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Grade vs. clade
Wessen-Simulating-human-origin-evo.pdf
Simulating Human Origins and Evolution by Ken Wessen (2005) p 19:
Any group of species may be classified according to the phylogenetic relationships of its members. A group that contains its most recent common ancestor and all its descendants is said to be monophyletic. If some, but not all, descendants are contained, it is a paraphyletic group. If the most recent common ancestor is not in the group, it is said to be polyphyletic. Traditionally, classification has been based on the concept of a grade, i.e. a grouping determined on the basis of overall morphological similarity. Such groupings often do not reflect the precise genetic relationships between the species, and are frequently paraphyletic or polyphyletic groups. The alternative is a clade-based classification, determined on the basis of common genetic origin, or monophyly. Because both morphological similarity and genetic relatedness between species are such primary concerns, both grades and clades remain important for taxonomy (Cronquist, 1987; Sokal, 1985). On the basis of the computer simulations mentioned in Section 1.3, Sepkoski and Kendrick (1993) found that, for incomplete data, polyphyletic groups may be just as useful ‘systematically’ as are clades (monophyletic groups). The species simulations in this book employ both techniques (see Section 3.1).
"Paraphyletic" is a word of convenience. It helps evolutionary biologists describe a group of creatures that have something meaningful in common, even if it means excluding another group.
When you or I say the word "ape," we usually mean every ape except humans, even though we are apes, an uncomfortable truth those racist speciesist Planet of the Apes apes would prefer to ignore.
So "ape" may mean chimps (both kinds), gorillas, orangutans, and those grumpy-faced B-listers, the gibbons, pictured above. Used this way, ape is paraphyletic. It includes all the descendants of some long-ago ape grandparent, but not one group. People.
We often use the word "animal" in a paraphyletic way, too -- again, excluding ourselves, but meaning all the other things we call animals.
Paraphyly might seem a little small-minded, particularly when it's used by people who see humans as being somehow superior to other living things. But it has its place. When someone asks you "Do you eat animals?" it's best "Yes" doesn't mean you're a cannibal.