R: Continuous Character Simulation

rTraitCont {ape} | R Documentation

## Continuous Character Simulation

### Description

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.

### 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.

### Author(s)

Emmanuel Paradis

### 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

`rTraitDisc`, `rTraitMult`, `ace`

### Examples

    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)

[Package ape version 5.1 Index]