Description

Infers a species network(s) with a specified number of reticulation nodes using maximum likelihood. The returned species network(s) will have inferred branch lengths and inheritance probabilities. To find the optimal network, simulated annealing is used. During the search, branch lengths and inheritance probabilities of a species network are sampled instead of optimized. After the search, users can ask the program to further optimize those parameters of the inferred network. In this case, 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 likelihood for that species network. The species network and gene trees must be specified in the Rich Newick Format. 

The inference can be made using only topologies of gene trees, or using both topologies and branch lengths of gene trees. The latter one requires the input gene trees to be ultrametric.

The input gene trees can be gene tree distributions inferred from Bayesian methods like MrBayes. See the second example below.

Usage

InferNetwork_ML geneTreeList numReticulations [-a taxa map] [-bl] [-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, the inference uses only the topologies of gene trees, however, users can also use both topologies and branch lengths of the gene trees to do the inference, by specifying option -bl. 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, only the first optimal species network will be returned. However, users can use -n option to ask for multiple optimal networks. 

By default, the method returns the species networks found by the search whose branch lengths and inheritance probabilities are sampled. However, if users want to see the species network with the optimized branch lengths and inheritance probabilities, along with its likelihood, users can use option -o. Then for every network the program returns, 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_ML (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_ML (geneTree1,geneTree2,geneTree3,geneTree4) 1;

END;

#NEXUS

BEGIN TREES;

Tree geneTree1 = ((C:3,((B:1,D:1):1,A:2):1):1,E:4);
Tree geneTree2 = (B:4,(D:3,(C:2,(A:1,E:1):1):1):1);
Tree geneTree3 = (D:4,(B:3,((C:1,E:1):1,A:2):1):1);
Tree geneTree4 = (D:3,((B:1,E:1):1,(C:1,A:1):1):1);

END;


BEGIN PHYLONET;

InferNetwork_ML (geneTree1,geneTree2,geneTree3,geneTree4) 1 -bl;

END;

Command References

• Y. Yu, N. Ristic and L. Nakhleh. Fast algorithms and Heuristics for Phylogenomics under hybridization and incomplete lineage sorting.  BMC Bioinformatics, vol. 14, no. Suppl 15, p. S6, 2013.

• Y. Yu, J. Dong, K. Liu, and L. Nakhleh, Maximum Likelihood Inference of Reticulate Evolutionary Histories, Proceedings of the National Academy of Sciences, vol. 111, no. 46, pp. 16448-16453, 2014.

  
  
  

See Also

• List of PhyloNet Commands