Original Article

Heredity (2008) 101, 92–103; doi:10.1038/hdy.2008.34; published online 30 April 2008

Revealing cryptic spatial patterns in genetic variability by a new multivariate method

T Jombart1, S Devillard1, A-B Dufour1 and D Pontier1

1Laboratoire de Biométrie et Biologie Evolutive, UMR-CNRS 5558, Université de Lyon, Université Lyon 1, Villeurbanne Cedex, France

Correspondence: Dr T Jombart, Laboratoire de Biométrie et Biologie Evolutive, UMR-CNRS 5558, Université Lyon 1—CNRS, 43 bd du 11 novembre 1918, Villeurbanne Cedex 69622, France. E-mail: jombart@biomserv.univ-lyon1.fr

Received 12 February 2008; Revised 19 March 2008; Accepted 26 March 2008; Published online 30 April 2008.



Increasing attention is being devoted to taking landscape information into account in genetic studies. Among landscape variables, space is often considered as one of the most important. To reveal spatial patterns, a statistical method should be spatially explicit, that is, it should directly take spatial information into account as a component of the adjusted model or of the optimized criterion. In this paper we propose a new spatially explicit multivariate method, spatial principal component analysis (sPCA), to investigate the spatial pattern of genetic variability using allelic frequency data of individuals or populations. This analysis does not require data to meet Hardy–Weinberg expectations or linkage equilibrium to exist between loci. The sPCA yields scores summarizing both the genetic variability and the spatial structure among individuals (or populations). Global structures (patches, clines and intermediates) are disentangled from local ones (strong genetic differences between neighbors) and from random noise. Two statistical tests are proposed to detect the existence of both types of patterns. As an illustration, the results of principal component analysis (PCA) and sPCA are compared using simulated datasets and real georeferenced microsatellite data of Scandinavian brown bear individuals (Ursus arctos). sPCA performed better than PCA to reveal spatial genetic patterns. The proposed methodology is implemented in the adegenet package of the free software R.


landscape genetics, Moran's I, multivariate analysis, principal component analysis, spatial genetics