kakusan: a computer program to automate the selection of a nucleotide substitution model and the configuration of a mixed model on multilocus data

The application of different substitution models to each gene (a.k.a. mixed model) should be considered in model‐based phylogenetic analysis of multigene sequences. However, a single molecular evolution model is still usually applied. There are no computer programs able to conduct model selection for multiple loci at the same time, though several recently developed types of software for phylogenetic inference can handle mixed model. Here, I have developed computer software named ‘kakusan’ that enables us to solve the above problems. Major running steps are briefly described, and an analysis of results with kakusan is compared to that obtained with other program.     

An asymptotic theory for model selection inference in general semiparametric problems

Hjort & Claeskens (2003) developed an asymptotic theoryfor model selection, model averaging and subsequent inferenceusing likelihood methods in parametric models, along with associatedconfidence statements. In this article, we consider a semiparametricversion of this problem, wherein the likelihood depends on parametersand an unknown function, and model selection/averaging is tobe applied to the parametric parts of the model. We show thatall the results of Hjort & Claeskens hold in the semiparametriccontext, if the Fisher information matrix for parametric modelsis replaced by the semiparametric information bound for semiparametricmodels, and if maximum likelihood estimators for parametricmodels are replaced by semiparametric efficient profile estimators.Our methods of proof employ Le Cam's contiguity lemmas, leadingto transparent results. The results also describe the behaviourof semiparametric model estimators when the parametric componentis misspecified, and also have implications for pointwise-consistentmodel selectors.     

Correlation Between Ka/Ks and Ks is Related to Substitution Model and Evolutionary Lineage

In 2005, Wyckoff and coworkers described a surprisingly strong correlation between Ka/Ks and Ks in several data sets using the LPB93 algorithm. This finding indicated the possibility of a paradigm shift in the way selection strength can be measured using the Ka/Ks ratio. We carried out a calculation of Ka and Ks using six different algorithms on three cross-species orthologous data sets and found a highly variable correlation among the algorithms and lineages. Algorithms based on the GY-HKY substitution model exhibit a weaker positive correlation or a stronger negative correlation than those based on the K2P and JC69 substitution model. Even if one algorithm shows a positive correlation between Ka/Ks and Ks in a warm-blooded lineage, it may show no correlation in a cold-blooded lineage. This algorithm-related and evolutionary lineage-related correlation indicates the need for great caution in drawing conclusions when using only one Ka and Ks algorithm in a genomewide analysis of selection strength. Our results indicated that currently used algorithms for Ka and Ks calculations are flawed and need improvements.     

Kakusan4 and Aminosan: two programs for comparing nonpartitioned, proportional and separate models for combined molecular phylogenetic analyses of multilocus sequence data

Proportional and separate models able to apply different combination of substitution rate matrix (SRM) and among-site rate variation model (ASRVM) to each locus are frequently used in phylogenetic studies of multilocus data. A proportional model assumes that branch lengths are proportional among partitions and a separate model assumes that each partition has an independent set of branch lengths. However, the selection from among nonpartitioned (i.e., a common combination of models is applied to all-loci concatenated sequences), proportional and separate models is usually based on the researcher's preference rather than on any information criteria. This study describes two programs, 'Kakusan4' (for DNA sequences) and 'Aminosan' (for amino-acid sequences), which allow the selection of evolutionary models based on several types of information criteria. The programs can handle both multilocus and single-locus data, in addition to providing an easy-to-use wizard interface and a noninteractive command line interface. In the case of multilocus data, SRMs and ASRVMs are compared at each locus and at all-loci concatenated sequences, after which nonpartitioned, proportional and separate models are compared based on information criteria. The programs also provide model configuration files for mrbayes, paup*, phyml, raxml and Treefinder to support further phylogenetic analysis using a selected model. When likelihoods are optimized by Treefinder, the best-fit models were found to differ depending on the data set. Furthermore, differences in the information criteria among nonpartitioned, proportional and separate models were much larger than those among the nonpartitioned models. These findings suggest that selecting from nonpartitioned, proportional and separate models results in a better phylogenetic tree. Kakusan4 and Aminosan are available at http://www.fifthdimension.jp/. They are licensed under gnugpl Ver.2, and are able to run on Windows, MacOS X and Linux.     

Model selection and estimation in the Gaussian graphical model

We propose penalized likelihood methods for estimating the concentrationmatrix in the Gaussian graphical model. The methods lead toa sparse and shrinkage estimator of the concentration matrixthat is positive definite, and thus conduct model selectionand estimation simultaneously. The implementation of the methodsis nontrivial because of the positive definite constraint onthe concentration matrix, but we show that the computation canbe done effectively by taking advantage of the efficient maxdetalgorithm developed in convex optimization. We propose a BIC-typecriterion for the selection of the tuning parameter in the penalizedlikelihood methods. The connection between our methods and existingmethods is illustrated. Simulations and real examples demonstratethe competitive performance of the new methods.