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Evolution of morphological structures results from the response to various selection pressures, constraints, gene flow, and random drift, but their relative importance is the subject of continuing debate (Maynard Smith et

Quantitative craniometrical traits have been successfully incorporated into population genetic methods to provide insight into human population structure. However, little is known about the degree of genetic and non-genetic influences on the phenotypic expression of functionally based traits. Many studies have assessed the heritability of craniofacial traits, but complex patterns of correlation among traits have been disregarded. This is a pitfall as the human skull is strongly integrated. Here we reconsider the evolutionary potential of craniometric traits by assessing their heritability values as well as their patterns of genetic and phenotypic correlation using a large pedigree-structured skull series from Hallstatt (Austria). The sample includes 355 complete adult skulls that have been analysed using 3D geometric morphometric techniques. Heritability estimates for 58 cranial linear distances were computed using maximum likelihood methods. These distances were assigned to the main functional and developmental regions of the skull. Results showed that the human skull has substantial amounts of genetic variation, and a t -test showed that there are no statistically significant differences among the heritabilities of facial, neurocranial and basal dimensions. However, skull evolvability is limited by complex patterns of genetic correlation. Phenotypic and genetic patterns of correlation are consistent but do not support traditional hypotheses of integration of the human shape, showing that the classification between brachy-and dolicephalic skulls is not grounded on the genetic level. Here we support previous findings in the mouse cranium and provide empirical evidence that covariation between the maximum widths of the main developmental regions of the skull is the dominant factor of integration in the human skull.

The Mean Measure of Divergence (MMD) is a formula that converts a battery of trait frequencies into a numerical value such that the more dissimilar two samples are, the greater the value. This measure of phenetic distance was developed by the statistician Cedric A. B. Smith and has become popular among dental anthropologists and osteologists for estimating the dissimilarity among groups in order to help reconstruct populations’ movements and structure over time and space. The purpose of the present study is to present the correct formulae and procedures for the MMD given that (1) numerous errors have entered into the literature concerning the formulae themselves, (2) improvements have been described that should be incorporated, and (3) various misunderstandings and misinterpretations have developed that need clarification.