Numerical analyses of Trypanozoon taxonomy are presented, based on the isoenzyme data of Stevens et al. (1992). The previous study used a reduced range of enzymes compared with earlier work; the analyses indicate the value of this rationalized system. Both recently isolated trypanosome stocks and previously studied populations were included, allowing detailed comparison with earlier studies. Relationships between zymodemes were calculated with an improved similarity coefficient program, using Jaccard's coefficient (1908), and by Nei's method (1972). Dendrograms were constructed from the matrices produced with the group-average method. The groupings produced by both numerical methods were in close agreement, and the clusters of related principal zymodemes largely matched the species, subspecies and strain groups proposed by previous workers. Trypanozoon biochemical taxonomy is reviewed and the groupings reinforced by this study are: the mainly East African strain groups, busoga, zambezi, kakumbi, kiboko and sindo; T.b. gambiense and the bouaflé strain group from West Africa, and T. evansi; an intermediate bouaflé/busoga group was also recognized.

Electrogena affinis (Eaton, 1883) is redescribed in all developmental stages. Larvae were analysed, in comparison with other congeneric european species, by a standard set of diagnostic characters which, in previous works, proved to be very useful in the taxonomy of Electrogena. The status of E. fascioculata (Sowa, 1974) is discussed and the synonymy E. fascioculata = E. affinis is stated. Finally, phenetic relationships between E. affinis and some other related european species are represented by cluster analysis, on the basis of quantitative characters of larvae.

This study reports on morphological variability of Eimeria species, which may be given either by drawings or as quantitative data. The drawings may be used to facilitate identification by eye of ‘unknown’ Eimeria specimens, whereas quantitative data may serve as a reference set for identification by multivariate statistical techniques. The morphology of 810 Eimeria specimens was defined in binary (b/w) digital images by pixels of their oocyst outline. A Fourier transform of pixel positions yielded size and shape features. To classify coccidia, the quantitative data were employed in an agglomerative clustering by average linkage algorithm with equal weight assigned to size and shape. An inverse Fourier transform served to reconstruct oocyst outlines, i.e. outlines of average shape and size, from mean values of features in resulting clusters. Clusters were subsequently identified based on their average morphology by comparison with drawings of species in an earlier taxonomical work. Five hundred oocyst outlines were simulated for each cluster representing a species, and shape/size variability was presented in contour diagrams. Differences in species shapes, and correspondence in length and width, were seen after reconstruction by inverse Fourier transform and comparison with earlier studies.

In this note we point out an inherent difficulty in numerical identification of bacteria. The problem is that of uniqueness of the taxonomic structure or, in mathematical terms, the lack of statistical identifiability of finite mixtures of multivariate Bernoulli probability distributions shown here.

It is common to represent taxonomic hierarchies of related objects (such as similar plant or animal species or languages of the same family) by rooted trees with labelled terminal vertices which represent the objects. The multivariate data comparing numerous characteristics of the objects is first reduced to indices of similarity (or more often of dissimilarity) between each pair of objects. These are used to classify the objects into groups which are then depicted on a tree.

This paper shows that an unrooted tree with labelled terminal vertices may provide a better representation of the relationships between the objects because the similarity indices are required to conform to fewer restrictions. Also for a given number of terminal vertices, there are fewer unrooted than rooted trees so that studies using probability distributions of trees or seeking the most suitable tree to represent the data are more practicable.