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Thierry, B. (1990). Feedback loop between kinship and dominance: the macaque model. J. Theor. Biol., 145(4), 511–522.
Abstract: There is growing evidence that macaque social systems represent sets of coadapted traits in which strength of hierarchies and degree of nepotism covary. A framework is developed to explain the link between dominance and kinship phenomena, assuming that power brought by alliances among non-kin is allometrically related to those involving relatives. This can account for the type of social relationships observed in “despotic” systems vs. “egalitarian” ones. When social bonds are mostly founded on kinship, lineages are closed and social power generated by coalitions among relatives may reach high levels; social power frequently outweighs the fighting abilities of single individuals, and asymmetry of dominance between group members may be marked. When lineages are more open, social bonds and alliances are less kin-biased, social relationships are more equal, and as the influence of coalitions is less important, the individual retains a certain degree of freedom in relation to the power of kin-networks. Acknowledging that the balance between individual and social power is not set at the same level across different species can explain a number of variations in rules of rank inheritance and relative dominance of males and females among macaques. The framework illustrates how epigenetic processes may shape complex features of primate social systems, and offers opportunities for testing.
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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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Hamilton, W. D. (1971). Geometry for the selfish herd. J. Theor. Biol., 31(2), 295–311.
Abstract: This paper presents an antithesis to the view that gregarious behaviour is evolved through benefits to the population or species. Following Galton (1871) and Williams (1964) gregarious behaviour is considered as a form of cover-seeking in which each animal tries to reduce its chance of being caught by a predator.
It is easy to see how pruning of marginal individuals can maintain centripetal instincts in already gregarious species; some evidence that marginal pruning actually occurs is summarized. Besides this, simply defined models are used to show that even in non-gregarious species selection is likely to favour individuals who stay close to others. Although not universal or unipotent, cover-seeking is a widespread and important element in animal aggregation, as the literature shows. Neglect of the idea has probably followed from a general disbelief that evolution can be dysgenic for a species. Nevertheless, selection theory provides no support for such disbelief in the case of species with outbreeding or unsubdivided populations. The model for two dimensions involves a complex problem in geometrical probability which has relevance also in metallurgy and communication science. Some empirical data on this, gathered from random number plots, is presented as of possible heuristic value. Keywords: Animals; Anura; *Behavior, Animal; Breeding; Communication; Evolution; Fear; Metallurgy; *Models, Biological; Probability; Snakes; *Spatial Behavior
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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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Mesterton-Gibbons, M., Gavrilets, S., Gravner, J., & Akçay, E. (2011). Models of coalition or alliance formation. J. Theor. Biol., 274(1), 187–204.
Abstract: More than half a century has now elapsed since coalition or alliance formation theory (CAFT) was first developed. During that time, researchers have amassed a vast amount of detailed and high-quality data on coalitions or alliances among primates and other animals. But models have not kept pace, and more relevant theory is needed. In particular, even though CAFT is primarily an exercise in polyadic game theory, game theorists have devoted relatively little attention to questions that motivate field research, and much remains largely unexplored. The state of the art is both a challenge and an opportunity. In this review we describe a variety of game-theoretic and related modelling approaches that have much untapped potential to address the questions that field biologists ask.
Keywords: Game theory; Cooperation
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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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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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Gueron, S., Levin, S. A., & Rubenstein, D. I. (1996). The Dynamics of Herds: From Individuals to Aggregations. J. Theor. Biol., 182(1), 85–98.
Abstract: The dynamic behavior of small herds is investigated by means of simulations of two-dimensional discrete-stochastic models. An individual-based approach is used to relate collective behavior to individual decisions. In our model, the motion of an individual in a herd is assumed to be the combined result of both density-independent and density-dependent decisions, in the latter case based on the influence of surrounding neighbors; assumed decision rules are hierarchical, balancing short range repulsion against long-range attraction. The probability of fragmentation of the model herd depends on parameter values. We explore the variety and characteristics of spatial patterns that develop during migration, for herds that are homogeneous and heterogeneous regarding intrinsic walking speeds. Group integrity can be maintained even in mixed populations, but fragmentation results for these more easily than for a homogeneous herd. Observations of natural populations suggest that animals move away from individuals that intrude too closely into their environment, but are attracted to individuals at a distance. Between these extremes, there appears to be a neutral zone, within which other individuals engender no response. We explore the importance of this neutral zone, and offer evolutionary interpretations. In particular, the neutral zone, if not too large, permits the individual to remain in contact with the herd, while reducing the frequency with which acceleration or deceleration must be undertaken. This offers obvious energetic benefits.
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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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