A GEOMETRIC MORPHOMETRIC APPROACH TO THE ANALYSIS OF THE SHAPE VARIABILITY OF THE HAPTORAL ATTACHMENT STRUCTURES OF LIGOPHORUS SPECIES (PLATYHELMINTHES: MONOGENEA)

The taxonomy of Ligophorus Euzet & Suriano, 1977, like the most of monopisthocotylean monogeneans, relies heavily on the morphology of sclerites of the posterior attachment organ (haptor). Geometric morphometric approach is used to analyse variability and compare the shapes of haptoral structures of these monogeneans. We outline the shapes of the sclerities by cubic Bezier curves and store results in SVG files. Every SVG outline is reduced to a set of harmonics of Elliptic Fourier transform using ElFourier program. Harmonics are the sequence of unique numbers that describe the shape of structures and are invariant to their sizes, rotation, and orientation. They allow reconstructing source outline images, finding their average form, analyzing variability and comparing shapes in combination with other numerical data like dimensions. We use that approach to investigate intra- and interspecific variability of 400 haptoral structures of seven representatives of Ligophorus, parasitising four mullet species from the Black Sea, and to discriminate these monogeneans. This method is perspective for the creation of semiautomatic key for identification of helminthes, which are mainly distinguished by the shape and dimensions of the attachment organs. The obtained results and method prospects are discussed.

Fourier analysis applied to Stephanomys (Rodentia, Muridae) molars: nonprogressive evolutionary pattern in a gradual lineage

Size and shape are analyzed for Pliocene lineages of the rodent genus Stephanomys Schaub 1938. Previous phylogenetic studies were based mainly on size variation and descriptive comparisons, without any attempt to quantify shape changes. Hence, on the basis of regular size increase, Stephanomys has been considered a prime example of phyletic gradualism. In order to quantify morphological variation within the lineage, a method for analyzing complex outlines, the elliptic Fourier transform, was applied to tooth contour (upper and lower first molars). It was then possible to compare evolution in size, estimated by tooth area, as well as evolution of shape, represented by Fourier coefficients.While size seems to change gradually through time, morphology gives a rather discontinuous evolutionary pattern for both the upper and lower molar. Such a discrepancy between the evolution of size and shape of a single structure suggests that different genetic determinisms and mechanical constraints may act on size and shape. Hence it may be misleading to infer generalized evolutionary processes from either size or shape alone.