As seen from the phylogeny in Figure 1, the predicted pattern of organisms at any given point in time can be described as "groups within groups", otherwise known as a nested hierarchy. The only known processes that specifically generate unique, nested, hierarchical patterns are branching evolutionary processes. Common descent is a genetic process in which the state of the present generation/individual is dependent only upon genetic changes that have occurred since the most recent ancestral population/individual. Therefore, gradual evolution from common ancestors must conform to the mathematics of Markov processes and Markov chains. Using Markovian mathematics, it can be rigorously proven that branching Markovian replicating systems produce nested hierarchies (Givnish and Sytsma 1997; Harris 1989; Norris 1997). For these reasons, biologists routinely use branching Markov chains to effectively model evolutionary processes, including complex genetic processes, the temporal distributions of surnames in populations (Galton and Watson 1874), and the behavior of pathogens in epidemics.
The nested hierarchical organization of species contrasts sharply with other possible biological patterns, such as the continuum of "the great chain of being" and the continuums predicted by Lamarck's theory of organic progression (Darwin 1872, pp. 552-553; Futuyma 1998, pp. 88-92). Mere similarity between organisms is not enough to support macroevolution; the nested classification pattern produced by a branching evolutionary process, such as common descent, is much more specific than simple similarity. Real world examples that cannot be objectively classified in nested hierarchies are the elementary particles (which are described by quantum chromodynamics), the elements (whose organization is described by quantum mechanics and illustrated by the periodic table), the planets in our Solar System, books in a library, or specially designed objects like buildings, furniture, cars, etc.
Although it is trivial to classify anything subjectively in a hierarchical manner, only certain things can be classified objectively in a consistent, unique nested hierarchy. The difference drawn here between "subjective" and "objective" is crucial and requires some elaboration, and it is best illustrated by example. Different models of cars certainly could be classified hierarchically—perhaps one could classify cars first by color, then within each color by number of wheels, then within each wheel number by manufacturer, etc. However, another individual may classify the same cars first by manufacturer, then by size, then by year, then by color, etc. The particular classification scheme chosen for the cars is subjective. In contrast, human languages, which have common ancestors and are derived by descent with modification, generally can be classified in objective nested hierarchies (Pei 1949; Ringe 1999). Nobody would reasonably argue that Spanish should be categorized with German instead of with Portugese.
The difference between classifying cars and classifying languages lies in the fact that, with cars, certain characters (for example, color or manufacturer) must be considered more important than other characters in order for the classification to work. Which types of car characters are more important depends upon the personal preference of the individual who is performing the classification. In other words, certain types of characters must be weighted subjectively in order to classify cars in nested hierarchies; cars do not fall into natural, unique, objective nested hierarchies.
Because of these facts, a cladistic analysis of cars will not produce a unique, consistent, well-supported tree that displays nested hierarchies. A cladistic analysis of cars (or, alternatively, a cladistic analysis of imaginary organisms with randomly assigned characters) will of course result in a phylogeny, but there will be a very large number of other phylogenies, many of them with very different topologies, that are as well-supported by the same data. In contrast, a cladistic analysis of organisms or languages will generally result in a well-supported nested hierarchy, without arbitrarily weighting certain characters (Ringe 1999). Cladistic analysis of a true genealogical process produces one or relatively few phylogenetic trees that are much more well-supported by the data than the other possible trees.
Interestingly, Linnaeus, who originally discovered the objective hierarchical classification of living organisms, also tried to classify rocks and minerals hierarchically. However, his classification for non-living objects eventually failed, as it was found to be very subjective. Hierarchical classifications for inanimate objects don't work for the very reason that unlike organisms, rocks and minerals do not evolve by descent with modification from common ancestors.