# rTraitDisc

##### Discrete Character Simulation

This function simulates the evolution of a discrete character along a
phylogeny. If `model`

is a character or a matrix, evolution is
simulated with a Markovian model; the transition probabilities are
calculated for each branch with \(P = e^{Qt}\) where \(Q\) is the
rate matrix given by `model`

and \(t\) is the branch length.
The calculation is done recursively from the root. See Paradis (2006,
p. 101) for a general introduction applied to evolution.

- Keywords
- datagen

##### Usage

```
rTraitDisc(phy, model = "ER", k = if (is.matrix(model)) ncol(model) else 2,
rate = 0.1, states = LETTERS[1:k], freq = rep(1/k, k),
ancestor = FALSE, root.value = 1, ...)
```

##### Arguments

- phy
an object of class

`"phylo"`

.- model
a character, a square numeric matrix, or a function specifying the model (see details).

- k
the number of states of the character.

- rate
the rate of change used if

`model`

is a character; it is*not*recycled if`model = "ARD"`

of`model = "SYM"`

.- states
the labels used for the states; by default ``A'', ``B'', …

- freq
a numeric vector giving the equilibrium relative frequencies of each state; by default the frequencies are equal.

- ancestor
a logical value specifying whether to return the values at the nodes as well (by default, only the values at the tips are returned).

- root.value
an integer giving the value at the root (by default, it's the first state). To have a random value, use

`root.value = sample(k)`

.- …
further arguments passed to

`model`

if it is a function.

##### Details

There are three possibilities to specify `model`

:

A matrix:it must be a numeric square matrix; the diagonal is always ignored. The arguments

`k`

and`rate`

are ignored.A character:these are the same short-cuts than in the function

`ace`

:`"ER"`

is an equal-rates model,`"ARD"`

is an all-rates-different model, and`"SYM"`

is a symmetrical model. Note that the argument`rate`

must be of the appropriate length, i.e., 1, \(k(k - 1)\), or \(k(k - 1)/2\) for the three models, respectively. The rate matrix \(Q\) is then filled column-wise.A function:it must be of the form

`foo(x, l)`

where`x`

is the trait of the ancestor and`l`

is the branch length. It must return the value of the descendant as an integer.

##### Value

A factor with names taken from the tip labels of `phy`

. If
`ancestor = TRUE`

, the node labels are used if present,
otherwise, ``Node1'', ``Node2'', etc.

##### References

Paradis, E. (2006) *Analyses of Phylogenetics and Evolution with
R.* New York: Springer.

##### See Also

##### Examples

```
# NOT RUN {
data(bird.orders)
### the two followings are the same:
rTraitDisc(bird.orders)
rTraitDisc(bird.orders, model = matrix(c(0, 0.1, 0.1, 0), 2))
### two-state model with irreversibility:
rTraitDisc(bird.orders, model = matrix(c(0, 0, 0.1, 0), 2))
### simple two-state model:
tr <- rcoal(n <- 40, br = runif)
x <- rTraitDisc(tr, ancestor = TRUE)
plot(tr, show.tip.label = FALSE)
nodelabels(pch = 19, col = x[-(1:n)])
tiplabels(pch = 19, col = x[1:n])
### an imaginary model with stasis 0.5 time unit after a node, then
### random evolution:
foo <- function(x, l) {
if (l < 0.5) return(x)
sample(2, size = 1)
}
tr <- rcoal(20, br = runif)
x <- rTraitDisc(tr, foo, ancestor = TRUE)
plot(tr, show.tip.label = FALSE)
co <- c("blue", "yellow")
cot <- c("white", "black")
Y <- x[1:20]
A <- x[-(1:20)]
nodelabels(A, bg = co[A], col = cot[A])
tiplabels(Y, bg = co[Y], col = cot[Y])
# }
```

*Documentation reproduced from package ape, version 4.1, License: GPL (>= 2)*