The scaling of expansive energy under the Red Queen predicts Cope’s Rule

Abstract

The Red Queen’s hypothesis portrays evolution as a never-ending competition for expansive energy, where one species’ gain is another species’ loss. The Red Queen is neutral with respect to body size, implying that neither small nor large species have a universal competitive advantage. The maximum population growth in ecology; however, clearly depends on body size – the smaller the species, the shorter the generation length, and the faster it can expand. Here we ask whether, and if so how, the Red Queen’s hypothesis can accommodate a spectrum of body sizes. We theoretically analyse scaling of expansive energy with body mass and demonstrate that in the Red Queen’s zero-sum game for resources, neither small nor large species have a universal evolutionary advantage. We argue that smaller species have an evolutionary advantage only when resources in the environment are not fully occupied, such as after mass extinctions or following key innovations allowing expansion into freed up or previously unoccupied resource space. Under such circumstances, we claim, generation length is the main limiting factor for population growth. When competition for resources is weak, smaller species can indeed expand faster, but to sustain this growth they also need more resources. In the Red Queen’s realm, where resources are fully occupied and the only way for expansion is to outcompete other species, acquisition of expansive energy becomes the limiting factor and small species lose their physiological advantage. A gradual transition from unlimited resources to a zero-sum game offers a direct mechanistic explanation for observed body mass trends in the fossil record, known as Cope’s Rule. When the system is far from the limit of resources and competition is not maximally intense, small species take up ecological space faster. When the system approaches the limits of its carrying capacity and competition tightens, small species lose their evolutionary advantage and we observe a wider range of successful body masses, and, as a result, an increase in the average body mass within lineages.