Phylogenetic conservation prioritization with uncertainty

We consider a set of species S and are interested in the assessment of the subsets of S from a phylogenetic diversity viewpoint. Several measures can be used for this assessment. Here we have retained phylogenetic diversity (PD) in the sense of Faith, a measure widely used to reflect the evolutionary history accumulated by a group of species. The PD of a group of species X included in S is easy to calculate when the phylogenetic tree associated with S is perfectly known but this situation is rarely verified. We are interested here in cases where uncertainty regarding the length of branches and the topology of the tree is reflected in the fact that several phylogenetic trees are considered to be plausible for the set S. We propose several measures of the phylogenetic diversity to take account of the uncertainty arising from this situation. A natural problem in the field of biological conservation is to select the best subset of species to protect from a group of threatened species. Here, the best subset is the one that optimizes the proposed measures. We show how to solve these optimal selection problems by integer linear programming. The approach is illustrated by several examples.     

Phylogenetic analysis of some Neogene phasianid genera (Aves: Phasianidae)

Phylogenetic analysis based on osteological characters of some Neogene and Recent phasianids is performed. Phylogenetic tree shows close relationships of Plioperdix with Ammoperdix and Tologuica with Excalfactoria. Chauvireria is at the base of the clade (Alectoris + (Coturnix + (Excalfactoria + Tologuica))). Palaeoperdix is relatively close to the lineage of large pheasants.     

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.

     

Distribution and abundance of a keystone tree, <Emphasis Type="Italic">Schinziophyton rautanenii</Emphasis>, and factors affecting its structure in Zambia,southern Africa

Schinziophyton rautanenii is a keystone tree species whose fruits are eaten by wildlife and livestock, nuts are used to extract oil for human use and its wood is used for making curios that are sold to tourists. The species occurs in southern African countries of Angola, Namibia, Botswana, Mozambique, Zambia, Zimbabwe and the Democratic Republic of Congo but little is known about its population and conservation status. The objectives of this study were to (i) assess factors determining the distribution and abundance of the species in Zambia, (ii) evaluate its regeneration potential and population status and (iii) assess whether the main determinants of forest and species stand structures also favour S. rautanenii. The study is based on three forest surveys conducted in 2004, 2005–2008 and 2015. In Zambia S. rautanenii abundance and population structure are controlled by soil, climate and human factors. The species is most abundant in southwest Zambia where population recruitment is good but is rare and recruitment is poor elsewhere in the country. Fire appears to be a major cause of tree damage and possibly death. The elephant is a major disperser of S. rautanenii nuts and the low recruitment levels in the country may partly be attributed to the decline in the elephant population from about 250,000 in 1960 to 28,000 in 2008. Different conservation strategies will be required for areas where the species is rare and for those where the species is abundant. Whatever the strategies, it will be important to address issues of fire management, fruit harvesting and the role of wildlife in the conservation of S. rautanenii in Zambia.     

Enumeration of Viral Capsid Assembly Pathways: Tree Orbits Under Permutation Group Action

This paper uses combinatorics and group theory to answer questions about the assembly of icosahedral viral shells. Although the geometric structure of the capsid (shell) is fairly well understood in terms of its constituent subunits, the assembly process is not. For the purpose of this paper, the capsid is modeled by a polyhedron whose facets represent the monomers. The assembly process is modeled by a rooted tree, the leaves representing the facets of the polyhedron, the root representing the assembled polyhedron, and the internal vertices representing intermediate stages of assembly (subsets of facets). Besides its virological motivation, the enumeration of orbits of trees under the action of a finite group is of independent mathematical interest. If G is a finite group acting on a finite set X, then there is a natural induced action of G on the set \(\mathcal{T}_{X}\) of trees whose leaves are bijectively labeled by the elements of X. If G acts simply on X, then |X|:=|X _n |=n?|G|, where n is the number of G-orbits in X. The basic combinatorial results in this paper are (1) a formula for the number of orbits of each size in the action of G on \(\mathcal{T}_{X_{n}}\), for every n, and (2) a simple algorithm to find the stabilizer of a tree \(\tau\in\mathcal{T} _{X}\) in G that runs in linear time and does not need memory in addition to its input tree. These results help to clarify the effect of symmetry on the probability and number of assembly pathways for icosahedral viral capsids, and more generally for any finite, symmetric macromolecular assembly.     

Taxonomy and pathogenicity of <Emphasis Type="Italic">Leptographium</Emphasis> species associated with <Emphasis Type="Italic">Ips subelongatus</Emphasis> infestations of <Emphasis Type="Italic">Larix</Emphasis> spp. in northern China,including two new species

The larch bark beetle (Ips subelongatus), which occurs in larch plantations over a vast area of eastern Asia, infects both dying and fallen trees. When its population reaches a high density, the beetle may also infect healthy trees, resulting in tree decline and, eventually, death. Leptographium spp., in both their sexual and asexual states, are mainly associated with conifer-infesting bark beetles; some species are important tree pathogens. The aims of this study were to identify the Leptographium spp. associated with I. subelongatus infestations of Larix spp. in northern China and to examine their pathogenicity towards the tree. Morphological studies and phylogenetic approaches based on multilocus DNA sequence data (ITS2- partial r28S, partial β-tubulin, and EF-1α gene regions) showed that three Leptographium species occur in association with I. subelongatus in the areas investigated: Leptographium taigense, which is recorded in China for the first time, and two new species, namely L. innermongolicum sp. nov. and L. zhangii sp. nov. Leptographium innermongolicum is closely related to L. taigense, whereas L. zhangii belongs to the Grosmannia piceaperda species complex. The pathogenicity of these Leptographium species towards mature Larix spp. was tested by stem inoculation in forests. All inoculations only resulted in small lesions on the inner bark; therefore, the three Leptographium species were not considered to be pathogenic.     

Growth and biochemical analysis of evergreen haloxeric tree species <Emphasis Type="Italic">Salvadora oleoides</Emphasis> and <Emphasis Type="Italic">Salvadora persica</Emphasis> under NaCl stress

In vitro growth, development, total soluble proteins and peroxidase profiles of Salvadora oleoides and Salvadora persica under NaCl stress were analysed in the present investigation. The plants are evergreen haloxeric tree species of family Salvadoraceae. Shoot apex from natural plants were initially used for screening of NaCl tolerance on MS culture medium. Shoot apex of S. oleoides and S. persica could survive optimally up to 200 and 100 mM NaCl. Axillary buds from nodal shoot segments of S. oleoides and S. persica were activated on 6 and 4 μM BAP, and were used further for extraction of total soluble proteins and peroxidases. Total soluble proteins were increased up to 150 mM NaCl in S. oleoides, but decline above 50 mM NaCl in S. persica. Peroxidase activity remained almost constant in S. oleoides at all the concentrations and duration of NaCl, but increased at 100 mM NaCl during fourth week of treatment in S. persica. Eleven peroxidase isozymes were observed in zymogram of S. oleoides. Isozymes P1, P2, P3, and P4 were slightly appeared, but P6 isozyme was lacking in S. persica. The P5 isozyme was more prominent in S. persica than S. oleoides. Isozyme P9 of S. persica was visible during the first week of NaCl treatment, but disappeared in the fourth week. Molecular biology of these plants can be useful further for the understanding of stress tolerance mechanisms for prospects.     

<Emphasis Type="Italic">A2144G</Emphasis> Is the Main Mutation in the <Emphasis Type="Italic">23S</Emphasis> rRNA Gene of <Emphasis Type="Italic">Helicobacter pylori</Emphasis> Associated with Clarithromycin Resistance

To detect point mutations A2115C, A2143G/C, and A2144G in the 23S rRNA gene of Helicobacter pylori associated with resistance of the microorganism to clarithromycin, a new powerful way of analysis was used. This method involved the reaction of minisequencing followed by MALDI-TOF mass spectrometry of reaction products. In ten analyzed clarithromycin-resistant clinical isolates of H. pylori obtained in Russia, the resistance was found to be mediated only by mutation A2144G in the 23S rRNA gene.     

Molecular genetic analysis of the suprageneric system of casebearer moths,with a description of a new genus from the tribe Carpochenini Cǎpuşe, 1973 (Lepidoptera,Coleophoridae)

Based on a complex approach including morphological and molecular genetic methods, the taxonomic position of two casebearer moth species Coleophora tsherkesi Falkovitsh, 1970 and C. isabellina Falkovitsh, 1970 (Lepidoptera, Coleophoridae) is discussed. On the phylogenetic tree based on the cytochrome oxidase subunit I gene (COI), two species form a common cluster with species of the genera Ionescumia, Carpochena, and Goniodoma. Data on the molecular phylogeny and morphology justify the placement of Coleophora tsherkesi and C. isabellina in a separate genus Falkmisa Anikin et Dyomin, gen. n. Thus, the tribe Carpochenini includes three genera: Ionescumia, Carpochena, and Falkmisa.     

Identification of 21 novel <Emphasis Type="Italic">S-RNase</Emphasis> alleles and determination of <Emphasis Type="Italic">S</Emphasis>-genotypes in 66 loquat (<Emphasis Type="Italic">Eriobotrya</Emphasis>) accessions

As observed in other self-incompatible species in the Pyrinae subtribe, loquat (Eriobotrya japonica) demonstrates gametophytic self-incompatibility that is controlled by the S-locus, which encodes a polymorphic stylar ribonuclease (S-RNase). This allows the female reproductive organ (style) to recognize and reject the pollen from individuals with the same S-alleles, but allows the pollen from individuals with different S-alleles to effect fertilization. The S-genotype is therefore an important consideration in breeding strategies and orchard management. In an attempt to optimize the selection of parental lines in loquat production, the S-RNase alleles of 35 loquat cultivars and their 26 progeny, as well as five wild loquat species, were identified and characterized in this study. The best pollinizer cultivar combinations were also explored. A total of 28 S-alleles were detected, 21 of which constituted novel S-RNase alleles. The S-haplotypes S₂ and S₆ were the most frequent, followed by S ₂₉ , S ₃₁ , S ₅ , S ₂₄ , S ₂₈ , S ₃₃ , S ₃₄ , S ₃₂ , and S ₁₅ , while the rare alleles S ₁ , S ₉ , S ₁₄ , S ₁₆ , S ₁₇ , S ₁₈ , S ₁₉ , S ₂₀ , S ₂₁ , S ₂₂ , S ₂₃ , S ₂₇ , and S ₃₅ were only observed in one of the accessions tested. Moreover, the S-genotypes of five wild loquat species (E. prinoides, E. bengalensis, E. prinoides var. dadunensis, E. deflexa, and E. japonica) are reported here for the first time. The results will not only facilitate the selection of suitable pollinators for optimal orchard management, but could also encourage the crossbreeding of wild loquat species to enhance the genetic diversity of loquat cultivars.     

Steroid Compounds from Far Eastern Starfishes <Emphasis Type="Italic">Henricia aspera</Emphasis> and <Emphasis Type="Italic">H. tumida</Emphasis>

Six new natural compounds were isolated from two Far Eastern starfish species, Henricia aspera and H. tumida, collected in the Sea of Okhotsk. Two new glycosylated steroid polyols were obtained from H. aspera: asperoside A and asperoside B, which were shown to be (20R,24R, 25S)-3-O-(2,3-di-O-methyl-β -D-xylopyranosyl)-24-methyl-5α-cholest-4-ene-3β, 6β,8,15α,16β,26-hexaol and (20R, 24R,25S,22E)-3-O-(2,4-di-O-methyl-β-D-xylopyranosyl)-24-methyl-5α-cholest-22-ene-3β,4β,6β,8,15α,26-hexaol, respectively. Two other glycosylated polyols, tumidoside A, with the structure elucidated as (20R, 22E)-3-O-(2,4-di-O-methyl-β -D-xylopyranosyl)-26,27-dinor-24-methyl-5α-cholest-22-ene-3β,4β,6β,8,15α,25-hexaol, and tumidoside B, whose structure was elucidated as (20R,24S)-3-O-(2,3-di-O-methyl-β-D-xylopyranosyl)-5α-cholestan-3β,4β,6β,8,15α,24-hexaol, were isolated from the two starfish species. (20R, 24S)-5α-Cholestan-3β,6β,15α,24-tetraol and (20R, 24S)-5α-cholestan-3β,6β,8,15α,24-pentaol were identified only in H. tumida. The known monoglycosides henricioside H1 and laeviuscolosides H and G were also identified in both species.     

Comprehensive dataset of mangrove tree weights in Southeast Asia

We assembled a dataset tabulating the weights of Thai and Indonesian mangrove trees that we measured between 1982 and 2001. We selected four Thai study sites in Phang Nga, Ranong, Satun, and Trat Provinces and one site in eastern Indonesia on Halmahera Island in Maluku Province. The stands in Ranong Province and on Halmahera Island were in primary forests with data collected in the 1980s and the remaining stands were in secondary forests with data collected later. We collected 124 tree samples from ten species (Avicennia alba, Bruguiera cylindrica, B. gymnorrhiza, Ceriops tagal, Rhizophora apiculata, R. mucronata, Sonneratia alba, S. caseolaris, Xylocarpus granatum, and X. moluccensis) and measured the root weights of 32 individuals of nine species (A. alba, B. cylindrica, B. gymnorrhiza, C. tagal, R. apiculata, R. mucronata, S. alba, S. caseolaris, and X. granatum). All sampled trees were subjected to a standardized protocol to obtain aboveground weights. The trunks were divided into horizontal segments from which the leaves and branches were collected separately. Roots were collected by winching them out of the ground, by trench digging, or by complete excavation. Thus, we were able to compile the weights of the trunk, branches, leaves, and roots of each tree sampled. Aerial roots were included in root weight measurements, although they were collected above ground. We compiled separate lists of trunk diameters, trunk heights, heights of the lowest living branches, and the heights of aerial roots on the trunks of trees in different size categories. Our dataset includes a wide range of tree sizes (maximum trunk diameter 48.9 cm), geographical locations (1°10′N–12°24′N, 98°32′E–123°49′E) and organ weights (trunks, branches, leaves, and roots), and therefore should prove useful in future biomass studies of mangrove forests.     

Molecular evidence for hybridization between invasive <Emphasis Type="Italic">Solidago canadensis</Emphasis> and native <Emphasis Type="Italic">S</Emphasis>. <Emphasis Type="Italic">virgaurea</Emphasis>

Hybridization between alien and native species is biologically very important and could lead to genetic erosion of native taxa. Solidago × niederederi was discovered over a century ago in Austria and described by Khek as a natural hybrid between the alien (nowadays regarded also as invasive) S. canadensis and native S. virgaurea. Although interspecific hybridization in the genus Solidago is considered to be relatively common, hybrid nature of S. × niederederi has not been independently proven using molecular tools, to date. Because proper identification of the parentage for the hybrid Solidago individuals solely based on morphological features can be misleading, in this paper we report an additive polymorphism pattern expressed in the ITS sequences obtained from individuals representing S. × niederederi, and confirm the previous hypothesis that the parental species of this hybrid are S. canadensis and S. virgaurea. Additionally, based on variability at the cpDNA rpl32-trnL locus, we showed that in natural populations hybridization occurs in both directions.     

Pistil-function breakdown in a new <Emphasis Type="Italic">S</Emphasis>-allele of European pear, <Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">21</Emphasis></Subscript>°, confers self-compatibility

European pear exhibits RNase-based gametophytic self-incompatibility controlled by the polymorphic S-locus. S-allele diversity of cultivars has been extensively investigated; however, no mutant alleles conferring self-compatibility have been reported. In this study, two European pear cultivars, ‘Abugo’ and ‘Ceremeño’, were classified as self-compatible after fruit/seed setting and pollen tube growth examination. S-genotyping through S-PCR and sequencing identified a new S-RNase allele in the two cultivars, with identical deduced amino acid sequence as S ₂₁ , but differing at the nucleotide level. Test-pollinations and analysis of descendants suggested that the new allele is a self-compatible pistil-mutated variant of S ₂₁ , so it was named S ₂₁ °. S-genotypes assigned to ‘Abugo’ and ‘Ceremeño’ were S ₁₀ S ₂₁ ° and S ₂₁ °S ₂₅ respectively, of which S ₂₅ is a new functional S-allele of European pear. Reciprocal crosses between cultivars bearing S ₂₁ and S ₂₁ ° indicated that both alleles exhibit the same pollen function; however, cultivars bearing S ₂₁ ° had impaired pistil-S function as they failed to reject either S ₂₁ or S ₂₁ ° pollen. RT-PCR analysis showed absence of S ₂₁ °-RNase gene expression in styles of ‘Abugo’ and ‘Ceremeño’, suggesting a possible origin for S ₂₁ ° pistil dysfunction. Two polymorphisms found within the S-RNase genomic region (a retrotransposon insertion within the intron of S ₂₁ ° and indels at the 3′UTR) might explain the different pattern of expression between S ₂₁ and S ₂₁ °. Evaluation of cultivars with unknown S-genotype identified another cultivar ‘Azucar Verde’ bearing S ₂₁ °, and pollen tube growth examination confirmed self-compatibility for this cultivar as well. This is the first report of a mutated S-allele conferring self-compatibility in European pear.     

High genetic diversity in an endangered medicinal plant, <Emphasis Type="Italic">Saussurea involucrata</Emphasis> (<Emphasis Type="Italic">Saussurea</Emphasis>, Asteraceae), in western Tianshan Mountains,China

Saussurea involucrata (Asteraceae) is a medicinal and second-degree national priority endangered plant that is mainly distributed in the high latitude region of the western Tianshan Mountains. The population is fragmented and isolated, and extensive human impact merits a suitable and specific conservation strategy, which can be compiled based on the genetic diversity, population structure, and demographic history. Phylogeographic studies were conducted on a total of five natural populations and 150 individuals were sampled. Data from three cpDNA intergenic spacer regions (trnL-F, matK, and ndhF-rpl32) and nrDNA ITS sequences showed that twelve haplotypes in cpDNA and five haplotypes in nrDNA indicated high genetic diversity among populations sampled (H _T?=?0.820 and 0.756) and within populations sampled (H _S?=?0.792 and 0.721). Additionally, the high genetic diversity did not mirror genetic structure in either cpDNA (F _ST?=?0.03153, G _ST?>?N _ST, p?<?0.05) or nrDNA (F _ST?=?0.03666, meaningless G _ST and N _ST). Two groups (north and south) were determined for a SAMOVA analysis. Based on this analysis, the demographic history was conducted with a Bayesian Skyline Plot and Isolation with Migration analysis, which showed sustainable and stable extension without a marked bottleneck. Divergence time was indicated at c. 6.25 Mya (90%HPD: 15.30–0.22 Mya) in the Miocene, which is consistent with the formation of the Kelasu section of Tianshan. The southern populations in the Bayanbulak and Gonglu regions require additional attention and transplanting would be an effective way to restore rare cpDNA haplotypes, increase effective population size, and migration rate. Our results suggested that in situ conservation of S. involucrata in western Tianshan should be the main strategy for protection and recovery of the species.     

Updates on East Asian <Emphasis Type="Italic">Asterostroma</Emphasis> (Russulales,Basidiomycota): new species and new records from Thailand and China

Two new species from northern Thailand, Asterostroma bambusicola and A. vararioides, are described and illustrated. Asterostroma bambusicola is characterized by globose, echinulate, and amyloid basidiospores and growing on rotten bamboo. Asterostroma vararioides is distinguished by the presence of Vararia-like dichohyphae, subglobose, smooth, and amyloid basidiospores and growing on bark of living angiosperm trees. In the phylogenetic tree inferred from a combined dataset of ITS and nLSU sequence data of Peniophoraceae, A. bambusicola forms a distinct lineage in the sect. Asterostroma clade, whereas A. vararioides and A. laxum form the sect. Laevispora clade. Asterostroma andinum, reported from China for the first time, forms a distinct lineage sister to Gloiothele spp. and Scytinostroma portentosum group. Asterostroma muscicola is reported from Thailand and China for the first time. A key to the species of Asterostroma from Thailand and China is provided.     

Spatial distribution of algae in the <Emphasis Type="Italic">Ahnfeltia tobuchiensis</Emphasis> bed in Amursky Bay (Sea of Japan)

Horizontal and vertical distribution of algae in Ahnfeltia tobuchiensis beds was studied in the area of Mt. Stolovaya in Amursky Bay, Sea of Japan. Thirty-four species of macroalgae (2 species of Chlorophyta, 26 Rhodophyta, and 6 Ochrophyta) were found in the area of study. Two fields of the unattached alga Ahnfeltia were located opposite Mt. Stolovaya; they differed in area, macrophyte stock, number and biomass of attendant species, hydrochemical and light conditions. A monodominant Ahnfeltia tobuchiensis community formed in the southern field and a bidominant community of Ahnfeltia tobuchiensis + Ahnfeltiopsis flabelliformis developed in the northern field. It is suggested that the horizontal distribution of common macrophyte species in the Ahnfeltia beds at Mt. Stolovaya is conditioned by the amount of photosynthetically active radiation (PAR) reaching the surface of the algal bed. Differences in tolerance of Ahnfeltia and attendant species to shadowing and in light conditions across the alga stratum define the vertical distribution of algae within the bed. Chondrus armatus and Ptilota filicina were found mainly in the upper layer of the algal bed. A. tobuchiensis, A. flabelliformis, Chaetomorpha linum, and Coccotylus orientalis extended across the entire thickness of the bed.     

Heterobucephalopsine and prosorhynchine trematodes (Digenea: Bucephalidae) from teleost fishes of Moreton Bay,Queensland, Australia,with the description of two new species

Eight species of the trematode family Bucephalidae Poche, 1907 are reported from teleost fishes in Moreton Bay, Queensland, Australia. Heterobucephalopsis yongi n. sp. is described from Gymnothorax eurostus (Muraenidae); the new form is distinguished from its congeners in the possession of a tiny cirrus-sac relative to body length, the length of the caecum, the position of the mouth and pharynx, and the position of the testes and ovary. Two known species of Dollfustrema Eckmann, 1934, D. durum Nolan, Curran, Miller, Cutmore, Cantacessi & Cribb, 2015 and D. gibsoni Nolan & Cribb, 2010, are reported from Gymnothorax pseudothyrsoideus (Bleeker) (Muraenidae); although both species were described from Australian waters, this represents the first reports from Moreton Bay and G. pseudothyrsoideus. Four species of Prosorhynchus Odhner, 1905 are reported, including one new, P. brayi n. sp., which is described from Epinephelus coioides (Hamilton) (Serranidae); P. brayi n. sp. is distinguished from its congeners in the possession of vitelline follicles in a confluent arc distinctly posterior to a conical rhynchus, uterine coils that do not extend anterior to the vitelline arc, contiguous testes, a cirrus-sac that reaches anteriorly to at least the level of the posterior testis and a short excretory vesicle. Three known species of Prosorhynchus are reported from Australia, for the first time: P. luzonicus Velasquez, 1959 and P. maternus Bray & Justine, 2006 from E. coioides and Prosorhynchus platycephali (Yamaguti, 1934) Srivastava, 1938 from Ambiserrula jugosa (McCulloch) and Inegocia japonica (Cuvier) (Platycephalidae). Skrjabiniella Issaitschikow, 1928 is re-recognised for new specimens of Skrjabiniella uniporus (Ozaki, 1924) n. comb. collected from Conger cinereus Rüppell (Congridae); three additional species of Prosorhynchus are considered members of this genus, two of which are synonymised with S. uniporus.     

A safe and complete algorithm for metagenomic assembly

Background

Reconstructing the genome of a species from short fragments is one of the oldest bioinformatics problems. Metagenomic assembly is a variant of the problem asking to reconstruct the circular genomes of all bacterial species present in a sequencing sample. This problem can be naturally formulated as finding a collection of circular walks of a directed graph G that together cover all nodes, or edges, of G.

Approach

We address this problem with the “safe and complete” framework of Tomescu and Medvedev (Research in computational Molecular biology—20th annual conference, RECOMB 9649:152–163, 2016). An algorithm is called safe if it returns only those walks (also called safe) that appear as subwalk in all metagenomic assembly solutions for G. A safe algorithm is called complete if it returns all safe walks of G.

Results

We give graph-theoretic characterizations of the safe walks of G, and a safe and complete algorithm finding all safe walks of G. In the node-covering case, our algorithm runs in time \(O(m^2 + n^3)\), and in the edge-covering case it runs in time \(O(m^2n)\); n and m denote the number of nodes and edges, respectively, of G. This algorithm constitutes the first theoretical tight upper bound on what can be safely assembled from metagenomic reads using this problem formulation.