Ross Cressman

Migration Dynamics for the Ideal Free Distribution

This article verifies that the ideal free distribution (IFD) is evolutionarily stable, provided the payoff in each patch decreases with an increasing number of individuals. General frequency‐dependent models of migratory dynamics that differ in the degree of animal omniscience are then developed. These models do not exclude migration at the IFD where balanced dispersal emerges. It is shown that the population distribution converges to the IFD even when animals are nonideal (i.e., they do not know the quality of all patches). In particular, the IFD emerges when animals never migrate from patches with a higher payoff to patches with a lower payoff and when some animals always migrate to the best patch. It is shown that some random migration does not necessarily lead to undermatching, provided migration occurs at the IFD. The effect of population dynamics on the IFD (and vice versa) is analyzed. Without any migration, it is shown that population dynamics alone drive the population distribution to the IFD. If animal migration tends (for each fixed population size) to the IFD, then the combined migration‐population dynamics evolve to the population IFD independent of the two timescales (i.e., behavioral vs. population).

Ideal Free Distributions, Evolutionary Games, and Population Dynamics in Multiple‐Species Environments

In this article, we develop population game theory, a theory that combines the dynamics of animal behavior with population dynamics. In particular, we study interaction and distribution of two species in a two‐patch environment assuming that individuals behave adaptively (i.e., they maximize Darwinian fitness). Either the two species are competing for resources or they are in a predator‐prey relationship. Using some recent advances in evolutionary game theory, we extend the classical ideal free distribution (IFD) concept for single species to two interacting species. We study population dynamical consequences of two‐species IFD by comparing two systems: one where individuals cannot migrate between habitats and one where migration is possible. For single species, predator‐prey interactions, and competing species, we show that these two types of behavior lead to the same population equilibria and corresponding species spatial distributions, provided interspecific competition is patch independent. However, if differences between patches are such that competition is patch dependent, then our predictions strongly depend on whether animals can migrate or not. In particular, we show that when species are settled at their equilibrium population densities in both habitats in the environment where migration between habitats is blocked, then the corresponding species spatial distribution need not be an IFD. Thus, when species are given the opportunity to migrate, they will redistribute to reach an IFD (e.g., under which the two species can completely segregate), and this redistribution will also influence species population equilibrial densities. Alternatively, we also show that when two species are distributed according to the IFD, the corresponding population equilibrium can be unstable.

Costly punishment does not always increase cooperation

In a pairwise interaction, an individual who uses costly punishment must pay a cost in order that the opponent incurs a cost. It has been argued that individuals will behave more cooperatively if they know that their opponent has the option of using costly punishment. We examined this hypothesis by conducting two repeated two-player Prisoners Dilemma experiments, that differed in their payoffs associated to cooperation, with university students from Beijing as participants. In these experiments, the level of cooperation either stayed the same or actually decreased when compared with the control experiments in which costly punishment was not an option. We argue that this result is likely due to differences in cultural attitudes to cooperation and punishment based on similar experiments with university students from Boston that found cooperation did increase with costly punishment.

The Role of Behavioral Dynamics in Determining the Patch Distributions of Interacting Species

The effect of the behavioral dynamics of movement on the population dynamics of interacting species in multipatch systems is studied. The behavioral dynamics of habitat choice used in a range of previous models are reviewed. There is very limited empirical evidence for distinguishing between these different models, but they differ in important ways, and many lack properties that would guarantee stability of an ideal free distribution in a single‐species system. The importance of finding out more about movement dynamics in multispecies systems is shown by an analysis of the effect of movement rules on the dynamics of a particular two‐species–two‐patch model of competition, where the population dynamical equilibrium in the absence of movement is often not a behavioral equilibrium in the presence of adaptive movement. The population dynamics of this system are explored for several different movement rules and different parameter values, producing a variety of outcomes. Other systems of interacting species that may lack a dynamically stable distribution among patches are discussed, and it is argued that such systems are not rare. The sensitivity of community properties to individual movement behavior in this and earlier studies argues that there is a great need for empirical investigation to determine the applicability of different models of the behavioral dynamics of habitat selection.

Stability of the replicator equation with continuous strategy space

Abstract We extend previous work that analyzes the stability of evolutionary dynamics on probability distributions over continuous strategy spaces. The stability concept considered is that of “neighborhood” convergence to a rest point (i.e. an equilibrium distribution over the strategy space) under the dynamics in the weak topology for all initial distributions whose support is close to that of the rest point. Stability criteria involving strategy domination and neighborhood superiority are developed for monomorphic rest points (i.e. the equilibrium distribution is supported on a single strategy) and for distributions that have finite support.

The replicator equation and other game dynamics.

The replicator equation is the first and most important game dynamics studied in connection with evolutionary game theory. It was originally developed for symmetric games with finitely many strategies. Properties of these dynamics are briefly summarized for this case, including the convergence to and stability of the Nash equilibria and evolutionarily stable strategies. The theory is then extended to other game dynamics for symmetric games (e.g., the best response dynamics and adaptive dynamics) and illustrated by examples taken from the literature. It is also extended to multiplayer, population, and asymmetric games.

Local stability of smooth selection dynamics for normal form games

Abstract Economic game theorists have recently used the concept of dynamic stability to choose among the many solution concepts of noncooperative game theory. They are justifiably concerned that stability with respect to the replicator dynamic does not adequately reflect the economic assumption that players make rational decisions. The paper analyzes stability for general adjustment processes such as monotone selection that translate payoffs into an evolutionary dynamic. By the linearization technique of dynamical systems, it is shown that the replicator dynamic deserves a prominent position in questions of stability. In particular, for symmetric normal form games, stability of monotone selection dynamics at an interior rest point is completely determined by that of the replicator dynamic unless there is a trivial linearization. Linearizations are also analyzed for asymmetric normal form games and dynamic stability consequences established for evolutionarily stable strategies as well as other Nash equilibria.

A predator-prey refuge system: Evolutionary stability in ecological systems.

A refuge model is developed for a single predator species and either one or two prey species where no predators are present in the prey refuge. An individuals fitness depends on its strategy choice or ecotype (predators decide which prey species to pursue and prey decide what proportion of their time to spend in the refuge) as well as on the population sizes of all three species. It is shown that, when there is a single prey species with a refuge or two prey species with no refuge compete only indirectly (i.e. there is only apparent competition between prey species), that stable resident systems where all individuals in each species have the same ecotype cannot be destabilized by the introduction of mutant ecotypes that are initially selectively neutral. In game-theoretic terms, this means that stable monomorphic resident systems, with ecotypes given by a Nash equilibrium, are both ecologically and evolutionarily stable. However, we show that this is no longer the case when the two indirectly-competing prey species have a refuge. This illustrates theoretically that two ecological factors, that are separately stabilizing (apparent competition and refuge use), may have a combined destabilizing effect from the evolutionary perspective. These results generalize the concept of an evolutionarily stable strategy (ESS) to models in evolutionary ecology. Several biological examples of predator-prey systems are discussed from this perspective.

Cooperation and evolutionary dynamics in the public goods game with institutional incentives

The one-shot public goods game is extended to include institutional incentives (i.e. reward and/or punishment) that are meant to promote cooperation. It is shown that the Nash equilibrium (NE) outcomes predict either partial or fully cooperative behavior in these extended multi-player games with a continuous strategy space. Furthermore, for some incentive schemes, multiple NE outcomes are shown to emerge. Stability of all these equilibria under standard evolutionary dynamics (i.e. the replicator equation and the canonical equation of adaptive dynamics) is characterized.

Strong stability and density-dependent evolutionarily stable strategies.

Stability conditions for equilibria of the evolution of population strategies in a single species are developed by comparing frequency and density dependent fitnesses of pairs of strategies. Stability of such equilibria is shown for general haploid frequency and density dynamics. It is also shown that this stability is stronger than that of multispecies population dynamical systems. A biological interpretation of the conditions is provided in terms of the fitness of invading subpopulations.