2017a Turechek and Madden 2003).Ĭorrelation or ‘geostatistics-based’ analyses provide information to complement distributional techniques at the sampling unit level or above and can indicate the degree or strength of aggregation for a nonrandom pattern ( Turechek and Madden 1999a, b). Implementation of these approaches provides a direct measure of heterogeneity of disease incidence at the sampling unit level ( Hughes and Madden 1992 Shah et al. This approach applies where binary data (e.g., disease incidence) indicate the frequency distribution of the proportion of diseased individuals within a sampling unit ( Hughes and Madden 1993 Madden and Hughes 1994, 1995, 1999 Turechek and Mahaffee 2004 Turechek et al. One approach attempts to convert an overall pattern into a statistic that is not scalar and based on fit of the data to a theoretical distribution ( Hughes and Madden 1992). The common goal unifying these techniques is to provide robust, statistical evidence that at a point in time the spatial pattern of disease depicts specific, scale-dependent spatial heterogeneity ( Ferrandino 1998 Turechek and McRoberts 2013).ĭepending upon the types of data collected (binary versus continuous) to quantify an epidemic, the statistical approaches generally fall into two broad categories that analyze the spatial pattern in relation to the scale of the sampling ( Turechek and McRoberts 2013). 2007 Pielou 1977 Ripley 1981 Schwanck and Del Ponte 2016). The types of data used to quantify epidemics usually dictate the techniques and approaches applied to spatial analysis ( Baddeley and Turner 2005 Madden et al. In plant pathology, a comprehensive understanding of how spatial patterns evolve forms the basis of effective disease management strategies that minimize crop loss ( Hughes 1987 Madden et al. Quantification of spatial attributes and patterns in plant pathology and scientific disciplines such as biology, ecology, and geography is essential for hypothesis testing.
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The Cluster app is available as a free download for Apple computers at iTunes, with a link to a user guide website.
Provided examples demonstrate the utility of Cluster to analyze patterns at various spatial scales in plant pathology and ecology and highlight the limitations, trade-offs, and considerations for the sensitivities of variables and the biological interpretations of results. Each simulated map may be saved as an image and inspected. Cluster summarizes normalized attributes of clusters, including pixel number, axis length, axis width, compass orientation, and the length/width ratio, available to the user as a downloadable spreadsheet. These frames can assume any shape, from natural (e.g., leaf) to arbitrary (e.g., a rectangular or polygonal field). This is the basis for statistical testing of the null hypothesis that the clusters are randomly distributed within the frame of interest. A two-tailed probability t test compares the mean inter-cluster distances for the observed versus the values derived from randomly simulated maps. Up to 1,000 stochastic simulations randomly place the centroids of each cluster in ranked order of size (largest to smallest) within each matrix while preserving their calculated angles of orientation for the long axes.
Users can deselect anomalous clusters manually and/or automatically by specifying a size threshold value to exclude smaller targets from the analysis. The app calculates the percent area occupied by targeted pixels, identifies the centroids of targeted clusters, and computes the relative compass angle of orientation for each cluster. The user isolates target entities (clusters) by designating up to 24 pixel colors as nontargets and moves a threshold slider to visualize the targets. We developed a new approach for spatial analysis of pixelated data in digital imagery and incorporated the method in a stand-alone desktop application called Cluster. Data collection for spatial analysis requires substantial investment in time to depict patterns in various frames and hierarchies. Spatial analysis of epiphytotics is essential to develop and test hypotheses about pathogen ecology, disease dynamics, and to optimize plant disease management strategies.
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