Random processes describing the occurrence of behavioural patterns in a cichlid fish

Territorial males of the cichlid fish species Haplochromis burtoni were observed over periods of approximately 3 hr and seven different behaviours were recorded. A statistical analysis of the data led to the following results: The short-term sequential organization in the occurrence of the seven recorded behaviours can be described in terms of renewal processes (Figs 1,2 and 3). In order to cope with long-term fluctuations in the rate of occurrence of some behaviours one has to assume that some parameters characterizing the renewal processes involved may slowly fluctuate in time. Long-term fluctuations in the rate of occurrence show particular correlations among the seven behaviours investigated (Figs 4 and 5). The correlation pattern found (Fig. 5) suggests that the seven behaviours share at least four slow ‘basic’ processes, ν₁, …, ν₄, which to different extents contribute to long-term fluctuations in the rate of different behaviours. A linear model representing slow fluctuations in the rate of a particular behaviour as a linear combination of four basic processes yields a reasonable approximation to the long-term correlation pattern observed (Figs 6 and 8).