Organised By

Mark Lewis


Modelling invasive species control as a linear programming
problem: Spartina alterniflora and other examples

Alan Hastings
University of California, Davis, USA

The control of invasive species is one of the most pressing problems environmental problems in the world today. Working from a particular invasion of Spartina alterniflora in the Northwestern United States, I present a model for determining optimal control strategies based on the observation that in the initial stages of an invasion, density dependent (nonlinear) effects are less important. Thus many control problems, such as limiting area, or limiting spatial extent, subject to constraints, that would appear to be dynamic programming problems, can be solved as linear programming problems. Specific examples are used to show: 1) the importance of taking early action, and 2) that the stages that should be the subject of control with finite resources change through time. Extensions, including the role of stochasticity, are also discussed. The research is supported by the National Science Foundation (NSF).

Home Range Patterns: mechanistic approaches to the analysis
of animal movement

Paul Moorcroft
Harvard University, USA

Coauthor(s): Mark A. Lewis

Since its introduction in the 1950s, radio telemetry has become a mainstream technique in wildlife studies, documenting a diverse array of patterns of space-use within many mammalian groups including ungulates, rodents, primates and carnivores. However, until recently, the models used to analyze telemetry data have had no mechanistic basis underlying their descriptions of space-use, and as a result, the analysis of animal home ranges has been an entirely descriptive endeavor. In this paper, we characterize coyote (Canis latrans) home range patterns, using partial differential equations for expected space use that are derived from an underlying mechanistic description of individual movement behavior. The results provide empirical support for a model formulation in which the movement of individuals is affected by both landscape characteristics and the scent-marks of neighboring groups. We then show how the model can be used to obtain predictions for individual movement and scent-marking behavior and to predict changes in home range patterns. More generally, our findings illustrate how mechanistic models permit the development of a predictive theory for the relationship between movement behavior and animal spatial distribution.

Exploring transient behaviours in host-pathogen interactions

K.A. Jane White
University of Bath, UK

Many biological and agricultural systems are subject to disturbance and often, even routinely, fail to achieve equilibrium levels within the natural time scales of the biological and agricultural processes. The behaviour of transients in population growth and the state of the system at interruption may be of immense economic importance, for example, in determining whether or not disease achieves a threshold density to persist and to cause significant losses in crop production.

I will present two deterministic models which have been developed to explore the transient behaviours of host-pathogen interactions. Analysis of the models explores the impact of initial and boundary conditions on the disease transmission process and allows us to distinguish temporal regions in which primary and secondary infection processes dominate. The results of the analysis are discussed in relation to some economically important agricultural diseases.