J1Index: Robust universal tree balance index

Description

Calculate tree balance index J¹ (when nonRootDominance = FALSE) or J^1c (when nonRootDominance = TRUE) from Lemant2022TreeTools.

Usage

J1Index(tree, q = 1, nonRootDominance = FALSE)
JQIndex(tree, q = 1, nonRootDominance = FALSE)

Arguments

tree: Either an object of class 'phylo', or a dataframe with column names Parent, Identity and (optionally) Population. The latter is similar to tree$edge, where tree is an object of class 'phylo'; the differences are in class (data.frame versus matrix) and column names. The dataframe may (but isn't required to) include a row for the root node. If population sizes are omitted then internal nodes will be assigned population size zero and leaves will be assigned population size one.
q: Numeric between zero and one specifying sensitivity to type frequencies. If q < 1, the J^q index - based on generalized entropy - will be returned; see Lemant2022;textualTreeTools, page 1223.
nonRootDominance: Logical specifying whether to use non-root dominance factor.

Author

Rob Noble, adapted by Martin R. Smith

Details

If population sizes are not provided, then the function assigns size 0 to internal nodes, and size 1 to leaves.

References

Examples

Run this code

# Using phylo object as input:
phylo_tree <- read.tree(text="((a:0.1)A:0.5,(b1:0.2,b2:0.1)B:0.2);")
J1Index(phylo_tree)
phylo_tree2 <- read.tree(text='((A, B), ((C, D), (E, F)));')
J1Index(phylo_tree2)

# Using edges lists as input:
tree1 <- data.frame(Parent = c(1, 1, 1, 1, 2, 3, 4),
                    Identity = 1:7,
                    Population = c(1, rep(5, 6)))
J1Index(tree1)
tree2 <- data.frame(Parent = c(1, 1, 1, 1, 2, 3, 4),
                    Identity = 1:7,
                    Population = c(rep(0, 4), rep(1, 3)))
J1Index(tree2)
tree3 <- data.frame(Parent = c(1, 1, 1, 1, 2, 3, 4),
                    Identity = 1:7,
                    Population = c(0, rep(1, 3), rep(0, 3)))
J1Index(tree3)
cat_tree <- data.frame(Parent = c(1, 1:14, 1:15, 15),
                       Identity = 1:31,
                       Population = c(rep(0, 15), rep(1, 16)))
J1Index(cat_tree)

# If population sizes are omitted then internal nodes are assigned population
# size zero and leaves are assigned population size one:
sym_tree1 <- data.frame(Parent = c(1, rep(1:15, each = 2)),
                       Identity = 1:31,
                       Population = c(rep(0, 15), rep(1, 16)))
# Equivalently:                        
sym_tree2 <- data.frame(Parent = c(1, rep(1:15, each = 2)),
                       Identity = 1:31)
J1Index(sym_tree1)
J1Index(sym_tree2)

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