COOPERATION UNDER PREDATION RISK - A DATA-BASED ESS ANALYSIS

Two fish that jointly approach a predator in order to inspect it share the deadly risk of capture depending on the distance between them, Mo dels are developed that seek ESS inspection distances of both single p rey and pairs, based on experimental data of the risk that prey (stick lebacks) incur when they approach a predator (pike) to varying distanc es. Our analysis suggests that an optimal inspection distance can exis t for a single fish, and for two equal fish behaving entirely cooperat ively so as to maximize the fitness of the pair. Two equal fish inspec ting cooperatively should inspect at an equal distance from the predat or. The optimal distance is much closer to the predator for cooperativ e pairs than for single inspectors. However, optimal inspection for tw o equal fish behaving cooperatively operates across a rather narrow ba nd of conditions relating to the benefits of cooperation. Evolutionari ly stable inspection can also exist for two equal fish behaving non-co operatively such that each acts to make a best reply (in terms of its personal fitness) to its opponent's strategy. Non-cooperative pairs sh ould also inspect at equal distance from the pike. Unlike the 'single fish' and 'cooperative' optima, which are unique inspection distances, there exists a range of ESS inspection distances. If either fish choo ses to move to any point in this zone, the best reply of its opponent is to match it (move exactly alongside). Unilateral forward movement i n the 'match zone' may not be possible without some cooperation, but i f the pair can 'agree' to mwe forward synchronously, maintaining equal distance, inspection will occur at the nearest point in this zone to the predator. This 'near threshold' is an ESS and is closer to the pre dator than the single fish optimum-pairs behaving almost selfishly can thus attain greater benefits from inspection by the protection gained from Hamilton's dilution effect. That pairs should inspect more close ly than single fish conforms with empirical findings. Phenotypic asymm etries in costs and benefits between the fish are not yet included in the model.