Simulation model of universal law of school size distribution applied to southern bluefin tuna ( Thunnus maccoyii) in the Great Australian Bight

Abstract

A universal law of animal group size distribution correlates well to observed fish school size distribution from fisheries catch data. I applied the law to fisheries independent aerial survey data of southern bluefin tuna ( Thunnus maccoyii) collected over a 10-year period in the Great Australian Bight. The law does not correlate to the observed school size distribution. A computer model originally demonstrated the formation of the universal law from simple rules. I redesigned this model as an individual-based simulation model calibrated from acoustic tag observations and state a mathematical formula for a resultant new family of transient group size distributions. The new formula correlates accurately to the simulation and to the aerial survey data. I use the mathematical model to estimate area of aggregation and total abundance. This approach is new as it does not seek stationary states of group size distribution and because it demonstrates a quantitative relationship between individual behaviour and group size distribution. This work elevates the pattern of group size distribution from a curiosity to a useful tool, and introduces a new family of transient distributions that may have a general application to other grouping phenomena.