On prey grouping and predator confusion in artifical fish schools

In two simulation models the benefit of schooling under predatory pressure is investigated. It appears that if a pre dator cannot become confused by prey, grouping is seldom beneficial. If prey, however, can confuse a predator, schooling appears to protect prey under a whole range of parameters. Using an evolutionary approach we found that, in the case of a confusable predator, cohesive groups with a consistent forward movement evolve most frequently, but that milling stationary groups also prove to be effective. We suggest tha t the predator protection in moving and stationary groups rel y on different mechanisms, among other things, on a kind of altruistic behaviour. Introduction Similar to herds or flocks of other animals many species of fish gather in shoals or schools 1 without the need for leaders or external cues. Instead, it is thought that the (local) int eractions between the group members lead through processes of self-organisation(Camazineet al., 2001) to the evident gr oup structure. The character of these local interactions has be en the focus of many models, e.g. (Niwa, 1994; Huth and Wissel, 1992; Aoki, 1982). Conceptually these models are identical in that individual fish relate their orientation and sp eed to that of their neighbors according to a few behavioral rule s which we will refer to as avoidance (of collisions), attraction (centering) and alignment (matching speed and orientation). As has been demonstrated by means of computer simulations these behavioral rules lead to schooling behav ior which looks natural to the human observer. However, in these models the question of what the benefits are of school formation is not addressed. Of the many studies of the advantages of schooling (Pitcher and Parrish, 1993) there are indications for forag ing benefits (Street and Hart, 1985), hydrodynamic advantages (Svendsen et al., 2003) and anti-predator functions. Here we will concentrate on the anti-predator function of school s. We will study prey-survival in a model on direct benefits of 1Groups of fish that aggregate for social reasons are commonly referred to as shoals (Pitcher and Parrish, 1993). Schools a re shoals that swim coordinated and synchronized. schooling (Zheng et al., 2005; Nishimura, 2002) and in an evolutionary model (Oboshi et al., 2002). Shoaling fish counter predator attacks in many ways, e.g. by evasion such as flash expansion or by early detection of attacking predators (Pitcher and Parrish, 1993). Whereas these strategies are active and direct reactions of the prey fish to the presence of a predator or an ongoing attack, we will concentrate on two different effects, namely the effec t of grouping itself (it may reduce the probability of being found by the predator) and of confusion of the predator. Grouping may be advantageous because in water fish shoals are barely better detectable than individuals (Pitc her and Parrish, 1993). Therefore, when the visual range is low compared to the speed of the predators and the fish, the predator has a much lower chance of encountering a shoal (because of their low number) than encountering fish that swim independently (as there are many). Nevertheless, Treisman shows that grouping is only beneficial if the predator (once a shoal has been detected) can only eat a small number of individuals while the rest can flee (Treisman, 1975). Here, we will nevertheless investigate under which conditions shoals might successfully avoid predator s. Confusion of a predator reduces the success of an attack of a predator (Pitcher and Parrish, 1993; Krause and Ruxton, 2002) due to a multitude of available targets. Correspondingly, the decision of the predator about which individual t o attack has been shown to take a longer time for larger shoals (Landeau and Terborgh, 1986). The reason for this could be twofold – by overloading the visual system (Broadbent, 1965) or by the difficulty of choosing between equal targets, the so-called effect of ‘embarrassment of riches’. Here we will study the effects of grouping and confusion strategies on prey survival both for schooling and ungroupe d prey. In a first model we will show how the number of surviving fish depends on the speed of the predator, the time that is needed to consume a prey fish (handling time) and on whether the predator is confused by too many prey-items or not. Next we will present the behavioral strategies that evolve in prey in an evolutionary model. It is important to note that in these two models prey cannot Figure 1: The sensory field of the predator is divided into five sectors that are subdivided in three areas. The crowdednessci (identical for all prey in an area) is the sum of the number of fish located in the same area and in the one immediately further away. The higher the crowdedness in an area, the better the protection for the prey due to the confusion effect. perceive the predator, therefore they cannot take any evasi ve action. This allows us to study the effects of grouping by prey and confusion of the predator independently from other anti-predator behaviours such as evasion and startling. We plan to incorporate evasion strategies in future work. Methods This section outlines the two types of prey agents used in the models and the predator, which is the same for both models. At the start of each simulation, the prey and the predator were set at random positions with random orientation. The initial positions were confined to a limited area, in order th at all the agents were in sensory range.