Score-dependent fertility model for the evolution of cooperation in a lattice

Metapopulation models for extinction threshold in spatially correlated landscapes

Simple analytical models assuming homogeneous space have been used to examine the effects of habitat loss and fragmentation on metapopulation size. The models predict an extinction threshold, a critical amount of suitable habitat below which the metapopulation goes deterministically extinct. The consequences of non-random loss of habitat for species with localized dispersal have been studied mainly numerically. In this paper, we present two analytical approaches to the study of habitat loss and its metapopulation dynamic consequences incorporating spatial correlation in both metapopulation dynamics as well as in the pattern of habitat destruction. One approach is based on a measure called metapopulation capacity, given by the dominant eigenvalue of a "landscape" matrix, which encapsulates the effects of landscape structure on population extinctions and colonizations. The other approach is based on pair approximation. These models allow us to examine analytically the effects of spatial structure in habitat loss on the equilibrium metapopulation size and the threshold condition for persistence. In contrast to the pair approximation based approaches, the metapopulation capacity based approach allows us to consider species with long as well as short dispersal range and landscapes with spatial correlation at different scales. The two methods make dissimilar assumptions, but the broad conclusions concerning the consequences of spatial correlation in the landscape structure are the same. Our results show that increasing correlation in the spatial arrangement of the remaining habitat increases patch occupancy, that this increase is more evident for species with short-range than long-range dispersal, and that to be most beneficial for metapopulation size, the range of spatial correlation in landscape structure should be at least a few times greater than the dispersal range of the species.

Evolution of altruism in stepping-stone populations with overlapping generations

We study the evolution of altruism in one- and two-dimensional stepping-stone populations with discrete overlapping generations. We find that increasing survival probability facilitates the evolution of altruism, in agreement with recent results for a patch-structured population. We allow the altruistic behaviour to affect either fecundity or survival probability. In the first case, altruism is favoured compared to a randomly interacting population, but in the second case, altruism is less likely to evolve. We consider the iterated prisoner's dilemma as a description of an altruistic interaction and compare our results with recent simulations of lattice populations.

Antibiotic and insecticide resistance modeling--is it time to start talking?

Mathematical models have played an important part in understanding both antibiotic and insecticide resistance. However, there has been little, if any, interdisciplinary work between these two areas of active research. One primary reason for this is that bacterial population genetics differ substantially from the population genetics of diploid organisms. This article examines these differences and their effect on resistance. It explores what efforts have gone into modeling resistance mathematically in both arenas, and offers suggestions on how the two groups could work together to gain a more comprehensive understanding of the resistance phenomenon

On the dynamic persistence of cooperation: how lower individual fitness induces higher survivability

We study a model in which cooperation and defection coexist in a dynamical steady state. In our model, subpopulations of cooperators and defectors inhabit sites on a lattice. The interactions among the individuals at a site, in the form of a prisoner's dilemma (PD) game, determine their fitnesses. The chosen PD payoff allows cooperators, but not defectors, to maintain a homogeneous population. Individuals mutate between types and migrate to neighboring sites with low probabilities. We consider both density-dependent and density-independent versions of the model. The persistence of cooperation in this model can be explained in terms of the life cycle of a population at a site. This life cycle starts when one cooperator establishes a population. Then defectors invade and eventually take over, resulting finally in the death of the population. During this life cycle, single cooperators migrate to empty neighboring sites to found new cooperator populations. The system can reach a steady state where cooperation prevails if the global "birth" rate of populations is equal to their global "death" rate. The dynamic persistence of cooperation ranges over a large section of the model's parameter space. We compare these dynamics to those from other models for the persistence of altruism and to predator-prey models.

Overlapping generations can promote altruistic behavior

We use an inclusive fitness model to study the evolution of altruism in a patch-structured population in which there is positive probability of breeder survival from one generation to the next. We find first that breeder survival promotes altruism and second that there is a marked difference between benefits of fecundity and benefits of survival. Under the first altruism is more strongly favored, and under the second altruism is less strongly favored than in a randomly mixing population.

Population viscosity and the evolution of altruism

The term population viscosity refers to limited dispersal, which increases the genetic relatedness of neighbors. This effect both supports the evolution of altruism by focusing the altruists' gifts on relatives of the altruist, and also limits the extent to which altruism may emerge by exposing clusters of altruists to stiffer local competition. Previous analyses have emphasized the way in which these two effects can cancel, limiting the viability of altruism. These papers were based on models in which total population density was held fixed. We present here a class of models in which population density is permitted to fluctuate, so that patches of altruists are supported at a higher density than patches of non-altruists. Under these conditions, population viscosity can support the selection of both weak and strong altruism.

Competition by allelopathy proceeds in traveling waves: colicin-immune strain aids colicin-sensitive strain

Producing toxic chemicals to suppress both the growth and survivorship of local competitors is called allelopathy; some strains of the bacteria Escherichia coli produce a toxin (named colicin) which may kill colicin-sensitive neighbors while they themselves are immune. In a previous paper, the competitive outcome between colicin-producing and colicin-sensitive strains was shown to differ between a spatially structured and a completely mixed population. In this paper, we analyze the role of a third, "colicin-immune," strain, which does not produce colicin but is immune to it. Without spatial structure, the colicin-immune strain suppresses the colicin-producing strain and enables the colicin-sensitive strain to win. In a spatially structured population, modeled as a reaction-diffusion system, we examine the speed of boundaries between areas dominated by different strains in traveling waves and the events after the collision of two such boundaries. The colicin-immune strain passes through the area dominated by the colicin-sensitive strain and drives the colicin-producing strain to extinction. Subsequently the colicin-sensitive strain occupies the whole population.