Extinction models typically base continued species existence on the tug-of-war between resource density and population growth, generally in a linear relationship.

But a new model that incorporates other facets, including body size and metabolic rates, purports to show a more complex picture based on energy intake, as presented in the latest issue of Nature Communications.

The new mathematical model is the Nutritional State-structured Model, or NSM, and it is a product of a collaboration between scientists at the Santa Fe Institute and the University of California – Merced.

“The energetics associated with somatic maintenance, growth and reproduction are important elements that influence the dynamics of all populations,” the study authors write, in the paper. “The NSM incorporates the dynamics of starvation and recovery that are expected to occur in resource-limited environments.”

The formula holds a few precepts, with one of the foremost being that only “full” animals have reproduction capacity. Also, hungry animals are more likely to die individually.

The quantitative evaluations produced demonstrations of two biological observations: one called Damuth’s law, and the other called Cope’s rule.

Damuth’s law holds that the bigger the individuals of a species, the fewer cohabitate in the same area; and the opposite is true, with smaller species showing more density in living arrangements.

Cope’s rule maintains that land-based mammals evolve toward bigger body sizes. That bigger physicality means more stability against starvation from short-term resource depletion.

The NSM showed both phenomena in the calculations, according to the paper. The NSM showed Damuth’s law in that large species with smaller numbers are less likely to starve, and thus survive. The findings showed Cope’s rule through less potential starvation – and it even predicted that the “ideal” surviving mammal would be a whopping 2.5 times the size of an African elephant – a history that recalls some of the largest fossils ever found.

“Most surprising was the observation that the NSM accurately predicts the maximum mammalian body size observed in the fossil record,” said Justin Yeakel, of UC Merced, one of the authors.

“Unlike many previous forager models, this one accounts for body size and metabolic scaling,” said Chris Kempes, one of the Santa Fe authors. “It allows for predictions about extinction risk, and also gives us a systematic way of assessing how far populations are form their most stable states.”

“I hope some of this will have relevance in managing resources and ensuring species don’t go extinct,” added Sidney Redner, another of the Santa Fe Institute authors.