Monophyletic

In phylogeny, a group is monophyletic if all organisms included in it have evolved from a common ancestral population, and all descendants of that ancestor are included in the group.
In contrast, a group that contains some but not all of the descendants of the most recent common ancestor is called paraphyletic, and a taxonomic group that contains organisms but lacks a common ancestor is called polyphyletic.
Example
All organisms in the genus Homo are thought to derive from the same ancestral form in the family Hominidae. Thus, the genus Homo is monophyletic.
On the other hand, if Homo habilis were found to have evolved from a different ancestor than Homo sapiens, and this ancestor was not included in the genus, then the genus would turn out to be polyphyletic. Since biologists on the whole prefer monophyletic groups, in this case they would probably either split the genus to fit the new circumstances, or expand it to include the additional forms.
Other uses
The usage explained above was introduced by Willi Hennig, and the success of the cladistic school of systematics has made it the dominant usage. However, according to other taxonomists such as Ernst Mayr and the tradition that he calls «evolutionary taxonomy», monophyletic is any group whose most recent common ancestor is a member of the clade, regardless of whether or not it includes all the descendants of said common ancestor; if it excludes some offspring it is paraphyletic, but if it excludes none it is holophyletic. The only groups that do not meet this broader definition of "monophyly" are polyphyletic groups.
This is the definition that was used almost universally in biological publications until about 1990. In cladistic terminology, the term "convex group" is used, although not in a general way, to refer to the same concept.
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