Concept of "Natural Groups" in systematics

The diagram depicts the evolutionary relationships of five species of vertebrate animals as a "family tree". The evolution of particular characters is indicated on the appropriate branches of the tree. The distribution of characters among species allows construction of a "natural taxonomy" that reflects their evolutionary relationships. Given that all five species have a vertebral column (Vertebrata), recognition that all except the Lamprey have jaws suggests that these four are more closely related to each other than any are to the Lamprey. They form a "natural group", the Gnathostomata, that includes the first jawed vertebrate and all of its descendants. Within this group, note that although Bass & Lizards do not have hair, this pair does not constitute a natural group, since other hairless vertebrates are excluded.