On the scaling of habitat specificity with body size

Larger species tend to occupy more habitats, but a theoretical framework fo r the pattern is lacking. I modified the continuous-time logistic equation of population growth in two ways to allow for such a habitat-based theoreti cal framework. First, I separated birth rate from death rate. Second, I inc luded two new terms in the equation: (1)an explicit spatial variable for ha bitat quality that reflects the match between a habitat and a population (s pecies-habitat match), and (2) a demand/supply function that depends on the ratio between the energy used by all populations occurring in a habitat, a nd energy available in that habitat. Energy was used as a common currency t o overcome differences between species of different body sizes as well as t o overcome differences caused by disproportional intra- and interspecific e ffects. Allometric relations were used to characterize parameter values tha t correlate with body size, such as metabolic rate, birth rate, and death r ate. The analytical solution of the: equation for carrying capacity shows t hat, for a population to have a positive carrying capacity, its ratio of de ath rate to birth rate should be less than its match to the habitat it occu pies. Literature-based body-size-dependent birth and death rates of Eutheri an mammals show that the death-rate:birth-rate ratio decreases with body si ze. Combining the analytical solution and the death-rate:birth-rate ratio r eveals that habitat generality should positively scale with body size. I us ed this model to simulate simple spatially explicit landscapes having diver se habitats and combinations of species of various body sizes. Using realis tic parameters, the model generates results that are consistent with field observations. Thus, one can focus on specific processes to explore macroeco logical questions.