AModel-Driven Approach to Experimental Validation of Predator-Prey Dynamics in a System of Terrestrial Arthropod

The application of mathematical models to ecological communities in order to describe behavior under varying conditions is fundamental to the field of predictive ecology. Although the data-driven validation of population models is well-practiced, it is an unfortunate reality that many ecological study systems are uncontrolled as well as spatially and temporally expansive. Observing these systems is costly and time intensive, and the information obtained can be messy or driven by unexpected factors.We are therefore interested in the effective validation of mathematical models in population ecology.;In this dissertation,we specifically study predator-prey interactions between arthropods (aphids, beetles, and spiders) in an agricultural field. Our interest stems from the potential for the biological control of aphids, an agricultural pest, by natural predators. Although this focus is fairly specific, we still expect to encounter diverse populations of predators in natural communities.We therefore rely on a generalizable model, in which interactions are parameterized by measurable species traits. To evaluate the viability of this model in describing natural communities, we conduct least-squares parameter estimation and fit the model to empirical data.;We begin by introducing the methodology for parameter estimation and motivating our choice of mathematical model.We then detail initial attempts at fitting our model to aphid abundance data in barley fields. The data used in this first attempt at model validation was opportunistically obtained and primarily intended as a study of community complexity instead of temporal dynamics. We demonstrate that insufficient sampling in time, along with mortality driven by unknown factors, prevents the estimation of model parameters with any degree of certainty.;Motivated by the shortcomings of this first attempt, we move on to the design of greenhouse experiments for model validation.We explicitly link the protocol for our experiment to the anticipated mathematical and statistical properties of our parameter estimation problem.We consider the time-dependent sensitivity of the model to parameters in determining the temporal mesh for data collection and the population-level observation error in determining feasible sampling strategies.We attempt to validate our model against the resulting experimental data, with marked improvement over our earlier work.;Returning to our initial question, we again consider the problem of validating our model in an agricultural field. Although we do not have sufficient data to estimate model parameters in the field, we motivate a simple partial differential equation model for predator-prey interactions. We investigate the effect of temporal and spatial sampling protocols on the estimation of model parameters over a single growing season.