An Eigenvalue Test for spatial Principal Component Analysis

The spatial Principal Component Analysis (sPCA, Jombart 2008) is designed to investigate non-random spatial distributions of genetic variation. Unfortunately, the associated tests used for assessing the existence of spatial patterns (global and local test; Jombart et al. 2008) lack statistical power and may fail to reveal existing spatial patterns. Here, we present a non-parametric test for the significance of specific patterns recovered by sPCA. We compared the performance of this new test to the original global and local tests using datasets simulated under classical population genetic models. Results show that our test outperforms the original global and local tests, exhibiting improved statistical power while retaining similar, and reliable type I errors. Moreover, by allowing to test various sets of axes, it can be used to guide the selection of retained sPCA components. As such, it represents a valuable complement to the original analysis, and should prove useful for the investigation of spatial genetic patterns.