Localised vs. Centralised Management Of Spatially Distributed Populations

Abstract

We consider management strategies for spatially distributed natural populations. The thesis considers two types of dynamical systems modelling approaches: rstly, population projection matrix models for spatially distributed meta-populations, and secondly, integral projection models. The rst approach combines localised observation and adaptive control strategies with information sharing to manage the dynamics of meta-populations e ectively. We consider meta-populations of N 2 N locally distinct equivalent stage-structured populations that are coupled via dispersal of one or more stages. Dispersal is modelled through a directed graph on the set of N nodes. This directional dispersal allows for wind-born dispersal, e.g. of seed stages, or nearest neighbour dispersal of stages able to disperse between di erent locations. Information sharing is captured by a second directed graph on the set of N nodes. This directional information sharing allows modelling of communication between the nodes, e.g., farmers sharing pesticide application strategies via a preferential attachment network. The novelty lies in the use of information sharing between managers of neighbouring populations, which acts to anticipate potential outbreaks. We explore situations when information sharing is and is not matched with dispersal. Information sharing improves the outcomes in that the size and extent of a pest outbreak and the amount of pesticide sprayed is reduced. Second, integral projection models (IPMs) can be used as models for spatio-temporal processes. Here we borrow ideas from Kot et al. [1], who use IPMs to model spatially distributed biological invasions. The speed of the biological invasion is a key property which may act as a proxy for the damage caused by the pest. The speed of invasion, or invasive wave speed, in the IPM depends on the form of the IPM kernel, for example, Gaussian or exponential distributions. These kernels depend on parameters which control the per-time-step spread of the pest. Parameters yielding narrower kernels lead to slower speed of spread. Now suppose we want to reduce the speed of spread (aka damage) to some below some pre-determined threshold. Assuming that increasing volume of pesticide narrows the kernel, we propose an adaptive algorithm which drives the speed to below the set threshold using an estimate of current speed. We apply our results to the control of invasion speed in D.pseudoobscura.