Mode score distributions and relations across the
(no gradient) dataset. R (reflective) modes are symmetrically distributed around the mean shape, while S (symmetric) and M (mixed) modes have skewed distributions. This is because they contain a ‘thinness versus fatness’ component, which has a hard lower limit. We also examined the joint distributions of pairs of modes. No linear correlations were expected since the shape modes are by definition orthogonal, and no obvious structure was visually apparent. However, a statistical test for nonlinear relationships  showed some dependencies between modes, particularly S1/M1 and S1/M2 (values shown in table; the measure varies between 0 and 1, with 0 indicating statistical independence).