Larger species tend to occupy more habitats, but a theoretical framework for the pattern is lacking. I modified the continuous-time logistic equation of population growth in two ways to allow for such a habitat-based theoretical framework. First, I separated birth rate from death rate. Second, I included two new terms in the equation: (1) an explicit spatial variable for habitat quality that reflects the match between a habitat and a population (species-habitat match), and (2) a demand/supply function that depends on the ratio between the energy used by all populations occurring in a habitat, and energy available in that habitat. Energy was used as a common currency to overcome differences between species of different body sizes as well as to overcome differences caused by disproportional intra- and interspecific effects. Allometric relations were used to characterize parameter values that correlate with body size, such as metabolic rate, birth rate, and death rate. The analytical solution of the equation for carrying capacity shows that, for a population to have a positive carrying capacity, its ratio of death rate to birth rate should be less than its match to the habitat it occupies. Literature-based body-size-dependent birth and death rates of Eutherian mammals show that the death-rate:birth-rate ratio decreases with body size. Combining the analytical solution and the death-rate:birth-rate ratio reveals that habitat generality should positively scale with body size. I used this model to simulate simple spatially explicit landscapes having diverse habitats and combinations of species of various body sizes. Using realistic parameters, the model generates results that are consistent with field observations. Thus, one can focus on specific processes to explore macroecological questions.
|Number of pages||7|
|State||Published - 1 Jan 2000|
- Body size and habitat specificity
- Demand/supply function
- Logistic equation
- Range-abundance distribution
- Species-habitat match