AbstractsMathematics

Estimating the size of an insect pest population in an agricultural field is an integral part of insect pest monitoring. An abundance estimate can be used to decide if action is needed to bring the population size under control, and accuracy is important in ensuring that the correct decision is made. Conventionally, statistical techniques are used to formulate an estimate from population density data obtained via sampling. This thesis thoroughly investigates an alternative approach of applying numerical integration techniques. We show that when the pest population is spread over the entire field, numerical integration methods provide more accurate results than the statistical counterpart. Meanwhile, when the spatial distribution is more aggregated, the error behaves as a random variable and the conventional error estimates do not hold. We thus present a new probabilistic approach to assessing integration accuracy for such functions, and formulate a mathematically rigorous estimate of the minimum number of sample units required for accurate abundance evaluation in terms of the species diffusion rate. We show that the integration error dominates the error introduced by noise in the density data and thus demonstrate the importance of formulating numerical integration techniques which provide accurate results for sparse spatial data.