Confronting Intuition in Disease Ecology and Evolution with Models
Keywords: Disease ecology
Disease evolution
Mathematical biology
Theoretical biology
Theoretical biology

Mathematical models have been used to address a wide range of central questions and ideas in ecology and evolutionary biology. For example, models are crucial for understanding the ecological processes that govern interactions between species (e.g., predator-prey dynamics) and the contributions of different evolutionary forces (e.g., the interaction between genetic drift and selection). Such models are useful for a number of reasons, including efficiently and expansively exploring– and questioning– ecological and evolutionary hypotheses and assumptions. My research applies this utility to three different questions, each from a different level of biological organization. First, I challenge the inference that rodent malaria parasite Plasmodium berghei experiences delayed development when in a host experiencing an active infection. Through the development of a series of delay differential equations, I simulate within-host infection dynamics and transform this data to reflect several documented measurement biases to which experimental data are subject. Subsequent fitting and parameter estimation of these transformed data reveal a potential to incorrectly infer delayed parasite developmental cycle length, as well as biased estimates of other important biological processes, including parasite clearance and replication. Moving from within-host ecology to selection within a population, I use both a structured coalescent model and forward-time population simulations to document the unique signatures following “negative frequency-dependent, positive” (NFDP) selection compared to constant, positive selection. This form of selection is to be expected for many disease resistance alleles: as the frequency of such an allele increases in a host population, the prevalence of disease– and thus the force of infection and thus selection– will decrease. I demonstrate that while these two forms of selection do produce different signatures, such signatures are insufficient when attempting to classify empirical data as originating from constant versus NFDP selection. Further, failure to correctly classify selection form can bias estimates of selection strength, with the assumption of constant selection producing stronger selection estimates. Finally, I move to consider coevolution between hosts and parasites and its consequences for the maintenance of host genetic diversity over time. In particular, I seek to reconcile disagreement in the literature by parsing the effects of population structure and time structure for the maintenance of host genetic diversity under host- parasite coevolution in finite populations. Through analytical and stochastic treatment of six models of host-parasite coevolution, I demonstrate that while host-parasite coevolution in finite populations may deplete diversity relative to the neutral expectation via directional selection, it may also contribute to its maintenance when 1) coevolution pushes the system away from its boundary equilibria and 2) there is sufficient perturbation from the boundary equilibria through introduction of genetic diversity via migration. All three projects employ mathematical models– and computational methods– and demonstrate their usefulness for challenging both recent and long-standing biological hypotheses.