Scaling relationships that describe variation in population density with body size in ecological communities, such as the thinning law in plant ecology, can be explained in terms of how individuals use resources as a function of their size. Data for rates of xylem transport as a function of stem diameter show that rates of resource use in individual plants scale as approximately the 3/4 power of body mass, which is the same as metabolic rates of animals. Here we use this relationship to develop a mechanistic model for relationships between density and mass in resource-limited plants. It predicts that average plant size should scale as the -4/3 power of maximum population density, in agreement with empirical evidence and comparable relationships in animals, but significantly less than the -3/2 power predicted by geometric models. Our model implies that fundamental constraints on metabolic rate are reflected in the scaling of population density and other ecological and evolutionary phenomena, including the finding that resource allocation among species in ecosystems is independent of body size.
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