James Brown,, Eric Charnov, Brian Enquist, Geoffrey West
Paper #: 99-10-072
A prominent feature of comparative life histories in the well-documented negative correlation between growth rate and life span [1,2]. Patterns of resource allocation during growth reflect life-history differences between species [1,2]. This is particularly striking in tropical forests, where tree species can differ greatly in their rates of growth and ages of maturity but still attain similar canopy sizes [3,4]. We provide a theoretical framework to relate life-history variables to rates of production $\partial M/\partial t$, where $M$ is above ground body mass and $t$ is time. Assuming that metabolic rate limits production as an individual grows, $\partial M/\partial t$ proportional to $M^3/4$ and incorporating interspecific variation in wood density we derive a universal growth law which quantitatively fits data for large sample of tropical tree species with diverse life histories. Combined with evolutionary life-history theory,  the growth law also predicts several qualitative features of tree demography and reproduction. This framework also provides a general answer to why relative growth rate $1/M(partial M/partial t$) decreases with increasing plant size and varies differing allocation strategies [5-8].