To refine our knowledge and to adequately test hypotheses concerning theoretical and applied aspects of invasion biology, successful and unsuccessful invaders should be compared. This study investigated insect establishment patterns by comparing the climatic preferences and biological attributes of two groups of polyphagous insect species that are constantly intercepted at New Zealand's border. One group of species is established in New Zealand (n = 15), the other group comprised species that are not established (n = 21). In the present study the two groups were considered to represent successful and unsuccessful invaders. To provide background for interpretation of results of the comparative analysis, global areas that are climatically analogous to sites in New Zealand were identified by an eco-climatic assessment model, CLIMEX, to determine possible sources of insect pest invasion. It was found that south east Australia is one of the regions that are climatically very similar to New Zealand. Furthermore, New Zealand shares 90% of its insect pest species with that region. South east Australia has close trade and tourism links with New Zealand and because of its proximity a new incursion in that analogous climate should alert biosecurity authorities in New Zealand. Other regions in western Europe and the east coast of the United States are also climatically similar and share a high proportion of pest species with New Zealand. Principal component analysis was used to investigate patterns in insect global distributions of the two groups of species in relation to climate. Climate variables were reduced to temperature and moisture based principal components defining four climate regions, that were identified in the present study as, warm/dry, warm/wet, cool/dry and cool/moist. Most of the insect species established in New Zealand had a wide distribution in all four climate regions defined by the principal components and their global distributions overlapped into the cool/moist, temperate climate where all the New Zealand sites belong. The insect species that have not established in New Zealand had narrow distributions within the warm/wet, tropical climates. Discriminant analysis was then used to identify which climate variables best discriminate between species presence/absence at a site in relation to climate. The discriminant analysis classified the presence and absence of most insect species significantly better than chance. Late spring and early summer temperatures correctly classified a high proportion of sites where many insect species were present. Soil moisture and winter rainfall were less effective discriminating the presence of the insect species studied here. Biological attributes were compared between the two groups of species. It was found that the species established in New Zealand had a significantly wider host plant range than species that have not established. The lower developmental threshold temperature was on average, 4°C lower for established species compared with non-established species. These data suggest that species that establish well in New Zealand have a wide host range and can tolerate lower temperatures compared with those that have not established. No firm conclusions could be drawn about the importance of propagule pressure, body size, fecundity or phylogeny for successful establishment because data availability constrained sample sizes and the data were highly variable. The predictive capacity of a new tool that has potential for eco-climatic assessment, the artificial neural network (ANN), was compared with other well used models. Using climate variables as predictors, artificial neural network predictions were compared with binary logistic regression and CLIMEX. Using bootstrapping, artificial neural networks predicted insect presence and absence significantly better than the binary logistic regression model. When model prediction success was assessed by the kappa statistic there were also significant differences in prediction performance between the two groups of study insects. For established species, the models were able to provide predictions that were in moderate agreement with the observed data. For non-established species, model predictions were on average only slightly better than chance. The predictions of CLIMEX and artificial neural networks when given novel data, were difficult to compare because both models have different theoretical bases and different climate databases. However, it is clear that both models have potential to give insights into invasive species distributions. Finally the results of the studies in this thesis were drawn together to provide a framework for a prototype pest risk assessment decision support system. Future research is needed to refine the analyses and models that are the components of this system.