Homoplasy in the context of "Polyphyletic"

A polyphyletic group is an assemblage that includes organisms with mixed evolutionary origin but does not include their most recent common ancestor. The term is often applied to groups that share similar features known as homoplasies, which are explained as a result of convergent evolution. The arrangement of the members of a polyphyletic group is called a polyphyly /ˈpɒlɪˌfaɪli/. It is contrasted with monophyly and paraphyly.

For example, the biological characteristic of warm-bloodedness evolved separately in the ancestors of mammals and the ancestors of birds; "warm-blooded animals" is therefore a polyphyletic grouping. Other examples of polyphyletic groups are algae, C4 photosynthetic plants, and edentates.

In phylogenetics and computational phylogenetics, maximum parsimony is an optimality criterion under which the phylogenetic tree that minimizes the total number of character-state changes (or minimizes the cost of differentially weighted character-state changes) is constructed. Under the maximum-parsimony criterion, the optimal tree will minimize the amount of homoplasy (i.e., convergent evolution, parallel evolution, and evolutionary reversals). In other words, under this criterion, the shortest possible tree that explains the data is considered best. Some of the basic ideas behind maximum parsimony were presented by James S. Farris in 1970 and Walter M. Fitch in 1971.

Maximum parsimony is an intuitive and simple criterion, and it is popular for this reason. However, although it is easy to score a phylogenetic tree (by counting the number of character-state changes), there is no algorithm to quickly generate the most-parsimonious tree. Instead, the most-parsimonious tree must be sought in "tree space" (i.e., amongst all possible trees). For a small number of taxa (i.e., fewer than nine) it is possible to do an exhaustive search, in which every possible tree is scored, and the best one is selected. For nine to twenty taxa, it will generally be preferable to use branch-and-bound, which is also guaranteed to return the best tree. For greater numbers of taxa, a heuristic search must be performed.