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GEOMETRIC ESTIMATES OF HERITABILITY IN BIOLOGICAL SHAPE
Author(s) -
MONTEIRO LEANDRO R.,
DINIZFILHO JOSÉ ALEXANDRE F.,
REIS SÉRGIO F.,
ARAÚJO EDILSON D.
Publication year - 2002
Publication title -
evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.84
H-Index - 199
eISSN - 1558-5646
pISSN - 0014-3820
DOI - 10.1111/j.0014-3820.2002.tb01367.x
Subject(s) - shape analysis (program analysis) , heritability , morphometrics , geometric shape , procrustes analysis , quantitative genetics , biology , wing , landmark , covariance , mathematics , covariance matrix , tangent , multivariate statistics , statistics , evolutionary biology , geometry , genetic variation , artificial intelligence , computer science , ecology , genetics , static analysis , aerospace engineering , gene , engineering
The recently developed geometric morphometrics methods represent an important contribution of statistics and geometry to the study of biological shapes. We propose simple protocols using shape distances that incorporate geometric techniques into linear quantitative genetic models that should provide insights into the contribution of genetics to shape variation in organisms. The geometric approaches use Procrustes distances in a curved shape space and distances in tangent spaces within and among families to estimate shape heritability. We illustrate the protocols with an example of wing shape variation in the honeybee, Apis mellifera . The heritability of overall shape variation was small, but some localized components depicting shape changes on distal wing regions showed medium to large heritabilities. The genetic variance‐covariance matrix of the geometric shape variables was significantly correlated with the phenotypic shape variance‐covariance matrix. A comparison of the results of geometric methods with the traditional multivariate analysis of interlandmark distances indicated that even with a larger dimensionality, the interlandmark distances were not as rich in shape information as the landmark coordinates. Quantitative genetics studies of shape should greatly benefit from the application of geometric methods.