LTT: Theoretical Lineage-Through Time Plots

Description

This function draws the lineage-through time (LTT) plots predicted under a speciation-extinction model (aka birth-death model) with specified values of speciation and extinction rates (which may vary with time).

A prediction interval is plotted by default which requires to define a sample size (100 by default), and different curves can be combined.

Usage

LTT(birth = 0.1, death = 0, N = 100, Tmax = 50, PI = 95,
    scaled = TRUE, eps = 0.1, add = FALSE, backward = TRUE,
    ltt.style = list("black", 1, 1), pi.style = list("blue", 1, 2))

Arguments

Details

For the moment, this works well when birth and death are constant. Some improvements are under progress for time-dependent rates (but see below for and example).

References

Paradis, E. (2011) Time-dependent speciation and extinction from phylogenies: a least squares approach. Evolution, 65, 661--672.

Examples

Run this code

### predicted LTT plot under a Yule model with lambda = 0.1
### and 50 species after 50 units of time...
LTT(N = 50)
### ... and with a birth-death model with the same rate of
### diversification (try with N = 500):
LTT(0.2, 0.1, N = 50, PI = 0, add = TRUE, ltt.style = list("red", 2, 1))
### predictions under different tree sizes:
layout(matrix(1:4, 2, 2, byrow = TRUE))
for (N in c(50, 100, 500, 1000)) {
    LTT(0.2, 0.1, N = N)
    title(paste("N =", N))
}
layout(1)
### speciation rate decreasing with time
birth.logis <- function(t) 1/(1 + exp(0.02 * t + 4))
LTT(birth.logis)
LTT(birth.logis, 0.05)
LTT(birth.logis, 0.1)