New Model Predicts the 'Ideal' Mammal Is 2.5 Times Bigger Than an Elephant

A more nuanced approach to studying animal populations shows that when it comes to extinction, size matters.

The ecological and evolutionary circumstances that drive a species to extinction are manifold and related to one another in complex ways. There’s predation, ecological collapse, and disease, or as may have been the case with most critters around at the end of the Mesozoic era, plain cosmic bad luck. The important point is that what drives a species to extinction is highly dependent on the idiosyncrasies of the organism and its local environment.


Nevertheless, ecologists attempt to model general population dynamics in order to better understand the population fluctuations of a particular species, and why some eventually go extinct. The world is currently experiencing an alarmingly high rate of species extinction, so having accurate insight into this process is more important than ever.

Many ecological models used to assess extinction risk look at the interplay of two main factors: resource availability and the size of the population. Generally speaking, if resources are abundant, the population increases; if resources are scarce, the population decreases.

Implicit in these models is the idea that if resources are abundant, an animal will be able to harvest enough energy from its environment to reproduce. On the flip side, if resources are scarce, the animal will devote these meagre resources to sustaining itself, rather than trying to produce offspring. This theory has seen validation in species ranging from reindeer to zooplankton, which have been observed to delay reproduction in times of scarcity.

The question, then, is how to make this implicit relationship between resource availability and reproduction explicit in order to create a more nuanced and accurate model of extinction risk for a population. A new eco-evolutionary model published in Nature Communications on Tuesday purports to do just that, and also generated some unexpected results in the process, such as the ideal size for a land mammal.


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Developed by three scientists at the Santa Fe Institute, a nonprofit research organization specializing in complex adaptive systems, the new nutritional state-structured model (NSM) describes the timescales involved when an organism switches from being a ‘full’ animal capable of reproduction, to a starving animal focused on self-maintenance as a function of resource availability.

According to Justin Yeakel, an UC Merced ecologist who formally did postdoctoral work at the Santa Fe Institute, the NSM took insights from allometry—the science of how an animal’s body size relates to its anatomy and behavior—to derive realistic parameters on how fast a population of land mammals could accumulate or deplete its energy resources based on what’s available in the environment.

Yeakel and his colleagues derived the amount of time it takes for an “average” land mammal to burn its excess energy, which is stored as body fat, by looking at allometric data from around 100 land mammals. The idea of an “average” land mammal sounds a bit strange, since everything from mice to humans to grizzly bears technically fall into this category, but the Santa Fe Institute researchers weren’t trying to model dynamics for a specific mammal. Instead, they were trying to create a general model that would apply broadly to all terrestrial mammals.

“When you boil life down to its essential ingredients, organisms have to reproduce to pass on our genes and we have to have enough energy to reproduce,” Yeakel told me on the phone. “Individual animals do really strange things that our model wouldn't capture. We were looking at average trends over this large class of organisms.”


What Yeakel and his colleagues found in their “simple model” was surprising. In the first place, it reproduced Cope’s Rule, a cornerstone of ecological theory. Cope’s Rule states that in general, animals of the same lineage tend to evolve toward larger body sizes. This trend continues until certain inflection point where evolutionary pressures then begin to move in the opposite direction. Put another way, larger animals have a greater evolutionary advantage.

The reason for this, Santa Fe Institute biologist Chris Kempes told me, is that larger organisms are able to drive resources to lower levels through consumption, while also being able to store more of this energy. Since the larger animals are able to store more consumed resources as energy (read: body fat), they can survive at lower levels of resource availability than animals with smaller body sizes.

Yet animals can’t keep growing forever. At a certain point, there won’t be enough resources available to a population of huge animals to allow them to create the energy stores necessary to survive resource shortages created by their own consumption of these very resources in the first place. In other words, animals of this size would basically be eating themselves into a state of starvation.

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The point where these two macro-evolutionary trends meet, the pressure towards larger body sizes and the pressure towards smaller body sizes, is considered the ‘ideal’ body size in the sense that this body size is the most robust against resource-driven extinction. The NSM was able to predict the ideal body size for terrestrial mammals and found that it was about 2.5 times the size of an African elephant, the largest land mammal in the world.


When Yeakel and his colleagues checked the fossil record, it turns out that one of the largest animals in history—the deinotherium, which lived around 10 million years ago and is a relative to modern elephants—was almost exactly the size their model predicted it would be.

“We didn't really have in mind that this model could predict the things that we ended up predicting,” Yeakel told me. “That made it all the more surprising when we started filling in the gaps and realizing that this meshes pretty well with what we see in nature.”

So why don’t we see land mammals around the ‘ideal’ size predicted by the NSM? According to Yeakel, this is because the model is only focused on starvation and recovery dynamics of mammalian populations, and doesn’t take into account all the other ecological forces acting on animal populations, such as predation or competition from other species.

“We would expect the optimal mass that we calculate to be an upper bound and one that is not often attained in nature,” Yeakel told me. “Organisms are not just constrained by starvation dynamics, so we observe many varieties of body sizes, which are optimal solutions (in a dynamic ever-changing way) to their particular environments and constraints.”

For now, the NSM is limited to terrestrial mammals, which Kempes said were selected because of the large amount of data available about their energetics. Nevertheless, both Kempes and Yeakel told me that the general model could be applied to other types of animals after appropriate changes were made in the parameters and that given the extinction risks faced by aquatic animals, this could be a fruitful research direction.

“There’s a lot of research about energetics and body composition for terrestrial mammals so we felt really confident in those scaling relationships,” Kempes said. “Of course, thinking about aquatic mammals in the same detailed way in the future would be very interesting.”