• distribution–abundance relationship;
  • marsupials;
  • Rapoport's Rule;
  • rodents;
  • species richness

1. In many groups of species, range size and population density are positively correlated (the ‘distribution−abundance relationship’) and range size is positively correlated with latitude (‘Rapoport's Rule’). This study investigated these two relationships among Australian forest mammals, and also tested for the existence of a relationship between population density and latitude in the same fauna.

2. All three relationships were significant, with the distribution–abundance relationship the strongest pattern of the three, and Rapoport's Rule the weakest. Partial correlation analysis showed that: (i) range size and population density remained positively correlated when latitude was held constant; and (ii) population density and latitude remained positively correlated when range size was held constant; but (iii) latitude and range size were not significantly correlated when population density was held constant. For (i) and (ii), partial correlation did not reveal stronger relationships than were revealed by simple correlation. These results suggest that the distribution–abundance relationship is conditioned by latitude to produce small ranges and low population densities in the tropics, and that tropical species tend to have low population densities relative to range size.

3. Body mass accounted for little variation in population density, and for no variation in range size and latitudinal position. The small ranges and low population densities of tropical species were not related to a latitudinal gradient in species richness, which did not occur in this fauna.

4. The latitudinal gradient in population density held within widespread species as well as among species. The effect of Bergmann's Rule (the tendency for organisms in cool environments to be larger bodied than organisms in warm environments) meant that in some species, population energy use rose more steeply with latitude than did population density.

5. I argue that all three relationships might be due to a tendency for the foraging efficiency of animals to be lower in tropical than in temperate ecosystems, as a result of a lower concentration of nutrients in tropical ecosystems. For resource-limited species, foraging efficiency should influence both range size and population density. Differences in foraging efficiency may therefore produce the distribution−abundance relationship as well as latitudinal gradients in range size and population density.