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In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

Recurrent neural networks with memory and attention mechanisms are widely used in natural language processing because they can capture short and long term sequential information for diverse tasks. We propose an integrated deep learning model for microbial DNA sequence data, which exploits convolutional neural networks, recurrent neural networks, and attention mechanisms to predict taxonomic classifications and sample-associated attributes, such as the relationship between the microbiome and host phenotype, on the read/sequence level. In this paper, we develop this novel deep learning approach and evaluate its application to amplicon sequences. We apply our approach to short DNA reads and full sequences of 16S ribosomal RNA (rRNA) marker genes, which identify the heterogeneity of a microbial community sample. We demonstrate that our implementation of a novel attention-based deep network architecture, Read2Pheno, achieves read-level phenotypic prediction. Training Read2Pheno models will encode sequences (reads) into dense, meaningful representations: learned embedded vectors output from the intermediate layer of the network model, which can provide biological insight when visualized. The attention layer of Read2Pheno models can also automatically identify nucleotide regions in reads/sequences which are particularly informative for classification. As such, this novel approach can avoid pre/post-processing and manual interpretation required with conventional approaches to microbiome sequence classification. We further show, as proof-of-concept, that aggregating read-level information can robustly predict microbial community properties, host phenotype, and taxonomic classification, with performance at least comparable to conventional approaches. An implementation of the attention-based deep learning network is available at https://github.com/EESI/sequence_attention (a python package) and https://github.com/EESI/seq2att (a command line tool)., Author summary Microbiomes are communities of microscopic organisms found everywhere, including on and in the human body. For example, the gut microbiome plays an important role in digestion, and changes in composition are associated with changes in health or disease, e.g., inflammatory bowel disease (IBD). Today, microbiome composition is often obtained from high-throughput sequencing, which generates many short DNA reads from multiple organisms in a sample. In this paper, we present a novel deep learning framework, Read2Pheno, to predict phenotype from all the reads in a set of biological samples. An attention mechanism allows visualization of specific subregions (sets of bases) which are important in classifying the reads according to phenotype or taxon labels. We evaluate the framework on sequencing data for 16S rRNA genes, genetic markers used to identify microbial taxonomy. We show that Read2Pheno performs comparably as conventional methods on three distinct data sets from the American Gut Project, IBD patients and controls, and a comprehensive taxonomic database. Moreover, Read2Pheno results can be readily interpreted—e.g., to identify regions of the 16S rRNA gene to target for PCR diagnostics—without additional pre/post-processing steps that can introduce complexity and error.

Stochastic models of biomolecular reaction networks are commonly employed in systems and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. For such models, the Kolmogorov’s forward equation is called the chemical master equation (CME), and it is a fundamental system of linear ordinary differential equations (ODEs) that describes the evolution of the probability distribution of the random state-vector representing the copy-numbers of all the reacting species. The size of this system is given by the number of states that are accessible by the chemical system, and for most examples of interest this number is either very large or infinite. Moreover, approximations that reduce the size of the system by retaining only a finite number of important chemical states (e.g. those with non-negligible probability) result in high-dimensional ODE systems, even when the number of reacting species is small. Consequently, accurate numerical solution of the CME is very challenging, despite the linear nature of the underlying ODEs. One often resorts to estimating the solutions via computationally intensive stochastic simulations. The goal of the present paper is to develop a novel deep-learning approach for computing solution statistics of high-dimensional CMEs by reformulating the stochastic dynamics using Kolmogorov’s backward equation. The proposed method leverages superior approximation properties of Deep Neural Networks (DNNs) to reliably estimate expectations under the CME solution for several user-defined functions of the state-vector. This method is algorithmically based on reinforcement learning and it only requires a moderate number of stochastic simulations (in comparison to typical simulation-based approaches) to train the “policy function”. This allows not just the numerical approximation of various expectations for the CME solution but also of its sensitivities with respect to all the reaction network parameters (e.g. rate constants). We provide four examples to illustrate our methodology and provide several directions for future research., Author summary We develop a deep learning framework for estimating solutions of the chemical master equation (CME) that is fundamental to stochastic analysis of reaction networks. The CME is a system of ordinary differential equations that describes the time-evolution of the probability density of the random state-vector, and owing to an inherent curse of dimensionality, directly solving the CME is generally impractical with existing approaches. Moreover, the commonly employed simulation-based approaches for estimating CME solutions often require an exorbitant amount of computational time, even for moderately-sized networks. To counter these issues, we develop a deep reinforcement learning based method, called DeepCME, in this paper. DeepCME not only estimates function expectations based on the CME solution, but it also solves the more challenging problem of estimating their sensitivities with respect to all the model parameters. We illustrate our approach with four carefully chosen reaction network examples with varying sizes. Our results demonstrate that DeepCME reliably estimates the expectations of interest, along with all the parametric sensitivities, at a fraction of the computational cost of simulation-based estimators. We present many directions for future research and suggest further improvements to DeepCME that can greatly enhance its accuracy and applicability.

High-throughput data such as metabolomics, genomics, transcriptomics, and proteomics have become familiar data types within the “-omics” family. For this work, we focus on subsets that interact with one another and represent these “pathways” as graphs. Observed pathways often have disjoint components, i.e., nodes or sets of nodes (metabolites, etc.) not connected to any other within the pathway, which notably lessens testing power. In this paper we propose the Pathway Integrated Regression-based Kernel Association Test (PaIRKAT), a new kernel machine regression method for incorporating known pathway information into the semi-parametric kernel regression framework. This work extends previous kernel machine approaches. This paper also contributes an application of a graph kernel regularization method for overcoming disconnected pathways. By incorporating a regularized or “smoothed” graph into a score test, PaIRKAT can provide more powerful tests for associations between biological pathways and phenotypes of interest and will be helpful in identifying novel pathways for targeted clinical research. We evaluate this method through several simulation studies and an application to real metabolomics data from the COPDGene study. Our simulation studies illustrate the robustness of this method to incorrect and incomplete pathway knowledge, and the real data analysis shows meaningful improvements of testing power in pathways. PaIRKAT was developed for application to metabolomic pathway data, but the techniques are easily generalizable to other data sources with a graph-like structure., Author summary PaIRKAT is a tool for improving testing power on high dimensional data by including graph topography in the kernel machine regression setting. Studies on high-dimensional data can struggle to include the complex relationships between variables. The semi-parametric kernel machine regression model is a powerful tool for capturing these types of relationships. They provide a framework for testing for relationships between outcomes of interest and high dimensional data such as metabolomic, genomic, or proteomic pathways. Our paper proposes a kernel machine method for including known biological connections between high dimensional variables by representing them as edges of ‘graphs’ or ‘networks.’ It is common for nodes (e.g., metabolites) to be disconnected from all others within the graph, which leads to meaningful decreases in testing power when graph information is ignored. We include a graph regularization or ‘smoothing’ approach for managing this issue. We demonstrate the benefits of this approach through simulation studies and an application to the metabolomic data from the COPDGene study.

Read-depths (RDs) are frequently used in identifying structural variants (SVs) from sequencing data. For existing RD-based SV callers, it is difficult for them to determine breakpoints in single-nucleotide resolution due to the noisiness of RD data and the bin-based calculation. In this paper, we propose to use the deep segmentation model UNet to learn base-wise RD patterns surrounding breakpoints of known SVs. We integrate model predictions with an RD-based SV caller to enhance breakpoints in single-nucleotide resolution. We show that UNet can be trained with a small amount of data and can be applied both in-sample and cross-sample. An enhancement pipeline named RDBKE significantly increases the number of SVs with more precise breakpoints on simulated and real data. The source code of RDBKE is freely available at https://github.com/yaozhong/deepIntraSV., Author summary In this paper, we used the deep segmentation model UNet to alleviate the bin size limitation of RD-based SV callers. UNet was initially proposed for image data. Here, we demonstrated that the UNet model could also be applied for one-dimensional genomic data. We formalized the breakpoint prediction as a segmentation task and inferred breakpoints in single-nucleotide resolution from predicted label marks. Through a set of experiments on both simulated and real WGS data, we demonstrated that the UNet model could be trained with a small amount of data, and an enhancement pipeline called RDBKE significantly increased the number of SVs with more precise breakpoints.

The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of mutational robustness and bistability. Living systems have developed their functions through evolutionary processes. To understand the particularities of this process theoretically, evolutionary simulation (ES) alone is insufficient because the outcomes of ES depend on evolutionary pathways. We need a reference system for comparison. An appropriate reference system for this purpose is an ensemble of the randomly sampled genotypes. However, generating high-fitness genotypes by simple random sampling is difficult because such genotypes are rare. In this study, we used the multicanonical Monte Carlo method developed in statistical physics to construct a reference ensemble of GRNs and compared it with the outcomes of ES. We obtained the following results. First, mutational robustness was significantly higher in ES than in the reference ensemble at the same fitness level. Second, the emergence of a new phenotype, bistability, was delayed in evolution. Third, the bistable group of GRNs contains many mutationally fragile GRNs compared with those in the non-bistable group. This suggests that the delayed emergence of bistability is a consequence of the mutation-selection mechanism., Comment: 14 pages, 12 figures

Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks., Author summary Biological systems display a remarkable diversity of functionalities, many of which can be conceived as the response of a large network composed of small interconnecting modules. Unravelling the connection pattern, i.e. design principles, behind important biological functionalities is one of the most challenging problems in systems biology. One such phenomenon is perfect adaptation, which merits special attention owing to its universal presence ranging from chemotaxis in bacterial cells to calcium homeostasis in mammalian cells. The present work focuses on finding the design principles for perfect adaptation in the presence of a stair-case type disturbance. To this end, the current work proposes a systems-theoretic approach to deduce precise mathematical (hence structural) conditions that comply with the key performance parameters for adaptation. The approach is agnostic to the particularities of the reaction kinetics, underlining the dominant role of the topological structure on the response of the network. Notably, the design principles obtained in this work serve as the most strict necessary structural conditions for a network of any size to provide perfect adaptation.

Working memory is a cognitive function involving the storage and manipulation of latent information over brief intervals of time, thus making it crucial for context-dependent computation. Here, we use a top-down modeling approach to examine network-level mechanisms of working memory, an enigmatic issue and central topic of study in neuroscience. We optimize thousands of recurrent rate-based neural networks on a working memory task and then perform dynamical systems analysis on the ensuing optimized networks, wherein we find that four distinct dynamical mechanisms can emerge. In particular, we show the prevalence of a mechanism in which memories are encoded along slow stable manifolds in the network state space, leading to a phasic neuronal activation profile during memory periods. In contrast to mechanisms in which memories are directly encoded at stable attractors, these networks naturally forget stimuli over time. Despite this seeming functional disadvantage, they are more efficient in terms of how they leverage their attractor landscape and paradoxically, are considerably more robust to noise. Our results provide new hypotheses regarding how working memory function may be encoded within the dynamics of neural circuits., Author summary The ability to remember information for brief periods of time before using it is a key human ability. For example, retaining a phone number for a few moments prior to entering it into a keypad. Such ability, known as working memory, enables many more complex functions such as planning and reasoning. In this paper, we use theory and computational modeling approaches to try and better understand how circuits and networks in the brain might be achieving working memory. Specifically, we construct hypothetical network models to perform a task that embodies essential aspects of working memory. We then dissect our model to reveal how its components—simulated neural units—interact with each other to represent and maintain information. It turns out that some models can achieve memory by maintaining a fixed representation over time, i.e., the units remain ‘still’ during memory. However, other models fluctuate their activity during memory in a particular way that is seemingly quite efficient and less susceptible to distraction. In total, our computational study provides new theory for how this form of memory might be implemented in brain networks.

© 2021 Moore et al., Bioinformatics training is required at every stage of a scientist’s research career. Continual bioinformatics training allows exposure to an ever-changing and growing repertoire of techniques and databases, and so biologists, computational scientists, and healthcare practitioners are all seeking learning opportunities in the use of computational resources and tools designed for data storage, retrieval, and analysis. There are abundant opportunities for accessing bioinformatics training for scientists in high-income countries (HICs), with well-equipped facilities and participants and trainers requiring minimal travel and financial costs alongside a range of general advice for developing short bioinformatics training courses [1–3]. However, regionally targeted bioinformatics training in low- and middle-income countries (LMICs) often requires more extensive local and external support, organization, and travel. Due to the limited expertise in bioinformatics in LMICs in general, most bioinformatics training requires a fair amount of collaboration with experts beyond the local community, country, or region. A common model of training, used as the basis of this article, includes a local host collaborating with local, regional, and international experts gathering to train local or regional participants. Recently, there has been a growth of capacity strengthening initiatives in LMICs, such as the Pan African Bioinformatics Network for Human Heredity and Health in Africa (H3ABioNet) Initiative [4–6], the Capacity Building for Bioinformatics in Latin America (CABANA) Project [7], the Asia Pacific BioInformatics Network (APBioNet) [8], and the Wellcome Connecting Science Courses and Conferences program [9]. One of the important strands of these initiatives is a drive to organize and deliver valuable bioinformatics training, but organizing and delivering short bioinformatics training workshops in an LMIC present a unique set of challenges. This paper attempts to build upon the sage advice for organizing bioinformatics workshops with specific guidance for organizing and delivering them in LMICs. It describes the processes to follow in organizing courses taking into consideration the low-resource setting. We should also note that LMICs are not a monolithic group and that setting, context, temporality, and specific location matters. LMICs are a complex regional grouping [10] and should be treated as such; however, we will present some common lessons that we hope will help organizers and trainers of bioinformatics training events in LMICs to navigate the often different, challenging, and rewarding experience., The authors who contributed to this manuscript are funded as follows: BM receives salary support from Wellcome Trust grants [WT108749/Z/15/Z, WT108749/Z/15/A], PC, VR, NM, AG’s salaries are funded in whole, or in part, by the NIH Common Fund H3ABioNet grant [U24HG006941], MC, SLFV, AR, PG, PCL’s salaries were partly funded by the UKRI-BBSRC ‘Capacity building for bioinformatics in Latin America’ (CABANA) grant, on behalf of the Global Challenges Research Fund [BB/P027849/1], JDLR is funded by ISCiii AES [ref. PI18/00591] at the CSIC/USAL (Spain) and by CYTED, RIABIO (Red Iberoamericana 521RT0118), AM’s salary is funded by [WT206194/Z/17/Z], GO is funded by the CABANA grant and SM is funded by the EMBL-EBI.

Decision-making about pandemic mitigation often relies upon simulation modelling. Models of disease transmission through networks of contacts--between individuals or between population centres--are increasingly used for these purposes. Real-world contact networks are rich in structural features that influence infection transmission, such as tightly-knit local communities that are weakly connected to one another. In this paper, we propose a new flow-based edge-betweenness centrality method for detecting bottleneck edges that connect nodes in contact networks. In particular, we utilize convex optimization formulations based on the idea of diffusion with p-norm network flow. Using simulation models of COVID-19 transmission through real network data at both individual and county levels, we demonstrate that targeting bottleneck edges identified by the proposed method reduces the number of infected cases by up to 10% more than state-of-the-art edge-betweenness methods. Furthermore, the proposed method is orders of magnitude faster than existing methods., Comment: 38 pages, 21 figures

The origin of life involved complicated evolutionary processes. Computer modeling is a promising way to reveal relevant mechanisms. However, due to the limitation of our knowledge on prebiotic chemistry, it is usually difficult to justify parameter-setting for the modeling. Thus, typically, the studies were conducted in a reverse way: the parameter-space was explored to find those parameter values “supporting” a hypothetical scene (that is, leaving the parameter-justification a later job when sufficient knowledge is available). Exploring the parameter-space manually is an arduous job (especially when the modeling becomes complicated) and additionally, difficult to characterize as regular “Methods” in a paper. Here we show that a machine-learning-like approach may be adopted, automatically optimizing the parameters. With this efficient parameter-exploring approach, the evolutionary modeling on the origin of life would become much more powerful. In particular, based on this, it is expected that more near-reality (complex) models could be introduced, and thereby theoretical research would be more tightly associated with experimental investigation in this field–hopefully leading to significant steps forward in respect to our understanding on the origin of life., Author summary People have long been interested in the evolutionary processes through which life on our planet could have arisen from a non-life background. However, it seems that experimental studies in this field are proceeding slowly, perhaps owing to the complication of such processes. In the meantime, computer modeling has shown its potential to disclose the evolutionary mechanisms involved. Now a major difficulty of the computer modeling work is to justify the parameter-setting–on account of our limited knowledge on prebiotic chemistry and environments. Thus, people tend to explore the parameter space to seek parameter values in favor of the hypothetic scene and leave the parameter-justification a later job when sufficient knowledge is available. To date, the parameter-exploration is usually conducted manually (in many cases by trial and error), thus arduous and unpredictable. Inspired by the algorithm of machine-learning, we designed an automatic approach of parameter-exploration. The results showed that the approach is quite effective–that is, “good” parameter-sets in favor of hypothetic scenes in the origin of life can be found automatically. It is expected that such a machine-learning-like method would greatly enhance the efficiency of our evolutionary modeling studies on the origin of life in future.

Machine learning algorithms, including recent advances in deep learning, are promising for tools for detection and classification of broadband high frequency signals in passive acoustic recordings. However, these methods are generally data-hungry and progress has been limited by challenges related to the lack of labeled datasets adequate for training and testing. Large quantities of known and as yet unidentified broadband signal types mingle in marine recordings, with variability introduced by acoustic propagation, source depths and orientations, and interacting signals. Manual classification of these datasets is unmanageable without an in-depth knowledge of the acoustic context of each recording location. A signal classification pipeline is presented which combines unsupervised and supervised learning phases with opportunities for expert oversight to label signals of interest. The method is illustrated with a case study using unsupervised clustering to identify five toothed whale echolocation click types and two anthropogenic signal categories. These categories are used to train a deep network to classify detected signals in either averaged time bins or as individual detections, in two independent datasets. Bin-level classification achieved higher overall precision (>99%) than click-level classification. However, click-level classification had the advantage of providing a label for every signal, and achieved higher overall recall, with overall precision from 92 to 94%. The results suggest that unsupervised learning is a viable solution for efficiently generating the large, representative training sets needed for applications of deep learning in passive acoustics., Author summary Machine learning algorithms have proven to be effective for tools for detection and classification tasks in many fields, however, these processes are generally data-hungry and their use in marine acoustics has been limited by a lack of large labeled datasets for algorithms to learn from. In underwater acoustic recordings, many signals generated by animals, human activities and physical processes mingle together, and their sounds can change depending on ocean temperatures, locations, and behavior. Manual classification of these datasets is unmanageable without an in-depth knowledge of the acoustic context of each recording location. This paper presents a process which combines unsupervised and supervised learning phases and expert oversight to generate and use large datasets for acoustic classification of marine mammal and human-generated signals. Unsupervised learning is used to automatically generate the large training datasets needed to teach a supervised learning algorithm to correctly classify seven different signal types commonly recorded in the Southern California Bight. Using this process, researchers with large unlabeled acoustic datasets can begin to take advantage of widespread advances in machine learning.

There has been a spate of interest in association networks in biological and medical research, for example, genetic interaction networks. In this paper, we propose a novel method, the extended joint hub graphical lasso (EDOHA), to estimate multiple related interaction networks for high dimensional omics data across multiple distinct classes. To be specific, we construct a convex penalized log likelihood optimization problem and solve it with an alternating direction method of multipliers (ADMM) algorithm. The proposed method can also be adapted to estimate interaction networks for high dimensional compositional data such as microbial interaction networks. The performance of the proposed method in the simulated studies shows that EDOHA has remarkable advantages in recognizing class-specific hubs than the existing comparable methods. We also present three applications of real datasets. Biological interpretations of our results confirm those of previous studies and offer a more comprehensive understanding of the underlying mechanism in disease., Author summary Reconstruction of multiple association networks from high dimensional omics data is an important topic, especially in biology. Previous studies focused on estimating different networks and detecting common hubs among all classes. Integration of information over different classes of data while allowing the difference in the hub nodes is also biologically plausible. Therefore, we propose a method, EDOHA, to jointly construct multiple interaction networks with the capacity in finding different hub networks for each class of data. Simulation studies show better performance over conventional methods. The method has been demonstrated in three real-world data.

8 pages.-- This is an open access article distributed under the terms of the Creative Commons Attribution License, A recent paper published in PLOS Computational Biology [1] introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the possibility of determining the values of the parameters (identifiability) and states (observability) of a dynamic model by observing its output. In this note we warn that SIM considers scaling symmetries as the only possible cause of non-identifiability and non-observability. We show that other types of symmetries can cause the same problems without being detected by SIM, and that in those cases the method may lead one to conclude that the model is identifiable and observable when it is actually not, AFV has received funding from a Ramón y Cajal Fellowship (RYC-2019-027537-I) and from the Spanish Ministry of Science, Innovation and Universities and the European Union FEDER under project grant SYNBIOCONTROL (DPI2017-82896-C2-2-R). GM was funded by the CSIC intramural project grant MOEBIUS (PIE 202070E062)

A current strategy for obtaining haplotype information from several individuals involves short-read sequencing of pooled amplicons, where fragments from each individual is identified by a unique DNA barcode. In this paper, we report a new method to recover the phylogeny of haplotypes from short-read sequences obtained using pooled amplicons from a mixture of individuals, without barcoding. The method, AFPhyloMix, accepts an alignment of the mixture of reads against a reference sequence, obtains the single-nucleotide-polymorphisms (SNP) patterns along the alignment, and constructs the phylogenetic tree according to the SNP patterns. AFPhyloMix adopts a Bayesian inference model to estimate the phylogeny of the haplotypes and their relative abundances, given that the number of haplotypes is known. In our simulations, AFPhyloMix achieved at least 80% accuracy at recovering the phylogenies and relative abundances of the constituent haplotypes, for mixtures with up to 15 haplotypes. AFPhyloMix also worked well on a real data set of kangaroo mitochondrial DNA sequences., Author summary In evolutionary studies, it is customary to obtain homologous sequences from different individuals in a population or a species to construct a phylogeny. Frequently, sequences from different individuals will be identical; we refer to a set of identical sequences as a haplotype. If short-read sequencing technologies are used to obtain sequences from many individuals, the sequence from each individual is tagged with a unique barcode, and a mixed sample of tagged sequences is subsequently sequenced. The tagged sequences can be identified using the appropriate bioinformatics tools, for further downstream analyses. We have developed a novel method, AFPhyloMix, to reconstruct the phylogeny of a mixed sample of homologous sequences, and the relative abundance of different haplotypes, from different individuals without the need for barcoding. AFPhyloMix aligns the short reads obtained to a reference alignment, and identifies the variable sites along the alignment. On the basis of the patterns of nucleotide frequencies at these and neighbouring sites, AFPhyloMix uses a Bayesian inference model to compute the phylogenetic tree and the haplotype relative abundances. Our results show that AFPhyloMix works well on both the simulated data set and the real data set.