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Constraining spatial neighbourhoods delineated in marine environmentsCesar Suarez 1 , Trisalyn Nelson 1 & Rosaline Canessa 21 Spatial Pattern Analysis and Research Laboratory, Department of Geography, University of Victoria, Victoria, BC, V8W 3R4,Canadasuarezc@uvic.ca, trisalyn@uvic.ca2 Coastal and Ocean Resource Analysis Lab, Department of Geography, University of Victoria, Victoria, BC, V8W 3R4, Canadarosaline@uvic.caAbstractSpatial analysis in a marine environment can be challenging due the irregular shape of marine areas and coastlines,the dynamic nature of the ocean environment, and species’ location. One aspect of spatial analysis that is particularlycomplicated in marine environments is the definition and delineation of spatial neighbourhoods. Spatialneighbourhoods are geographic regions where spatial interaction is defined. All spatial analyses require spatialneighbourhoods be defined. The most common types of spatial neighbourhoods are k-neighbours, distance, adjacency,and spatial dependency. However, spatial neighbourhood delineation in marine environments should considermore complex factors such as land (barrier) and ocean currents, and accommodate irregularly shaped study areas. Inthis paper a review of the common definitions of spatial neighbourhood for marine environments and a new approachto constraining spatial neighbourhood when conducting analysis in a marine environment are presented.IntroductionSpatial analysis has been used to conduct exploratory and descriptive spatially explicit marine studies. Studieshave been developed to analyze the abundance (Mellin et al., 2010), distribution (Grech et al., 2011) and impacts ondifferent marine species on diverse ecosystems (West and van Woesik, 2001). As spatial data become more common,it is anticipated that the spatial analysis of marine phenomena will also increase.When conducting spatial analysis, the region of spatial interaction must be defined. Whether preforming an interpolation,quantifying spatial autocorrelation, or conducting spatially explicit regression methods, spatial neighbourhoodsare defined by the analysts. For instance, in order to determine patterns in spatial distribution of contaminantsin marine environments, researchers identified the neighbourhood, based on distance, at which contaminants wouldinteract with the environment (Magesh et al., 2011). The output of the spatial analysis will depend on how the spatialneighbourhood was selected (Nelson and Robertson, 2012).The dynamic nature of marine environments makes defining spatial neighbourhoods particularly challenging in amarine context. For example, defining a neighbourhood for spatial analysis of marine mammals can be complex asthose species can be found in both open water and between islands. However, coastlines with indentations and protrusionsand islands may impede spatial interaction among areas that are nearby based on Euclidean distance(straight line). Appropriate definition of spatial neighbourhoods would benefit from taking into account physicalbarriers in marine environments such as islands and keys.ObjectiveThe goal of this paper is to review opportunities and challenges of neighbourhood definition in marine spatialstudies. To meet this goal we first provide an overview of what a spatial neighbourhood is and common definitionsused in marine application. Secondly, we present a case study to show how spatial neighbourhoods can be constrainedwhen applying spatial approaches to marine environments. The approach for this paper is based on spatialneighbourhoods for point objects (e.g., shipping vessels, marine mammals or samples of nutrients or organisms),based on coastlines (polyline).Spatial neighbourhoods in marine applicationsThe most common spatial neighbourhood definition used in marine studies is the definition by distance, whichrepresents the region of space (defined by a buffer of a given distance) associated around an object under study217