A comparison of phylogenetic network methods using computer simulation

Background

We present a series of simulation studies that explore the relative performance of several phylogenetic network approaches (statistical parsimony, split decomposition, union of maximum parsimony trees, neighbor-net, simulated history recombination upper bound, median-joining, reduced median joining and minimum spanning network) compared to standard tree approaches, (neighbor-joining and maximum parsimony) in the presence and absence of recombination.

Principal Findings

In the absence of recombination, all methods recovered the correct topology and branch lengths nearly all of the time when the substitution rate was low, except for minimum spanning networks, which did considerably worse. At a higher substitution rate, maximum parsimony and union of maximum parsimony trees were the most accurate. With recombination, the ability to infer the correct topology was halved for all methods and no method could accurately estimate branch lengths.

Conclusions

Our results highlight the need for more accurate phylogenetic network methods and the importance of detecting and accounting for recombination in phylogenetic studies. Furthermore, we provide useful information for choosing a network algorithm and a framework in which to evaluate improvements to existing methods and novel algorithms developed in the future.     

Maximum Parsimony on Phylogenetic networks

Background

Phylogenetic networks are generalizations of phylogenetic trees, that are used to model evolutionary events in various contexts. Several different methods and criteria have been introduced for reconstructing phylogenetic trees. Maximum Parsimony is a character-based approach that infers a phylogenetic tree by minimizing the total number of evolutionary steps required to explain a given set of data assigned on the leaves. Exact solutions for optimizing parsimony scores on phylogenetic trees have been introduced in the past.

Results

In this paper, we define the parsimony score on networks as the sum of the substitution costs along all the edges of the network; and show that certain well-known algorithms that calculate the optimum parsimony score on trees, such as Sankoff and Fitch algorithms extend naturally for networks, barring conflicting assignments at the reticulate vertices. We provide heuristics for finding the optimum parsimony scores on networks. Our algorithms can be applied for any cost matrix that may contain unequal substitution costs of transforming between different characters along different edges of the network. We analyzed this for experimental data on 10 leaves or fewer with at most 2 reticulations and found that for almost all networks, the bounds returned by the heuristics matched with the exhaustively determined optimum parsimony scores.

Conclusion

The parsimony score we define here does not directly reflect the cost of the best tree in the network that displays the evolution of the character. However, when searching for the most parsimonious network that describes a collection of characters, it becomes necessary to add additional cost considerations to prefer simpler structures, such as trees over networks. The parsimony score on a network that we describe here takes into account the substitution costs along the additional edges incident on each reticulate vertex, in addition to the substitution costs along the other edges which are common to all the branching patterns introduced by the reticulate vertices. Thus the score contains an in-built cost for the number of reticulate vertices in the network, and would provide a criterion that is comparable among all networks. Although the problem of finding the parsimony score on the network is believed to be computationally hard to solve, heuristics such as the ones described here would be beneficial in our efforts to find a most parsimonious network.     

Efficient parsimony-based methods for phylogenetic network reconstruction

MOTIVATION: Phylogenies--the evolutionary histories of groups of organisms-play a major role in representing relationships among biological entities. Although many biological processes can be effectively modeled as tree-like relationships, others, such as hybrid speciation and horizontal gene transfer (HGT), result in networks, rather than trees, of relationships. Hybrid speciation is a significant evolutionary mechanism in plants, fish and other groups of species. HGT plays a major role in bacterial genome diversification and is a significant mechanism by which bacteria develop resistance to antibiotics. Maximum parsimony is one of the most commonly used criteria for phylogenetic tree inference. Roughly speaking, inference based on this criterion seeks the tree that minimizes the amount of evolution. In 1990, Jotun Hein proposed using this criterion for inferring the evolution of sequences subject to recombination. Preliminary results on small synthetic datasets. Nakhleh et al. (2005) demonstrated the criterion's application to phylogenetic network reconstruction in general and HGT detection in particular. However, the naive algorithms used by the authors are inapplicable to large datasets due to their demanding computational requirements. Further, no rigorous theoretical analysis of computing the criterion was given, nor was it tested on biological data. RESULTS: In the present work we prove that the problem of scoring the parsimony of a phylogenetic network is NP-hard and provide an improved fixed parameter tractable algorithm for it. Further, we devise efficient heuristics for parsimony-based reconstruction of phylogenetic networks. We test our methods on both synthetic and biological data (rbcL gene in bacteria) and obtain very promising results.     

Detecting phylogenetic incongruence using BIONJ: an improvement of the ILD test

The problem of testing for congruence between phylogenetic data has long been debated among phylogeneticists, but reaches a critical point with the availability of large amount of biological sequences. Notably in prokaryotes, where the amount of lateral transfers is believed to be important, the inference of phylogenies using multiple genes requires testing for incongruence before concatenating the genes. On another scale, incongruence tests can be used to detect recombination points within single gene alignments. The incongruence length difference test (ILD), based on parsimony, has been proved to be useful for finding incongruent data sets, but its application remains limited to small data sets for computational time reasons. Here, we have adapted the principle of ILD to the BIONJ algorithm. This algorithm is based on a tree length minimisation criterion and is suitable to replace parsimony in this test when used with uncorrected distance (model-free approach). We show that this new test, ILD-BIONJ, while being much faster, is often more accurate than the ILD test, especially when the alignments compared are simulated under different evolutionary models.     

Statistical Parsimony Networks and Species Assemblages in Cephalotrichid Nemerteans (Nemertea)

Background

It has been suggested that statistical parsimony network analysis could be used to get an indication of species represented in a set of nucleotide data, and the approach has been used to discuss species boundaries in some taxa.

Methodology/Principal Findings

Based on 635 base pairs of the mitochondrial protein-coding gene cytochrome c oxidase I (COI), we analyzed 152 nemertean specimens using statistical parsimony network analysis with the connection probability set to 95%. The analysis revealed 15 distinct networks together with seven singletons. Statistical parsimony yielded three networks supporting the species status of Cephalothrix rufifrons, C. major and C. spiralis as they currently have been delineated by morphological characters and geographical location. Many other networks contained haplotypes from nearby geographical locations. Cladistic structure by maximum likelihood analysis overall supported the network analysis, but indicated a false positive result where subnetworks should have been connected into one network/species. This probably is caused by undersampling of the intraspecific haplotype diversity.

Conclusions/Significance

Statistical parsimony network analysis provides a rapid and useful tool for detecting possible undescribed/cryptic species among cephalotrichid nemerteans based on COI gene. It should be combined with phylogenetic analysis to get indications of false positive results, i.e., subnetworks that would have been connected with more extensive haplotype sampling.     

Reconstructible Phylogenetic Networks: Do Not Distinguish the Indistinguishable

Phylogenetic networks represent the evolution of organisms that have undergone reticulate events, such as recombination, hybrid speciation or lateral gene transfer. An important way to interpret a phylogenetic network is in terms of the trees it displays, which represent all the possible histories of the characters carried by the organisms in the network. Interestingly, however, different networks may display exactly the same set of trees, an observation that poses a problem for network reconstruction: from the perspective of many inference methods such networks are indistinguishable. This is true for all methods that evaluate a phylogenetic network solely on the basis of how well the displayed trees fit the available data, including all methods based on input data consisting of clades, triples, quartets, or trees with any number of taxa, and also sequence-based approaches such as popular formalisations of maximum parsimony and maximum likelihood for networks. This identifiability problem is partially solved by accounting for branch lengths, although this merely reduces the frequency of the problem. Here we propose that network inference methods should only attempt to reconstruct what they can uniquely identify. To this end, we introduce a novel definition of what constitutes a uniquely reconstructible network. For any given set of indistinguishable networks, we define a canonical network that, under mild assumptions, is unique and thus representative of the entire set. Given data that underwent reticulate evolution, only the canonical form of the underlying phylogenetic network can be uniquely reconstructed. While on the methodological side this will imply a drastic reduction of the solution space in network inference, for the study of reticulate evolution this is a fundamental limitation that will require an important change of perspective when interpreting phylogenetic networks.     

A microbial population-species interface: nested cladistic and coalescent inference with multilocus data

Using sequence data from seven nuclear loci in 385 isolates of the haploid, plant parasitic, ascomycete fungus, Sclerotinia, divergence times of populations and of species were distinguished. The evolutionary history of haplotypes on both population and species scales was reconstructed using a combination of parsimony, maximum likelihood and coalescent methods, implemented in a specific order. Analysis of site compatibility revealed recombination blocks from which alternative (marginal) networks were inferred, reducing uncertainty in the network due to recombination. Our own modifications of Templeton and co-workers' cladistic inference method and a coalescent approach detected the same phylogeographic processes. Assuming neutrality and a molecular clock, the boundary between divergent populations and species is an interval of time between coalescence (to a common ancestor) of populations and coalescence of species.     

Parsimony Score of Phylogenetic Networks: Hardness Results and a Linear-Time Heuristic

Phylogenies—the evolutionary histories of groups of organisms—play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set of species can be represented by a binary tree. Although many biological processes can be effectively modeled and summarized in this fashion, others cannot: recombination, hybrid speciation, and horizontal gene transfer result in networks of relationships rather than trees of relationships. In previous works, we formulated a maximum parsimony (MP) criterion for reconstructing and evaluating phylogenetic networks, and demonstrated its quality on biological as well as synthetic data sets. In this paper, we provide further theoretical results as well as a very fast heuristic algorithm for the MP criterion of phylogenetic networks. In particular, we provide a novel combinatorial definition of phylogenetic networks in terms of “forbidden cycles,” and provide detailed hardness and hardness of approximation proofs for the "small” MP problem. We demonstrate the performance of our heuristic in terms of time and accuracy on both biological and synthetic data sets. Finally, we explain the difference between our model and a similar one formulated by Nguyen et al., and describe the implications of this difference on the hardness and approximation results.     

Characterization of phylogenetic networks with NetTest

Background  

Typical evolutionary events like recombination, hybridization or gene transfer make necessary the use of phylogenetic networks to properly depict the evolution of DNA and protein sequences. Although several theoretical classes have been proposed to characterize these networks, they make stringent assumptions that will likely not be met by the evolutionary process. We have recently shown that the complexity of simulated networks is a function of the population recombination rate, and that at moderate and large recombination rates the resulting networks cannot be categorized. However, we do not know whether these results extend to networks estimated from real data.     

ACOHAP: an efficient ant colony optimization for the haplotype inference by pure parsimony problem

Haplotype information plays an important role in many genetic analyses. However, the identification of haplotypes based on sequencing methods is both expensive and time consuming. Current sequencing methods are only efficient to determine conflated data of haplotypes, that is, genotypes. This raises the need to develop computational methods to infer haplotypes from genotypes.Haplotype inference by pure parsimony is an NP-hard problem and still remains a challenging task in bioinformatics. In this paper, we propose an efficient ant colony optimization (ACO) heuristic method, named ACOHAP, to solve the problem. The main idea is based on the construction of a binary tree structure through which ants can travel and resolve conflated data of all haplotypes from site to site. Experiments with both small and large data sets show that ACOHAP outperforms other state-of-the-art heuristic methods. ACOHAP is as good as the currently best exact method, RPoly, on small data sets. However, it is much better than RPoly on large data sets. These results demonstrate the efficiency of the ACOHAP algorithm to solve the haplotype inference by pure parsimony problem for both small and large data sets.     

Characterization of reticulate networks based on the coalescent with recombination

Phylogenetic networks aim to represent the evolutionary history of taxa. Within these, reticulate networks are explicitly able to accommodate evolutionary events like recombination, hybridization, or lateral gene transfer. Although several metrics exist to compare phylogenetic networks, they make several assumptions regarding the nature of the networks that are not likely to be fulfilled by the evolutionary process. In order to characterize the potential disagreement between the algorithms and the biology, we have used the coalescent with recombination to build the type of networks produced by reticulate evolution and classified them as regular, tree sibling, tree child, or galled trees. We show that, as expected, the complexity of these reticulate networks is a function of the population recombination rate. At small recombination rates, most of the networks produced are already more complex than regular or tree sibling networks, whereas with moderate and large recombination rates, no network fit into any of the standard classes. We conclude that new metrics still need to be devised in order to properly compare two phylogenetic networks that have arisen from reticulating evolutionary process.     

Trees and/or networks to display intraspecific DNA sequence variation?

Phylogenetic trees and networks are both used in the scientific literature to display DNA sequence variation at the intraspecific level. Should we rather use trees or networks? I argue that the process of inferring the most parsimonious genealogical relationships among a set of DNA sequences should be dissociated from the problem of displaying this information in a graph. A network graph is probably more appropriate than a strict consensus tree if many alternative, equally most parsimonious, genealogies are to be included. Within the maximum parsimony framework, current phylogenetic inference and network‐building algorithms are both unable to guarantee the finding of all most parsimonious (MP) connections. In fact, each approach can find MP connections that the other does not. Although it should be possible to improve at least the maximum parsimony approach, current implementations of these algorithms are such that it is advisable to use both approaches to increase the probability of finding all possible MP connections among a set of DNA sequences.     

Direct maximum parsimony phylogeny reconstruction from genotype data

Background  

Maximum parsimony phylogenetic tree reconstruction from genetic variation data is a fundamental problem in computational genetics with many practical applications in population genetics, whole genome analysis, and the search for genetic predictors of disease. Efficient methods are available for reconstruction of maximum parsimony trees from haplotype data, but such data are difficult to determine directly for autosomal DNA. Data more commonly is available in the form of genotypes, which consist of conflated combinations of pairs of haplotypes from homologous chromosomes. Currently, there are no general algorithms for the direct reconstruction of maximum parsimony phylogenies from genotype data. Hence phylogenetic applications for autosomal data must therefore rely on other methods for first computationally inferring haplotypes from genotypes.     

Outgroup misplacement and phylogenetic inaccuracy under a molecular clock--a simulation study

We conducted a simulation study of the phylogenetic methods UPGMA, neighbor joining, maximum parsimony, and maximum likelihood for a five-taxon tree under a molecular clock. The parameter space included a small region where maximum parsimony is inconsistent, so we tested inconsistency correction for parsimony and distance correction for neighbor joining. As expected, corrected parsimony was consistent. For these data, maximum likelihood with the clock assumption outperformed each of the other methods tested. The distance-based methods performed marginally better than did maximum parsimony and maximum likelihood without the clock assumption. Data correction was generally detrimental to accuracy, especially for short sequence lengths. We identified another region of the parameter space where, although consistent for a given method, some incorrect trees were each selected with up to twice the frequency of the correct (generating) tree for sequences of bounded length. These incorrect trees are those where the outgroup has been incorrectly placed. In addition to this problem, the placement of the outgroup sequence can have a confounding effect on the ingroup tree, whereby the ingroup is correct when using the ingroup sequences alone, but with the inclusion of the outgroup the ingroup tree becomes incorrect.     

The evolutionary value of recombination is constrained by genome modularity

Genetic recombination is a fundamental evolutionary mechanism promoting biological adaptation. Using engineered recombinants of the small single-stranded DNA plant virus, Maize streak virus (MSV), we experimentally demonstrate that fragments of genetic material only function optimally if they reside within genomes similar to those in which they evolved. The degree of similarity necessary for optimal functionality is correlated with the complexity of intragenomic interaction networks within which genome fragments must function. There is a striking correlation between our experimental results and the types of MSV recombinants that are detectable in nature, indicating that obligatory maintenance of intragenome interaction networks strongly constrains the evolutionary value of recombination for this virus and probably for genomes in general.     

Supervised Lowess normalization of comparative genome hybridization data – application to lactococcal strain comparisons

Background

Visualising the evolutionary history of a set of sequences is a challenge for molecular phylogenetics. One approach is to use undirected graphs, such as median networks, to visualise phylogenies where reticulate relationships such as recombination or homoplasy are displayed as cycles. Median networks contain binary representations of sequences as nodes, with edges connecting those sequences differing at one character; hypothetical ancestral nodes are invoked to generate a connected network which contains all most parsimonious trees. Quasi-median networks are a generalisation of median networks which are not restricted to binary data, although phylogenetic information contained within the multistate positions can be lost during the preprocessing of data. Where the history of a set of samples contain frequent homoplasies or recombination events quasi-median networks will have a complex topology. Graph reduction or pruning methods have been used to reduce network complexity but some of these methods are inapplicable to datasets in which recombination has occurred and others are procedurally complex and/or result in disconnected networks.

Results

We address the problems inherent in construction and reduction of quasi-median networks. We describe a novel method of generating quasi-median networks that uses all characters, both binary and multistate, without imposing an arbitrary ordering of the multistate partitions. We also describe a pruning mechanism which maintains at least one shortest path between observed sequences, displaying the underlying relations between all pairs of sequences while maintaining a connected graph.

Conclusion

Application of this approach to 5S rDNA sequence data from sea beet produced a pruned network within which genetic isolation between populations by distance was evident, demonstrating the value of this approach for exploration of evolutionary relationships.     

Inferring domain-domain interactions from protein-protein interactions in the complex network conformation

Background

As protein domains are functional and structural units of proteins, a large proportion of protein-protein interactions (PPIs) are achieved by domain-domain interactions (DDIs), many computational efforts have been made to identify DDIs from experimental PPIs since high throughput technologies have produced a large number of PPIs for different species. These methods can be separated into two categories: deterministic and probabilistic. In deterministic methods, parsimony assumption has been utilized. Parsimony principle has been widely used in computational biology as the evolution of the nature is considered as a continuous optimization process. In the context of identifying DDIs, parsimony methods try to find a minimal set of DDIs that can explain the observed PPIs. This category of methods are promising since they can be formulated and solved easily. Besides, researches have shown that they can detect specific DDIs, which is often hard for many probabilistic methods. We notice that existing methods just view PPI networks as simply assembled by single interactions, but there is now ample evidence that PPI networks should be considered in a global (systematic) point of view for it exhibits general properties of complex networks, such as 'scale-free' and 'small-world'.

Results

In this work, we integrate this global point of view into the parsimony-based model. Particularly, prior knowledge is extracted from these global properties by plausible reasoning and then taken as input. We investigate the role of the added information extensively through numerical experiments. Results show that the proposed method has improved performance, which confirms the biological meanings of the extracted prior knowledge.

Conclusions

This work provides us some clues for using these properties of complex networks in computational models and to some extent reveals the biological meanings underlying these general network properties.

     

DTL reconciliation repair

Background

Maximum parsimony phylogenetic tree reconciliation is an important technique for reconstructing the evolutionary histories of hosts and parasites, genes and species, and other interdependent pairs. Since the problem of finding temporally feasible maximum parsimony reconciliations is NP-complete, current methods use either exact algorithms with exponential worst-case running time or heuristics that do not guarantee optimal solutions.

Results

We offer an efficient new approach that begins with a potentially infeasible maximum parsimony reconciliation and iteratively “repairs” it until it becomes temporally feasible.

Conclusions

In a non-trivial number of cases, this approach finds solutions that are better than those found by the widely-used Jane heuristic.

     

Inferring angiosperm phylogeny from EST data with widespread gene duplication

Background

Most studies inferring species phylogenies use sequences from single copy genes or sets of orthologs culled from gene families. For taxa such as plants, with very high levels of gene duplication in their nuclear genomes, this has limited the exploitation of nuclear sequences for phylogenetic studies, such as those available in large EST libraries. One rarely used method of inference, gene tree parsimony, can infer species trees from gene families undergoing duplication and loss, but its performance has not been evaluated at a phylogenomic scale for EST data in plants.

Results

A gene tree parsimony analysis based on EST data was undertaken for six angiosperm model species and Pinus, an outgroup. Although a large fraction of the tentative consensus sequences obtained from the TIGR database of ESTs was assembled into homologous clusters too small to be phylogenetically informative, some 557 clusters contained promising levels of information. Based on maximum likelihood estimates of the gene trees obtained from these clusters, gene tree parsimony correctly inferred the accepted species tree with strong statistical support. A slight variant of this species tree was obtained when maximum parsimony was used to infer the individual gene trees instead.

Conclusion

Despite the complexity of the EST data and the relatively small fraction eventually used in inferring a species tree, the gene tree parsimony method performed well in the face of very high apparent rates of duplication.

     

Bayesian estimation of genomic distance

We present a Bayesian approach to the problem of inferring the number of inversions and translocations separating two species. The main reason for developing this method is that it will allow us to test hypotheses about the underlying mechanisms, such as the distribution of inversion track lengths or rate constancy among lineages. Here, we apply these methods to comparative maps of eggplant and tomato, human and cat, and human and cattle with 170, 269, and 422 markers, respectively. In the first case the most likely number of events is larger than the parsimony value. In the last two cases the parsimony solutions have very small probability.