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The group of "warm-blooded animals" is polyphyletic.

In phylogenetics, a taxon is polyphyletic (Greek for "of many races") if the trait its members have in common evolved separately in different places in the phylogenetic tree. Equivalently, a polyphyletic taxon does not contain the most recent common ancestor of all its members.

For example, the group 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, so it is not a true phylogenetic grouping.

Scientific classification aims to group species together such that every group is descended from a single common ancestor, and the elimination of groups that are found to be polyphyletic is therefore a common goal, and 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. contain only the descendants of a common ancestor, but do not contain all its descendants.

• The group of all warm-blooded animals is polyphyletic because it includes birds and mammals, yet descendents of their nearest ancestor include cold-blooded animals, such as reptiles.

• The group of all organisms that use photosynthesis is polyphyletic, because it includes plants and some bacteria, and the nearest common ancestor includes many non-photosynthetic organisms, such as animals.

• The group of flying animals is polyphyletic, because it includes bats (mammals) and birds, and the nearest common ancestor includes non-flying animals such as primates.

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 organisims, for the following reaons:

• Clades are simple to define: a typical clade definition is "All descendents of the nearest common ancestor of species X and Y". On the other hand, polyphyletic and paraphyletic groups are always defined in terms of clades, for example "reptiles are the Synapsid clade, minus the Aves clade". Or "Warm-blooded animals are the Aves clade plus the Mammals clade". Because polyphyletic an paraphyletic groups are defined in terms of clades, they are considered less important than clades.

• For a given evolutionary tree of, say, N nodes, there are exactly N clades (one per node). However, the number of paraphyletic groups and polyphyletic groups is exponentially larger than that, on the order of N². Yet only a small fraction of the paraphyletic groups are given names or discussed.

• Polyphyletic groups often have their origin in traditional taxonomy, based on similar morphological characteristics. The original perception may have been that the group was entirely descended from a single ancestor. If such a group is later discovered (for instance, due to convergent evolution) to be polyphyletic, rather than monophyletic, then such a group loses its original significance.

• Colin Tudge (2000). The Variety of Life. Oxford University Press. ISBN 0198604262.