varLeafDepI | R Documentation |

This function calculates the variance of leaf depths index `VLD(T)`

for a given rooted tree `T`

. The tree must not necessarily be binary.
`VLD(T)`

is defined as

`VLD(T)=\frac{1}{n}\cdot\sum_{x\in V_L(T)} (\delta(x)-N(T))^2`

in which `n`

denotes the number of leaves of `T`

, `V_L(T)`

denotes the set of leaves of `T`

, `\delta(x)`

denotes the depth of
the leaf `x`

and `N(T)`

denotes the average leaf depth of `T`

.

For `n=1`

the function returns `VLD(T)=0`

and a warning.

For details on the variance of leaf depths, see
also Chapter 7 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_7).

```
varLeafDepI(tree)
```

`tree` |
A rooted tree in phylo format. |

`varLeafDepI`

returns the variance of leaf depths index of the given tree.

Sophie Kersting

T. M. Coronado, A. Mir, F. Rossello, and L. Rotger. On Sackin's original proposal: the variance of the leaves' depths as a phylogenetic balance index. BMC Bioinformatics, 21(1), 2020. doi: 10.1186/s12859-020-3405-1. URL https://doi.org/10.1186/s12859-020-3405-1.

M. J. Sackin. "Good" and "Bad" Phenograms. Systematic Biology, 21(2):225-226, 1972. doi: 10.1093/sysbio/21.2.225.

K.-T. Shao and R. R. Sokal. Tree Balance. Systematic Zoology, 39(3):266, 1990. doi: 10.2307/2992186.

```
tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
varLeafDepI(tree)
```

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