Invasive Allele Spread under Preemptive Competition

We study a discrete spatial model for invasive allele spread in which two alleles compete preemptively, initially only the "residents" (weaker competitors) being present. We find that the spread of the advantageous mutation is well described by homogeneous nucleation; in particular, in large systems the time-dependent global density of the resident allele is well approximated by Avrami's law.Comment: Computer Simulation Studies in Condensed Matter Physics XVIII, edited by D.P. Landau, S.P. Lewis, and H.-B. Schuttler, (Springer, Heidelberg, Berlin, in press

Spatial heterogeneity promotes coexistence of rock-paper-scissor metacommunities

The rock-paper-scissor game -- which is characterized by three strategies R,P,S, satisfying the non-transitive relations S excludes P, P excludes R, and R excludes S -- serves as a simple prototype for studying more complex non-transitive systems. For well-mixed systems where interactions result in fitness reductions of the losers exceeding fitness gains of the winners, classical theory predicts that two strategies go extinct. The effects of spatial heterogeneity and dispersal rates on this outcome are analyzed using a general framework for evolutionary games in patchy landscapes. The analysis reveals that coexistence is determined by the rates at which dominant strategies invade a landscape occupied by the subordinate strategy (e.g. rock invades a landscape occupied by scissors) and the rates at which subordinate strategies get excluded in a landscape occupied by the dominant strategy (e.g. scissor gets excluded in a landscape occupied by rock). These invasion and exclusion rates correspond to eigenvalues of the linearized dynamics near single strategy equilibria. Coexistence occurs when the product of the invasion rates exceeds the product of the exclusion rates. Provided there is sufficient spatial variation in payoffs, the analysis identifies a critical dispersal rate $d^*$ required for regional persistence. For dispersal rates below $d^*$, the product of the invasion rates exceed the product of the exclusion rates and the rock-paper-scissor metacommunities persist regionally despite being extinction prone locally. For dispersal rates above $d^*$, the product of the exclusion rates exceed the product of the invasion rates and the strategies are extinction prone. These results highlight the delicate interplay between spatial heterogeneity and dispersal in mediating long-term outcomes for evolutionary games.Comment: 31pages, 5 figure

Interaction between habitat quality and an Allee-like effect in metapopulations

We construct a stochastic patch occupancy metapopulation model that incorporates variation in habitat quality and an Allee-like effect. Using some basic results from stochastic ordering, we investigate the effect of habitat degradation on the persistence of the metapopulation. In particular, we show that for a metapopulation with Allee-like effect habitat degradation can cause a dramatic decrease in the level of persistence while in the absence of an Allee-like effect this decrease is more gradual

A graphical theory of competition on spatial resource gradients

Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two consumers for two resources in a one-dimensional habitat in which the resources are supplied from opposite sides. We show that the success of an invading species crucially depends on the slope of the resource gradients shaped by the resident. Our analysis reveals that parameter combinations which lead to coexistence in a uniform environment may favor alternative stable states in a spatial system, and vice versa. Furthermore, differences in growth rate, mortality or dispersal abilities allow a consumer to coexist stationarily with - or even outcompete - a competitor with lower resource requirements. Applying our theory to a phytoplankton model, we explain shifts in the community structure that are induced by environmental changes