If \code{type = "continuous"}, the default model is Brownian motion
where characters evolve randomly following a random walk. This model
can be fitted by residual maximum likelihood (the default), maximum
- likelihood (Schluter et al. 1997), least squares (\code{method =
- "pic"}, Felsenstein 1985), or generalized least squares (\code{method
- = "GLS"}, Martins and Hansen 1997, Cunningham et al. 1998). In the
- last case, the specification of \code{phy} and \code{model} are
- actually ignored: it is instead given through a correlation structure
- with the option \code{corStruct}.
+ likelihood (Felsenstein 1973, Schluter et al. 1997), least squares
+ (\code{method = "pic"}, Felsenstein 1985), or generalized least
+ squares (\code{method = "GLS"}, Martins and Hansen 1997, Cunningham et
+ al. 1998). In the last case, the specification of \code{phy} and
+ \code{model} are actually ignored: it is instead given through a
+ correlation structure with the option \code{corStruct}.
In the setting \code{method = "ML"} and \code{model = "BM"} (this used
- to be the default until ape 3.0-7) the maximum likelihood estimation
- is done simultaneously on the ancestral values and the variance of the
- Brownian motion process; these estimates are then used to compute the
- confidence intervals in the standard way. The REML method first
- estimates the ancestral value at the root (aka, the phylogenetic
- mean), then the variance of the Brownian motion process is estimated
- by optimizing the residual log-likelihood. The ancestral values are
- finally inferred from the likelihood function giving these two
- parameters. If \code{method = "pic"} or \code{"GLS"}, the confidence
- intervals are computed using the expected variances under the model,
- so they depend only on the tree.
+ to be the default until \pkg{ape} 3.0-7) the maximum likelihood
+ estimation is done simultaneously on the ancestral values and the
+ variance of the Brownian motion process; these estimates are then used
+ to compute the confidence intervals in the standard way. The REML
+ method first estimates the ancestral value at the root (aka, the
+ phylogenetic mean), then the variance of the Brownian motion process
+ is estimated by optimizing the residual log-likelihood. The ancestral
+ values are finally inferred from the likelihood function giving these
+ two parameters. If \code{method = "pic"} or \code{"GLS"}, the
+ confidence intervals are computed using the expected variances under
+ the model, so they depend only on the tree.
It could be shown that, with a continous character, REML results in
unbiased estimates of the variance of the Brownian motion process
an equal-rates model (e.g., the first and third examples above),
\code{"ARD"} is an all-rates-different model (the second example), and
\code{"SYM"} is a symmetrical model (e.g., \code{matrix(c(0, 1, 2, 1,
- 0, 3, 2, 3, 0), 3)}). If a short-cut is used, the number of states
- is determined from the data.
+ 0, 3, 2, 3, 0), 3)}). If a short-cut is used, the number of states is
+ determined from the data.
With discrete characters it is necessary to compute the exponential of
the rate matrix. By default (and the only possible choice until
reappraisal. \emph{Trends in Ecology & Evolution}, \bold{13},
361--366.
+ Felsenstein, J. (1973) Maximum likelihood estimation
+ of evolutionary trees from continuous characters. \emph{American Journal of Human Genetics}, \bold{25}, 471--492.
+
Felsenstein, J. (1985) Phylogenies and the comparative
method. \emph{American Naturalist}, \bold{125}, 1--15.