ILS-Aware Analysis of Low-Homoplasy Retroelement Insertions: Inference of Species Trees and Introgression Using Quartets

DNA sequence alignments have provided the majority of data for inferring phylogenetic relationships with both concatenation and coalescent methods. However, DNA sequences are susceptible to extensive homoplasy, especially for deep divergences in the Tree of Life. Retroelement insertions have emerged as a powerful alternative to sequences for deciphering evolutionary relationships because these data are nearly homoplasy-free. In addition, retroelement insertions satisfy the “no intralocus-recombination” assumption of summary coalescent methods because they are singular events and better approximate neutrality relative to DNA loci commonly sampled in phylogenomic studies. Retroelements have traditionally been analyzed with parsimony, distance, and network methods. Here, we analyze retroelement data sets for vertebrate clades (Placentalia, Laurasiatheria, Balaenopteroidea, Palaeognathae) with 2 ILS-aware methods that operate by extracting, weighting, and then assembling unrooted quartets into a species tree. The first approach constructs a species tree from retroelement bipartitions with ASTRAL, and the second method is based on split-decomposition with parsimony. We also develop a Quartet-Asymmetry test to detect hybridization using retroelements. Both ILS-aware methods recovered the same species-tree topology for each data set. The ASTRAL species trees for Laurasiatheria have consecutive short branch lengths in the anomaly zone whereas Palaeognathae is outside of this zone. For the Balaenopteroidea data set, which includes rorquals (Balaenopteridae) and gray whale (Eschrichtiidae), both ILS-aware methods resolved balaeonopterids as paraphyletic. Application of the Quartet-Asymmetry test to this data set detected 19 different quartets of species for which historical introgression may be inferred. Evidence for introgression was not detected in the other data sets.

Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition

Forbidden characterizations may sometimes be the most natural way to describe families of graphs, and yet these characterizations are usually very hard to exploit for enumerative purposes.By building on the work of Gioan and Paul (2012) and Chauve et al.(2014), we show a methodology by which we constrain a split-decomposition tree to avoid certain patterns, thereby avoiding the corresponding induced subgraphs in the original graph.We thus provide the grammars and full enumeration for a wide set of graph classes: ptolemaic, block, and variants of cactus graphs (2,3-cacti, 3-cacti and 4-cacti). In certain cases, no enumeration was known (ptolemaic, 4-cacti); in other cases, although the enumerations were known, an abundant potential is unlocked by the grammars we provide (in terms of asymptotic analysis, random generation, and parameter analyses, etc.).We believe this methodology here shows its potential; the natural next step to develop its reach would be to study split-decomposition trees which contain certain prime nodes. This will be the object of future work.

Isotropic Matroids III: Connectivity

The isotropic matroid $M[IAS(G)]$ of a graph $G$ is a binary matroid, which is equivalent to the isotropic system introduced by Bouchet. In this paper we discuss four notions of connectivity related to isotropic matroids and isotropic systems. We show that the isotropic system connectivity defined by Bouchet is equivalent to vertical connectivity of $M[IAS(G)]$, and if $G$ has at least four vertices, then $M[IAS(G)]$ is vertically 5-connected if and only if $G$ is prime (in the sense of Cunningham's split decomposition). We also show that $M[IAS(G)]$ is $3$-connected if and only if $G$ is connected and has neither a pendant vertex nor a pair of twin vertices. Our most interesting theorem is that if $G$ has $n\geq7$ vertices then $M[IAS(G)]$ is not vertically $n$-connected. This abstract-seeming result is equivalent to the more concrete assertion that $G$ is locally equivalent to a graph with a vertex of degree $<\frac{n-1}{2}$.

Separability for weakly irreducible matrices

This paper is devoted to the study of the separability problem in the field of Quantum information theory. We focus on the bipartite finite dimensional case and on two types of matrices: SPC and PPT matrices (see definitions 32 and 33). We prove that many results hold for both types. If these matrices have specific Hermitian Schmidt decompositions then they are separable in a very strong sense (see theorem 38 and corollary 39). We prove that both types have what we call \textbf{split decompositions} (see theorems 41 and 42). We also define the notion of weakly irreducible matrix (see definition 43), based on the concept of irreducible state defined recently in \cite{chen1}, \cite{chen} and \cite{chen2}.}{These split decomposition theorems imply that every SPC $($PPT$)$ matrix can be decomposed into a sum of $s+1$ SPC $($PPT$)$ matrices of which the first $s$ are weakly irreducible, by theorem 48, and the last one has a further split decomposition of lower tensor rank, by corollary 49. Thus the SPC $($PPT$)$ matrix is decomposed in a finite number of steps into a sum of weakly irreducible matrices. Different components of this sum have support on orthogonal local Hilbert spaces, therefore the matrix is separable if and only if each component is separable. This reduces the separability problem for SPC $($PPT$)$ matrices to the case of weakly irreducible SPC $($PPT$)$ matrices. We also provide a complete description of weakly irreducible matrices of both types (see theorem 46).}{Using the fact that every positive semidefinite Hermitian matrix with tensor rank 2 is separable (see theorem 58), we found sharp inequalites providing separability for both types (see theorems 61 and 62).

Lactobacillus delbrueckii subsp. jakobsenii subsp. nov., isolated from dolo wort, an alcoholic fermented beverage in Burkina Faso

Lactobacillus delbrueckii is divided into five subspecies based on phenotypic and genotypic differences. A novel isolate, designated ZN7a-9T, was isolated from malted sorghum wort used for making an alcoholic beverage (dolo) in Burkina Faso. The results of 16S rRNA gene sequencing, DNA–DNA hybridization and peptidoglycan cell-wall structure type analyses indicated that it belongs to the species L. delbrueckii . The genome sequence of isolate ZN7a-9T was determined by Illumina-based sequencing. Multilocus sequence typing (MLST) and split-decomposition analyses were performed on seven concatenated housekeeping genes obtained from the genome sequence of strain ZN7a-9T together with 41 additional L. delbrueckii strains. The results of the MLST and split-decomposition analyses could not establish the exact subspecies of L. delbrueckii represented by strain ZN7a-9T as it clustered with L. delbrueckii strains unassigned to any of the recognized subspecies of L. delbrueckii . Strain ZN7a-9T additionally differed from the recognized type strains of the subspecies of L. delbrueckii with respect to its carbohydrate fermentation profile. In conclusion, the cumulative results indicate that strain ZN7a-9T represents a novel subspecies of L. delbrueckii closely related to Lactobacillus delbrueckii subsp. lactis and Lactobacillus delbrueckii subsp. delbrueckii for which the name Lactobacillus delbrueckii subsp. jakobsenii subsp. nov. is proposed. The type strain is ZN7a-9T = DSM 26046T = LMG 27067T.