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Broom, M. (2002). A unified model of dominance hierarchy formation and maintenance. J. Theor. Biol., 219(1), 63–72.
Abstract: In many different species it is common for animals to spend large portions of their lives in groups. Such groups need to divide available resources amongst the individuals they contain and this is often achieved by means of a dominance hierarchy. Sometimes hierarchies are stable over a long period of time and new individuals slot into pre-determined positions, but there are many situations where this is not so and a hierarchy is formed out of a group of individuals meeting for the first time. There are several different models both of the formation of such dominance hierarchies and of already existing hierarchies. These models often treat the two phases as entirely separate, whereas in reality, if there is a genuine formation phase to the hierarchy, behaviour in this phase will be governed by the rewards available, which in turn depends upon how the hierarchy operates once it has been formed. This paper describes a method of unifying models of these two distinct phases, assuming that the hierarchy formed is stable. In particular a framework is introduced which allows a variety of different models of each of the two parts to be used in conjunction with each other, thus enabling a wide range of situations to be modelled. Some examples are given to show how this works in practice.
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Broom, M., & Cannings, C. (2002). Modelling Dominance Hierarchy formation as a Multi-player game. J. Theor. Biol., 219(3), 397–413.
Abstract: Animals who live in groups need to divide available resources amongst themselves. This is often achieved by means of a dominance hierarchy, where dominant individuals obtain a larger share of the resources than subordinate individuals. This paper introduces a model of dominance hierarchy formation using a multi-player extension of the classical Hawk-Dove game. Animals play non-independent pairwise games in a Swiss tournament which pairs opponents against those which have performed equally well in the conflict so far, for a fixed number of rounds. Resources are divided according to the number of contests won. The model, and its emergent properties, are discussed in the context of experimental observations.
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Dugatkin, L. A., & Hoglund, J. (1995). Delayed breeding and the evolution of mate copying in lekking species. J. Theor. Biol., 174(3), 261–267.
Abstract: Recent experimental evidence indicates that females may copy the mate choice of others. Here, we present a model for the evolution of mate copying strategies in lekking species. In the model, all females (copiers and non-copiers) assess male quality, but a copier's assessment of a male's quality increases after males have mated with other females. The model demonstrates that mate copying is favored when breeding late in the season has a relatively high cost. We hope that our results will spur empirical work quantifying the time constraints associated with breeding, thus allowing more direct tests of the model's predictions.
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Dugatkin, L. A., Perlin, M., & Atlas, R. (2003). The Evolution of Group-beneficial Traits in the Absence of Between-group Selection. J. Theor. Biol., 220(1), 67–74.
Abstract: One specific prediction emerging from trait-group models of natural selection is that when individuals possess traits that benefit other group members, natural selection will favor “cheating” (i.e. not possessing the group-beneficial trait) within groups. Cheating is selected within groups because it allows individuals to avoid bearing the relative costs typically associated with group-beneficial traits, but to still reap the benefits associated with the acts of other group members. Selection between groups favors traits that benefit other group members. The relative strength of within- and between-group selection then determines the equilibrium frequency of those who produce group-beneficial traits and those that do not. Here we demonstrate that individual-level selection, that is selection within groups can also produce an intermediate frequency of such group-beneficial traits by frequency-dependent selection. The models we develop are general in nature, but were inspired by the evolution of antibiotic resistance in bacteria. The theory developed here is distinct from prior work that relies on reciprocity or kinship per'se to achieve cooperation and altruism among group members.
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Fishman, M. A. (1999). Predator Inspection: Closer Approach as a Way to Improve Assessment of Potential Threats. J. Theor. Biol., 196(2), 225–235.
Abstract: When detecting a predator, some prey animals respond in a counterintuitive fashion by approaching, rather than fleeing, that potential threat of extinction. This seemingly paradoxical behaviour, known aspredator inspection, has been reported for a wide variety of taxa--and therefore can be assumed to be adaptive. However, the view of predator inspection as a paradoxical behaviour rests on two implicit assumptions: (a) initial predator detecting is unambiguous, with no uncertainty in discriminating between hunting and non hunting members of predator species, or members of predator species and unrelated phenomena; (b) the costs of flight are negligible relative to the risk of predation. Upon reflection assumption (a) is not really tenable. Whereas assumption (b) is not consistent with experimental evidence [Godin & Crossman (1994)Behav. Ecol. Sociobiol.34,359-366]. Given that predator detection is ambiguous and the costs of flight are not negligible, a prey individual may benefit by a closer approach to the source of the alarming signals, thus improving its assessment of the situation--despite the increased risk of predation. In this paper, the above statement is given rigor by reformulating the problem in game theoretical terms. The results indicate that a prey will minimize its costs by performing predator inspection whenever its degree of certainty regarding predator identification and/or assessment of its intentions is less than a threshold, which is determined by the model's parameters.
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James, R., Bennett, P. G., & Krause, J. (2004). Geometry for mutualistic and selfish herds: the limited domain of danger. J. Theor. Biol., 228(1), 107–113.
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.
Keywords: Aggregation; Selfish herd; Limited domains
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Reluga, T. C., & Viscido, S. (2005). Simulated evolution of selfish herd behavior. J. Theor. Biol., 234(2), 213–225.
Abstract: Single species aggregations are a commonly observed phenomenon. One potential explanation for these aggregations is provided by the selfish herd hypothesis, which states that aggregations result from individual efforts to reduce personnel predation risk at the expense of group-mates. Not all movement rules based on the selfish herd hypothesis are consistent with observed animal behavior. Previous work has shown that herd-like aggregations are not generated by movement rules limited to local interactions between nearest neighbors. Instead, rules generating realistic herds appear to require delocalized interactions. To date, it has been an open question whether or not the necessary delocalization can emerge from local interactions under natural selection. To address this question, we study an individual-based model with a single quantitative genetic trait that controls the influence of neighbors as a function of distance. The results indicate that predation-based selection can increase the influence of distant neighbors relative to near neighbors. Our results lend support for the idea that selfish herd behavior can arise from localized movement rules under natural selection.
Keywords: Selfish herd; Behavior; Evolution; Predation risk
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Viscido, S. V., Miller, M., & Wethey, D. S. (2002). The dilemma of the selfish herd: the search for a realistic movement rule. J. Theor. Biol., 217(2), 183–194.
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.
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Viscido, S. V., Miller, M., & Wethey, D. S. (2001). The response of a selfish herd to an attack from outside the group perimeter. J. Theor. Biol., 208(3), 315–328.
Abstract: According to the selfish herd hypothesis, animals can decrease predation risk by moving toward one another if the predator can appear anywhere and will attack the nearest target. Previous studies have shown that aggregations can form using simple movement rules designed to decrease each animal's Domain of Danger. However, if the predator attacks from outside the group's perimeter, these simple movement rules might not lead to aggregation. To test whether simple selfish movement rules would decrease predation risk for those situations when the predator attacks from outside the flock perimeter, we constructed a computer model that allowed flocks of 75 simulated fiddler crabs to react to one another, and to a predator attacking from 7 m away. We attacked simulated crab flocks with predators of different sizes and attack speeds, and computed relative predation risk after 120 time steps. Final trajectories showed flight toward the center of the flock, but curving away from the predator. Path curvature depended on the predator's size and approach speed. The average crab experienced a greater decrease in predation risk when the predator was small or slow moving. Regardless of the predator's size and speed, however, predation risk always decreased as long as crabs took their flock-mates into account. We conclude that, even when flight away from an external predator occurs, the selfish avoidance of danger can lead to aggregation.
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Suzuki, Y., & Toquenaga, Y. (2005). Effects of information and group structure on evolution of altruism: analysis of two-score model by covariance and contextual analyses. J. Theor. Biol., 232(2), 191–201.
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.
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