Clines: character number and the multivariate analysis of simple patterns of geographic variation

The stability of a clinal pattern geographic variation in relation to character number was investigated by the random selection of real characters. The characters used were selected from a set of 18 significant characters, drawn from four different character systems, and had a low within-group correlation. Principal component/coordinate analysis was used to elucidate the main pattern of geographic variation and the first principal coordinate was plotted against a geographical transect to illustrate this pattern. The existence of ‘clinal’ or ‘monotically clinal’ variation was assessed by the rank correlation between geographic position and coordinate score and the congruence between patterns of geographic variation was assessed by the correlation between the first principal coordinates of the appropriate analyses. Two procedural models were used: A, the congruence between completely independent character sets based on 1–9 characters, and B, congruence between the ‘total’ analysis and those analyses based on 1–16 characters. The frequency of the types of pattern of geographic variation shown by these Model B analyses was also determined. Congruence is asymptotic in relation to character number and is described by various mathematical models, depending upon parameter and procedure. A broad pattern of clinal variation occurred in all analyses based on six or more characters and appears to be a stable feature of the racial affinities that is unlikely to be influenced by character choice. The details of the clinal pattern cannot be shown to be stable and may be influenced by the choice of character. This study had several findings in common with a previous study of categorical variation, e.g. the approximately hyperbolic relationship between character number and congruence in Model B, which may prove to be generally true in comparable situations.