An Eigenvalue test for spatial principal component analysis

V Montano,T Jombart

doi:10.1186/s12859-017-1988-y

Abstract

BackgroundThe spatial Principal Component Analysis (sPCA, Jombart (Heredity 101:92-103, 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; (Heredity 101:92-103, 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.ResultsWe 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.ConclusionsAs such, our test represents a valuable complement to the original analysis, and should prove useful for the investigation of spatial genetic patterns.

Highlights

The spatial Principal Component Analysis (sPCA, Jombart (Heredity 101:92-103, 2008) is designed to investigate non-random spatial distributions of genetic variation
Our simulated local spatial patterns turned out more difficult to detect than global patterns, the spca_randtest is twice to five times more effective than the local test (Table 1 and 2)
Both spca_randtest and global and local tests have a lower sensitivity in presence of island migratory schemes, while results for stepping stone and isolation by distance models are more satisfying (Table 1 and 2)

Summary

Introduction

The spatial Principal Component Analysis (sPCA, Jombart (Heredity 101:92-103, 2008) is designed to investigate non-random spatial distributions of genetic variation. The global and local tests have been developed for detecting the presence of global and local patterns, respectively [5] While these tests have robust type I error, they typically lack power, and can fail to identify existing spatial genetic patterns [5]. They can only be used to diagnose the presence or absence of spatial patterns, and are unable to test the significance of specific structures revealed by sPCA axes

Methods

Results

Discussion

Conclusion