Locus-aware decomposition of gene trees with respect to polytomous species trees

Background

Horizontal gene transfer (HGT), a process of acquisition and fixation of foreign genetic material, is an important biological phenomenon. Several approaches to HGT inference have been proposed. However, most of them either rely on approximate, non-phylogenetic methods or on the tree reconciliation, which is computationally intensive and sensitive to parameter values.

Results

We investigate the locus tree inference problem as a possible alternative that combines the advantages of both approaches. We present several algorithms to solve the problem in the parsimony framework. We introduce a novel tree mapping, which allows us to obtain a heuristic solution to the problems of locus tree inference and duplication classification.

Conclusions

Our approach allows for faster comparisons of gene and species trees and improves known algorithms for duplication inference in the presence of polytomies in the species trees. We have implemented our algorithms in a software tool available at https://github.com/mciach/LocusTreeInference.

     

Isometric gene tree reconciliation revisited

Background

Isometric gene tree reconciliation is a gene tree/species tree reconciliation problem where both the gene tree and the species tree include branch lengths, and these branch lengths must be respected by the reconciliation. The problem was introduced by Ma et al. in 2008 in the context of reconstructing evolutionary histories of genomes in the infinite sites model.

Results

In this paper, we show that the original algorithm by Ma et al. is incorrect, and we propose a modified algorithm that addresses the problems that we discovered. We have also improved the running time from \(O(N^2)\) to \(O(N\log N)\), where N is the total number of nodes in the two input trees. Finally, we examine two new variants of the problem: reconciliation of two unrooted trees and scaling of branch lengths of the gene tree during reconciliation of two rooted trees.

Conclusions

We provide several new algorithms for isometric reconciliation of trees. Some questions in this area remain open; most importantly extensions of the problem allowing for imprecise estimates of branch lengths.

     

Time-consistent reconciliation maps and forbidden time travel

Background

In the absence of horizontal gene transfer it is possible to reconstruct the history of gene families from empirically determined orthology relations, which are equivalent to event-labeled gene trees. Knowledge of the event labels considerably simplifies the problem of reconciling a gene tree T with a species trees S, relative to the reconciliation problem without prior knowledge of the event types. It is well-known that optimal reconciliations in the unlabeled case may violate time-consistency and thus are not biologically feasible. Here we investigate the mathematical structure of the event labeled reconciliation problem with horizontal transfer.

Results

We investigate the issue of time-consistency for the event-labeled version of the reconciliation problem, provide a convenient axiomatic framework, and derive a complete characterization of time-consistent reconciliations. This characterization depends on certain weak conditions on the event-labeled gene trees that reflect conditions under which evolutionary events are observable at least in principle. We give an \(\mathcal {O}(|V(T)|\log (|V(S)|))\)-time algorithm to decide whether a time-consistent reconciliation map exists. It does not require the construction of explicit timing maps, but relies entirely on the comparably easy task of checking whether a small auxiliary graph is acyclic. The algorithms are implemented in C++ using the boost graph library and are freely available at https://github.com/Nojgaard/tc-recon.

Significance

The combinatorial characterization of time consistency and thus biologically feasible reconciliation is an important step towards the inference of gene family histories with horizontal transfer from orthology data, i.e., without presupposed gene and species trees. The fast algorithm to decide time consistency is useful in a broader context because it constitutes an attractive component for all tools that address tree reconciliation problems.

     

Maximum likelihood models and algorithms for gene tree evolution with duplications and losses

Background

The abundance of new genomic data provides the opportunity to map the location of gene duplication and loss events on a species phylogeny. The first methods for mapping gene duplications and losses were based on a parsimony criterion, finding the mapping that minimizes the number of duplication and loss events. Probabilistic modeling of gene duplication and loss is relatively new and has largely focused on birth-death processes.

Results

We introduce a new maximum likelihood model that estimates the speciation and gene duplication and loss events in a gene tree within a species tree with branch lengths. We also provide an, in practice, efficient algorithm that computes optimal evolutionary scenarios for this model. We implemented the algorithm in the program DrML and verified its performance with empirical and simulated data.

Conclusions

In test data sets, DrML finds optimal gene duplication and loss scenarios within minutes, even when the gene trees contain sequences from several hundred species. In many cases, these optimal scenarios differ from the lca-mapping that results from a parsimony gene tree reconciliation. Thus, DrML provides a new, practical statistical framework on which to study gene duplication.

     

Towards sub-quadratic time and space complexity solutions for the dated tree reconciliation problem

Background

Recent coevolutionary analysis has considered tree topology as a means to reduce the asymptotic complexity associated with inferring the complex coevolutionary interrelationships that arise between phylogenetic trees. Targeted algorithmic design for specific tree topologies has to date been highly successful, with one recent formulation providing a logarithmic space complexity reduction for the dated tree reconciliation problem.

Methods

In this work we build on this prior analysis providing a further asymptotic space reduction, by providing a new formulation for the dynamic programming table used by a number of popular coevolutionary analysis techniques. This model gives rise to a sub quadratic running time solution for the dated tree reconciliation problem for selected tree topologies, and is shown to be, in practice, the fastest method for solving the dated tree reconciliation problem for expected evolutionary trees. This result is achieved through the analysis of not only the topology of the trees considered for coevolutionary analysis, but also the underlying structure of the dynamic programming algorithms that are traditionally applied to such analysis.

Conclusion

The newly inferred theoretical complexity bounds introduced herein are then validated using a combination of synthetic and biological data sets, where the proposed model is shown to provide an \(O(\sqrt{n})\) space saving, while it is observed to run in half the time compared to the fastest known algorithm for solving the dated tree reconciliation problem. What is even more significant is that the algorithm derived herein is able to guarantee the optimality of its inferred solution, something that algorithms of comparable speed have to date been unable to achieve.

     

Biologically feasible gene trees,reconciliation maps and informative triples

Background

The history of gene families—which are equivalent to event-labeled gene trees—can be reconstructed from empirically estimated evolutionary event-relations containing pairs of orthologous, paralogous or xenologous genes. The question then arises as whether inferred event-labeled gene trees are biologically feasible, that is, if there is a possible true history that would explain a given gene tree. In practice, this problem is boiled down to finding a reconciliation map—also known as DTL-scenario—between the event-labeled gene trees and a (possibly unknown) species tree.

Results

In this contribution, we first characterize whether there is a valid reconciliation map for binary event-labeled gene trees T that contain speciation, duplication and horizontal gene transfer events and some unknown species tree S in terms of “informative” triples that are displayed in T and provide information of the topology of S. These informative triples are used to infer the unknown species tree S for T. We obtain a similar result for non-binary gene trees. To this end, however, the reconciliation map needs to be further restricted. We provide a polynomial-time algorithm to decide whether there is a species tree for a given event-labeled gene tree, and in the positive case, to construct the species tree and the respective (restricted) reconciliation map. However, informative triples as well as DTL-scenarios have their limitations when they are used to explain the biological feasibility of gene trees. While reconciliation maps imply biological feasibility, we show that the converse is not true in general. Moreover, we show that informative triples neither provide enough information to characterize “relaxed” DTL-scenarios nor non-restricted reconciliation maps for non-binary biologically feasible gene trees.

     

Anchoring quartet-based phylogenetic distances and applications to species tree reconstruction

Background

Inferring species trees from gene trees using the coalescent-based summary methods has been the subject of much attention, yet new scalable and accurate methods are needed.

Results

We introduce DISTIQUE, a new statistically consistent summary method for inferring species trees from gene trees under the coalescent model. We generalize our results to arbitrary phylogenetic inference problems; we show that two arbitrarily chosen leaves, called anchors, can be used to estimate relative distances between all other pairs of leaves by inferring relevant quartet trees. This results in a family of distance-based tree inference methods, with running times ranging between quadratic to quartic in the number of leaves.

Conclusions

We show in simulated studies that DISTIQUE has comparable accuracy to leading coalescent-based summary methods and reduced running times.

     

Gene tree parsimony for incomplete gene trees: addressing true biological loss

Motivation

Species tree estimation from gene trees can be complicated by gene duplication and loss, and “gene tree parsimony” (GTP) is one approach for estimating species trees from multiple gene trees. In its standard formulation, the objective is to find a species tree that minimizes the total number of gene duplications and losses with respect to the input set of gene trees. Although much is known about GTP, little is known about how to treat inputs containing some incomplete gene trees (i.e., gene trees lacking one or more of the species).

Results

We present new theory for GTP considering whether the incompleteness is due to gene birth and death (i.e., true biological loss) or taxon sampling, and present dynamic programming algorithms that can be used for an exact but exponential time solution for small numbers of taxa, or as a heuristic for larger numbers of taxa. We also prove that the “standard” calculations for duplications and losses exactly solve GTP when incompleteness results from taxon sampling, although they can be incorrect when incompleteness results from true biological loss. The software for the DP algorithm is freely available as open source code at https://github.com/smirarab/DynaDup.

     

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.

     

rDolphin: a GUI R package for proficient automatic profiling of 1D <Superscript>1</Superscript>H-NMR spectra of study datasets

Introduction

Adoption of automatic profiling tools for ¹H-NMR-based metabolomic studies still lags behind other approaches in the absence of the flexibility and interactivity necessary to adapt to the properties of study data sets of complex matrices.

Objectives

To provide an open source tool that fully integrates these needs and enables the reproducibility of the profiling process.

Methods

rDolphin incorporates novel techniques to optimize exploratory analysis, metabolite identification, and validation of profiling output quality.

Results

The information and quality achieved in two public datasets of complex matrices are maximized.

Conclusion

rDolphin is an open-source R package (http://github.com/danielcanueto/rDolphin) able to provide the best balance between accuracy, reproducibility and ease of use.

     

OCTAL: Optimal Completion of gene trees in polynomial time

Background

For a combination of reasons (including data generation protocols, approaches to taxon and gene sampling, and gene birth and loss), estimated gene trees are often incomplete, meaning that they do not contain all of the species of interest. As incomplete gene trees can impact downstream analyses, accurate completion of gene trees is desirable.

Results

We introduce the Optimal Tree Completion problem, a general optimization problem that involves completing an unrooted binary tree (i.e., adding missing leaves) so as to minimize its distance from a reference tree on a superset of the leaves. We present OCTAL, an algorithm that finds an optimal solution to this problem when the distance between trees is defined using the Robinson–Foulds (RF) distance, and we prove that OCTAL runs in \(O(n^2)\) time, where n is the total number of species. We report on a simulation study in which gene trees can differ from the species tree due to incomplete lineage sorting, and estimated gene trees are completed using OCTAL with a reference tree based on a species tree estimated from the multi-locus dataset. OCTAL produces completed gene trees that are closer to the true gene trees than an existing heuristic approach in ASTRAL-II, but the accuracy of a completed gene tree computed by OCTAL depends on how topologically similar the reference tree (typically an estimated species tree) is to the true gene tree.

Conclusions

OCTAL is a useful technique for adding missing taxa to incomplete gene trees and provides good accuracy under a wide range of model conditions. However, results show that OCTAL’s accuracy can be reduced when incomplete lineage sorting is high, as the reference tree can be far from the true gene tree. Hence, this study suggests that OCTAL would benefit from using other types of reference trees instead of species trees when there are large topological distances between true gene trees and species trees.

     

Root fungal colonisations of the understory grass <Emphasis Type="Italic">Deschampsia flexuosa</Emphasis> after top-canopy harvesting

Aims

Root fungal relationships in forest understory may be affected by tree harvesting. Deschampsia flexuosa forms a mutualistic symbiosis with arbuscular mycorrhizal (AM) fungi functioning in nutrient uptake, and a more loose association with dark septate endophytic (DSE) fungi. We asked how harvesting affects fungal colonisations and whether DSE is more prone to change than AM.

Methods

Deschampsia flexuosa plants were sampled close to a control or a cut tree after top-canopy harvesting in a primary successional site. Colonisations were studied using light microscopy. Shoot N%, vegetation cover and soil nutrients were determined.

Results

Tree harvesting did not affect vegetation and soil parameters, except potassium (K⁺) increasing near cut trees. AM colonisation did not change, while DSE increased. Shoot N% increased with increasing DSE near cut trees. Hyaline septate (HSE) hyphae and soil K⁺ and magnesium (Mg²⁺) were positively correlated near control trees. Lichen cover and HSE correlated negatively.

Conclusions

DSE colonisation increased but AM did not change after harvesting. Positive correlation of DSE with shoot N% near cut trees may suggest a role for DSE in favouring plant nitrogen uptake after disturbance in an open microsite. HSE may play a role in K⁺ and Mg²⁺ uptake.

     

A clique-based method for the edit distance between unordered trees and its application to analysis of glycan structures

Background

Measuring similarities between tree structured data is important for analysis of RNA secondary structures, phylogenetic trees, glycan structures, and vascular trees. The edit distance is one of the most widely used measures for comparison of tree structured data. However, it is known that computation of the edit distance for rooted unordered trees is NP-hard. Furthermore, there is almost no available software tool that can compute the exact edit distance for unordered trees.

Results

In this paper, we present a practical method for computing the edit distance between rooted unordered trees. In this method, the edit distance problem for unordered trees is transformed into the maximum clique problem and then efficient solvers for the maximum clique problem are applied. We applied the proposed method to similar structure search for glycan structures. The result suggests that our proposed method can efficiently compute the edit distance for moderate size unordered trees. It also suggests that the proposed method has the accuracy comparative to those by the edit distance for ordered trees and by an existing method for glycan search.

Conclusions

The proposed method is simple but useful for computation of the edit distance between unordered trees. The object code is available upon request.

     

Tree-microbial biomass competition for nutrients in a temperate deciduous forest,central Germany

Aims

Our goals were (1) to determine whether tree species diversity affects nutrient (N, P and K) cycling, and (2) to assess whether there is competition for these nutrients between microbial biomass and trees.

Methods

We measured nutrient resorption efficiency by trees, nutrient contents in leaf litterfall, decomposition rates of leaf litter, nutrient turnover in decomposing leaf litter, and plant-available nutrients in the soil in mono-species stands of beech, oak, hornbeam and lime and in mixed-species stands, each consisting of three of these species.

Results

Cycling of nutrients through leaf litter input and decomposition were influenced by the types of tree species and not simply by tree species diversity. Trees and microbial biomass were competing strongly for P, less for K and only marginally for N. Such competition was most pronounced in mono-species stands of beech and oak, which had low nutrient turnover in their slow decomposing leaf litter, and less in mono-species stands of hornbeam and lime, which had high nutrient turnover in their fast decomposing leaf litter.

Conclusions

The low soil P and K availability in beech stands, which limit the growth of beech at Hainich, Germany, were alleviated by mixing beech with hornbeam and lime. These species-specific effects on nutrient cycling and soil nutrient availability can aid forest management in improving productivity and soil fertility.

     

Resolution effects in reconstructing ancestral genomes

Background

The reconstruction of ancestral genomes must deal with the problem of resolution, necessarily involving a trade-off between trying to identify genomic details and being overwhelmed by noise at higher resolutions.

Results

We use the median reconstruction at the synteny block level, of the ancestral genome of the order Gentianales, based on coffee, Rhazya stricta and grape, to exemplify the effects of resolution (granularity) on comparative genomic analyses.

Conclusions

We show how decreased resolution blurs the differences between evolving genomes, with respect to rate, mutational process and other characteristics.

     

Fine-root growth in a forested bog is seasonally dynamic,but shallowly distributed in nutrient-poor peat

Background and aims

Fine roots contribute to ecosystem carbon, water, and nutrient fluxes through resource acquisition, respiration, exudation, and turnover, but are understudied in peatlands. We aimed to determine how the amount and timing of fine-root growth in a forested, ombrotrophic bog varied across gradients of vegetation density, peat microtopography, and changes in environmental conditions across the growing season and throughout the peat profile.

Methods

We quantified fine-root peak standing crop and growth using non-destructive minirhizotron technology over a two-year period, focusing on the dominant woody species in the bog: Picea mariana, Larix laricina, Rhododendron groenlandicum, and Chamaedaphne calyculata.

Results

The fine roots of trees and shrubs were concentrated in raised hummock microtopography, with more tree roots associated with greater tree densities and a unimodal peak in shrub roots at intermediate tree densities. Fine-root growth tended to be seasonally dynamic, but shallowly distributed, in a thin layer of nutrient-poor, aerobic peat above the growing season water table level.

Conclusions

The dynamics and distribution of fine roots in this forested ombrotrophic bog varied across space and time in response to biological, edaphic, and climatic conditions, and we expect these relationships to be sensitive to projected environmental changes in northern peatlands.