R: Theoretical Lineage-Through Time Plots

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).

### Author(s)

Emmanuel Paradis

### 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.

### See Also

`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 5.6 Index]