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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.
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Izar, P., Ferreira, R. G., & Sato, T. (2006). Describing the organization of dominance relationships by dominance-directed tree method. Am. J. Primatol., 68(2), 189–207.
Abstract: Methods to describe dominance hierarchies are a key tool in primatology studies. Most current methods are appropriate for analyzing linear and near-linear hierarchies; however, more complex structures are common in primate groups. We propose a method termed “dominance-directed tree.” This method is based on graph theory and set theory to analyze dominance relationships in social groups. The method constructs a transitive matrix by imposing transitivity to the dominance matrix and produces a graphical representation of the dominance relationships, which allows an easy visualization of the hierarchical position of the individuals, or subsets of individuals. The method is also able to detect partial and complete hierarchies, and to describe situations in which hierarchical and nonhierarchical principles operate. To illustrate the method, we apply a dominance tree analysis to artificial data and empirical data from a group of Cebus apella.
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Zhou, W. - X., Sornette, D., Hill, R. A., & Dunbar, R. I. M. (2005). Discrete hierarchical organization of social group sizes. Proc Biol Sci, 272(1561), 439–444.
Abstract: The 'social brain hypothesis' for the evolution of large brains in primates has led to evidence for the coevolution of neocortical size and social group sizes, suggesting that there is a cognitive constraint on group size that depends, in some way, on the volume of neural material available for processing and synthesizing information on social relationships. More recently, work on both human and non-human primates has suggested that social groups are often hierarchically structured. We combine data on human grouping patterns in a comprehensive and systematic study. Using fractal analysis, we identify, with high statistical confidence, a discrete hierarchy of group sizes with a preferred scaling ratio close to three: rather than a single or a continuous spectrum of group sizes, humans spontaneously form groups of preferred sizes organized in a geometrical series approximating 3-5, 9-15, 30-45, etc. Such discrete scale invariance could be related to that identified in signatures of herding behaviour in financial markets and might reflect a hierarchical processing of social nearness by human brains.
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Scheffer, M., & van Nes, E. H. (2006). Self-organized similarity, the evolutionary emergence of groups of similar species. Proc. Natl. Acad. Sci. U.S.A., 103(16), 6230–6235.
Abstract: Ecologists have long been puzzled by the fact that there are so many similar species in nature. Here we show that self-organized clusters of look-a-likes may emerge spontaneously from coevolution of competitors. The explanation is that there are two alternative ways to survive together: being sufficiently different or being sufficiently similar. Using a model based on classical competition theory, we demonstrate a tendency for evolutionary emergence of regularly spaced lumps of similar species along a niche axis. Indeed, such lumpy patterns are commonly observed in size distributions of organisms ranging from algae, zooplankton, and beetles to birds and mammals, and could not be well explained by earlier theory. Our results suggest that these patterns may represent self-constructed niches emerging from competitive interactions. A corollary of our findings is that, whereas in species-poor communities sympatric speciation and invasion of open niches is possible, species-saturated communities may be characterized by convergent evolution and invasion by look-a-likes.
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Johnson, D. D. P., Stopka, P., & Knights, S. (2003). Sociology: The puzzle of human cooperation. Nature, 421(6926), 911–2; discussion 912.
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Cameron, E. Z. (2004). Facultative adjustment of mammalian sex ratios in support of the Trivers-Willard hypothesis: evidence for a mechanism. Proc Biol Sci, 271(1549), 1723–1728.
Abstract: Evolutionary theory predicts that mothers of different condition should adjust the birth sex ratio of their offspring in relation to future reproductive benefits. Published studies addressing variation in mammalian sex ratios have produced surprisingly contradictory results. Explaining the source of such variation has been a challenge for sex-ratio theory, not least because no mechanism for sex-ratio adjustment is known. I conducted a meta-analysis of previous mammalian sex-ratio studies to determine if there are any overall patterns in sex-ratio variation. The contradictory nature of previous results was confirmed. However, studies that investigated indices of condition around conception show almost unanimous support for the prediction that mothers in good condition bias their litters towards sons. Recent research on the role of glucose in reproductive functioning have shown that excess glucose favours the development of male blastocysts, providing a potential mechanism for sex-ratio variation in relation to maternal condition around conception. Furthermore, many of the conflicting results from studies on sex-ratio adjustment would be explained if glucose levels in utero during early cell division contributed to the determination of offspring sex ratios.
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