Interpretation of animal behavior, especially as cooperative or selfish, is a challenge for evolutionary theory. Strategy of a competition should follow from corresponding Darwinian payoffs for the available behavioral options. The payoffs and decision making processes, however, are difficult to observe and quantify. Here we present a general method for the derivation of evolutionary payoffs from observable statistics of interactions. The method is applied to combat of male bowl and doily spiders, to predator inspection by sticklebacks and to territorial defense by lions, demonstrating animal behavior as a new type of game theoretical equilibrium. Games animals play may be derived unequivocally from their observable behavior, the reconstruction, however, can be subjected to fundamental limitations due to our inability to observe all information exchange mechanisms (communication).
Animals in the wild or laboratory environment are involved in coordinated, game-like interactions. It can be a fight for mating opportunities with basic individual choices to attack or retreat, or cooperation vs. selfishness dilemma such as participation in territory defence or predator inspection. The corresponding Darwinian rewards and costs are significant, exacting even the life of a player. Animal behavior in these contests, therefore, must be affected by natural selection, converging with time to some evolutionary optimum.
Modeling of animal behavior in the framework of evolutionary game theory [1,2,3], requires a-priori assumptions of available behavioral options and of a decision making mechanism, followed by subsequent analysis of evolutionary optimal behavior. For instance, a combat for mating opportunities or territorial possession can be modeled by the War of Attrition game [4,5]: competitors decide whether to retreat or pursue the fighting under time increasing cost for competition. An alternative description is a strategy choice game, such as Hawk-Dove, with options for selfish (Hawk) and cooperative (Dove) behaviors. Evolutionary payoffs for possible outcomes of the contest (retreat vs. pursue, Hawk vs. Dove etc.) define evolutionarily stable strategies (ESS), capable of outperforming any other behavior. In the case of War of Attrition, for instance, evolutionarily stable strategy is to pursue fighting with a probability exponentially decaying with time. The notion of evolutionarily stable behavior stems from game theoretical Nash equilibrium [6], though may significantly deviate from it in interactions containing significant information exchange [7].
Predictions of animal behavior by its evolutionary stability are, in some cases, ambiguous and paradoxical. There is a longstanding argument concerning emergence and maintenance of cooperation or even altruism, which * Electronic address: sasha@soreq.gov.il are apparently in discord with the Darwinian ban to increase fitness of others [8,9]. For instance, contrary to the evolutionarily stable strategy for War of Attrition, nonexponential statistics of combat durations takes place in some species. The models, therefore, lack the ability to account for the variety of behavioral strategies in nature.
Back in 1983, S. Austad proposed the combat of male bowl and doily spider (Frontinella pyramitela) as a quantitative test of evolutionary game theory [10]. In nature, mature males of this species wander in search of female webs with eggs to fertilize and determine their evolutionary success by fighting with other males. The contests end when one of the combatants gains access to the eggs while his opponent either retreats or dies. The statistics of fight outcomes (percentage of fatal injuries) together with expected evolutionary payoffs (average eggs per female) were accurately documented.
One can expect a self-consistent evolutionary theory predicting spiders’ behavior in a given fight from the expected number of eggs per female and from lifetime male reproductive success: mortal combat becomes more reasonable if a future evolutionary gain is unlikely. In laboratory conditions, two virgin spiders of the same size with no previous knowledge of females’ value, finish their fight in 67% of cases by death of one of the competitors. The surviving looser gets less than δ = 5% of eggs. According to field data, average value of a female is V F = 10 eggs and the male’s lifetime reproductive success in the absence of fighting costs is V L = 16.2 eggs.
The main impediment to derive the spider’s observable behavior from the corresponding evolutionary payoffs is the lack of a general theory for biological cognitive processes. Assumption of random choice by a spider whether to retreat or continue the fight leads to a fallacious conclusion that sometimes they do not fight at all. Hypothesis of war of attrition (fight until one of the competitors retreats) predicts much shorter fight durations than observed [10]. It indicates that even natural seeming assumptions, such as the skill to recognize a re-treating competitor, may be beyond the spiders abilities and have to be incorporated in evolutionary models with great caution.
In this work, the complex process of choosing either selfish S (e.g. continue the fight) or cooperative C (e.g. retreat) behavior is described by conditional probabilities α and β, where α and 1 -α are respectively the probabilities to choose cooperation C and selfish S behaviors against the competitor’s unconditional selfish behavior S, while β and 1 -β are the probabilities to choose cooperation C and selfish S behaviors against the competitor’s unconditional cooperation behavior C. In this context, α and β can be viewed as selfishness aversion and cooperation attraction respectively. These two parameters suffice to describe all four types of interactions: S vs. S, S vs. C, C vs. S and C vs. C. This approach generalizes previous works bas
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