Simulate multivariate Ornstein-Uhlenbeck evolutionary sequence data sets

Function to simulate a multivariate Ornstein-Uhlenbeck evolutionary sequence data set.

Usage

sim.multi.OU(
  ns = 30,
  anc = c(0, 0),
  optima = c(3, 2),
  A = matrix(c(7, 0, 0, 6), nrow = 2, byrow = TRUE),
  R = matrix(c(0.05, 0, 0, 0.05), nrow = 2, byrow = TRUE),
  vp = 0.1,
  nn = rep(30, ns),
  tt = 0:(ns - 1)
)

Arguments

ns

number of samples in time-series

anc

the ancestral trait values

optima

the optimal trait values

A

the pull matrix.

R

the drift matrix

vp

within-population trait variance

nn

vector of the number of individuals in each sample (identical sample sizes for all time-series is assumed)

tt

vector of sample ages, increases from oldest to youngest

Value

A multivariate evolutionary sequence (time-series) data set.

Note

The Ornstein Uhlenbeck model is reduced to an Unbiased Random Walk when the alpha parameter is zero. It is therefore possible to let a trait evolve as an Unbiased Random Walk by setting the diagonal element for that trait to a value close to zero (e.g. 1e-07). Elements in the diagonal of A cannot be exactly zero as this will result in a singular variance-covariance matrix.

Author

Kjetil Lysne Voje

Examples

##Define the A and R matrices

A_matrix<-matrix(c(4,-2,0,3), nrow=2, byrow = TRUE)
R_matrix<-matrix(c(4,0.2,0.2,4), nrow=2, byrow = TRUE)

## Generate an evoTS object by simulating a multivariate dataset
data_set<-sim.multi.OU(40, optima = c(1.5,2),A=A_matrix , R = R_matrix)

## plot the data
plotevoTS.multivariate(data_set)