Kevin Gross

PhD 2003

Advisor: Tony Ives / Rick Nordheim

Ph.D. Thesis: The aphid, the wasp, adn the matrix: aspects of modeling host-parasitoid and single-species dynamics

In southern Wisconsin, pea aphids (Acyrthosiphon pisum) in alfalfa provide a model system for studying biological control. Aphid populations appear to be regulated by a suite of natural enemies, including the specialist parasitoid wasp Aphidius ervi and several species of generalist predators (e.g., coccinellids, nabids). This dissertation contains four projects motivated by the population regulation of pea aphids.
Chapter 1 proposes a method for estimating time-varying vital rates from observational time-series data. The model is used to analyze monitoring data from the pea aphid system, with the goal of understanding how parasitism impacts aphid dynamics. We find that although parasitism reduces aphid population growth rates substantially, this reduction is not density dependent, suggesting that the decreases in aphid densities observed in some cutting cycles are not the beginning of host-parasitoid cycles. In a larger context, this method provides a way to estimate the fluctuations in vital rates that produced observed dynamics, without requiring strong assumptions about dynamic feedback.
Chapters 2 and 3 study aspects of demographic matrix models, common tools for analyzing single-species dynamics. Chapter 2 uses Bayesian techniques to estimate the parameters in a demographic matrix model from time series of stage-specific abundances. We use the method to analyze pea aphid data collected by previous researchers, before Aphidius ervi had established widely. Chapter 3 derives an approximation for the sampling variance in population growth rates estimated from a matrix model, as a function of the number of individuals monitored in each stage. This approximation can be used to design more efficient data collection protocols.
Chapter 4 re-examines the practice of using the heterogeneity in parasitism among host patches to infer stabilizing aggregation of risk among hosts. The project shows that multiple parasitoid foraging behaviors can produce aggregated patterns of observed parasitism, but not all of these behaviors generate the aggregation of risk that stabilizes host-parasitoid dynamics.