simulate_ou_model {castor}

Simulate an Ornstein-Uhlenbeck model for continuous trait evolution.

Description

Given a rooted phylogenetic tree and an Ornstein-Uhlenbeck (OU) model for the evolution of a continuous (numeric) trait, simulate random outcomes of the model on all nodes and/or tips of the tree. The function traverses nodes from root to tips and randomly assigns a state to each node or tip based on its parent's previously assigned state and the specified model parameters. The generated states have joint distributions consistent with the OU model. Optionally, multiple independent simulations can be performed using the same model.

Usage

simulate_ou_model(tree, stationary_mean, stationary_std, decay_rate,
                  include_tips=TRUE, include_nodes=TRUE, 
                  Nsimulations=1, drop_dims=TRUE)

Arguments

tree

A rooted tree of class "phylo". The root is assumed to be the unique node with no incoming edge.

stationary_mean

Numeric. The mean (center) of the stationary distribution of the OU model.

stationary_std

Positive numeric. The standard deviation of the stationary distribution of the OU model.

decay_rate

Positive numeric. Exponential decay rate (stabilization rate) of the OU model (in units 1/edge_length_units).

include_tips

Include random states for the tips. If FALSE, no states will be returned for tips.

include_nodes

Include random states for the nodes. If FALSE, no states will be returned for nodes.

Nsimulations

Number of random independent simulations to perform. For each node and/or tip, there will be Nsimulations random states generated.

drop_dims

Logical, specifying whether the returned tip_states and node_states (see below) should be vectors, if Nsimulations==1. If drop_dims==FALSE, then tip_states and tip_nodes will always be 2D matrices.

Details

For each simulation, the state of the root is picked randomly from the stationary distribution of the OU model, i.e. from a normal distribution with mean = stationary_mean and standard deviation = stationary_std.

If tree$edge.length is missing, each edge in the tree is assumed to have length 1. The tree may include multi-furcations (i.e. nodes with more than 2 children) as well as mono-furcations (i.e. nodes with only one child). The asymptotic time complexity of this function is O(Nedges*Nsimulations), where Nedges is the number of edges in the tree.

Value

A list with the following elements:

tip_states

Either NULL (if include_tips==FALSE), or a 2D numeric matrix of size Nsimulations x Ntips, where Ntips is the number of tips in the tree. The [r,c]-th entry of this matrix will be the state of tip c generated by the r-th simulation. If drop_dims==TRUE and Nsimulations==1, then tip_states will be a vector.

node_states

Either NULL (if include_nodes==FALSE), or a 2D numeric matrix of size Nsimulations x Nnodes, where Nnodes is the number of nodes in the tree. The [r,c]-th entry of this matrix will be the state of node c generated by the r-th simulation. If drop_dims==TRUE and Nsimulations==1, then node_states will be a vector.

Author(s)

Stilianos Louca

See Also

simulate_bm_model, simulate_mk_model, simulate_rou_model

Examples

# generate a random tree
tree = generate_random_tree(list(birth_rate_intercept=1),max_tips=10000)$tree

# simulate evolution of a continuous trait
tip_states = simulate_ou_model( tree, 
                                stationary_mean = 10, 
                                stationary_std = 1, 
                                decay_rate = 0.1)$tip_states

# plot histogram of simulated tip states
hist(tip_states, breaks=20, xlab="state", main="Trait probability distribution", prob=TRUE)