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.

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

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.

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.

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.

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.

# 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) # }