Life is organized as a pattern of a tree, with lineages diverging from common ancestors.

Over time, the lineages acquire new adaptations that are passed on (sometimes with modification) to their descendants.

Example:

• Lions, tigers, bears, cows, platypi, and lizards all had a common ancestor with a backbone, limbs with digits, etc.: these adaptations (specializations) were passed down to all these descendant groups.
• Lions, tigers, bears, cows, and platypi (but not lizards) all had a common ancestor that had fur and gave milk.
• Lions, tigers, bears, and cows (but not platypi and lizards) all had a common ancestor that had a placenta.
• Lions, tigers, and bears (but not cows, platypi, and lizards) all had a common ancestor that had molar teeth modified for shearing.
• Lions and tigers (but not bears, cows, platypi, and lizards) both had a common ancestor that had retractable claws.

Or by a braching diagram:

In 1950s, German entomologist Willi Hennig realized that one could use this method to organize taxonomy (systematics) by reconstructing the phylogeny (family tree) of life.

The branching diagram above is called a cladogram.

• A sort of map showing the simplest (most parsimonious) arrangement of organisms
• Inferred to best represent the evolutionary branching arrangements

Here is another, more comprehensive, cladogram of living terrestrial vertebrates:

The taxa along the top line are terminal taxa

Nodes:

• Where two branches of a cladogram meet
• Represents the most recent common ancestor of the terminal taxa they join
• Are also taxa (named, or at least “nameable” groups of organisms)

In the above example, Amphibia, Mammalia, Testudines, Lepidosauria, Crocodylia, and Aves are all terminal taxa; Tetrapoda, Amniota, Reptilia, Diapsida, and Archosauria are named nodes.

Each node contains ALL taxa further up the tree!

The above arrangement can also be written in outline form:
Tetrapoda

I. Amphibia
II. Amniota
A. Mammalia
B. Reptilia
1. Testudines
2. Diapsida
a. Lepidosauria
b. Archosauria
i. Crocodylia
ii. Aves

So:

• Crocodiles are archosaurs, and diapsids, and reptiles, and amniotes, and tetrapods.
• Lepidosaurs are diapsids, and reptiles, and amniotes, and tetrapods.
• Etc.

Two taxa which meet at a node are called sister taxa, and are each other's closest relatives (i.e., they represent the two lineages which diverged from that particular common ancestor).

So:

• Crocodylia is the sister taxon to Aves
• Aves is the sister taxon to Crocodylia
• Lepidosauria is the sister taxon to ALL Archosauria (not just Crocodylia)
• Etc.

The ingroup represents the assemblage of taxa of primary interest in any particular study; the outgroup is the sister taxon to the ingroup.

Sometimes the relationship between three or more terminal taxa is uncertain. These are drawn as polytomies: multiple branches stemming from the same node.

For example, some evidence suggests that, unlike the cladogram above, turtles might be closer to lepidosaurs than lepidosaurs are to archosaurs, or that turtles might be closer to archosaurs than archosaurs are to lepidosaurs. This uncertainty can be shown by the following polytomy:

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