The use of Mixed Distribution Models to Determine Bout Criteria for Analysis of Animal Behaviour

Feeding behaviour consists of feeding events, separated by non-feeding intervals. Feeding events are often clustered into bouts, which may be called meals. Grouping feeding events into meals requires the determination of a bout or meal criterion, that is, the longest interval accepted as part of a meal. Tolkamp & Kyriazakis (1999a) proposed a three-Gaussian model to estimate meal criteria. The three Gaussians each described the frequency distribution of the loge-transformed lengths of a population of intervals. These populations were thought to be: (1) short intervals within meals; (2) intervals within meals during which animals drink; (3) intervals between meals. This model predicted that the probability of an animal starting a meal would first increase, and then decrease with time since the last meal. This contrasts with expectations based on the satiety concept, which predicts that the probability of an animal starting a meal will increase with time since the last meal. This discrepancy is related to the symmetrical nature of the Gaussian distribution. Alternatively, the two-parameter Weibull distribution can take a skewed form and perhaps is more suitable to describe the different populations of intervals. In this study, models consisting of combinations of Gaussian and Weibull distributions were examined for their suitability to describe the observed feeding behaviour of cows. Weibulls did not improve the description of the populations of within-meal intervals, compared to Gaussians. However, the Weibull distribution was found to describe the between-meal population of intervals statistically better than the Gaussian. Additionally, this inclusion of a Weibull, as opposed to a Gaussian, resulted in predictions that were in better agreement with the satiety concept over the entire range of interval lengths observed. A model based on Gaussians to describe the within-meal populations of intervals and a Weibull to describe the population of between-meal intervals is, therefore, proposed. This model leads to biologically more satisfactory estimates of bout criteria than previous models and is likely to be applicable both across species and behaviours.