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Standard multivariate analysis methods aim to identify and summarize the mainstructures in large data sets containing the description of a number ofobservations by several variables. In many cases, spatial information is alsoavailable for each observation, so that a map can be associated to themultivariate data set. Two main objectives are relevant in the analysis ofspatial multivariate data: summarizing covariation structures and identifyingspatial patterns. In practice, achieving both goals simultaneously is astatistical challenge, and a range of methods have been developed that offertrade-offs between these two objectives. In an applied context, thismethodological question has been and remains a major issue in communityecology, where species assemblages (i.e., covariation between speciesabundances) are often driven by spatial processes (and thus exhibit spatialpatterns). In this paper we review a variety of methods developed in communityecology to investigate multivariate spatial patterns. We present different waysof incorporating spatial constraints in multivariate analysis and illustratethese different approaches using the famous data set on moral statistics inFrance published by Andr\'{e}-Michel Guerry in 1833. We discuss and compare theproperties of these different approaches both from a practical and theoreticalviewpoint.

Revisiting Guerry's data: Introducing spatial constraints in multivariate analysis