hsp_empirical_probabilities {castor}

Hidden state prediction via empirical probabilities.

Description

Reconstruct ancestral discrete states of nodes and predict unknown (hidden) states of tips on a tree based on empirical state probabilities across tips. This is a very crude HSP method, and other more sophisticated methods should be preferred (e.g. hsp_mk_model).

Usage

hsp_empirical_probabilities(tree, tip_states, 
                            Nstates=NULL, check_input=TRUE)

Arguments

tree

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

tip_states

An integer vector of size Ntips, specifying the state of each tip in the tree as an integer from 1 to Nstates, where Nstates is the possible number of states (see below). tip_states can include NA to indicate an unknown tip state that is to be predicted.

Nstates

Either NULL, or an integer specifying the number of possible states of the trait. If NULL, then it will be computed based on the maximum non-NA value encountered in tip_states

check_input

Logical, specifying whether to perform some basic checks on the validity of the input data. If you are certain that your input data are valid, you can set this to FALSE to reduce computation.

Details

For this function, the trait's states must be represented by integers within 1,..,Nstates, where Nstates is the total number of possible states. If the states are originally in some other format (e.g. characters or factors), you should map them to a set of integers 1,..,Nstates. You can easily map any set of discrete states to integers using the function map_to_state_space.

Any NA entries in tip_states are interpreted as unknown states. Prior to ancestral state reconstruction, the tree is temporarily prunned, keeping only tips with known state. The function then calculates the empirical state probabilities for each node in the pruned tree, based on the states across tips descending from each node. The state probabilities of tips with unknown state are set to those of the most recent ancestor with reconstructed states, as described by Zaneveld and Thurber (2014).

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). This function has asymptotic time complexity O(Nedges x Nstates).

Tips must be represented in tip_states in the same order as in tree$tip.label. The vector tip_states need not include names; if it does, however, they are checked for consistency (if check_input==TRUE).

This function is meant for reconstructing ancestral states in all nodes of a tree as well as predicting the states of tips with an a priory unknown state. If the state of all tips is known and only ancestral state reconstruction is needed, consider using functions such as asr_empirical_probabilities for improved efficiency.

Value

A list with the following elements:

success

Logical, indicating whether HSP was successful. If FALSE, some return values may be NULL.

likelihoods

A 2D numeric matrix, listing the probability of each tip and node being in each state. This matrix will have (Ntips+Nnodes) rows and Nstates columns, where Nstates was either explicitly provided as an argument or inferred based on the number of unique values in tip_states (if Nstates was passed as NULL). In the latter case, the column names of this matrix will be the unique values found in tip_states. The rows in this matrix will be in the order in which tips and nodes are indexed in the tree, i.e. the rows 1,..,Ntips store the probabilities for tips, while rows (Ntips+1),..,(Ntips+Nnodes) store the probabilities for nodes. Each row in this matrix will sum up to 1. Note that the return value is named this way for compatibility with other HSP functions.

states

Integer vector of length Ntips+Nnodes, with values in {1,..,Nstates}, specifying the maximum-likelihood estimate of the state of each tip & node.

Author(s)

Stilianos Louca

References

J. R. Zaneveld and R. L. V. Thurber (2014). Hidden state prediction: A modification of classic ancestral state reconstruction algorithms helps unravel complex symbioses. Frontiers in Microbiology. 5:431.

See Also

hsp_max_parsimony, hsp_mk_model, map_to_state_space

Examples

## Not run: 
# generate random tree
Ntips = 100
tree = generate_random_tree(list(birth_rate_intercept=1),max_tips=Ntips)$tree

# simulate a discrete trait
Nstates = 5
Q = get_random_mk_transition_matrix(Nstates, rate_model="ER", max_rate=0.1)
tip_states = simulate_mk_model(tree, Q)$tip_states

# print states of first 20 tips
print(tip_states[1:20])

# set half of the tips to unknown state
tip_states[sample.int(Ntips,size=as.integer(Ntips/2),replace=FALSE)] = NA

# reconstruct all tip states via MPR
likelihoods = hsp_empirical_probabilities(tree, tip_states, Nstates)$likelihoods
estimated_tip_states = max.col(likelihoods[1:Ntips,])

# print estimated states of first 20 tips
print(estimated_tip_states[1:20])

## End(Not run)