Detection of length-dependent effects of tandem repeat alleles by 3-D geometric decomposition of craniofacial variation.

Topologically conservative morphological transformations typify the succession of species in the fossil record and also typify more subtle morphological variation within species. Isolation and quantification of morphological variation along its various intermingled modes becomes increasingly difficult as the structures under consideration increase in complexity. Here, we describe a comparative morphometric and genomic study in dogs in which complex three-dimensional craniofacial variation is mathematically distilled into simpler geometric components to test the hypothesis that incremental mutations at developmental loci result in simple geometric deformations of morphology. Combinations of candidate transforms are computationally evaluated for their ability to accurately transform a reference three-dimensional skull model into those of distinct breeds. A set of five simple basis functions are found to be sufficient to describe most craniofacial variation among dogs. Allele lengths of amino acid repeat length variants in developmental regulator genes, which frequently have quantitative effects on phenotype, were compared to geometric terms using Pearson correlation and regression. The coordinated quantitative representation of both phenotype and genotype improves the statistical power for the detection of causative genotype-phenotype relationships and enabled the characterization of the influence of Runx-2 coding repeat length on craniofacial variation among domestic dogs.