3,955 research outputs found
Recommended from our members
Evolutionary games on graphs and the speed of the evolutionary process
In this paper, we investigate evolutionary games with the invasion process updating rules on three simple non-directed graphs: the star, the circle and the complete graph. Here, we present an analytical approach and derive the exact solutions of the stochastic evolutionary game dynamics. We present formulae for the fixation probability and also for the speed of the evolutionary process, namely for the mean time to absorption (either mutant fixation or extinction) and then the mean time to mutant fixation. Through numerical examples, we compare the different impact of the population size and the fitness of each type of individual on the above quantities on the three different structures. We do this comparison in two specific cases. Firstly, we consider the case where mutants have fixed fitness r and resident individuals have fitness 1. Then, we consider the case where the fitness is not constant but depends on games played among the individuals, and we introduce a ‘hawk–dove’ game as an example
An analysis of the fixation probability of a mutant on special classes of non-directed graphs
There is a growing interest in the study of evolutionary dynamics on populations with some non-homogeneous structure. In this paper we follow the model of Lieberman et al. (Lieberman et al. 2005 Nature 433, 312–316) of evolutionary dynamics on a graph. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. We further demonstrate that finding similar solutions on graphs outside these classes is far more complex. Finally, we investigate our chosen classes numerically and discuss a number of features of the graphs; for example, we find the fixation probabilities for different initial starting positions and observe that average fixation probabilities are always increased for advantageous mutants as compared with those of unstructured populations
Effect of migration in a diffusion model for template coexistence in protocells
The compartmentalization of distinct templates in protocells and the exchange
of templates between them (migration) are key elements of a modern scenario for
prebiotic evolution. Here we use the diffusion approximation of population
genetics to study analytically the steady-state properties of such prebiotic
scenario. The coexistence of distinct template types inside a protocell is
achieved by a selective pressure at the protocell level (group selection)
favoring protocells with a mixed template composition. In the degenerate case,
where the templates have the same replication rate, we find that a vanishingly
small migration rate suffices to eliminate the segregation effect of random
drift and so to promote coexistence. In the non-degenerate case, a small
migration rate greatly boosts coexistence as compared with the situation where
there is no migration. However, increase of the migration rate beyond a
critical value leads to the complete dominance of the more efficient template
type (homogeneous regime). In this case, we find a continuous phase transition
separating the homogeneous and the coexistence regimes, with the order
parameter vanishing linearly with the distance to the transition point
- …