Relationship is essential to understanding the identities of organisms. To reconstruct relationships, branching diagrams called cladograms are used. Organisms are grouped on these using the presence of shared, derived (or diagnostic) characters; the groups of organisms that result are all inferred to be more closely related to each other than to anything else; that is, they are monophyletic. The evolution of new types of organisms is represented on the cladogram with the novel features, which make the descendants unlike their ancestors, being the shared, derived characters.
Cladograms differ from "trees of life" in several fundamental aspects. Cladograms are based upon shared derived characters; they do not show time; they do not show ancestors (although they specify what the ancestral condition of an organism must have been like); and, most importantly, they are testable.
Testability is a key part of science; any scientific inference must be able to be tested. Scientists thus "prove" nothing; scientific hypotheses merely fail falsification via careful testing. Something that is not testable, no matter how significant to us, is not science. In the case of cladograms, falsification consists of the prediction on the cladogram that a character will be present that is not (or vice versa). Because cladograms are falsifiable, they are merely hypotheses of the relationships of organisms.
With several hypotheses of relationship (cladograms) to choose among, the cladogram requiring the least number of steps (that is, the most parsimonious) is the preferred one.
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