Dimensional consideration of the relationship between organism abundance and body size

Abstract

The relationship between organism size and abundance, or population density, has been well characterized by a scaling relationship, with different studies reporting a range of scaling exponents. Various mechanistic explanations have been put forth, more recently leveraging metabolic scaling, but there is still considerable debate about the value of exponents. In this paper, I take a phenomenological approach and use dimensional analysis to address the determinants of organism abundance. By considering four variables—energy input, body size, length, and time—a scaling law for organism abundance as a function of body size emerges, most parsimoniously with an exponent of −1. I also consider how abundance is likely to scale with variables with dimensions of length and time: velocity, acceleration, variance, and covariance. Different scaling exponents for the abundance–body size scaling relationship, including −3/4, can easily be obtained by considering life history components or interactions with the abiotic environment.