The stationary variance of an Ornstein-Uhlenbeck process

Description

This function returns the stationary variance for an Ornstein-Uhlenbeck process (object of class "ou").

Usage

stationary(object)

Arguments

Details

This function computes the dispersion parameter of the Ornstein-Uhlenbeck process (i.e., the expected variance when the process is stationary). The multivariate normal stationary distribution of the Ornstein-Uhlenbeck process is computed following Bartoszek et al. (2012).

Value

The stationary variance-covariance matrix of the OU process

Author(s)

Julien Clavel

References

Bartoszek K., Pienaar J., Mostad P., Andersson S., Hansen T.F. 2012. A phylogenetic comparative method for studying multivariate adaptation. J. Theor. Biol. 314:204-215.

See Also

mvMORPH mvOU halflife

Examples

# Simulated dataset
set.seed(14)
# Generating a random tree
tree<-pbtree(n=50)

# Setting the regime states of tip species
sta<-as.vector(c(rep("Forest",20),rep("Savannah",30))); names(sta)<-tree$tip.label

# Making the simmap tree with mapped states
tree<-make.simmap(tree,sta , model="ER", nsim=1)
col<-c("blue","orange"); names(col)<-c("Forest","Savannah")

# Plot of the phylogeny for illustration
plotSimmap(tree,col,fsize=0.6,node.numbers=FALSE,lwd=3, pts=FALSE)

# Simulate the traits
alpha<-matrix(c(2,0.5,0.5,1),2)
sigma<-matrix(c(0.1,0.05,0.05,0.1),2)
theta<-c(2,3,1,1.3)
data<-mvSIM(tree, param=list(sigma=sigma, alpha=alpha, ntraits=2, theta=theta,
            names_traits=c("head.size","mouth.size")), model="OUM", nsim=1)

## Fitting the models
# OUM - Analysis with multiple optima
result<-mvOU(tree, data)

stationary(result)

# Expected values when the process is stationary
expected<-list(alpha=alpha,sigma=sigma)
class(expected)<-c("mvmorph","mvmorph.ou")
stationary(expected)

Results