Mantel test
The Mantel test, named after Nathan Mantel, is a statistical test of the correlation between two matrices. The matrices must be of the same rank; in most applications, they are matrices of interrelations between the same vectors of objects. The test was first published by Nathan Mantel, a biostatistician at the National Institutes of Health, in 1967. Accounts of it can be found in advanced statistics books (e.g., Sokal & Rohlf 1995).
The test is commonly used in ecology, where the data are usually estimates of the "distance" between objects such as species of organisms. For example, one matrix might contain estimates of the genetic distances (i.e., the amount of difference between two different genomes) between all possible pairs of species in the study, obtained by the methods of molecular systematics; while the other might contain estimates of the geographical distance between the ranges of each species to every other species.
If there are n objects, and the matrix is symmetrical (so the distance from object a to object b is the same as the distance from b to a) such a matrix contains
distances. Because distances are not independent of each other – since changing the "position" of one object would change of these distances (the distance from that object to each of the others) – we can not assess the relationship between the two matrices by simply evaluating the correlation coefficient between the two sets of distances and testing its statistical significance. The Mantel test deals with this problem.
...
Wikipedia