The Signed Mantel test to cope with autocorrelation in comparative analyses

In biology, medicine and anthropology, scientists try to reveal general patterns when comparing different sampling units such as biological taxa, diseases or cultures. A problem of such comparative data is that standard statistical procedures are often inappropriate due to possible autocorrelation within the data. Widespread causes of autocorrelation are a shared geography or phylogeny of the sampling units. To cope with possible autocorrelations within comparative data, we suggest a new kind of the Mantel test. The Signed Mantel test evaluates the relationship between two or more distance matrices and allows trait variables facultatively to be represented as signed distances (calculated as signed differences or quotients). Considering the sign of distances takes into account the direction of an effect found in the data. Since different metrics exist to calculate the distance between two sampling units from the raw data and because the test results often depend on the kind of metric used, we suggest validating analysis by comparing the structures of the raw and the distance data. We offer a computer program that is able to construct both signed and absolute distance matrices, to perform both customary and Signed Mantel tests, and to explore raw and distance data visually.