LTT: Theoretical Lineage-Through Time Plots In ape: Analyses of Phylogenetics and Evolution

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

 ```1 2 3``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```### 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) ```

Example output

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ape documentation built on Sept. 24, 2018, 9:03 a.m.