3.1.1.2.2. Geometric wing shape morphometry

The geometric morphometric method is based on the coordinates of landmarks located at vein intersections of the wing (Bookstein, 1991; Smith et al., 1997). The fundamental advances of geometric morphometrics over traditional approaches include (i) the way the amount of difference between shapes can be measured (using Procrustes distance), (ii) the elucidation of the properties of the multidimensional shape space defined by this distance coefficient, (iii) the development of specialized statistical methods for the study of shape, and (iv) the development of new techniques for the graphical representations of the results (Bookstein, 1991; Rohlf, 2000; Mendes et. al., 2007).

In the measuring process, landmark coordinates are superimposed using a Generalized least Squares (GLS) Procrustes Superimposition (Rohlf and Slice, 1990): Specimens are centered, normalized to unit centered-size (Bookstein, 1991) and interactively rotated to minimize the sum-of squared distances between each location and its sample mean. Shape differences are then analysed by multivariate analysis of variance (MANOVA), Canonical Variate Analyses (CVA) and Multiple Discriminate Analyses, and shape patterns along the canonical axes are estimated by multivariate regression (Monteiro, 1999). For this kind of analysis, the software packages Morpheus (Slice, 2002), NTSYS (Rohlf, 1990), MORPHOJ (Klingenberg, 2011) and DrawWing (Tofilslki 2004) are commonly used. The new methods of automated measures and geometric morphometry have been used to distinguish Africanized honey bees from African and European subspecies, and to characterize the evolutionary lineages of A. mellifera (Francoy et al., 2006, 2008; Baylac et al., 2008; Tofilski, 2008; Miguel et al., 2010; Kandemir et al., 2011). This method has also been used to analyse differences between three honey bee subspecies in Poland: A. m. mellifera, A. m. carnica, and A. m. caucasica (Tofilski, 2004, 2008). The high rates of correct classification obtained with the geometric method indicate that forewings carry sufficient information to distinguish between different groups of bees. Discrimination results obtained with this method proved superior to classical wing angles, although the degree of improvement was moderate (Tofilski, 2008).