Abstract: We present a two-dimensional individual-based model of aggregation behaviour in animals by introducing the concept of a “limited domain of danger”, which represents either a limited detection range or a limited attack range of predators. The limited domain of danger provides a suitable framework for the analysis of individual movement rules under real-life conditions because it takes into account the predator's prey detection and capture abilities. For the first time, a single geometrical construct can be used to analyse the predation risk of both peripheral and central individuals in a group. Furthermore, our model provides a conceptual framework that can be equally applied to aggregation behaviour and refuge use and thus presents a conceptual advance on current theory that treats these antipredator behaviours separately. An analysis of individual movement rules using limited domains of danger showed that the time minimization strategy outcompetes the nearest neighbour strategy proposed by Hamilton's (J. Theor. Biol. 31 (1971) 295) selfish herd model, whereas a random strategy confers no benefit and can even be disadvantageous. The superior performance of the time minimization strategy highlights the importance of taking biological constraints, such as an animal's orientation relative to its neighbours, into account when searching for efficient movement rules underlying the aggregation process.

Abstract: The selfish herd hypothesis predicts that aggregations form because individuals move toward one another to minimize their own predation risk. The “dilemma of the selfish herd” is that movement rules that are easy for individuals to follow, fail to produce true aggregations, while rules that produce aggregations require individual behavior so complex that one may doubt most animals can follow them. If natural selection at the individual level is responsible for herding behavior, a solution to the dilemma must exist. Using computer simulations, we examined four different movement rules. Relative predation risk was different for all four movement rules (p<0.05). We defined three criteria for measuring the quality of a movement rule. A good movement rule should (a) be statistically likely to benefit an individual that follows it, (b) be something we can imagine most animals are capable of following, and (c) result in a centrally compact flock. The local crowded horizon rule, which allowed individuals to take the positions of many flock-mates into account, but decreased the influence of flock-mates with distance, best satisfied these criteria. The local crowded horizon rule was very sensitive to the animal's perceptive ability. Therefore, the animal's ability to detect its neighbors is an important factor in the dynamics of group formation.

Abstract: An altruistic individual has to gamble on cooperation to a stranger because it does not know whether the stranger is trustworthy before direct interaction. Nowak and Sigmund (Nature 393 (1998a) 573; J. Theor. Biol. 194 (1998b) 561) presented a new theoretical framework of indirect reciprocal altruism by image scoring game where all individuals are informed about a partner's behavior from its image score without direct interaction. Interestingly, in a simplified version of the image scoring game, the evolutionarily stability condition for altruism became a similar form of Hamilton's rule, i.e. inequality that the probability of getting correct information is more than the ratio of cost to benefit. Since the Hamilton's rule was derived by evolutionarily stable analysis, the evolutionary meaning of the probability of getting correct information has not been clearly examined in terms of kin and group selection. In this study, we applied covariance analysis to the two-score model for deriving the Hamilton's rule. We confirmed that the probability of getting correct information was proportional to the bias of altruistic interactions caused by using information about a partner's image score. The Hamilton's rule was dependent on the number of game bouts even though the information reduced the risk of cooperation to selfish one at the first encounter. In addition, we incorporated group structure to the two-score model to examine whether the probability of getting correct information affect selection for altruism by group selection. We calculated a Hamilton's rule of group selection by contextual analysis. Group selection is very effective when either the probability of getting correct information or that of future interaction, or both are low. The two Hamilton's rules derived by covariance and contextual analyses demonstrated the effects of information and group structure on the evolution of altruism. We inferred that information about a partner's behavior and group structure can produce flexible pathways for the evolution of altruism.

Abstract: Theoretical models have demonstrated the possibility of stable cost-free signalling of need between relatives. The stability of these cost-free equilibria depends on the indirect fitness cost of cheating and deceiving a donor into giving away resources. We show that this stability is highly sensitive to the distribution of need among signallers and receivers. In particular, cost-free signalling is likely to prove stable only if there is very large variation in need (such that the least-needy individuals stand to gain much less than the most-needy individuals from additional resources). We discuss whether these conditions are likely to be found in altricial avian breeding systems--the most intensively studied instance of signalling of need between relatives. We suggest that cost-free signalling is more likely to prove stable and will provide parents with more information during the earlier phases of chick growth, when parents can more easily meet the demands of a brood (and chicks are more likely to reach satiation). Later, informative yet cost-free signalling is unlikely to persist.

Abstract: Models of costly signalling are commonly employed in evolutionary biology in order to explain how honest communication between individuals with conflicting interests can be stable. These models have focused primarily on a single type of honest signalling equilibrium, the separating equilibrium in which any two different signallers send distinct signals, thereby providing signal receivers with complete information. In this paper, we demonstrate that in signalling among relatives (modelled using the Sir Philip Sidney game), there is not one but a large number of possible signalling equilibria, most of which are pooling equilibria in which different types of signallers may share a common signal. We prove that in a general Sir Philip Sidney game, any partition of signallers into equi-signalling classes can have a stable signalling equilibrium if and only if it is a contiguous partition, and provide examples of such partitions. A similar (but slightly stricter) condition is shown to hold when signals are transmitted through a medium with signalling error. These results suggest a solution to a problem faced by previous signalling theory models: when we consider the separating equilibrium, signal cost is independent of the frequency of individuals sending that signal and, consequently, even very rare signaller types can drastically affect signal cost. Here, we show that by allowing these rare signallers to pool with more common signallers, signal cost can be greatly reduced. Copyright 1998 Academic Press.