THEORETICAL-ANALYSIS OF THE RELATIONSHIP BETWEEN PRODUCTION PER UNIT BIOMASS AND ANIMAL BODY-SIZE

An empirical generalization in ecology states that the relationship be tween production per unit biomass (PIE) and body mass (W) is an allome tric (power) function with an exponent around -1/3, for species assemb lages covering a wide spectrum of phyla. Despite its lack of theoretic al support, the empirical relation has been used to estimate productio n of populations and communities. We present here a theoretical analys is showing that asymptotic individual growth and the cubic relation be tween length and mass are sufficient to explain the pattern and the nu merical value of the exponent for multispecies assemblages, with no ne ed to invoke ecological processes above the individual level. Our resu lts imply that body size at sexual maturity is a fixed fraction of asy mptotic 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. Furthe rmore, the allometric equation does not hold for cohorts of a populati on, although it may be considered as a good approximation to the curve expected under our model for fish populations.