Altruism, the prisonerís dilemma,
and the components of selection
Jeffrey A. Fletcher and Martin Zwick
Systems Science Ph.D. Program
The mechanisms by which altruistic behavior may evolve in biological systems has been vigorously debated over the last several decades. Alternative explanations include reciprocal altruism where the self-interest of individuals is served by the exchange of cooperation with others, inclusive fitness where the self-interest of genes is served by benefiting copies of themselves in other organisms (usually relatives), and multilevel selection (often called group selection) where the self-interest of groups may favor those with more altruistic, cooperative members. Although these explanations may to some degree be mathematically equivalent, they clearly differ in their view of the level at which self-interest can select for self-sacrifice. The purpose of our research is to demonstrate the usefulness of game theory as a framework for understanding the evolution of altruistic behaviors. Previously we have shown that an n-player prisonerís dilemma (PD) with minimal group structure can serve as a model of multilevel selection favoring altruism. This framework highlights the non-zero sum fitness relationships necessary for selection of altruistic traits as well as the tension between selection within groups (which favors selfish individuals) and selection between groups (which favors altruistic individuals). Here we more formally connect the parameters of a simple n-player PD and these two opposing components of selection.
Dynamic evolutionary computer simulations based on a simple n-player PD in multiple groups are used in which utility payoffs from the PD determine fitness, i.e. the relative number of progeny in the next generation. We demonstrate how an altruistic trait can be selected for in a global population despite being selected against in each sub-population. This is an example of Simpsonís paradox and is due to the disproportionate contribution to the whole population by groups containing a higher percentage of cooperators. Using the Price covariance equation we partition the change in overall altruism frequency into two components. The first represents the contribution to the global frequency change due to the disproportionate success of groups; the second component represents the contribution to change due to the advantage of individual defectors over cooperators within any group. In the multilevel selection explanation of altruism, these two components of selection oppose one another, i.e. have opposite sign.
We find that the two components of hierarchical selection predicted by the Price equation can be directly interpreted in terms of two features of our PD model. Specifically the between group selection component is given by the weighted average of the utilities for cooperators and defectors within a group. This value varies with the frequency of cooperators in each group. The within group individual selection component is given by the difference between cooperator and defector utilities independent of group cooperator frequency.
Although computer simulations of the PD including n-player versions have been used to study reciprocal altruism, surprisingly, the n-player PD has not been used to model multilevel selection. Previously we have made this connection and here for the first time we formally demonstrate the connection between PD parameters in our model and the hierarchical components of selection specified by the Price equation.
The tension between hierarchical levels of selection can be modeled by an n-player PD in multiple groups such that the between and within group selection components can be precisely represented by two features of the n-player PD.
 Here we use the term altruistic to describe any behavior that gives benefit to others at a relative cost to the provider of the benefit. Psychological or moral aspects of altruism are not investigated nor implied by our use of this term.