Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry

Table 5 Procrustes ANOVA for the coral example, with a symmetry group consisting of reflection and rotation of order 2

Source	Degrees of freedom	Sums of squares	Mean squares	F	P
Individual	1127	4.9380	0.0043815	1.82	< 0.000001
Rotation	23	0.096360	0.0041896	4.20	< 0.000001
Reflection	23	0.16058	0.0069818	1.34	0.13
Rotation × reflection	23	0.072451	0.0031501	3.17	< 0.000001
Rotation × individual	1127	1.1251	0.0009983	4.95	< 0.000001
Reflection × individual	1127	5.8839	0.0052209	25.87	< 0.000001
Rotation × reflection × individual	1127	1.1184	0.0009924	4.92	< 0.000001
[Total FA]	3381	8.1274	0.0024039
Imaging error	4600	0.92842	0.0002018	1.26	< 0.000001
Digitizing error	9200	1.4789	0.0001607

The main effect of individuals is tested against the mean square for the total fluctuating asymmetry ("Total FA": pooling sums of squares and degrees of freedom across all three subspaces with asymmetric variation: rotation × individual, reflection × individual and rotation × reflection × individual). This total asymmetry is not used otherwise in the analysis.

ISSN: 2730-7182