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.

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.

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.

Abstract: The view is examined that the adaptive value of conventional aspects of fighting behaviour is for assessment of relative RHP (resource holding power) of the combatants. Outcomes of aggressive disputes should be decided by each individual's fitness budget available for expenditure during a fight (determined by the fitness difference between adoption of alternative strategies, escalation or withdrawal without escalation) and on the rate of expenditure of the fitness budget if escalation occurs (determined by the RHPs of the combatants). Thus response thresholds for alternative strategies (“assessments”) will be determined by natural selection on a basis of which opponent is likely to expend its fitness budget first, should escalation occur. This “loser” should retreat (before escalation) and the winner should stay in possession of the resource. Many aggressive decisions depend on whether one is a resource holder, or an attacker. Assuming the RHP of the combatants to be equal, there are many instances of fitness pay-off imbalances between holder and attacker which should weight the dispute outcome in favour of one or other opponent by allowing it a greater expendable fitness budget. Usually the weighting favours the holder; the attacker therefore needs a correspondingly higher RHP before it may be expected to win. This is not invariably the case, and much observed data fits the predictions of this sort of model. If assessments are perfect and budget expenditure rates exactly predictable, then there would never seem to be any case for escalation. Escalation can be explained in terms of injury inflictions (expenditures) occurring as discrete events; i.e. as “bouts” won or lost during fighting. Assessment can give only a probabilistic prediction of the outcome of a bout. A simple model is developed to investigate escalation situations. Each combatant assesses relative RHP; this correlates with an absolute probability of winning the next bout (cabs). The stake played for is infliction of loss of RHP and is determined by the fitness budgets of the opponents. (Each individual plays for the withdrawal of its opponent.) This defines a critical probability of winning (ccrit) for each combatant, above which escalation is the favourable strategy (cabs > ccrit) and below which withdrawal is favourable (cabs < ccrit). Escalation should occur only where cabs-ccrit is positive for both combatants. This model gives predictions compatible with the observations, indicating that RHP loss alone can be adequate to explain withdrawal: escalation behaviour. Withdrawal tendency will be increased by low searching costs. Escalations should be restricted to closely matched RHP opponents if RHP disparity is the major imbalance. Outside the “escalation range” of a given individual, the higher RHP individual wins and the lower one loses (i.e. it should withdraw after conventional display). RHP disparity and holder: attacker imbalance should both interact to shape the observed pattern, though their relative importances will depend on species and situation. In some instances selection may favour immediate withdrawal from an occupied territory even without assessment of RHP.

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.