Abstract
BackgroundThe introduction and statistical formalisation of landmark-based methods for analysing biological shape has made a major impact on comparative morphometric analyses. However, a satisfactory solution for including information from 2D/3D shapes represented by ‘semi-landmarks’ alongside well-defined landmarks into the analyses is still missing. Also, there has not been an integration of a statistical treatment of measurement error in the current approaches.ResultsWe propose a procedure based upon the description of landmarks with measurement covariance, which extends statistical linear modelling processes to semi-landmarks for further analysis. Our formulation is based upon a self consistent approach to the construction of likelihood-based parameter estimation and includes corrections for parameter bias, induced by the degrees of freedom within the linear model. The method has been implemented and tested on measurements from 2D fly wing, 2D mouse mandible and 3D mouse skull data. We use these data to explore possible advantages and disadvantages over the use of standard Procrustes/PCA analysis via a combination of Monte-Carlo studies and quantitative statistical tests. In the process we show how appropriate weighting provides not only greater stability but also more efficient use of the available landmark data. The set of new landmarks generated in our procedure (‘ghost points’) can then be used in any further downstream statistical analysis.ConclusionsOur approach provides a consistent way of including different forms of landmarks into an analysis and reduces instabilities due to poorly defined points. Our results suggest that the method has the potential to be utilised for the analysis of 2D/3D data, and in particular, for the inclusion of information from surfaces represented by multiple landmark points.
Highlights
The introduction of geometric morphometrics has laid the foundations for a quantitative description of shapes and shape differences, revolutionising the century old quest for comparing anatomical features of organisms [1]
For Procrustes we use the residuals from the fitted models to make an estimate of landmark measurement error
Our analysis approach has been driven by the requirements of statistical estimation, quantitation and self consistency, i.e. distributions assumed during likelihood construction match the data and estimated parameters match those generating the data
Summary
The introduction of geometric morphometrics has laid the foundations for a quantitative description of shapes and shape differences, revolutionising the century old quest for comparing anatomical features of organisms [1]. It is increasingly used to link quantitative descriptions of shape with developmental processes and associated genetic factors [2] This process generally involves the construction of a parametric model based upon exemplar biological shape specimens, and the most popular of these are linear models. As a consequence of these efforts, the standard method for analysis of variation in landmark position is generally regarded as ‘Procrustes’ It comprises a least-squares alignment of a set of landmark features to a mean shape, and this is often followed by eigenvector analysis of the linear correlations in variation around that mean. While the technique is very popular the approach has several limitations with regard to the types of variation with which it can deal One of these limitations is due to the assumption associated with taking least-squares differences and eigenvector summaries of distributions. There has not been an integration of a statistical treatment of measurement error in the current approaches
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