Description Usage Arguments Details Value Author(s) References See Also Examples
Fits the Ornstein-Uhlenbeck-based Hansen model to data.
The fitting is done using optim
or subplex
.
1 2 3 4 |
data |
Phenotypic data for extant species, i.e., species at the terminal twigs of the phylogenetic tree.
This can either be a single named numeric vector, a list of |
tree |
A phylogenetic tree, specified as an |
regimes |
A vector of codes, one for each node in the tree, specifying the selective regimes hypothesized to have been operative.
Corresponding to each node, enter the code of the regime hypothesized for the branch segment terminating in that node.
For the root node, because it has no branch segment terminating on it, the regime specification is irrelevant.
If there are |
sqrt.alpha, sigma |
These are used to initialize the optimization algorithm. The selection strength matrix alpha and the random drift variance-covariance matrix sigma^2 are parameterized by their matrix square roots. Specifically, these initial guesses are each packed into lower-triangular matrices (column by column). The product of this matrix with its transpose is the alpha or sigma^2 matrix. See Details, below. |
fit |
If |
method |
The method to be used by the optimization algorithm, |
hessian |
If |
... |
Additional arguments will be passed as |
The Hansen model for the evolution of a multivariate trait X along a lineage can be written as a stochastic differential equation (Ito diffusion)
dX = alpha (theta(t)-X(t)) dt + sigma dB(t),
where t is time along the lineage, theta(t) is the optimum trait value, B(t) is a standard Wiener process (Brownian motion), and alpha and sigma are matrices quantifying, respectively, the strength of selection and random drift. Without loss of generality, one can assume sigma is lower-triangular. This is because only the infinitesimal variance-covariance matrix sigma^2 = sigma%*%transpose(sigma) is identifiable, and for any admissible variance-covariance matrix, we can choose sigma to be lower-triangular. Moreover, if we view the basic model as describing evolution on a fitness landscape, then alpha will be symmetric and if we further restrict ourselves to the case of stabilizing selection, alpha will be positive definite as well. We make these assumptions and therefore can assume that the matrix alpha has a lower-triangular square root.
The hansen
code uses unconstrained numerical optimization to maximize the likelihood.
To do this, it parameterizes the alpha and sigma^2 matrices in a special way:
each matrix is parameterized by nchar*(nchar+1)/2
parameters, where nchar
is the number of quantitative characters.
Specifically, the parameters initialized by the sqrt.alpha
argument of hansen
are used to fill the nonzero entries of a lower-triangular matrix (in column-major order), which is then multiplied by its transpose to give the selection-strength matrix.
The parameters specified in sigma
fill the nonzero entries in the lower triangular sigma matrix.
When hansen
is executed, the numerical optimizer maximizes the likelihood over these parameters.
The print
, show
, and summary
methods for the resulting hansentree
object display (among other things) the estimated alpha and sigma^2 matrices.
The coef
method extracts a named list containing not only these matrices (given as the alpha.matrix
and sigma.sq.matrix
elements) but also the MLEs returned by the optimizer (as sqrt.alpha
and sigma
, respectively).
The latter elements should not be interpreted, but can be used to restart the algorithm, etc.
hansen
returns an object of class hansentree
.
For details on the methods of that class, see hansentree
.
Aaron A. King <kingaa at umich dot edu>
Butler, M.A. and A.A. King (2004) Phylogenetic comparative analysis: a modeling approach for adaptive evolution. American Naturalist 164:683-695.
ouchtree
, hansentree
, optim
, bimac
, anolis.ssd
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 | ## Not run:
if (require(geiger)) {
### an example data set (Darwin's finches)
data(geospiza)
str(geospiza)
sapply(geospiza,class)
### check the correspondence between data and tree tips:
print(nc <- with(geospiza,name.check(geospiza.tree,geospiza.data)))
### looks like one of the terminal twigs has no data associated
### drop that tip:
tree <- with(geospiza,drop.tip(geospiza.tree,nc$tree_not_data))
dat <- as.data.frame(geospiza$dat)
### make an ouchtree out of the phy-format tree
ot <- ape2ouch(tree)
### merge data with tree info
otd <- as(ot,"data.frame")
### in these data, it so happens that the rownames correspond to node names
### we will exploit this correspondence in the 'merge' operation:
dat$labels <- rownames(dat)
otd <- merge(otd,dat,by="labels",all=TRUE)
rownames(otd) <- otd$nodes
print(otd)
### this data-frame now contains the data as well as the tree geometry
### now remake the ouch tree
ot <- with(otd,ouchtree(nodes=nodes,ancestors=ancestors,times=times,labels=labels))
b1 <- brown(tree=ot,data=otd[c("tarsusL","beakD")])
summary(b1)
### evaluate an OU model with a single, global selective regime
otd$regimes <- as.factor("global")
h1 <- hansen(
tree=ot,
data=otd[c("tarsusL","beakD")],
regimes=otd["regimes"],
sqrt.alpha=c(1,0,1),
sigma=c(1,0,1),
maxit=10000
)
summary(h1)
}
## End(Not run)
|
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