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Microbial ecologists have made exceptional improvements in our understanding of microbiomes in the last decade due to breakthroughs in sequencing technologies. These advances have wide-ranging implications for fields ranging from agriculture to human health. Due to limitations in databases, the majority of microbial ecology studies use a binning approach to approximate taxonomy based on DNA sequence similarity. There remains extensive debate on the best way to bin and approximate this taxonomy. Here we examine two popular approaches using a large field-based data set examining both bacteria and fungi and conclude that there are not major differences in the ecological outcomes. Thus, it appears that standard microbial community analyses are not overly sensitive to the particulars of binning approaches. Recent discussion focuses on the best method for delineating microbial taxa, based on either exact sequence variants (ESVs) or traditional operational taxonomic units (OTUs) of marker gene sequences. We sought to test if the binning approach (ESVs versus 97% OTUs) affected the ecological conclusions of a large field study. The data set included sequences targeting all bacteria (16S rRNA) and fungi (internal transcribed spacer [ITS]), across multiple environments diverging markedly in abiotic conditions, over three collection times. Despite quantitative differences in microbial richness, we found that all α and β diversity metrics were highly positively correlated ( r > 0.90) between samples analyzed with both approaches. Moreover, the community composition of the dominant taxa did not vary between approaches. Consequently, statistical inferences were nearly indistinguishable. Furthermore, ESVs only moderately increased the genetic resolution of fungal and bacterial diversity (1.3 and 2.1 times OTU richness, respectively). We conclude that for broadscale (e.g., all bacteria or all fungi) α and β diversity analyses, ESV or OTU methods will often reveal similar ecological results. Thus, while there are good reasons to employ ESVs, we need not question the validity of results based on OTUs. IMPORTANCE Microbial ecologists have made exceptional improvements in our understanding of microbiomes in the last decade due to breakthroughs in sequencing technologies. These advances have wide-ranging implications for fields ranging from agriculture to human health. Due to limitations in databases, the majority of microbial ecology studies use a binning approach to approximate taxonomy based on DNA sequence similarity. There remains extensive debate on the best way to bin and approximate this taxonomy. Here we examine two popular approaches using a large field-based data set examining both bacteria and fungi and conclude that there are not major differences in the ecological outcomes. Thus, it appears that standard microbial community analyses are not overly sensitive to the particulars of binning approaches.

The Noetherian property of the generalized power series module can determine in several ways. This paper uses the sub-exact sequence of modules over a ring R to determine this property. This investigation not only determines the Noetherian property of the generalized power series module but also the Noetherian property of its submodule. Furthermore, we give a construction of R[[S]]-homomorphism between the generalized power series modules.

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.

In this paper, the notion of (short) quasi-exact sequence of S-acts is introduced. We study the behaviour of quasi-exact sequences in regard to some algebraic properties of S-acts including principal weak injectivity, principal weak flatness, regularity and torsion freeness. Moreover, some results concerning commutative diagrams of modules are generalized to acts over monoids.

In this paper, we will present a new result that clarify the relationship between divisible module and Injective module. But before starting to give the most important results, we need to present the following lemma with some basic definitions that help us reach the desired goal.

The phylogenetic depth at which arbuscular mycorrhizal (AM) fungi harbor a coherent ecological niche is unknown, which has consequences for operational taxonomic unit (OTU) delineation from sequence data and the study of their biogeography. We tested how changes in AM fungi community composition across habitats (beta diversity) vary with OTU phylogenetic resolution. We inferred exact sequence variants (ESVs) to resolve phylotypes at resolutions finer than provided by traditional sequence clustering and analyzed beta diversity profiles up to order-level sequence clusters. At the ESV level, we detected the environmental predictors revealed with traditional OTUs or at higher genetic distances. However, the correlation between environmental predictors and community turnover steeply increased at a genetic distance of c. 0.03 substitutions per site. Furthermore, we observed a turnover of either closely or distantly related taxa (respectively at or above 0.03 substitutions per site) along different environmental gradients. This study suggests that different axes of AM fungal ecological niche are conserved at different phylogenetic depths. Delineating AM fungal phylotypes using DNA sequences should screen different phylogenetic resolutions to better elucidate the factors that shape communities and predict the fate of AM symbioses in a changing environment.

Let XX be a simply connected rational elliptic space of formal dimension nn and let E(X)\\mathcal {E}(X) denote the group of homotopy classes of self-equivalences of XX. If X[k]X^{[k]} denotes the kkth Postikov section of XX and XkX^{k} denotes its kkth skeleton, then making use of the models of Sullivan and Quillen we prove that E(X)≅E(X[n])\\mathcal {E}(X)\\cong \\mathcal {E}(X^{[n]}) and if n>m=max{k|πk(X)≠0}n>m=\\mathrm {max}\\big \\{k \\,| \\,\\pi _{k}(X)\\neq 0\\big \\}, then E(X)≅E(Xm+1)\\mathcal {E}(X)\\cong \\mathcal {E}(X^{m+1}). Moreover, in case when XX is 2-connected, we show that if πn(X)≠0\\pi _{n}(X)\\neq 0, then the group E(X)\\mathcal {E}(X) is infinite.

We provide a purely combinatorial proof of a skein exact sequence obeyed by double-point enhanced grid homology. We also extend the theory to coefficients over $\\mathbb {Z},$ and discuss alternatives to the Ozsváth–Szabó $\\tau $ invariant.

DNA metabarcoding is used to generate species composition data for entire communities. However, sequencing errors in high-throughput sequencing instruments are fairly common, usually requiring reads to be clustered into operational taxonomic units (OTUs), losing information on intraspecific diversity in the process. While Cytochrome c oxidase subunit I (COI) haplotype information is limited in resolving intraspecific diversity it is nevertheless often useful e.g. in a phylogeographic context, helping to formulate hypotheses on taxon distribution and dispersal. This study combines sequence denoising strategies, normally applied in microbial research, with additional abundance-based filtering to extract haplotype information from freshwater macroinvertebrate metabarcoding datasets. This novel approach was added to the R package \"JAMP\" and can be applied to COI amplicon datasets. We tested our haplotyping method by sequencing (i) a single-species mock community composed of 31 individuals with 15 different haplotypes spanning three orders of magnitude in biomass and (ii) 18 monitoring samples each amplified with four different primer sets and two PCR replicates. We detected all 15 haplotypes of the single specimens in the mock community with relaxed filtering and denoising settings. However, up to 480 additional unexpected haplotypes remained in both replicates. Rigorous filtering removes most unexpected haplotypes, but also can discard expected haplotypes mainly from the small specimens. In the monitoring samples, the different primer sets detected 177-200 OTUs, each containing an average of 2.40-3.30 haplotypes per OTU. The derived intraspecific diversity data showed population structures that were consistent between replicates and similar between primer pairs but resolution depended on the primer length. A closer look at abundant taxa in the dataset revealed various population genetic patterns, e.g. the stonefly and the caddisfly showed a distinct north-south cline with respect to haplotype distribution, while the beetle and the isopod displayed no clear population pattern but differed in genetic diversity. We developed a strategy to infer intraspecific genetic diversity from bulk invertebrate metabarcoding data. It needs to be stressed that at this point this metabarcoding-informed haplotyping is not capable of capturing the full diversity present in such samples, due to variation in specimen size, primer bias and loss of sequence variants with low abundance. Nevertheless, for a high number of species intraspecific diversity was recovered, identifying potentially isolated populations and taxa for further more detailed phylogeographic investigation. While we are currently lacking large-scale metabarcoding datasets to fully take advantage of our new approach, metabarcoding-informed haplotyping holds great promise for biomonitoring efforts that not only seek information about species diversity but also underlying genetic diversity.