Elliptic Fourier shape analysis of fossil bivalves: some practical considerations

TLDR: Elliptic Fourier shape analysis is a powerful, though underutilized, biometric tool that is particularly suited for the description of fossils lacking many homologous landmarks, such as several common bivalve groups as discussed by the authors.

Abstract: Elliptic Fourier shape analysis is a powerful, though under-utilized, biometric tool that is particularly suited for the description of fossils lacking many homologous landmarks, such as several common bivalve groups. The method is conceptually more parsimonious than more traditional biometric methods based on discrete linear and angular measurements. Most importantly, however, shape analysis captures a much higher proportion of the morphological information resident in any fossil than analyses based on discrete measurements. The number of harmonics required in an elliptic Fourier analysis can be estimated from a series of inverse Fourier reconstructions, or from the power spectrum. In most studies it is appropriate to normalize Fourier coefficients for size, although this information can be reincorporated at a later stage. The coefficients should probably not be standardized, unless there is evidence to suggest that high-frequency information was genetically as important as low-frequency information. Depending upon the aims of a particular study and the morphological disparity of the fossils in question, it might be appropriate to eliminate the first harmonic (‘best-fitting’) ellipse from an analysis. Meaningful comparison of the left and right valves of bivalves requires the digitized coordinates of one or other to be mirrored prior to computation of the Fourier coefficients. □Biometric analysis, Bivalvia, elliptic Fourier analysis, morphometrics.