Life-history models reconstruct mammalian evolution

While ecologists sometimes bemoan the complexities of the discipline, several of the overarching patterns of nature can be boiled down to surprisingly simple terms. One of the most intriguing of these is Damuth’s law (1) that population density is scaled with body mass raised to the power of −3/4 irrespective of taxa or time. Because metabolic demand is allometrically scaled in identical fashion, a local population of 5-kg hares requires essentially the same energy to sustain itself as a herd of 50-kg deer. This implies that different species of organisms are energetically equivalent and hence interchangeable in a very basic sense. On the other hand, reconstructions of mammalian lineages consistently demonstrate gradual replacement of small species with larger versions over evolutionary time. This pattern, known as Cope’s rule (2), suggests that fundamental selective advantages accrue with increase in body size, seemingly at odds with Damuth’s law. If large animals are no more energetically efficient than their smaller brethren, why would one expect any directional trajectory over evolutionary time? This paradox is neatly explained by Bhat et al.’s paper (3) in PNAS.

Linking a body of metabolic theory championed by J. H. Brown et al. (4) with fractal-based conjectures (5, 6) about the degree of patchiness in food supply experienced by animals of different size, Bhat et al. (3) use energetic cost−benefit analysis to construct a minimalist model of mammalian life-history constraints. Because the process of gathering food items is inherently stochastic, whereas metabolic costs of foraging are continuous, the energy state of each individual gradually drifts upward or downward over time, much like wind-borne grains of pollen (2). This diffusive process occasionally results in a lucky individual acquiring sufficient energy to facilitate a reproductive event, at which point the energy balance is reset to a new lower level, much like an electrical capacitor. The probabilistic nature of diffusion processes similarly implies, however, that the energy state sometimes slips below the level required to meet ongoing metabolic demand, resulting in death by misadventure (2). Individual lives are accordingly characterized as repeated episodes of food gathering punctuated by reproductive events, until a run of bad foraging luck (sometimes referred to by mathematicians as the principle of gambler’s ruin) ends the game. Very basic ecology, indeed.

Because diffusion processes recur in many physical and biological contexts, their statistical properties are well understood (7). The simplicity of the energy state diffusion envisaged by Bhat et al. (3) allows them to predict, from first principles, the probability of one, two, or more breeding events, and, as a result, both the mean and variance in fitness expected for any given population. The predicted fitness can be neatly encapsulated in an equation incorporating the mean and variance in energy obtained through feeding each day, metabolic costs, the energetic investment in each offspring, litter size, and the somatic energy reserves remaining after each reproductive event. Inevitable trade-offs between the influence of the latter three variables define what ecologists term an organism’s life history: the species-specific set of traits that define the strategic response to ecological challenges set by their natural environment. Environments in which mean rates of energetic gain exceed metabolic costs encourage investment in reproduction and larger litter sizes, but only up to a point. The optimality model predicts that particularly rich environments should select for organisms with large somatic energy reserves, short intervals between breeding events, and minimal investment in each offspring, a demographic strategy termed by evolutionary ecologists an r-selected life history (8). Harsh environments, in which costs exceed energy gain or those that are highly variable in energy acquisition, are predicted to favor longer intervals between smaller litters and increased energetic investment in each offspring, a so-called K-selected life history (8). Since metabolic costs are almost always substantially greater for endotherms than ecotherms, differences in energetic efficiency lead to taxon-specific contrasts in optimal life-history strategies that are well supported by empirical studies.

Because both lifetime reproduction and mortality risk due to energy shortfall are predictable from first principles using Bhat et al.’s (3) optimal life-history formulation, it is relatively straightforward to solve for the level of energy gain at which a typical individual is just able to replace itself over the course of its lifetime. By dividing the resource supply rate by the critical rate of energy gain, the equilibrium population density is predictable on the basis of body size. Such calculations applied across the spectrum of animal body sizes intriguingly resurrect Damuth’s law.

What makes Bhat et al.’s (3) life-history model truly unique, however, is the recognition that spatial clustering of food items relative to the ecological demands of consumers can play a crucial role in shaping life-history responses. Consider, first, a relatively uniform food resource such as a grassland. Variation in energy gain for a population of grazing buffalo would be much less than for a population of voles, largely because of mass-specific differences in their mobility and consequently home range (Fig. 1). In contrast, the obviously patchy food distribution experienced by a giraffe wandering across the African savannah would be more directly comparable to resource variation of much smaller folivores. To the extent that system-specific differences in resource clustering can be neatly encapsulated by mass-specific scaling coefficients, the optimality model makes intriguing predictions about how fitness is influenced by mean resource supply rates, spatial and potentially temporal variation in resource supply rates, and mass-specific constraints on metabolic rates, mobility, and home range size.

Fig. 1.

Over the course of the Miocene period, ancestral horses were gradually replaced by bigger species with larger home ranges, making them better adapted to forage across heterogenous grasslands.

Incorporation of an appropriate scaling coefficient to accommodate resource clustering introduces the potential for a critical density threshold, termed an Allee effect in the ecological literature, below which organisms of a given size cannot persist, regardless of the resource supply rate. Such tipping points are predicted to have particularly severe effects on smaller organisms, resulting in higher probability of extinction and reduced competitive success when faced with larger organisms or organisms feeding on more spatially uniform resources.

Bhat et al. (3) use this approach to explain the evolutionary history of mammalian herbivore lineages. In the mid-Miocene, the ancient progenitors of modern pigs, rhinos, and horses were all relatively small in size and fed largely on herbaceous plants that tend to occur in clusters. Isotope analysis of the ratio of ¹³C/¹²C isotopes from plant fragments recovered from fossilized teeth suggests that, by the end of the Miocene, these early browsers had been replaced by species that shifted increasingly to a grazing lifestyle, allowing them to gain most of their energy from more uniformly distributed graminoid plants (9–11). This conversion to grazing was accompanied by increase in body size, as predicted by the optimal life-history model. In other words, Bhat et al.’s scale-dependent energetic model explains Cope’s rule regarding the gradual replacement of small species by larger versions over evolutionary time as well as the simultaneous transition to grazing.

Linking a body of metabolic theory championed by J. H. Brown et al. with fractal-based conjectures about the degree of patchiness in food supply experienced by animals of different size, Bhat et al. use energetic cost−benefit analysis to construct a minimalist model of mammalian life-history constraints.

The strength of any minimalist model is that it readily focuses our attention on key processes. Bhat et al.’s (3) scale-dependent energetic life-history model offers an appealingly simple way to think about life-history strategies. Its obvious strength is that it does not require any major assumptions about the structure of age- or size-dependent demography. On the other hand, there is abundant evidence that structure can play a major role in animal population dynamics, defining the outcome of ecological interactions and sensitivity to changing environmental conditions (12, 13). Similarly, the optimal life-history model requires only a single coefficient to completely characterize the complex spatial structure of resources. Resource heterogeneity is thought to have a profound impact on herbivore population dynamics (14), but, even in savannah ecosystems, spatial variation in food resources is shaped by a complex mix of factors: geomorphology, seasonality, local variation in rainfall, both aboveground and belowground plant abundance, and previous exposure to grazing. These factors will surely strain the predictive power of a single scaling coefficient.

Other simplifying assumptions of Bhat et al.’s (3) model will no doubt attract immediate attention. Perhaps the most glaring is that the model treats organisms as if they were, in principle, immortal—individuals only die by chance. This assumption clearly makes the models more tractable mathematically, but obviously flies in the face of empirical reality. Of particular concern is that foraging herbivores inevitably incur some risk of predation, and that risk often influences patterns of habitat use, resource acquisition, and herbivore demography (15). How such complications alter demographic and life-history predictions of Bhat et al.’s central model will no doubt be of fundamental interest. The exciting potential demonstrated in the initial outline clearly calls for a more comprehensive analysis of the Bhat et al. model to further clarify how its predictions differ from those arising from alternative life-history hypotheses in the evolutionary ecology literature. More important still will be thorough evaluation of its explanatory power relative to that of alternative models.

The core stochastic foraging process that dictates demographic rates in Bhat et al.’s (3) model could also be usefully employed to model implicit movement by multiple species across clustered resource landscapes. It would be fascinating, for example, to apply such logic to explore the dynamics of paleocommunities. One can readily imagine a guild of prehistoric herbivores of different sizes living in a structured Early Pleistocene landscape populated with appropriate carnivores driven by the same mass-specific energetic rules of engagement. Adding early ancestral humans to this size-structured scenario would provide a useful vantage for evaluating the relative contribution of landscape change vs. hominid hunting to mass mammalian extinction over the past 14,000 y [the so-called Pleistocene overkill hypothesis (16)]. Energetically scaled models of contemporary communities could similarly cast fascinating light on the perplexing power relationship observed in the ratio of predator biomass to prey biomass in modern ecosystems across the globe (17). Perhaps Bhat et al.’s model of optimal life history will provide a useful key to unlock other ecological mysteries.