Number of trees with m steps

Calculate the number of trees in which Fitch parsimony will reconstruct m steps, where a leaves are labelled with one state, and b leaves are labelled with a second state.

Usage

Carter1(m, a, b)

Log2Carter1(m, a, b)

LogCarter1(m, a, b)

Arguments

m

Number of steps.

a, b

Number of leaves labelled 0 and 1.

Details

Implementation of theorem 1 from Carter1990;textualTreeTools

References

See also:

Steel1993TreeSearch

Steel1995TreeSearch

(Steel1996TreeSearch)

See also

Other profile parsimony functions: PrepareDataProfile(), StepInformation(), WithOneExtraStep(), profiles

Author

Martin R. Smith (martin.smith@durham.ac.uk)

Examples

# The character `0 0 0 1 1 1`
Carter1(1, 3, 3) # Exactly one step
#> [1] 9
Carter1(2, 3, 3) # Two steps (one extra step)
#> [1] 54

# Number of trees that the character can map onto with exactly _m_ steps
# if non-parsimonious reconstructions are permitted:
cumsum(sapply(1:3, Carter1, 3, 3))
#> [1]   9  63 105

# Three steps allow the character to map onto any of the 105 six-leaf trees.