Gregory B. Pollock

Can altruism evolve in purely viscous populations

SummaryLimited dispersal is often thought to facilitate the evolution of altruism by increasing the degree of relatedness among interacting individuals. Limited dispersal can have additional effects, however, such as local population regulation, that inhibits the evolution of altruism. Many models of structured populations assume that a viscous stage of the life cycle alternates with a global mixing stage, which allows the advantages of interactions among close relatives without the disadvantages of local population regulation. Here we analyse a computer simulation model of ‘pure’ population viscosity, in which offspring are always deposited close to parents and no global mixing stage exists. As expected, limited dispersal generates a high coefficient of relatedness among interacting individuals. Patches of altruists, however, are unable to ‘export’ their productivity to other regions of the landscape and are easily invaded by selfish types from neighbouring patches. Unlike models of alternating viscosity, in which high relatedness and local population regulation can be decoupled, these two opposing effects are inextricably linked in purely viscous populations, which therefore are not conducive to the evolution of altruistic traits.

Reciprocity and the emergence of reputation

Before reputation can be cultivated it must be conferred; individuals must seek information relevant to a future social partner prior to actual interaction. Such information may be gathered by observing a future social partner in interaction with another. Use of vicarious observation to direct initial play in actual encounter we term minimal attributed reputation. We model minimal attributed reputation by the strategy Observer Tit For Tat (OTFT), which behaves like Tit For Tat (TFT) when ignorant of a new partner but begins by defecting on a new partner if that partner was seen defecting on another. TFT can resist invasion by OTFT in the presence of recurring mutant unilateral defectors. Yet OTFT is evolutionarily stable when TFT is not; similarly, OTFT requires less clustering than TFT to invade a world of unilateral defection. OTFT is evolutionarily superior to TFT under low probabilities of future interaction between partners; indeed, in principle OTFT requires no future interaction between partners. As the probability of future interaction increases, TFT supplants OTFT. Thus, minimal reputation evolves when the duration of pair-wise interaction is relatively uncertain.

Viscous Population Equilibria

Viscosity in a biological population is the tendency of individuals to have a higher rate of interactions with their closer relatives than with similar numbers of more distantly related individuals. This paper presents a simple method of equilibrium analysis to predict the effect of viscosity in biological games. Taking the limit as viscosity goes to zero, a set of fluid population equilibria is defined. The set of fluid population equilibria is nonempty and includes all evolutionary stable strategies.

Population Viscosity and Kin Selection

Kin selection may be broken down into two components: intrafamily and interfamily selection. When an altruism coding allele is rare (i.e., at its emergence) within the family the frequency of the altruism coding genotype necessarily declines; it is only by differential production of reproductives between families that kin selection can act to increase the frequency of this genotype in the population. Thus kin selection acts on a partitioned population: families with altruists disperse more offspring than families without altruists. This has implications for current theories on the evolution of eusociality, especially with respect to the role of population viscosity. In an environment with limited resources, population viscosity, by preventing offspring dispersal, creates a population structure where, locally, the proportion of altruism coded genotypes is declining. If the population is at carrying capacity, and if survivorship is unrelated to altruistic genotype, over generations fewer of this genotype survive to reproduce. In effect, continual population viscosity disrupts kin selection. This suggests that theories which invoke population viscosity to provide high values of r are wanting. In particular, contrary to the polygynous family hypothesis (see text), kin selection in the presence of population viscosity cannot yield evolutionarily stable semisociality. Rather, effective kin selection requires parental mediation to form temporary groups of related conspecifics. Thus explanations invoking kin selection must ultimately focus on the parent.

Evolutionary stability of reciprocity in a viscous lattice

Abstract In randomly mixing populations, reciprocity cannot resist invasion by appropriate concurrent multiple mutants (Boyd and Lorberbaum 1987). Here I show how reciprocity can resist such invasion when the clustering (“viscous”) population structure necessary for the emergence of reciprocity in a world of defection is retained after reciprocity has saturated the population. A mutation heuristic is introduced under which only forgiving reciprocity can resist Boyd/Lorberbaum invasion in viscous populations; this provides a selective basis for forgiveness and extends TIT FOR TATs collective stability to evolutionary stability under multiple mutation. The results are generalized to n -person games, where Boyd/Lorberbaum invasion is precluded among insular commons, whether or not reciprocators are forgiving. Non-insular commons are, however, invadable, providing a selection rationale for the maintenance of in/out group distinctions under n -person social ecologies.

Kin selection, kin avoidance and correlated strategies

SummaryKin selection of correlated strategies is examined for both weak and strong altruism under simple haploid inheritance. While kin assortment enhances the range of evolutionary stability for (strongly altruistic) correlated strategies (defined herein), kin avoidance is possible under a weakly altruistic correlated strategy. When social competition induces role assignments of variable fitness, group mates may ‘prefer’ association with non-relatives. Even when group life is mandatory, an individual may accept the risk of abandonment (and reproductive death) rather then associate with kin: a competitive superior may behave altruistically by permitting competitively inferior kin to emigrate. Thus, kin selection and social competition are not necessarily mutually supportive processes within groups. I conclude by interpreting dominance as a strongly altruistic correlated strategy in two social hymenopteran contexts.

Social competition or correlated strategy

SummaryCooperation need not be expressed identically among individuals in a group to enhance the fitness of all. Complementary tasks can be allocated differentially, with task assignment differentially affecting individual absolute fitness. Such differential task assignment is often considered a consequence of social competition to avoid fitness-limiting tasks. I suggest an alternative, evoking an area of evolutionary game theory often overlooked in analyses of cooperation, where task assignment can be fundamentally arbitrary relative to competitive ability. Dominance, implied, ritual or actual, need not be a consequence of social competition for resources within groups.

Pareto efficiency, simple game stability, and social structure in finitely repeated games

Simple game (sensu Brown and Vincent, 1987) evolutionary theory, when coupled with social structure measured as non‐random encounter of strategy “clones”, often permits equilibrium refinement leading to Pareto superior outcomes (e.g., Axelrod, 1981; Myerson et al., 1991), a foundational goal of economic game theory (Myerson, 1991: 370–375). This conclusion, derived from analyses of one‐shot and infinitely repeated games, fails for finitely repeated games. While mutant cluster invasion enhances Pareto efficiency of equilibria in the former, it can depress Pareto efficiency in the latter. Cooperative equilibria of finitely repeated games (under economic analysis) can be susceptible to cluster‐invasion by even more Pareto efficient strategies which are not themselves evolutionarily stable. Evolutionary (simple) game theorys ability to eliminate Pareto inferior Nash equilibrium strategies induces vulnerabilities foreign to economic analysis. Simple game analysis of finitely repeated games suggests that socia...