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Another aspect of the imperfect nature of biological symmetry rests on the existence of deviations from the symmetric expectation (Ludwig 1932). These deviations manifest themselves to varying degrees and have distinct developmental causes. Let us consider the general case of a biological structure, whose symmetry emerges from the coherent spatial repetition of a finite number of units (e.g. the two wings of the drosophila, the five arms of the starfish). Different types of asymmetry are recognized (see also Graham et al. (1993) and Palmer (1996, 2004)):

 – directional asymmetry corresponds to the case where one of the units tends to systematically differ from the others in terms of size or shape. A classic example is the narwhal, whose “horn” is in fact the enlarged canine tooth of the left maxilla, while the vestigial right canine tooth remains embedded in the gum;

 – antisymmetry is comparable in magnitude to directional asymmetry, but the unit that differs from the others in size or shape is not the same from one individual to another. The claws of the fiddler crab show this type of asymmetry, the most developed claw being the right or the left, depending on the individual;

 – fluctuating asymmetry is an asymmetry of very small magnitude and is therefore much more difficult to detect. It is the result of random inaccuracies in the developmental processes during the formation of the units that compose the biological structure. Fluctuating asymmetry is a priori always present, even if it is not always measurable. Its magnitude is considered a measure of developmental precision and has often been used (albeit sometimes controversially) as a marker of stress.

Geometrically, the morphological variation in a sample of biological shapes exhibiting a symmetric arrangement can thus be decomposed into symmetric and asymmetric variations. There is only one way to be perfectly symmetric with respect to the symmetry group of the considered structure (this is the case when all the isometries of the group are respected), but there are one less many ways to deviate from perfect symmetry as there are isometries in the group. Thus, the total variation always includes one symmetric component and at least one asymmetric component. Geometric morphometrics offers mathematical and statistical tools to quantify and explore this empirical variation.