Mathematical modelling of dominance hierarchies

Abstract

In this research we analyse the formation of dominance hierarchies from different viewpoints and various models of dominance hierarchy formation have been proposed, one important class being winner--loser models and another being Swiss tournaments. We start by understanding the structure of hierarchies emerging under the influence of winner and loser effects and two situations are considered: (i) when each individual has the same, fixed (unchanged) aggression threshold, meaning that all of them use the same rule when deciding whether to fight or retreat, and (ii) when individuals select an aggression threshold comparing their own and their opponent's abilities, and fighting if and only if the situation is sufficiently favourable to themselves. For both situations, we investigate if we can achieve hierarchy linearity, and if so, when it is established. We are particularly interested in the question of how many fights are necessary to establish dominance hierarchy. To examine these questions we use existing and new statistical measures. Besides understanding the structure and the temporal dynamic of the hierarchy formation, we also analyse the effect of the information that each individual has about the strength of their opponents on linearity. For the second situation, where individuals choose different aggression threshold, we find the appropriate level of aggression and examine the conditions when an individual needs to be more aggressive and when not. Lastly, we develop a model which allows only the individuals with the same number of wins and losses to fight each other. We show that linear hierarchies are always established. A formula for the total number of fights is derived, and the effect of group size on the level of aggressiveness is analysed