Truncated power laws: a tool for understanding aggregation patterns in animals?

Statistical distributions like the negative binomial distribution are commonly used to describe aggregation patterns in animals. However, recently it has been suggested that truncated power laws (TPLs) may also be used for this kind of analysis. A TPL consists of two power functions separated by a cut-off size (C*). The cut-off size and the slope of power function one (beta(1)) for the smallest group sizes have been suggested to have a biological explanatory value. We applied TPLs to aggregation data of tephritid seed predators on a composite plant, aphids on willows and grey seals on a haulout site. beta(1) varied between 0.60 and and -0.72, which is higher than predicted. In addition, resource distribution and animal density influenced beta(1) and C*. This indicates that environmental dimensionality suggested to affect beta(1) is masked by ecological factors. We conclude that TPLs are useful due to their simplicity and, in comparison with traditional methods, provide additional biologically relevant information. Truncated power laws can therefore prove to be useful in studies of animal behaviour and population dynamics.