This function estimates ancestral character states, and the associated uncertainty, for continuous characters. It mainly works as the ace function, from which it differs, first, in the fact that computations are not performed by numerical optimisation but through matrix calculus. Second, besides classical Brownian-based reconstruction methods, it reconstructs ancestral states under Arithmetic Brownian Motion (ABM, i.e. Brownian with linear trend) and Ornstein-Uhlenbeck process (OU, i.e. Brownian with an attractive optimum).
reconstruct(x, phyInit, method = "ML", alpha = NULL, CI = TRUE)an object of class "ace" with the following elements:
the estimates of the ancestral character values.
the estimated 95% confidence intervals.
if method = "ML", the maximum likelihood estimate
of the Brownian parameter.
if method = "ML", the maximum log-likelihood.
a numerical vector.
an object of class "phylo".
a character specifying the method used for
estimation. Six choices are possible: "ML", "REML",
"GLS", "GLS_ABM", "GLS_OU" or
"GLS_OUS".
a numerical value which accounts for the attractive
strength parameter of "GLS_OU" or "GLS_OUS" (used only
in these cases). If alpha = NULL (the default), then it is estimated
by maximum likelihood using optim which may lead to
convergence issue.
a logical specifying whether to return the 95% confidence intervals of the ancestral state estimates.
Manuela Royer-Carenzi, Gilles Didier
For "ML", "REML" and "GLS", the default model is
Brownian motion. This model can be fitted by maximum likelihood
(method = "ML", Felsenstein 1973, Schluter et al. 1997) - the
default, residual maximum likelihood (method = "REML"), or
generalized least squares (method = "GLS", Martins and Hansen
1997, Garland T and Ives AR 2000).
"GLS_ABM" is based on Brownian motion with trend model. Both
"GLS_OU" and "GLS_OUS" are based on Ornstein-Uhlenbeck
model.
"GLS_OU" and "GLS_OUS" differs in the fact that
"GLS_OUS" assume that the process starts from the optimum,
while the root state has to be estimated for "GLS_OU", which
may rise some issues (see Royer-Carenzi and Didier, 2016). Users may
provide the attractive strength parameter alpha, for these two
models.
"GLS_ABM", "GLS_OU" and "GLS_OUS" are all fitted
by generalized least squares (Royer-Carenzi and Didier, 2016).
Felsenstein, J. (1973) Maximum likelihood estimation of evolutionary trees from continuous characters. American Journal of Human Genetics, 25, 471--492.
Garland T. and Ives A.R. (2000) Using the past to predict the present: confidence intervals for regression equations in phylogenetic comparative methods. American Naturalist, 155, 346--364.
Martins, E. P. and Hansen, T. F. (1997) Phylogenies and the comparative method: a general approach to incorporating phylogenetic information into the analysis of interspecific data. American Naturalist, 149, 646--667.
Royer-Carenzi, M. and Didier, G. (2016) A comparison of ancestral state reconstruction methods for quantitative characters. Journal of Theoretical Biology, 404, 126--142.
Schluter, D., Price, T., Mooers, A. O. and Ludwig, D. (1997) Likelihood of ancestor states in adaptive radiation. Evolution, 51, 1699--1711.
Yang, Z. (2006) Computational Molecular Evolution. Oxford: Oxford University Press.
MPR, corBrownian, compar.ou
Reconstruction of ancestral sequences can be done with the package
phangorn (see function ?ancestral.pml).
### Some random data...
data(bird.orders)
x <- rnorm(23, m=100)
### Reconstruct ancestral quantitative characters:
reconstruct(x, bird.orders)
reconstruct(x, bird.orders, method = "GLS_OUS", alpha=NULL)
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