Comparison of geometric morphometric outline methods in the discrimination of age-related differences in feather shape

BACKGROUND: Geometric morphometric methods of capturing information about curves or outlines of organismal structures may be used in conjunction with canonical variates analysis (CVA) to assign specimens to groups or populations based on their shapes. This methodological paper examines approaches to optimizing the classification of specimens based on their outlines. This study examines the performance of four approaches to the mathematical representation of outlines and two different approaches to curve measurement as applied to a collection of feather outlines. A new approach to the dimension reduction necessary to carry out a CVA on this type of outline data with modest sample sizes is also presented, and its performance is compared to two other approaches to dimension reduction. RESULTS: Two semi-landmark-based methods, bending energy alignment and perpendicular projection, are shown to produce roughly equal rates of classification, as do elliptical Fourier methods and the extended eigenshape method of outline measurement. Rates of classification were not highly dependent on the number of points used to represent a curve or the manner in which those points were acquired. The new approach to dimensionality reduction, which utilizes a variable number of principal component (PC) axes, produced higher cross-validation assignment rates than either the standard approach of using a fixed number of PC axes or a partial least squares method. CONCLUSION: Classification of specimens based on feather shape was not highly dependent of the details of the method used to capture shape information. The choice of dimensionality reduction approach was more of a factor, and the cross validation rate of assignment may be optimized using the variable number of PC axes method presented herein

Differences between sliding semi-landmark methods in geometric morphometrics, with an application to human craniofacial and dental variation

Over the last decade, geometric morphometric methods have been applied increasingly to the study of human form. When too few landmarks are available, outlines can be digitized as series of discrete points. The individual points must be slid along a tangential direction so as to remove tangential variation, because contours should be homologous from subject to subject whereas their individual points need not. This variation can be removed by minimizing either bending energy (BE) or Procrustes distance (D) with respect to a mean reference form. Because these two criteria make different assumptions, it becomes necessary to study how these differences modify the results obtained. We performed bootstrapped-based Goodall's F-test, Foote's measurement, principal component (PC) and discriminant function analyses on human molars and craniometric data to compare the results obtained by the two criteria. Results show that: (1) F-scores and P-values were similar for both criteria; (2) results of Foote's measurement show that both criteria yield different estimates of within- and between-sample variation; (3) there is low correlation between the first PC axes obtained by D and BE; (4) the percentage of correct classification is similar for BE and D, but the ordination of groups along discriminant scores differs between them. The differences between criteria can alter the results when morphological variation in the sample is small, as in the analysis of modern human populations