Final answer:
Derived characters are traits that arose in the most recent common ancestor of a particular lineage and are used to identify evolutionary relationships within a clade, while shared ancestral characters are older traits found across a clade and are less informative in distinguishing between lineages.
Step-by-step explanation:
A derived character is a trait that arose in the most recent common ancestor of a particular lineage and was passed along to its descendants. This contrasts with shared ancestral characters, which are traits that originated in ancestors that are older than the clade in question. Derived characters are immensely useful in cladistics because they help to identify evolutionary relationships within a clade. For example, the presence of an amniotic egg characterizes a clade that includes reptiles, birds, and mammals, but it does not include their more distant ancestors like fish or amphibians, which do not have this trait. Cladistics utilizes these characters to build phylogenetic trees, showcasing the branching patterns of evolution and clarifying the diverse lineages in the tree of life.
To further explain, consider a clade represented in a phylogenetic tree. Shared derived characters such as having hair or an amniotic egg help scientists determine more recent common ancestors and distinguish between different evolutionary lineages. In contrast, shared ancestral characters like vertebrae in vertebrates are found throughout the tree and do not provide information about the specific branching points of the clade. It is this distinction that allows researchers to infer the sequence of evolutionary events and assemble a more precise phylogenetic tree.