When some idea has been obtained of the constituent forms in a group and of the similarity and dissimilarity that they bear to each other, it is necessary to fit a hierarchical system to them. As already indicated, for groups with good fossil records, a dendritic, or branching, arrangement is desired, and classification must be partly arbitrary because of lack of knowledge. If the taxonomist has two compact groups of species, those within each group agreeing closely with each other in many characters and differing sharply from members of the other group in others, there is no difficulty in classification except in ranking. If each group contains a scattering of forms, any one close to another but the most divergent members in each group less like each other than they are like certain of the other group, breaking up the groups into definite classes becomes arbitrary.

A particularly difficult case arises when these forms also occur in time series: the present-day dogs, cats, hyenas, and other carnivores differ greatly from each other, but at one time their ancestors were much alike; presumably, therefore, they came from one ancestral stock. Paleontologists trace back each taxonomic line and are inclined to carry their separations of taxonomic groups as far backward in time as possible, until the earliest members of related groups are far more like each other than each is to the rest of the later members of the group to which it is assigned. This separation of groups is extreme phyletic splitting, but cutting off a large basal group containing all the primitive members may require arbitrary breaks in the many lines of descent and will obscure the evolutionary relationships. There is no answer to this dilemma except to avoid extremes.

A similar difficulty arises when the same character complex has arisen independently in related lines. The American paleontologist George Gaylord Simpson, for example, pointed out that mammalian characters such as the single jawbone (dentary) have arisen several times in groups of the extinct mammal-like reptiles. To use Sir Julian Huxley’s useful terminology, the definition of the Mammalia expresses a grade of organization (the attainment of a particular level of advancement), not a clade (a single phyletic group or line). Some taxonomists insist that in an evolutionary classification every group must be truly monophyletic—that is, spring from a single ancestral stock. Usually, this cannot be ascertained; the fossil material is insufficient or, as with many soft-bodied forms, nonexistent. Definite convergence must not be overlooked if it can be detected.

How far groups should be split to show phyletic lines and what rank should be given each group and subgroup thus are matters for reasonable compromise. The resulting classification, if fossils are unknown, may be frankly “natural” or phenetic, as is often explicitly the case with the flowering plants and is actually the case with many animal groups. If sufficient fossils are available, the resulting classification may be consonant with what is known about the evolution of the group or with what is merely conjectured. In reality, many classifications are conjectural or tendentious, and simpler and more natural ones might be closer to the available facts.

Even when only mere fragments are dealt with, a classification of some sort may still be necessary. Large numbers of leaves, some stems, trunks or roots, many seeds, and few flowers are known as fossils and may be of interest to the evolutionist. It may be many decades before a particular sort of fossilized leaf can be associated with a particular sort of branch, let alone trunk, flower, or seed. It is customary to construct form groups (i.e., a genus or species name is assigned to the fossilized material on the basis of its structure) in order to classify fossilized remains and to give them valid binomial names. When (if ever) two or more bits of fossil material are identified as belonging to one organism, one name only is retained. This procedure is best known for plants, but one phylum of animals (the Conodonta) is made up of enigmatic structures that are obviously some part of something animal.