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

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.