Applying Lanchester’s laws to the interspecific competition of coral reef fish

Abstract

Lanchester’s laws of combat are a mathematical framework describing the relative contributions of individual fighting ability and group size to overall group fighting ability. Since 1993, several studies have attempted to apply this framework to interspecific dominance relationships between nonhuman animals. However, this prior work addressed only the corollaries of Lanchester’s laws rather than the laws themselves. Here, we directly test Lanchester’s linear and square law to explain interspecific competition of coral reef fish. First, we analyzed the relationship between body size and dominance to find a biologically accurate proxy of individual fighting ability. We then tested whether group fighting ability was linearly (linear law) or quadratically (square law) related to group size while accounting for the different fighting abilities of competing species. We found support for the linear law; however, both laws were outperformed by a simpler model that only included body size. After accounting for possible outliers and data limitations, we suggest that Lanchester’s linear law may prove useful for explaining interspecific competition in marine ecosystems. Dominance hierarchies develop among fishes based on several factors such as group size and body size, whose interplay remains poorly understood. We investigated whether the relative contributions of these factors to overall competitive success can be quantified using Lanchester’s laws of combat, a mathematical framework that was originally developed to analyze human warfare. We found that for differently sized groups of coral reef fishes, Lanchester’s linear law can predict displacement outcomes.