# rTraitCont

##### Continuous Character Simulation

This function simulates the evolution of a continuous character along a phylogeny. The calculation is done recursively from the root. See Paradis (2012, pp. 232 and 324) for an introduction.

- Keywords
- datagen

##### Usage

```
rTraitCont(phy, model = "BM", sigma = 0.1, alpha = 1, theta = 0,
ancestor = FALSE, root.value = 0, ...)
```

##### Arguments

- phy
an object of class

`"phylo"`

.- model
a character (either

`"BM"`

or`"OU"`

) or a function specifying the model (see details).- sigma
a numeric vector giving the standard-deviation of the random component for each branch (can be a single value).

- alpha
if

`model = "OU"`

, a numeric vector giving the strength of the selective constraint for each branch (can be a single value).- theta
if

`model = "OU"`

, a numeric vector giving the optimum for each branch (can be a single value).- 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
a numeric giving the value at the root.

- …
further arguments passed to

`model`

if it is a function.

##### Details

There are three possibilities to specify `model`

:

`"BM"`

:a Browian motion model is used. If the arguments`sigma`

has more than one value, its length must be equal to the the branches of the tree. This allows to specify a model with variable rates of evolution. You must be careful that branch numbering is done with the tree in ``postorder'' order: to see the order of the branches you can use:`tr <- reorder(tr, "po"); plor(tr); edgelabels()`

. The arguments`alpha`

and`theta`

are ignored.`"OU"`

:an Ornstein-Uhlenbeck model is used. The above indexing rule is used for the three parameters`sigma`

,`alpha`

, and`theta`

. This may be interesting for the last one to model varying phenotypic optima. The exact updating formula from Gillespie (1996) are used which are reduced to BM formula if`alpha = 0`

.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. The arguments`sigma`

,`alpha`

, and`theta`

are ignored.

##### Value

A numeric vector with names taken from the tip labels of
`phy`

. If `ancestor = TRUE`

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

##### References

Gillespie, D. T. (1996) Exact numerical simulation of the
Ornstein-Uhlenbeck process and its integral. *Physical Review E*,
**54**, 2084--2091.

Paradis, E. (2012) *Analysis of Phylogenetics and Evolution with
R (Second Edition).* New York: Springer.

##### See Also

##### Examples

```
# NOT RUN {
data(bird.orders)
rTraitCont(bird.orders) # BM with sigma = 0.1
### OU model with two optima:
tr <- reorder(bird.orders, "postorder")
plot(tr)
edgelabels()
theta <- rep(0, Nedge(tr))
theta[c(1:4, 15:16, 23:24)] <- 2
## sensitive to 'alpha' and 'sigma':
rTraitCont(tr, "OU", theta = theta, alpha=.1, sigma=.01)
### an imaginary model with stasis 0.5 time unit after a node, then
### BM evolution with sigma = 0.1:
foo <- function(x, l) {
if (l <= 0.5) return(x)
x + (l - 0.5)*rnorm(1, 0, 0.1)
}
tr <- rcoal(20, br = runif)
rTraitCont(tr, foo, ancestor = TRUE)
### a cumulative Poisson process:
bar <- function(x, l) x + rpois(1, l)
(x <- rTraitCont(tr, bar, ancestor = TRUE))
plot(tr, show.tip.label = FALSE)
Y <- x[1:20]
A <- x[-(1:20)]
nodelabels(A)
tiplabels(Y)
# }
```

*Documentation reproduced from package ape, version 5.3, License: GPL (>= 2)*