On The Size of Spherical Cows: How Body-Mass Influences the Existence and Coexistence of Mammalian Herbivores.

The fundamental constraints governing the flow of energy through consumer-resource systems ultimately determines the structure and dynamics of food webs. As this is true generally, it is also true for plant-herbivore systems, where herbivores must compete with each other to obtain sufficient caloric return. Because diverse herbivore communities are com- posed of species spanning a large range in body sizes, the different life histories imposed by these body sizes, the different effects of mortalities upon them, and the different effects these species have on their resources interact in complex ways, perhaps playing a role in determining the conditions for coexistence. This dissertation describes a complex of ways in which herbivore body size governs the existence and coexistence of populations over three scales of inquiry: pair-wise consumer resource dynamics, adaptive food-webs, and food-webs in environmental and historical contexts. Firstly, we construct a minimal consumer-resource dynamic system where the vital rates determining life history attributes are established on process-based energetic trade-offs. For this system, we derive the timescales associated with four alternative sources of mortality for terrestrial mammals: starvation from resource limitation, mortality associated with aging, consumption by specialist to generalist predators, and mortality introduced by subsidized harvest. The incorporation of these allometric relationships into the consumer-resource system illuminates central constraints that may contribute to the structure of mammalian communities. Our framework reveals that while starvation largely impacts smaller-bodied species, external predation and subsidized harvest primarily influence larger-bodied species. Finally, we predict the harvest pressure required to induce mass-specific extinctions as well as the predator-prey mass ratios at which dynamic instabilities form that may limit the feasibility of megaherbivore populations Secondly, we expand the minimal consumer-resource model of Chapter 1 into an n- dimensional plant-herbivore food web model, and where foraging behaviors are adaptive. ix In addition, we explore three alternative relationships between body-mass and diet-breadth: that of increasing breadth with mass, decreasing breadth with mass, and a non-linear relationship with high diet breadth for large and small herbivores. Our results demonstrate that our approach accurately captures macroecological patterns such as Damuth’s Law. We ob- serve that the negative mass-breadth relationship maximizes herbivore survival, while the competitive dynamics of plant-herbivore systems heavily favours larger consumers, with smaller consumers adaptively avoiding competitive overlap to enable persistence. Finally, communities with high levels of dietary overlap, where small consumers cannot escape predation, display consistently reduced richness. Thirdly, we investigate mammalian herbivore body-mass distributions through the allometric, adaptive, plant-herbivore food-webs of Chapter 2 over two broad environmental axes: closed vs open environments and humid vs arid environments. The incorporation of diverse historical mass-distributions with environmental scenarios provides insight into the relationship between distribution structure and community stability. Our framework demonstrates that broad separation in body-mass increases community stability. It shows that large gaps in body-size can reverse the normally positive mass-fitness relationship. It shows that the distinction between humid and arid environments does not alter the patterns of herbivore competition that govern community stability. Finally, the distinction between closed and open environments can substantially alter competitive outcomes as closed environments can provide more opportunities for niche partitioning by smaller herbivores