Abstract

An empirical generalization in ecology states that the relationship between production per unit biomass (P/B) and body mass (W) is an allometric (power) function with an exponent around -1/3, for species assemblages covering a wide spectrum of phyla. Despite its lack of theoretical support, the empirical relation has been used to estimate production of populations and communities. We present here a theoretical analysis showing that asymptotic individual growth and the cubic relation between length and mass are sufficient to explain the pattern and the numerical value of the exponent for multispecies assemblages, with no need to invoke ecological processes above the individual level. Our results imply that body size at sexual maturity is a fixed fraction of asymptotic body size across the species for which the allometric equation holds. Our model supports previous reservations in the sense that the allometric relation may not be valid for some small metazoans. Furthermore, the allometric equation does not hold for cohorts of a population, although it may be considered as a good approximation to the curve expected under our model for fish populations.