Formal models, those which explicitly specify the postulates on which they are based, the development of their 'predictions' from those postulates, and the boundary conditions under which they apply, have the potential to be useful tools in archaeological inference and explanation. Detailed examination of one such model, the mathematical model commonly referred to as the diet breadth or prey choice model, shows that its archaeological application is severely complicated by two factors that are difficult or impossible to specify for prehistoric cases: 1) limits on the amount of meat consumable by a food-sharing group before spoilage or loss to scavengers and 2) hunting failure rates. The former introduce significant uncertainties into the food yield or energetic return term of resource rankings, while the latter affect both resource rankings and the resouce encounter rates leading to prey inclusion or exclusion from the diet. Together, these factors make rigorous diet breadth / prey choice model-based inferences from ungulate archaeofaunas impractical, especially in Paleolithic cases. Following success in recent years in making diet breadth model-based inferences about Paleolithic demography from small game analyses that involved computer simulation modeling of prey species' resilience to hunting pressure, the development and employment of a similar model applied to ungulate species reveals that, in general, the differences in the abilty of populations of different ungulate species to sustain harvest rates are not sufficient to allow the relative representation of ungulate remains in archaeological sites to be a viable basis for human demographic inferences. However, in cases where ungulate remains allow the determination of both prey age structure and sex ratio, it is possible to distinguish low exploitation rates, high exploitation rates, and overhunting. In some cases, the sex ratio data may also alter relative hunting resilience levels in such a way that it may be possible to infer that one species was capable of supporting a larger human population than another.