Biology · Introductory biology · Worked example

Compare two trees by parsimony

A second tree for the same five animals puts the frog beside the mammals, (Shark,(Lizard,(Frog,(Mouse,Human)))). Using the characters four limbs, amniotic egg and hair, how many changes does it need, and how does it compare with the tree (Shark,(Frog,(Lizard,(Mouse,Human)))), which needs $3$ ? How many rooted trees for five animals are there to choose from?

Score the first tree

On the vertebrate tree each character changes once, on the branch below its clade.

1 + 1 + 1 = 3

Score the second tree

Four limbs still change once, below (Lizard, …), and hair once, below (Mouse, Human). Why does the amniotic egg need two? The lizard and the mammals have it but the frog between them does not, so the egg either arose twice or arose once and was lost in frogs.

1 + 2 + 1 = 4

Compare the scores

The second tree needs one more change, one extra coincidence. Parsimony prefers the vertebrate tree.

4 - 3 = 1

Count the possible trees

There are many more ways to arrange five animals than these two. Build a tree one animal at a time. Each new animal can join any branch already on the tree, which gives $1 \times 3 \times 5 \times 7 = 105$ rooted trees. Once the shark is fixed as the outgroup, only the other four are arranged, which leaves $1 \times 3 \times 5 = 15$ .

1 \cdot 3 \cdot 5 \cdot 7 = 105

Read what parsimony says

No tree can need fewer than $3$ changes for these three characters, so the vertebrate tree is among the most parsimonious of the $105$ . It ties with the six other rootings of the same branching, because a score does not depend on the root. With the shark as the outgroup, it is the only one of the $15$ that scores $3$ . That makes it the best-supported hypothesis, not a proof. Many more characters, and DNA, support it too.

Result

The second tree needs $4$ changes, because the amniotic egg must change twice. The vertebrate tree needs $3$ , so parsimony prefers it by one change. There are $1 \times 3 \times 5 \times 7 = 105$ rooted trees for five animals, or $15$ once the shark is fixed as the outgroup.

Your turn

1. One like the example

A third tree for the five animals reads ((Shark,Frog),(Lizard,(Mouse,Human))). How many changes does it need, and why?

Show the answer and explanation

$3$ , the same as the vertebrate tree.

It has the same branches as the vertebrate tree, only rooted between the shark and the frog instead of on the shark. Each character still changes once, $1 + 1 + 1 = 3$ . Parsimony scores do not depend on the root, which is why an outgroup is needed to root the tree.

1 + 1 + 1 = 3

2. A variation

How many rooted trees are there for four taxa, and for six?

Show the answer and explanation

$15$ for four taxa, and $945$ for six.

For $n$ taxa the count is $1 \times 3 \times 5 \times \dots \times (2 n - 3)$ . Four taxa give $1 \times 3 \times 5 = 15$ . Six taxa multiply the five-taxon $105$ by $9$ , giving $945$ .

\begin{array}{l} 1 \cdot 3 \cdot 5 = 15 \\ 105 \cdot 9 = 945 \end{array}

3. Somewhere new

Dolphins and sharks both have a streamlined body and a dorsal fin. Dolphins are mammals that breathe air with lungs and feed their young milk. If a tree were built from body shape alone, what would it show, and why does parsimony over many characters fix it?

Show the answer and explanation

It would wrongly group dolphins with sharks. Counted over many characters, such as milk and lungs, the tree that puts dolphins among the mammals needs far fewer changes.

Body shape is homoplasy, a similarity that evolved separately in two lineages adapted to swimming. One character can mislead, but every mammal trait the dolphin shares would need extra changes on a dolphin-with-shark tree. Parsimony counts all of them and outvotes the one.

Keep exploring

The second tree opens in Phylogenetic tree with the same three characters and a parsimony score of $4$ . Under Compare a second tree the vertebrate tree is filled in, and Compare trees reports that the two are topologically different.

Return to the concept →

Sources and scope

Authored study material. Tool results depend on the stated inputs and model assumptions.

After reading

Study it, then try it

Practice the key terms as flashcards, then open the example in its tool, change a value and keep a useful result on your board.

Study the 13 key terms Open the second tree Count the changes in Math Open worked example on a board Taxonomy in Biology Reference

Your existing work stays on this device. Examples open as editable copies.

Score the first tree

Score the second tree

Compare the scores

Count the possible trees

Read what parsimony says

Result

Your turn

1. One like the example

33, the same as the vertebrate tree.

2. A variation

1515 for four taxa, and 945945 for six.

3. Somewhere new

It would wrongly group dolphins with sharks. Counted over many characters, such as milk and lungs, the tree that puts dolphins among the mammals needs far fewer changes.

Keep exploring

Study it, then try it

$3$ , the same as the vertebrate tree.

$15$ for four taxa, and $945$ for six.