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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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Gonzalez-Fernandez, J. M., & Atta, S. E. (1982). Facilitated transport of oxygen in the presence of membranes in the diffusion path. Biophys J, 38(2), 133–141.
Abstract: Most of the experimental observations on facilitated transport have been done with millipore filters, and all the theoretical studies have assumed homogeneous spatial properties. In striated muscle there exist membranes that may impede the diffusion of the carrier myoglobin. In this paper a theoretical study is undertaken to analyze the transport in the presence of membranes in the diffusion path. For the numerical computations physiologically relevant values of the parameters were chosen. The numerical results indicate that the presence of membranes tends to decrease the facilitation. For the nonlinear chemical kinetics of the reaction of oxygen with the carrier, this decrement also depends on the location of the membranes. At the higher oxygen concentration side of each membrane the flow of combined oxygen is transferred to the flow of dissolved oxygen. The reverse process occurs at the lower concentration side. Jump discontinuities of the concentration of the oxygen-carrier compound at each membrane are associated with these transfers. The decrement of facilitation is due to the cumulative effect of these jump discontinuities.
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Rands, S. A., Cowlishaw, G., Pettifor, R. A., Rowcliffe, J. M., & Johnstone, R. A. (2008). The emergence of leaders and followers in foraging pairs when the qualities of individuals differ. BMC Evol Biol, 8, 51.
Abstract: BACKGROUND: Foraging in groups offers animals a number of advantages, such as increasing their likelihood of finding food or detecting and avoiding predators. In order for a group to remain together, there has to be some degree of coordination of behaviour and movement between its members (which may in some cases be initiated by a decision-making leader, and in other cases may emerge as an underlying property of the group). For example, behavioural synchronisation is a phenomenon where animals within a group initiate and then continue to conduct identical behaviours, and has been characterised for a wide range of species. We examine how a pair of animals should behave using a state-dependent approach, and ask what conditions are likely to lead to behavioural synchronisation occurring, and whether one of the individuals is more likely to act as a leader. RESULTS: The model we describe considers how the energetic gain, metabolic requirements and predation risks faced by the individuals affect measures of their energetic state and behaviour (such as the degree of behavioural synchronisation seen within the pair, and the value to an individual of knowing the energetic state of its colleague). We explore how predictable changes in these measures are in response to changes in physiological requirements and predation risk. We also consider how these measures should change when the members of the pair are not identical in their metabolic requirements or their susceptibility to predation. We find that many of the changes seen in these measures are complex, especially when asymmetries exist between the members of the pair. CONCLUSION: Analyses are presented that demonstrate that, although these general patterns are robust, care needs to be taken when considering the effects of individual differences, as the relationship between individual differences and the resulting qualitative changes in behaviour may be complex. We discuss how these results are related to experimental observations, and how the model and its predictions could be extended.
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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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Seyfarth, R. M. (1977). A model of social grooming among adult female monkeys. J. Theor. Biol., 65(4), 671–698.
Abstract: Grooming networks among adult female monkeys exhibit two similar features across a number of different species. High-ranking animals receive more grooming than others, and the majority of grooming occurs between females of adjacent rank. A theoretical model which duplicates these features is presented, and the properties of the model are used to explain the possible causation and function of female grooming behaviour. The model illustrates how relatively simple principles governing the behaviour of individuals may be used to explain more complex aspects of the social structure of non-human primate groups.
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Tobin, T., & Combie, J. D. (1982). Performance testing in horses: a review of the role of simple behavioral models in the design of performance experiments. J Vet Pharmacol Ther, 5(2), 105–118.
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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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Bell, A. M. (2007). Evolutionary biology: animal personalities (Vol. 447).
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Conradt, L., & Roper, T. J. (2003). Group decision-making in animals. Nature, 421(6919), 155–158.
Abstract: Groups of animals often need to make communal decisions, for example about which activities to perform, when to perform them and which direction to travel in; however, little is known about how they do so. Here, we model the fitness consequences of two possible decision-making mechanisms: 'despotism' and 'democracy'. We show that under most conditions, the costs to subordinate group members, and to the group as a whole, are considerably higher for despotic than for democratic decisions. Even when the despot is the most experienced group member, it only pays other members to accept its decision when group size is small and the difference in information is large. Democratic decisions are more beneficial primarily because they tend to produce less extreme decisions, rather than because each individual has an influence on the decision per se. Our model suggests that democracy should be widespread and makes quantitative, testable predictions about group decision-making in non-humans.
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Rands, S. A., Cowlishaw, G., Pettifor, R. A., Rowcliffe, J. M., & Johnstone, R. A. (2003). Spontaneous emergence of leaders and followers in foraging pairs. Nature, 423(6938), 432–434.
Abstract: Animals that forage socially often stand to gain from coordination of their behaviour. Yet it is not known how group members reach a consensus on the timing of foraging bouts. Here we demonstrate a simple process by which this may occur. We develop a state-dependent, dynamic game model of foraging by a pair of animals, in which each individual chooses between resting or foraging during a series of consecutive periods, so as to maximize its own individual chances of survival. We find that, if there is an advantage to foraging together, the equilibrium behaviour of both individuals becomes highly synchronized. As a result of this synchronization, differences in the energetic reserves of the two players spontaneously develop, leading them to adopt different behavioural roles. The individual with lower reserves emerges as the 'pace-maker' who determines when the pair should forage, providing a straightforward resolution to the problem of group coordination. Moreover, the strategy that gives rise to this behaviour can be implemented by a simple 'rule of thumb' that requires no detailed knowledge of the state of other individuals.
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