Since multivariate techniques for studying the morphological changes of animals and plants using multivariate statistical analyses were introduced, their development has rapidly increased. Subsequently, a new era of multivariate morphometry, namely geometric morphometry, emerged (Reyment 1995a). Bookstein (1989, 1991) was the first to enhance the theory and practice of analyzing variation in shape by geometric methods.
Geometric morphometry in biology was pioneered by Thompson (1917) who expressed changes in shape in organisms by transforming the data into coordinates observed at diagnostic sites on the organism. These sites of reference are known as landmarks, a term borrowed from craniometry and previously from topographic surveying. Data in the form of coordinates are more comprehensive than those expressed as lengths, heights and breadths and "distances between" because they encompass not only all information on the relative positions of the points observed but also the distances between these points (see Reyment 1995a for details on general categories of landmarks and how to choose sites for landmarks).
It can be difficult to distinguish between ornamented and unornamented fossil ostracods. In taxonomic studies of this group, ornamented forms can be identified by standard methods of character recognition with a greater degree of confidence than can be accomplished with unornamented forms. In the absence of information about the internal characters of the carapace, the use of multivariate morphometric techniques can help resolve this dilemma, by providing additional information about the shape parameters of unornamented forms, so that they can be more easily differentiated.
Through study of the middle Eocene ostracods of a section on the western bank of the Nile Valley (Upper Egypt), the author has recognized that specimens of Cyamocytheridea? sp. Elewa (1994) have many characters different from that genus (see the taxonomic section below), but which may be attributed to the genus Digmocythere based on the shape of the carapace (note that all the specimens are closed carapaces and analysis of the internal characters is not available). Three species of the Family Brachycytheridae have been selected for the present study: Cyamocytheridea? sp. (defined as Digmocythere cronini n. sp. in the conclusion of this study), Digmocythere ismaili (Bassiouni), and Digmocythere omarai Cronin and Khalifa. These species were collected from the middle Eocene Maghagha Formation, from a section that lies opposite of Beni Mazar city on the western bank of the Nile Valley, about 50 km north of Minia city (Figure 1). The Maghagha Formation was first proposed by Bishay (1966) to designate the chalk-marl complex exposed in the Maghagha district on the Nile Valley in substitution for the informal "B formation" of Barker (1945). Taxa analyzed in this study were collected from a section of the Maghagha Formation illustrated in Figure 2. This section consists of yellowish white, moderately hard limestone alternating with yellow to yellowish brown, soft to moderately hard marl and marly limestone comprising a thickness of about 14 m and all within the Maghagha Formation of Bishay (1966). Twenty-one samples from 15 beds were collected by the author from the studied section; only bed numbers 1-5 and the top of bed number 8 contain specimens of the new species. For more detailed information about the age and lithology of the section from which the specimens were collected, see Elewa (1997). For descriptions and illustrations of holotypes of D. ismaili and D. omarai, see Bassiouni (1971, p. 170, pl. 7, figs. 5-6) and Cronin and Khalifa (1979, p. 403, pl. 1, figs. 9-10), respectively.
The purpose of this study is to differentiate between the shapes of the three related ostracod forms by means of multivariate statistics and geometric morphometrics, to establish whether there is adequate shape variation between the forms to separate them into different species, and to describe any resulting new species.