Internode intervals of a pure-birth process with lineage-dependent rates

With k lineages each splits at rate k^c, so the interval with k lineages is Exp(k^(1 + c)). c = 0 is Yule; c < 0 slows diversification as lineages accumulate (gamma < 0); c > 0 accelerates it (gamma > 0). The final interval (n lineages, up to the present) is drawn from the same law.

Usage

intervals_lineage_rate(n, c = 0)

Arguments

n

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

c

Lineage dependence of the split rate, a single finite number.

Value

Intervals g_2, ..., g_n (length n - 1), scaled to sum 1.

References

Pybus, O. G., & Harvey, P. H. (2000). Testing macro-evolutionary models using incomplete molecular phylogenies. Proceedings of the Royal Society B, 267, 2267–2272. doi:10.1098/rspb.2000.1278

Examples

set.seed(1)
intervals_lineage_rate(10, c = -1)
#> [1] 0.09121461 0.14272468 0.01759918 0.01688517 0.05267053 0.34966867 0.14851261
#> [8] 0.06518557 0.11553897