Long-range dispersal, stochasticity and the broken accelerating wave of advance.

Rare long distance dispersal events are thought to have a disproportionate impact on the spread of invasive species. Modelling using integrodifference equations suggests that, when long distance contacts are represented by a fat-tailed dispersal kernel, an accelerating wave of advance can ensue. Invasions spreading in this manner could have particularly dramatic effects. Recently, various authors have suggested that demographic stochasticity disrupts wave acceleration. Integrodifference models have been widely used in movement ecology, and as such a clearer understanding of stochastic effects is needed. Here, we present a stochastic non-linear one-dimensional lattice model in which demographic stochasticity and the dispersal regime can be systematically varied. Extensive simulations show that stochasticity has a profound effect on model behaviour, and usually breaks acceleration for fat-tailed kernels. Exceptions are seen for some power law kernels, K(l)∝|l|-β with β<3, for which acceleration persists despite stochasticity. Such kernels lack a second moment and are important in 'accelerating' phenomena such as Lévy flights. Furthermore, for long-range kernels the approach to the continuum limit behaviour as stochasticity is reduced is generally slow. Given that real-world populations are finite, stochastic models may give better predictive power when long-range dispersal is important. Insights from mean-field models such as integrodifference equations should be applied with caution in such circumstances

Nonequivalence of updating rules in evolutionary games under high mutation rates.

Moran processes are often used to model selection in evolutionary simulations. The updating rule in Moran processes is a birth-death process, i. e., selection according to fitness of an individual to give birth, followed by the death of a random individual. For well-mixed populations with only two strategies this updating rule is known to be equivalent to selecting unfit individuals for death and then selecting randomly for procreation (biased death-birth process). It is, however, known that this equivalence does not hold when considering structured populations. Here we study whether changing the updating rule can also have an effect in well-mixed populations in the presence of more than two strategies and high mutation rates. We find, using three models from different areas of evolutionary simulation, that the choice of updating rule can change model results. We show, e. g., that going from the birth-death process to the death-birth process can change a public goods game with punishment from containing mostly defectors to having a majority of cooperative strategies. From the examples given we derive guidelines indicating when the choice of the updating rule can be expected to have an impact on the results of the model

Nonequivalence of updating rules in evolutionary games under high mutation rates.

Moran processes are often used to model selection in evolutionary simulations. The updating rule in Moran processes is a birth-death process, i. e., selection according to fitness of an individual to give birth, followed by the death of a random individual. For well-mixed populations with only two strategies this updating rule is known to be equivalent to selecting unfit individuals for death and then selecting randomly for procreation (biased death-birth process). It is, however, known that this equivalence does not hold when considering structured populations. Here we study whether changing the updating rule can also have an effect in well-mixed populations in the presence of more than two strategies and high mutation rates. We find, using three models from different areas of evolutionary simulation, that the choice of updating rule can change model results. We show, e. g., that going from the birth-death process to the death-birth process can change a public goods game with punishment from containing mostly defectors to having a majority of cooperative strategies. From the examples given we derive guidelines indicating when the choice of the updating rule can be expected to have an impact on the results of the model

Effects of group size and memory on the evolution of cooperation

(INTRODUCTION) Human societies are characterised by high degrees of reciprocal altruism between unrelated individuals. It has even been suggested that humans have evolved a cognitive capacity for effective reasoning about social exchange transactions which does not readily generalise to other, non-social reasoning tasks (Cosmides 1989). Explaining the emergence of this capacity for cooperation is one of the fundamental goals of evolutionary anthropology.(DISCUSSION) Our results appear to resolve the contradiction identified at the start of this paper. Cooperation can evolve as a dominant and stable strategy in very large social groups, provided that certain conditions are met. We have shown that cooperation can be sustained in a large group with a limited number of interactions on each round, if players are able to base decisions about future play on the results of a number of rounds of past play and are permitted to refuse to play with others when necessary. In evolutionary terms the rewards for this cooperation would give a significant advantage to individuals in the group, who would, however, need to store more information to co-ordinate relationships with other players and would require greater processing power to do this effectively