of possible configurations. Upper and lower bounds on the fixation probability after any given number of iterations of the birth–death process are derived in terms of the transition matrix of this proc...

Evolution of Cooperation in a Heterogeneous Graph: Fixation Probabilities under Weak Selection

It has been shown that natural selection favors cooperation in a homogenous graph if the benefit-to-cost ratio exceeds the degree of the graph. However, most graphs related to interactions in real populations are heterogeneous, in which some individuals have many more neighbors than others. In this paper, we introduce a new state variable to measure the time evolution of cooperation in a hetero...

Supporting Information for “Evolution of cooperation in a heterogeneous graph: Fixation probabilities under neutral selection ”