ouqoumodel: Simulate traits under ouqou model given a set of parameters
In ouxy: Model of Adaptive Trait Evolution

Description Usage Arguments Details Value References Examples

Simulate traits under ouqou model given a set of model parameters, regression parameters, tree and ancestral values.

1	ouqoumodel(model.params, reg.params, root = root, tree = tree)

`model.params`	A vector of model parameters including alpha.y: force parameter of response trait, alpha.x: force parameter of covariate, theta.x: optimum parameter of covariate, sigmasq.x: rate parameter of covariate and tau rate parameter of response trait
`reg.params`	A vector of regression paramters including b0: intercept parameter of regression, b1: slope parameter of first covariate, b2: slope paramter of the second covariate
`root`	A vector of numerical values for root of species estimated from `OUprior`
`tree`	An ape: tree object stored in phylo format

The model requires user to input model parameters α_y,α_x,θ_x, σ^2_x,τ and regression parameters b_0,b_1,b_2, a tree object, trait dataset (one response, two covariate), ancestral values(root) which is estimated by BM or OU model from geiger. Then the algorithm starts from the root and apply the tree traversal algorithm to simulate trait on each node according the ouqou dynamics.

Returns the trait vectors Y=(y_1,y_2,\cdots,y_n)', X_1=(x_{1,1},x_{1.2},\cdots,x_{1,n})',X_2=(x_{2,1},x_{2,2},\cdots,x_{2,n})' simulated from the model.

Jhwueng, D-C. (2019) Statistical modeling for adaptive trait evolution. Under review.
Jhwueng, D-C., and Vasileios Maroulas. "Adaptive trait evolution in random environment." Journal of Applied Statistics 43.12 (2016): 2310-2324.
Hansen, Thomas F., Jason Pienaar, and Steven Hecht Orzack. "A comparative method for studying adaptation to a randomly evolving environment." Evolution: International Journal of Organic Evolution 62.8 (2008): 1965-1977.

library(ape)
tree<-rcoal(5)
tree<-reorder(tree,"postorder")
root<-list(y.ou.sigmsq=1 ,y.ou.root=0, x1.ou.root=0, x2.ou.root=0,x1.bm.root=0, x2.bm.root=0)
model.params<-c(0.5,0.25,0,1,0.2)
names(model.params)<-c("alpha.y","alpha.x","theta.x","sigmasq.x","tau")
reg.params<-c(0,1,1)
names(reg.params)<-c("b0","b1","b2")
ouqoumodel(model.params,reg.params,root=root,tree=tree)