Doctoral Dissertations
Date of Award
5-2021
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Mathematics
Major Professor
Suzanne M. Lenhart
Committee Members
Louis J. Gross, Judy D. Day, Christopher Strickland
Abstract
We present two models of the Adelges tsugae, the hemlock woolly adelgid, an invasive insect pest of Tsuga canadensis, eastern hemlock, in the eastern United States. An A. tsugae infestation often results in the death of T. canadensis within years, and has caused significant changes to hemlock forests. We construct two models composed of systems of ordinary differential equations with time dependent parameters to represent seasonality. The first model captures the coupled cycles in T. canadensis health and A. tsugae density. We use field data from Virginia to develop the model and to perform parameter estimation. The mechanisms we represent in the model, including an A. tsugae density dependent T. canadensis growth rate, a T. canadensis health dependent A. tsugae mortality rate and a density dependent A. tsugae mortality rate, produce the cycles in T. canadensis health and A. tsugae density commonly seen with the A. tsugae system in the eastern United States. We test sets of initial conditions to determine scenarios that will likely lead to T. canadensis mortality.
The second model represents the population dynamics of A. tsugae and two introduced biological control organisms, Laricobius nigrinus and Sasajiscymnus tsugae, released to attempt to control A. tsugae populations and allow T. canadensis survival. We use field data from the Great Smoky Mountains National Park to develop the model and to perform parameter estimation. The model is stage structured, with two classes per species. To represent the seasonality of the system, in addition to time dependent parameters, the model is composed of multiple systems of ordinary differential equations that control the system at different times of the year.
Recommended Citation
Thompson, Hannah M., "Data Driven Models of Hemlock Woolly Adelgid Impacts and Biological Control. " PhD diss., University of Tennessee, 2021.
https://trace.tennessee.edu/utk_graddiss/6736