Species-abundance distributions and Taylor’s power law of fluctuation scaling

Two widely investigated areas of theory in ecology over the past half century are species-abundance distributions (SADs) and Taylor’s power law of fluctuation scaling (TL). This paper connects TL with a classic SAD, MacArthur’s broken-stick model. Each of these models is more than 60 years old, but apparently the connection has not been observed previously. For large numbers of species, the broken-stick model asymptotically obeys TL with exponent 2: the variance of species abundance equals the square of the mean species abundance. Equivalently, in the broken-stick model, the coefficient of variation of abundance is asymptotically 1. Because both the broken-stick model and TL have interpretations and applications beyond ecology, the connection established here has broader than purely ecological interest. This simple but previously unnoticed relationship between the broken-stick model and the power-law variance function raises the question of how other species-abundance distributions are related to power law or other variance functions.