Invasive Species Models

Modeling the spread and control of invasive species is an important part of the Grid Computing project at UTK.

Optimal control for management of an invasive plant species. Preprint.

ABSTRACT: Invasive plant populations typically consist of a large (main) focus and several smaller outlier populations. Management of the spread of invasives requires repeated control measures, constrained by limited funding and effort. Posing this as a control problem, we investigate whether it is best to apply control to the main focus, the outlier populations, or some combination of these. We first formulate and solve a discrete-time optimal control problem to determine where control is best applied over a finite time horizon. However, if limited funds are available for control, this optimal solution may not be feasible. In this case, we add an additional constraint to account for the fixed budget and solve the new optimality system. Our results have a variety of practical implications for invasive species management.

Modeling the effect of growing season length on the spread of multi-brooded invasive species. Preprint

Ecologists and natural resource managers are deeply concerned about the potential effects of large-scale climate change on the spread of invasive species. Global warming trends and an increased intensity of severe weather may accelerate rates of spread for established exotics while encouraging new invasions. Models that project the long-term impacts of climate variation are therefore critcally needed. We introduce a new modeling approach that exploits predictable latitudinal variation in the growing season to make projections about the speed and ultimate extent of species invasions. Our Variable Breeding Season (VBS) model is particularly applicable to species capable of reproducing multiple times in a given breeding season, such as multivoltine insects, many bird species, and plants that spread by vegetative reproduction. The VBS model uses integro-difference equations which respresent space as a continuous variable and time as discrete. The model faithfully reproduces several aspects of the invasion of the Eurasian collared dove (Streptopelia decaocto) in North America, including differential rates of spread along different compass directions and an asymptotic slowing of the wave front corresponding to growing seasons that are too brief to support population growth. Data from the North American Breeding Bird Survey agree with a projected upper latitudinal limit for the collared dove distribution around a latitude of 48.5 degrees. In addition to capturing important dynamical aspects of the spread of multi-brooded species, the VBS model provides an alternative to metabolic-cost-based explanations for species' northern range boundaries.