A polyphyletic (Greek for "of many races") group is one whose members' last common ancestor is not a member of the group.
For example, the group consisting of warm-blooded animals is polyphyletic, because it contains both mammals and birds, but the most recent common ancestor of mammals and birds was cold-blooded. Warm-bloodedness evolved separately in the ancestors of mammals and the ancestors of birds.
Scientific classification aims to group species together such that every group is descended from a single common ancestor and therefore it is frequently a goal to eliminate groups that are found to be polyphyletic. This is often the stimulus for major revisions of the classification schemes. A polyphyletic group can be "fixed" either by excluding clades or by adding the common ancestor.
Opinions differ as to whether valid groups need to contain all the descendants of a common ancestor. Groups that do so are called monophyletic, and according to cladistics it should be the aim of classification to ensure that all groups have this property. However, many other taxonomists would argue that there is a valid place for groups that are paraphyletic, i.e. contains its most recent common ancestor but does not contain all the descendants of that ancestor.
In most cladistics-based schools of taxonomy, the existence of polyphyletic groups (as well as paraphyletic groups) in a classification is discouraged. Monophyletic groups (that is, clades) are considered by these schools of thought to be the most important grouping of organisms, for the following reasons:
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