Canonical Trend Surface Analysis: A Method for Describing Geographic Patterns

Characteristics of organisms often vary widely across geographic space as a result of natural selection, migration and environmental heterogeneity. I present canonical trend surface analysis as an approach to the study of this variation. The method is based on the canonical correlations between sets of orthogonal axes in the space defined by the characteristics of the organism and in the space defined by the coordinates of the localities (and their squares and crossproducts). I apply this method to simulated data sets of trends and patches; the basic patterns are recovered. Next, I analyze two real data sets: the distribution of 21 HLA human blood types at 58 localities in Europe; and the distribution of 26 species of Foraminifera in 61 sediment core top samples from the Atlantic and Indian oceans. The derived patterns are similar to those developed by other investigators using different methods on these same data. However, canonical trend surface analysis is shown to be less sensitive to geographically unpatterned data than the methods used in these earlier studies of the same data. The canonical trend surface method extracts that part of the character variation that is most nearly coincident with the geographic information, and leaves unresolved the other covariances.