Spatial analysis methods used for detecting, interpolating or predicting local patterns require a delineation of a neighbourhood defining the extent of spatial interaction in geographic data. The most common neighbourhood delineation techniques include fixed distance bands, k-nearest neighbours, or spatial adjacency (contiguity) matrices optimized to represent spatial dependency in data. However, these standard approaches do not take into consideration the geographic or environmental constraints such as impassable mountain ranges, road networks or coastline barriers. Specifically, complex marine landscapes and coastlines present common problematic neighbourhood definitions for standard neighbourhood matrices used in the spatial analysis of marine environments. Therefore, the goal of our research is to present a new approach to constraining spatial neighbourhoods when conducting geographical analysis in marine environments. To meet this goal, we developed methods and software (COnstraining SpatIal NEighbourhoods - COSINE) for modifying spatial neighbourhoods, and demonstrate their utility in two case studies. Our method enables delineation of neighbourhoods that are constrained by coastlines and the direction of marine currents. Our software calculates and evaluates whether neighbouring features are separated by land, or are within a user defined angle that excludes interaction based on directional processes. Using decision rules a modified spatial weight matrix is created, either in binary or row-standardized format. Within open source software (R), a graphical user interface enables users to modify the standard spatial neighbourhood definition distance, inverse distance and k-nearest neighbour. Two case studies are presented to demonstrate the usefulness of the new approach for detecting spatial patterns: the first case study observes marine mammals’ abundance and the second, oil spill observation. Our results indicate that constraining spatial neighbourhoods in marine environments is particularly important at larger spatial scales. The COSINE tool has many applications for modelling both environmental and human processes. / Graduate / 0463 / 0366 / suarezc@uvic.ca

In this study, we extend the spatial weight matrix defined by Getis and Aldstadt (2004) to a more general case. The modified spatial weight matrix performs better than the original spatial weight matrix since the modified spatial weight matrix adjusts weights of observations based on the distance from other observations. Both the simulation study and the application to the ecological process of invasion of non-native invasive plants (NNIPs) provide evidences for the better performance of the modified spatial weight matrix. We also develop procedures that can be used to quantify the invasion stages of NNIPs. The resultant map of invasion stage on county-level provides a useful and meaningful tool for policy makers; especially, it can be used to optimize allocation of management resources. The result of simultaneous autoregressive model shows that not only the biotic and abiotic factors but also human activities play an important role in the establishment and spread of multiflora rose in the Upper Midwest. It also shows the tendency of the establishment and spread of multiflora rose (Rosa Multiflora, Thunb. ex Murr.) in the Upper Midwest.