Objective functions for comparing simulations with insect trap catch data

Abstract

Targeted surveillance of high risk invasion sites using insect traps is becoming an important tool in border biosecurity, aiding in early detection and subsequent monitoring of eradication attempts. The mark-release-recapture technique is widely used to study the dispersal of insects, and to generate unbiased estimates of population density. It may also be used in the biosecurity context to quantify the efficacy of surveillance and eradication monitoring systems. Marked painted apple moths were released at three different locations in Auckland, New Zealand over six weeks during a recent eradication campaign. The results of the mark-release-recapture experiment were used to parameterise a process-based mechanistic dispersal model in order to understand the moth dispersal pattern in relation to wind patterns, and to provide biosecurity agencies with an ability to predict moth dispersal patterns. A genetic algorithm was used to fit some model parameters. Different objective functions were tested: 1) Cohen’s Kappa test, 2) the sum of squared difference on trap catches, 3) the sum of squared difference weighted by distance from the release site, 4) the sum of squared difference weighted on distance between best-fit paired data. The genetic algorithm proved to be a powerful fitting method, but the model results were highly dependant on the objective function used. Objective functions for fitting spatial data need to characterise spatial patterns as well as density (ie. recapture rate). For fitting stochastic models to datasets derived from stochastic spatial processes, objective functions need to accommodate the fact that a perfect fit is practically impossible, even if the models are the same. Applied on mark-release-recapture data, the Cohen’s Kappa test and the sum of squared difference on trap catches captured respectively the distance component of the spatial pattern and the density component adequately but failed to capture both requirements whereas the sum of squared difference weighted by distance from the release site did. However, in order to integrate the stochastic error generated by the model underlying stochastic process, only the sum of squared difference weighted on distance between best-fit paired data was adequate. The relevance of each of the fitting methods is detailed, and their respective strengths and weaknesses are discussed in relation to their ability to capture the spatial patterns of insect recaptures.