## The Wagner algorithm

Kluge and Farris' (1969) method minimizes the Manhattan distance between members of a set of taxa via the creation of hypothetical taxonomic units. The first Wagner algorithm (in later papers termed the "simple Wagner algorithm'') is constructed as follows:

Definition: X(A, i); state = X, of character i, for Taxon A D(A, B) is the difference between taxon A and taxon B;

### Step 1. Choose an ancestral taxon.

Step 2. Find the operational taxonomic unit (OTU) that is the least distance from the ancestor, using Eq. 1. Connect the taxon to the ancestor, forming an interval. Step 3. Find the next taxon that is next least distant from the ancestor. Step 4. Find the interval from which the taxon found in step 3 differs least, using Eq. 2.

Step 5. Attach the taxon found in step 3 to the interval found in step 4 by constructing an intermediate (hypothetical ancestor), Y, and insert it into the

D(A, INT(B)) is the difference between A and interval B;

tree at this interval. The character states of Y will be the median of the three nodes surrounding this newly created intermediate.

Step 6. If any taxa remain unplaced, go to step 3, otherwise stop.

Example:

Using the same four-taxon, five-character statement as was used in the groundplan-divergence example (O Table 5.1)

O Table 5.1

Exemplar of a four-taxon, five-character statement

O Table 5.1

Exemplar of a four-taxon, five-character statement