Analysing the spatial patterns of livestock anthrax in Kazakhstan in relation to environmental factors: a comparison of local (Gi*) and morphology cluster statistics

We compared a local clustering and a cluster morphology statistic using anthrax outbreaks in large (cattle) and small (sheep and goats) domestic ruminants across Kazakhstan. The Getis-Ord (Gi*) statistic and a multidirectional optimal ecotope algorithm (AMOEBA) were compared using 1st, 2nd and 3rd order Rook contiguity matrices. Multivariate statistical tests were used to evaluate the environmental signatures between clusters and non-clusters from the AMOEBA and Gi* tests. A logistic regression was used to define a risk surface for anthrax outbreaks and to compare agreement between clustering methodologies. Tests revealed differences in the spatial distribution of clusters as well as the total number of clusters in large ruminants for AMOEBA (n = 149) and for small ruminants (n = 9). In contrast, Gi* revealed fewer large ruminant clusters (n = 122) and more small ruminant clusters (n = 61). Significant environmental differences were found between groups using the Kruskall-Wallis and Mann- Whitney U tests. Logistic regression was used to model the presence/absence of anthrax outbreaks and define a risk surface for large ruminants to compare with cluster analyses. The model predicted 32.2% of the landscape as high risk. Approximately 75% of AMOEBA clusters corresponded to predicted high risk, compared with ~64% of Gi* clusters. In general, AMOEBA predicted more irregularly shaped clusters of outbreaks in both livestock groups, while Gi* tended to predict larger, circular clusters. Here we provide an evaluation of both tests and a discussion of the use of each to detect environmental conditions associated with anthrax outbreak clusters in domestic livestock. These findings illustrate important differences in spatial statistical methods for defining local clusters and highlight the importance of selecting appropriate levels of data aggregation.