How might you expect the average size of mammal species to vary from the tropics to the polar regions

"Bergmann's rule is an ecogeographic principle that states that within a broadly distributed taxonomic clade, populations and species of larger size are found in colder environments, and species of smaller size are found in warmer regions."

The rule arises from the fact that smaller objects have larger surface to volume ratios, so they lose heat more easily to the environment. Large animals therefore are able to conserve heat better and are therefore better adapted to colder climates. This rule can also be applied to sizes of mammals during ice ages. Ice age mammals are larger because they are better able to conserve heat.