Evolution of cooperation Mutualism Kin selection By-product mutualism –as a consequence of behaving selfishly, the donor inadvertantly benefits the recipient. –Example: cleaner wrasse selfishly consume ectoparasites of larger fish. The large fish cooperates by not eating the cleaner fish. –Cleaner wrasse have mimics that cheat! Reciprocal altruism
Reciprocal Altruism the trading of altruistic acts in which the benefit is larger than the cost so that over time participants enjoy a net gain. –Delay between donation cost and receipt of benefit separates mutualism from reciprocal altruism. –Delay allows for the possibility of cheating, thus cheaters must be detected and excluded –A sufficient number of interactions must occur to provide a net benefit to participants. Note that in many instances, the net benefit will increase with the number of exchanges. Thus, a large number of interactions favors reciprocity.
The prisoner’s dilemma PD is defined by T > R > P > S and R > (T + S) / 2 ESS for single round of the game: always defect! Two suspected criminals are jailed separately and encouraged to provide evidence that the other was involved in the crime
The Iterated Prisoner’s Dilemma Iterating this game allows for cheating - the key distinction between mutualism and reciprocity Iteration permits complicated strategies, e.g. one player can perform CDCDCCCD while another might do CCCCCCCC, etc. TFT (cooperate on the first move and thereafter mimic your opponent) is the best strategy because –Outscored all other strategies in computer tournament (Axelrod) –Is an ESS if the probability of future encounter, w, meets these criteria: –w > (T - R)/(T - P) and w > (T - R)/(R - S) –Obtain these inequalities by applying 1, w, w 2, w 3,... to successive future payoffs and noting that w + w 2 + w = 1/(1 - w)
Beyond tit-for-tat Once TFT evolves, can other strategies invade? Subsequent work indicates that other trajectories may occur, e.g. TFT-> Generous TFT-> Pavlov-> cooperation (Nowak & Sigmund) –If mistakes are made, Generous-tit-for-tat does better than TFT (GTFT cooperates after opponent cooperates but also after opponent defects with some probability) –Pavlov - win-stay, lose-shift does better than TFT because it corrects occasional mistakes and exploits unconditional cooperators.
Predator inspection - mirror expt Fish with parallel mirror approached closer than fish with oblique mirror But, same result is seen in The absence of any predator! Suggests that fish tend to school.