Description

Infers a species network(s) with a specified number of reticulation nodes using maximum pseudo-likelihood. The returned species network(s) will have inferred branch lengths and inheritance probabilities. To find the optimal network, simulated annealing is used. After the search, branch lengths and inheritance probabilities of all top species networks are optimized before being returned. In order to address the identifiability issue caused by the fact that networks are not necessarily encoded by their triplet system, users can ask the program to further optimize those parameters of the inferred network under full likelihood. We use Richard Brent's algorithm (from his book "Algorithms for Minimization without Derivatives", p. 79) to optimize the branch lengths and inheritance probabilities to obtain the maximum (pseudo-) likelihood for that species network. The species network and gene trees must be specified in the Rich Newick Format. 

The inference uses only topologies of gene trees. The input gene trees can be non-binary and can contain missing taxa. The input gene trees can be gene tree distributions inferred from Bayesian methods like MrBayes. See the second example below.

Usage

InferNetwork_MPL geneTreeList numReticulations [-a taxa map] [-b threshold] [-s startingNetwork] [-n numNetReturned] [-h {s1 [,s2...]}] [-w (w1,...,w7)] [-x numRuns] [-m maxNetExamined] [-md moveDiameter] [-rd reticulationDiameter] [-o] [-p (rel,abs)] [-r maxRounds] [-t maxTryPerBr] [-i improveThreshold] [-l maxBL] [-pl numProcessors] [-di] [result output file]

It is mandatory to specify the number of reticulation nodes to added to the starting network. By default, it is assumed that only one individual is sampled per species in gene trees. However, the option [-a taxa map] allows multiple alleles to be sampled. If users have a prior knowledge of the hybrid species, they can specify them using option -h. 

Simulated annealing is used for the search. Option -m allows users to specify the maximum number of networks examined during the search. See Salter and Pearl 2001 for details of settings for simulated annealing. Users can specify the weights of seven operations for network arrangement through option -w. The seven weights correspond to adding a reticulation node, deleting a reticulation node, relocating the head of a reticulation edge, relocating the tail of an edge, reversing the direction of a reticulation edge, replacing a reticulation edge and changing branch lengths and inheritance probabilities, respectively. Furthermore, users can use option -md to specify the maximum move diameter of an operation for network rearrangement, like what local-SPR does. Also, users can use option -rd to specify the maximum reticulation diameter which is the distance (the number of branches) between the two parents of a reticulation node. In order to avoid getting stuck at some local optimum, it is recommended to performed the search multiple times, which users can specify by option -x. The -s option allows the users to specify a starting network (can be a tree) for network search. Then starting from this network, numReticulations number of reticulation nodes will be added during the network search using steepest descent. If the starting network is not specified, the optimal tree under MDC (command infer_ST_MDC) will be used. If it is not binary, a random resolution will be used. By default, the top 5 species networks with optimized branch lengths and inheritance probabilities will be returned. However, users can use -n option to change the number of top species networks being returned. 

By default, the method returns the species networks inferred under maximum pseudo-likelihood. However, networks are not necessarily encoded by their triplet system. To address this issue, users can ask PhyloNet to further analyze those returned species networks by optimizing their branch lengths and inheritance probabilities under full likelihood using option -o. Keep in mind that this feature might not be feasible for large datasets.

We use Richard Brent's algorithm (from his book "Algorithms for Minimization without Derivatives", p. 79) to optimize the branch lengths and inheritance probabilities. Users can use different options to control this process. Option -p allows users to specify the original stopping criterion of Brent's algorithm. More precisely, abs and rel define a tolerance tol = rel |x| + abs. We optimize the branch lengths one by one. For every branch, it terminates when either maxTryPerBr (option -t) trials have been made or the Brent's algorithm suggests so. Users can put an upper bound of the branch lengths through option -l.Optimization of all branch lengths consists of a round. After every round, if the improvement in terms of likelihood score is greater than that from last round by at least improveThreshold (option -i), we starts next round. A maximum of maxRound (option -r) rounds will be tried. 

If users want to run the computation in parallel (in terms of the gene trees). Please specify the number of processors through option -pl.

Examples

#NEXUS

BEGIN TREES;

Tree geneTree1 = ((C,((B,D),A)),E);
Tree geneTree2 = (B,(D,(C,(A,E))));
Tree geneTree3 = (D,(B,((C,E),A)));
Tree geneTree4 = (D,((B,E),(C,A)));

END;


BEGIN PHYLONET;

InferNetwork_MPL (geneTree1,geneTree2,geneTree3,geneTree4) 1;

END;

#NEXUS

BEGIN TREES;

Tree geneTree1 = [&W 0.9] ((C,((B,D),A)),E);
Tree geneTree2 = [&W 0.1] (B,(D,(C,(A,E))));
Tree geneTree3 = [&W 0.6] (D,(B,((C,E),A)));
Tree geneTree4 = [&W 0.4] (D,((B,E),(C,A)));

END;


BEGIN PHYLONET;

InferNetwork_MPL (geneTree1,geneTree2,geneTree3,geneTree4) 1 -o;

END;

Command References

• Y. Yu and L. Nakhleh. A maximum pseudo-likelihood approach for phylogenetic networks. Under review.
  
  
  

See Also

• List of PhyloNet Commands