Table 6 Computed tree statistics from the illustrated tree in Fig. 1

Number of Cherries

Cherries are formed by tips 1 & 2 and 4 & 5. So the number of cherries is 2.

Standardized number of Cherries

From the formula, \(\frac{2}{0.5*5}=0.8\)

Sackin index

We consider each leaf and we count the edges to the root, e.g for leaf 1, there are 3 edges to the root. The value of the Sackin index becomes 14.

Standardized Sackin index

From the formula, \(\frac{14}{0.5 \times 5 \times 6 - 1}=\frac{14}{14}=1\)

Colless index

We consider each internal node, e.g for internal node C, the difference between left and right tips subtended is 1. Adding such values for each internal node results in 2 as the Colless index.

Standardized Colless index

From the formula, \(\frac{2}{4\times 3|2}=0.3333\)

Total cophenetic index

\((1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5) \& (4,5)\) are the possible pairs. The corresponding cophenetic values are \(2,0,0,0,0,0,0,1,1 \& 2\), respectively. Sum of all possible pairs is 6.

Ladder length

One internal node C has a single child descendant leaf, ladder length therefore is \(\frac{1}{5}=0.2.\)

Maximum depth

Depth for tips 1,2,3,4 & 5 are 3,3,2,3 & 3. Since 3 is the highest, it is the maximum depth.

Maximum width

Depth for tips 1,2,3,4 & 5 are 3,3,2,3 & 3 respectively. Depth for internal nodes A,B,C,D & E are 0,1,1,2 & 2. Depth 3 has the highest number of nodes and it is 4. Maximum width becomes 4.

Width-depth ratio

\(\frac{4}{3}=1.3333\)