UCLA

Consumer-resource interactions constitute the fundamental building block of foodwebs, and play an essential role in ecosystem services and biological pest control. The defining feature of consumer-resource interactions is their inherent tendency to oscillate in abundance. This oscillatory tendency can be both weakened and strengthened by abiotic environmental fluctuations such as seasonal temperature variation. My dissertation focuses on the role of abiotic and biotic oscillations mediate the persistence and diversity of consumer-resource communities.

I start by investigating how seasonal temperature variation influences the persistence of tritrophic food chains consisting of multicellular ectotherms (invertebrates, fish, amphibians and reptiles). Since ectotherm body temperature depends on the environmental temperature, temperature variation has a direct effect on the physiology, behavior and population dynamics of ectothermic species. I develop a trait-based mathematical framework to investigate tri-trophic interactions amongst ectotherm species inhabiting a seasonally varying thermal environment. By incorporating mechanistic trait response functions --- derived from the first principles of thermodynamics --- into a dynamical model constructed using ordinary differential equations, I find that the persistence of tri-trophic interactions requires that each trophic level be more cold-adapted than the level below it. The model predicts that tri-trophic food chain length should increase with increasing latitude, because higher latitudes experience higher-amplitude seasonal fluctuations and more opportunities for upper trophic levels to be more cold-adapted.

Next I expand the framework described above to develop predictions of how developmentally induced time delays affect niche partitioning in seasonal environment, using delay differential equations (DDEs) to capture the effects of temperature dependent maturation rates. I find that developmental delays reduce opportunities for thermal niche partitioning by reducing the temporal separation between species, since juveniles keep maturing after the environment has become unfavorable for the focal species and favorable for its competitor. The addition of developmental delays also leads to the emergence of uninvasible attack optimum or response breadth values which maximize the overlap between the consumer species' lifetime reproductive success and the resource's fundamental thermal niche. While these uninvasible strategies preclude niche partitioning, such partitioning becomes possible when species vary in their attack optima or response breadth \textit{and} temperature sensitivity of juvenile or adult mortality.

Finally, I study how stage structure and delayed negative feedback affect coexistence through relative nonlinearity. I use a DDE based model with in a constant thermal environment, using trait species values based on data from the harlequin bug and one of its parasitoids. I find that the presence of stage structure hinders coexistence through relative nonlinearity, since it reduces the differences in resource oscillations generated by consumers with different functional responses. This result is not generated by delayed application of negative feedback, and I posit that it is instead the delayed application of the positive feedback.

The work I present here addresses the interplay between a community's abiotic and biotic environments, with the latter encompassing both species life history and community structure. The frameworks developed here are based on first principles, which allows me to make general predictions on community structure, and can be parameterized with species specific data that can predict the outcomes of specific interactions. The data I use on our models include systems with important applications for pest control, so the results here can be applied to specific systems of high economic importance. Taken together, this dissertation represents a step towards a framework that advances our theoretical understanding of natural communities and their environments and has important practical applications.