zt: A Sofware Tool for Simple and Partial Mantel Tests

Different methods of data analysis (e.g. clustering and ordination) are based on distance matrices. In some cases, researchers may wish to compare several distance matrices with one another in order to test a hypothesis concerning a possible relationship between these matrices. However, this is not always self-evident. Usually, values in distance matrices are, in some way, correlated and therefore the usual assumption of independence between objects is violated in the classical tests approach. Furthermore, often, spurious correlations can be observed when comparing two distances matrices. A classic example is the comparison between genetic and environmental distances. Colonies that are in close proximity of each other tend to have similar environments and therefore there will be a positive correlation between environmental and geographical distances. Such colonies will also be more likely to exchange migrants so that genetic distances will be positively correlated with spatial distances. The consequence is that an observed positive association between genetic and environmental distances may be simply due to spatial effects. The most widely used method to account for distance correlations is a procedure known as the Mantel test (Mantel,'67; Mantel and Valand,'70 following the pioneering work of Daniels,'44 ; Daniels and Kendall'47). The simple Mantel test considers two matrices while an extension known as the partial Mantel test considers three matrices. These tools are widely used in different fields of research such as population genetics, ecology, anthropology, psychometrics and sociology.