Interaction of hemlock woolly adelgid populations with host tree health drives population oscillations

Adelges tsugae Annand, the hemlock woolly adelgid, is an invasive insect pest of Tsuga canadensis (L.) Carriere, 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. Cycles in T. canadensis health and A. tsugae densities seem to be an important feature in A. tsugae population dynamics in the eastern United States. To investigate mechanisms leading to such cycles, we construct a model composed of systems of ordinary differential equations with time-dependent parameters to represent seasonality. The 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 include 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, which produce 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 the scenarios that will likely lead to T. canadensis mortality and explore longer term dynamics of the system. In general, low and high T. canadensis health initial condition values result in likely T. canadensis mortality while T. canadensis with medium health initial condition values are predicted to survive.