LTT {ape} R Documentation

## 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

 `birth` the speciation rate, this may be either a numeric value or a funtion of time (named `t` in the code of the function). `death` id. for the extinction rate. `N` the size of the tree. `Tmax` the age of the root of the tree. `PI` the percentage value of the prediction interval; set this value to 0 to not draw this interval. `scaled` a logical values specifying whether to scale the y-axis between 0 and 1. `eps` a numerical value giving the resolution of the time axis. `add` a logical values specifying whether to make a new plot (the default). `backward` a logical value: should the time axis be traced from the present (the default), or from the root of the tree? `ltt.style` a list with three elements giving the style of the LTT curve with, respectively, the colour (`"col"`), the line thickness (`"lwd"`), and the line type (`"lty"`). `pi.style` id. for the prediction interval. `...` arguments passed to `plot` (e.g., `log="y"`).

### 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 an example).

### References

Hallinan, N. (2012) The generalized time variable reconstructed birth–death process. Journal of Theoretical Biology, 300, 265–276.

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

Paradis, E. (2015) Random phylogenies and the distribution of branching times. Journal of Theoretical Biology, 387, 39–45.

`ltt.plot`

### Examples

```### 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)
## Not run:
### 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)

## End(Not run)
```

[Package ape version 5.5 Index]