Random topology under Aldous' beta-splitting model

A clade of m tips splits into i and m - i tips with probability proportional to Gamma(beta + i + 1) Gamma(beta + m - i + 1) / (Gamma(i + 1) Gamma(m - i + 1)). beta = 0 is Yule, beta = -1.5 is PDA, beta close to -2 is caterpillar-like and large beta is balanced.

Usage

rtopology_beta(n, beta = 0)

Arguments

n

Number of tips, a single integer of at least 2.

beta

Aldous' beta, a single finite number greater than -2. Lower values give more imbalanced trees.

Value

A phylo object without branch lengths, with tips t1, ..., tn.

References

Aldous, D. (1996). Probability distributions on cladograms. In D. Aldous & R. Pemantle (Eds.), Random discrete structures (pp. 1–18). Springer. doi:10.1007/978-1-4612-0719-1_1

Examples

set.seed(1)
rtopology_beta(10, beta = -1)
#> 
#> Phylogenetic tree with 10 tips and 9 internal nodes.
#> 
#> Tip labels:
#>   t1, t2, t3, t4, t5, t6, ...
#> 
#> Rooted; no branch length.