title: Behavioural dominance: Some elementary probabilistic considerations and their behavioural implications.
abstract: Despite near ubiquity of behavioural dominance, its nature and implications remain uncertain. Criteria commonly used to detect and assess dominance are not easily referred to random expectation, and may be behaviourally inappropriate. Use of the final score , Wins to A:Wins to B, is insufficient on both counts, and does not consider temporal succession. Successive wins and losses for an individual can be scored as positive (p) and negative (q) units, whose sum at any encounter is the cumulative score (S). This indicates lead (+S), lag (-S) or equality (S=0), sums all prior experience in a single present state, and may then be of direct behavioural relevance. Lead so measured is appropriate to assessment of the overall direction of dominance, and allows distinction between 'reversals' which do or do not alter this. Exact random probabilities of all possible values of SN at encounter N, and of all possible win-loss sequences leading to these can be specified by reference to the arcsine probability distribution. Calculations of such expectations for situations of particular behavioural interest reveal counter-intuitively high degrees of consistency in lead (dominance). The need to establish reliable null hypotheses to avoid erroneous detection of behavioural dominance is stressed.
authors.affiliation: Le Petit Monthélon, 35690 Acigné, France.
authors.forename: P O
authors.initials: PO
authors.lastname: Hopkins