Population dynamics, demographic stochasticity, and the evolution of cooperation

Abstract

A basic evolutionary problem posed by the Iterated Prisoner's Dilemma game is to understand when the paradigmatic cooperative strategy Tit-for-Tat can invade a population of pure defectors. Deterministically, this is impossible. We consider the role of demographic stochasticity by embedding the Iterated Prisoner's Dilemma into a population dynamic framework. Tit-for-Tat can invade a population of defectors when their dynamics exhibit short episodes of high population densities with subsequent crashes and long low density periods with strong genetic drift. Such dynamics tend to have reddened power spectra and temporal distributions of population size that are asymmetric and skewed toward low densities. The results indicate that ecological dynamics are important for evolutionary shifts between adaptive peaks. The Prisoner's Dilemma game contains the basic paradox for the evolution of reciprocal altruism (1, 2). In this game, each of two players can either cooperate or defect. This leads to four possible payoffs S Ͻ P Ͻ R Ͻ T: if one player cooperates and the other defects, the cooperator gets S and the defector gets T, if both players cooperate they both get R, and if both defect they get P. No matter what the other does, it is always best to defect (R Ͻ T and S Ͻ P), but if both would cooperate they would both receive a higher payoff than if both defect (P Ͻ R). If payoffs are interpreted as Darwinian fitness, this game exemplifies the advantage of selfish mutants and the evolution of maladaptive noncooperative behavior. The paradox has a solution in the Iterated Prisoner's Dilemma (1), in which opponents meet again with a certain probability. In this new game, the Tit-for-Tat (TFT) strategy-cooperate in the first round, then do whatever the opponent did in the previous round-does very well against a wide variety of other strategies (3). TFT captures the essence of reciprocal altruism (4), and once established, TFT can catalyze the evolution of even more cooperative strategies (5, 6). Thus, TFT represents a cornerstone in the evolution of cooperation, and it is important to determine the conditions under which TFT can evolve in a population of pure defectors.We consider the evolutionary game between the strategies TFT and AD-always defect, regardless of the opponent's decisions-in the Iterated Prisoner's Dilemma. Let w be the probability that opponents meet again. Then the payoffs between TFT and AD are as shown in Table 1, in which the entries are the payoffs received by the strategy in the left column when playing against the strategy in the top row. For example, when TFT plays against AD, it gets S in the first round and P in all successive rounds, hence a total of S ϩ wP ϩ w 2 P ϩ . . . . AD gets T in the first round and P thereafter. Thus the payoff for TFT is S ϩ wP͞(1 Ϫ w), whereas that of AD is T ϩ wP͞(1 Ϫ w). The other payoffs are calculated similarly. In a population consisting of a mixture of TFT and AD, the payoffs of the two strategies depend on their frequencies. If p is the frequency of TFT...

Demography and ecology drive variation in cooperation across human populations

“…Theory predicts that factors like population size and age structures affect the balance of cooperation and competition within a population (21,22). It is possible that some of the behavioral variation between our study populations is driven by norms at the level of the population or village unit rather than at the level of the endogamous cultural unit; this hypothesis needs to be tested empirically.…”

Disordered environments in spatial games

“…For instance, in a round robin tournament, Axelrod [1] found that tit-for-tat (TFT) (starts cooperating and, after that, do what the opponent did in the previous step) was the most successful strategy, but other successful strategies have also been found [22]. Nevertheless, TFT cannot invade a population of defectors before reaching a minimum population, what can be achieved in several ways [8,23,24].…”

Eco-evolutionary dynamics of social dilemmas

“…For a complete understanding of evolutionary processes it is therefore important to incorporate ecological changes. Especially evolutionary changes occurring on timescales comparable to ecological changes necessitate an amalgamation into an eco-evolutionary framework [23,38,[73][74][75][76][77]. The importance of more comprehensive theoretical approaches is supported by recent experimental results [21,57].…”