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

Abstract

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.

New insights into pig taxonomy, domestication and human dispersal in Island South East Asia: molar shape analysis of Sus remains from Niah Caves, Sarawak

“…82 coefficients for the first 20 harmonics), we have performed data reduction through principal component analysis (PCA) which preserves both the statistical balance between number of variables versus the number of individuals, and the accuracy of outline parameterisation (Monti et al, 2001;Sheets et al, 2006). The numbers of retained principal components was determined according to a threshold of 95% of the variance explanation, in order to minimise cross-validated misclassification percentages.…”

Geometric morphometric approach to sex estimation of human pelvis

“…This provides an unbiased estimate of the percentage of individuals that were wrongly classified. Because discriminant analysis requires more individuals than variables per group, the use of outline methods poses difficulties due to the large number of semilandmarks needed per individual to describe outlines and due to the representation of semilandmark points by two coordinates (x-and y-) when there is only one degree of freedom per point [37]. Therefore, principal components analysis is used to reduce the dimensionality of the data by analyzing a limited number of scores instead of the original data.…”

Linear Discrimination, Ordination, and the Visualization of Selection Gradients in Modern Morphometrics

“…Smaller group mean differences can be represented only by a larger (and usually unknown) number of PCs, leading again to the problems described in this section (e.g., Jolliffe 2002). Some authors have computed CVA based on a set of scores resulting from a partial least squares analysis (PLS) between the measured variables and a set of group variables (Kemsley 1996;Sheets et al 2006); these basically are the scores of between-group PCA. Flury et al (1997) proposed a maximum likelihood approach for estimating a low-dimensional subspace for discrimination.…”

“…In such a case, one should avoid CVA and instead apply methods that do not require the inversion of a covariance matrix, such as PCA or PLS (between-group PCA). Otherwise, the number of variables must be reduced, for example to the first few principal components (e.g., Harvati 2003;Sheets et al 2006;Skinner et al 2009). If the number of relevant or significant PCs can be estimated from a scree plot or using Anderson's test (e.g., Coquerelle et al, in press), then these PCs might be used for CVA.…”

“…If the number of relevant or significant PCs can be estimated from a scree plot or using Anderson's test (e.g., Coquerelle et al, in press), then these PCs might be used for CVA. Sheets et al (2006) selected the number of PCs based on the rate of correct classifications in a crossvalidation. But only relatively large group mean differences will be represented by the first PCs.…”