phylolm (version 2.1)

phylolm: Phylogenetic Linear Model

Description

Fits a phylogenetic linear regression model. The likelihood is calculated with an algorithm that is linear in the number of tips in the tree.

Usage

phylolm(formula, data = list(), phy, model = c("BM", "OUrandomRoot",
       "OUfixedRoot", "lambda", "kappa", "delta", "EB", "trend"),
       lower.bound = NULL, upper.bound = NULL, 
       starting.value = NULL, ...)

Arguments

formula

a model formula.

data

a data frame containing variables in the model. If not found in data, the variables are taken from current environment.

phy

a phylogenetic tree of type phylo with branch lengths.

model

a model for the covariance (see Details).

lower.bound

optional lower bound for the optimization of the phylogenetic model parameter.

upper.bound

optional upper bound for the optimization of the phylogenetic model parameter.

starting.value

optional starting value for the optimization of the phylogenetic model parameter.

...

further arguments to be passed to the function optim.

Value

• coefficients
  the named vector of coefficients.
• sigma2
  the maximum likelihood estimate of the variance rate $\sigma^2$.
• optpar
  the optimized value of the phylogenetic correlation parameter (alpha, lambda, kappa, delta or rate).
• logLik
  the maximum of the log likelihood.
• p
  the number of all parameters of the model.
• aic
  AIC value of the model.
• vcov
  covariance matrix for the regression coefficients, given the phylogenetic correlation parameter (if any).
• fitted.values
  fitted values
• residuals
  raw residuals
• y
  response
• n
  number of observations (tips in the tree)
• d
  number of dependent variables
• mean.tip.height
  mean root-to-tip distance, which can help choose good starting values for the correlation parameter.
• formula
  the model formula
• call
  the original call to the function
• model
  the phylogenetic model for the covariance

encoding

latin1

Details

This function uses an algorithm that is linear in the number of tips in the tree to calculate the likelihood. Possible phylogenetic models for the error term are the Brownian motion model (BM), the Ornstein-Uhlenbeck model with an ancestral state to be estimated at the root (OUfixedRoot), the Ornstein-Uhlenbeck model with the ancestral state at the root having the stationary distribution (OUrandomRoot), Pagel's $\lambda$ model (lambda), Pagel's $\kappa$ model (kappa), Pagel's $\delta$ model (delta), the early burst model (EB), and the Brownian motion model with a trend (trend).

By default, the bounds on the phylogenetic parameters are $[10^{-7}/T,50/T]$ for $\alpha$, $[10^{-7},1]$ for $\lambda$, $[10^{-6},1]$ for $\kappa$, $[10^{-5},3]$ for $\delta$ and $[-3/T,0]$ for rate, where $T$ is the mean root-to-tip distance.

References

Ho, L. S. T. and An�, C. "A linear-time algorithm for Gaussian and non-Gaussian trait evolution models". Systematic Biology 63(3):397-408.

Butler, M. A. and King, A. A. 2004. "Phylogenetic comparative analysis: A modeling approach for adaptive evolution". The American Naturalist 164:683-695.

Hansen, T. F. 1997. "Stabilizing selection and the comparative analysis of adaptation". Evolution 51:1341-1351.

Harmon, L. J. et al. 2010. "Early bursts of body size and shape evolution are rare in comparative data". Evolution 64:2385-2396.

Ho, L. S. T. and An�, C. "Asymptotic theory with hierarchical autocorrelation: Ornstein-Uhlenbeck tree models". The Annals of Statistics 41(2):957-981.

Pagel, M. 1997. "Inferring evolutionary processes from phylogenies". Zoologica Scripta 26:331-348.

Pagel, M. 1999. "Inferring the historical patterns of biological evolution". Nature 401:877-884.

See Also

corBrownian, corMartins, corPagel, fitContinuous, pgls.

Examples

set.seed(123456)
tre = rcoal(60)
taxa = sort(tre$tip.label)
b0=0; b1=1;
x <- rTrait(n=1, phy=tre,model="BM",
            parameters=list(ancestral.state=0,sigma2=10))
y <- b0 + b1*x + 
     rTrait(n=1,phy=tre,model="lambda",parameters=list(
              ancestral.state=0,sigma2=1,lambda=0.5))
dat = data.frame(trait=y[taxa],pred=x[taxa])
fit = phylolm(trait~pred,data=dat,phy=tre,model="lambda")
summary(fit)