This paper proposes and analyzes a model of stochastic evolution in finite populations. The expected motion in our model resembles the standard replicator dynamic when the population is large, but is qualitatively different when the population size is small, due to the difference between maximizing payoff and maximizing relative payoff. Moreover, even in large populations the asymptotic behavio...

The Moran model is used in population genetics as a simple way to describe the stochastic evolution of a biological population. The model assumes that the population has a fixed size N and that it evolves through random reproduction events, in which one individual dies and is replaced by a newborn. Parents of the newborn individual are chosen at random from the population. In the classical Mora...

In this paper I illustrate the use of general conditions, derived by Pinkse (1999), under which Moran–flavoured tests for spatial correlation and spatial cross–correlation have a limiting normal distribution in the presence of nuisance parameters in six frequently encountered spatial models. The conditions are weaker than those in related work by other authors and the class of nuisance paramete...

We present a Moran-model approach to modeling general multiallelic selection in a finite population and show how it may be used to develop theoretical models of biological systems of balancing selection such as plant gametophytic self-incompatibility loci. We propose new expressions for the stationary distribution of allele frequencies under selection and use them to show that the continuous-ti...

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 population, or to become extinct. It is known that the expected absorption time for an advantageous mutation is O(n) on an n-vertex undirected graph, which allows ...

ELISABETH ROUDINESCO, Madness anid revolution: the lives and legends of Theroigne de Mericourt, transl. Martin Thom, London and New York, Verso, 1992, pp. xi, 284, illus., £12.95 (paperback 0-86091-597-2). Anne-Josephe Terwagne, from Marcourt in Belgium, gained notoriety during the French Revolution as Theroigne de Mericourt and ended her life confined in La Salpetri&e. Her "madness", integrate...

We study the Moran process as adapted by Lieberman, Hauert and Nowak. A family of directed graphs is said to be strongly amplifying if the extinction probability tends to 0 when the Moran process is run on graphs in this family. The most-amplifying known family of directed graphs is the family of megastars of Galanis et al. We show that this family is optimal, up to logarithmic factors, since e...

Equilibrium probabilities of identity by descent (IBD), for pairs of genes within individuals, for genes between individuals within subpopulations, and for genes between subpopulations are calculated in metapopulation models with fixed or varying colony sizes. A continuous-time analog to the Moran model was used in either case. For fixed-colony size both propagule and migrant pool models were c...

Among many organisms, offspring are constrained to occur at sites adjacent to their parents. This applies to plants and animals with limited dispersal ability, to colonies of microbes in biofilms, and to other genetically heterogeneous aggregates of cells, such as cancerous tumors. The spatial structure of such populations leads to greater relatedness among proximate individuals while increasin...