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S. Renaud and J. R. Michaux

Figure 1 Sampling localities of the animals considered in the present study. Open symbols: mainland (circles, western European clade;
triangles, Italo-Balkanic clade), filled symbols: islands.

An alternative approach to the analysis of outline data is (Renaud & Michaux, 2003), RFT was used for the analysis
the elliptic Fourier transform (EFT). This method is based of the simple molar outline whereas EFT was chosen to
on separate Fourier decompositions of the incremental describe the morphological variation of the mandible.
changes along x and y as a function of the cumulative Previous studies on related rodents showed that using the
length along the outline (Kuhl & Giardina, 1982; Ferson first nine harmonics for the M1 (Renaud, 1999) and the first
et al., 1985). Any harmonic corresponds to four coefficients: seven harmonics for the mandible (Renaud & Michaux,
A n and B n for x, and C n and D n for y, defining an ellipse in 2003) offer a good compromise between measurement error,
the xy-plane. The coefficients of the first harmonic, descri- information content and number of variables to be consid-
bing the ellipse best fitting the original outline, were used to ered.
standardize the size and orientation. The Fourier coefficients
(FC) of one harmonic cannot be considered as independent
Statistical analyses
because the variations along x and y are related when
considering a closed outline. Additionally, performing a
Estimation of size
Fourier analysis on both, the variations of x and y lead to
twice the number of FC as RFT for the same number of The size of the mandible or of the M1 was estimated by a
harmonics. Although the high number of variables can be univariate parameter, derived from the outline analysis. For
viewed as a shortcoming, EFT provides very accurate the M1, the RFT provides the zero-harmonic amplitude A 0 as a
reconstructions, even for complex outlines, and makes visual size estimator. The size of each mandible was estimated by the
inspection of the results easier, especially when dealing with area of the ellipse corresponding to the first harmonic (area
shape variations of a complex structure like the mandible. As H1). The relationship of these two parameters with latitude
both methods provide similar results when compared was investigated using simple linear regression.

342 Journal of Biogeography 34, 339–355
ª 2006 The Authors. Journal compilation ª 2006 Blackwell Publishing Ltd