On the metric dimension of Grassmann graphs

The {\em metric dimension} of a graph $\Gamma$ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph $G_q(n,k)$ (whose vertices are the $k$-subspaces of $\mathbb{F}_q^n$, and are adjacent if they intersect in a $(k-1)$-subspace) for $k\geq 2$, and find a constructive upper bound on its metric dimension. Our bound is equal to the number of 1-dimensional subspaces of $\mathbb{F}_q^n$.Comment: 9 pages. Revised to correct an error in Proposition 9 of the previous versio

Foreword : evolution in the century of biology

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DNA sonification for public engagement in bioinformatics

Funding: This work was funded by the Science and Technology Facilities Council (STFC) grant numbers ST/R000328/1 and ST/T000872/1.Objective: Visualisation methods, primarily color-coded representation of sequence data, have been a predominant means of representation of DNA data. Algorithmic conversion of DNA sequence data to sound – sonification – represents an alternative means of representation that uses a different range of human sensory perception. We propose that sonification has value for public engagement with DNA sequence information because it has potential to be entertaining as well as informative. We conduct preliminary work to explore the potential of DNA sequence sonification in public engagement with bioinformatics. We apply a simple sonification technique for DNA, in which each DNA base is represented by a specific note. Additionally, a beat may be added to indicate codon boundaries or for musical effect. We report a brief analysis from public engagement events we conducted that featured this method of sonification. Results: We report on use of DNA sequence sonification at two public events. Sonification has potential in public engagement with bioinformatics, both as a means of data representation and as a means to attract audience to a drop-in stand. We also discuss further directions for research on integration of sonification into bioinformatics public engagement and education.Publisher PDFPeer reviewe

Disassortative mating prevails in style-dimorphic Narcissus papyraceus despite low reciprocity and compatibility of morphs

Evolution to reduce inbreeding can favor disassortative (inter-morph) over assortative (intramorph) mating in hermaphroditic sexually polymorphic plant species. Heterostyly enhances disassortative pollination through reciprocal placement of stigmas and anthers of morphs and appropriate pollinators. Stylar dimorphism in which there is not reciprocal anther placement may compromise disassortative mating, particularly when there is not intra-morph incompatibility. Variable rates of disassortative mating along with differential female fecundity or siring success among floral morphs could lead to variation in morph ratio. We investigated mating patterns, female fecundity and siring success of style-length morphs in Narcissus papyraceus, a self-incompatible but morph-compatible species with dimorphic (long- and short-styled) and monomorphic (long-styled) populations in central and north regions of its range respectively. We established experimental populations in both regions and exposed them to ambient pollinators. Using paternity analysis, we found similar siring success of morphs and high disassortative mating in most populations. Female fecundity of morphs was similar in all populations. Although these results could not completely explain the loss of dimorphism in the species’ northern range, they provided evidence for the evolutionary stability of stylar dimorphism in N. papyraceus in at least some populations. Our findings support the hypothesis that prevailing inter-morph mating is key for the maintenance of stylar dimorphism.PostprintPeer reviewe

Do s genes or deleterious recessives control late-acting self-incompatibility in Handroanthus heptaphyllus (Bignoniaceae)? A diallel study with four full sib progeny arrays

MBB thanks the Consejo de Investigaciones de la Universidad Nacional de Rosario (CIUNR) for financial support.Background and Aims Genetically controlled self-incompatibility (SI) mechanisms constrain selfing and thus have contributed to the evolutionary diversity of flowering plants. In homomorphic gametophytic SI (GSI) and homomorphic sporophytic SI (SSI), genetic control is usually by a single multi-allelic locus S. Both GSI and SSI prevent self pollen tubes reaching the ovary and so are pre-zygotic in action. In contrast, in taxa with late-acting self-incompatibility (LSI), rejection is often post-zygotic, since self-pollen tubes grow to the ovary where fertilization may occur prior to floral abscission. Alternatively, lack of self fruit set could be due to early-acting inbreeding depression (EID). The aim of our study was to investigate mechanisms underlying lack of selfed fruit set in Handroanthus heptaphyllus in order to assess the likelihood of LSI versus EID. Methods We employed four full sib diallels to study the genetic control of LSI in Handroanthus heptaphyllus using a precociously flowering variant. We also used fluorescence microscopy to study the incidence of ovule penetration by pollen tubes in pistils that abscised following pollination or initiated fruits. Key Results All diallels showed reciprocally cross-incompatible full-sibs (RCI), reciprocally cross compatible full-sibs (RCC), and non-reciprocally compatible full-sibs (NRC) in almost equal proportions. There was no significant difference between the incidence of ovule penetrations in abscised pistils following self- and cross-incompatible pollinations, but those in successful cross pollinations were around twofold greater. Conclusions A genetic model postulating a single S locus with four s alleles, one of which, in the maternal parent, is dominant to the other three, will produce RCI, RCC and NRC situations each at 33 %, consistent with our diallel results. We favour this simple genetic control over an early-acting inbreeding depression (EID) explanation since none of our pollinations, successful or unsuccessful, resulted in partial embryo development, as would be expected under a whole genome EID effect.PostprintPeer reviewe

The role of edaphic environment and climate in structuring phylogenetic pattern in seasonally dry tropical plant communities

This study was made possible through the kind financial support of the São Paulo Research Foundation - http://fapesp.br/en (Fundação de Amparo à Pesquisa do Estado de São Paulo - Fapesp 2013/15280-9).Seasonally dry tropical plant formations (SDTF) are likely to exhibit phylogenetic clustering owing to niche conservatism driven by a strong environmental filter (water stress), but heterogeneous edaphic environments and life histories may result in heterogeneity in degree of phylogenetic clustering. We investigated phylogenetic patterns across ecological gradients related to water availability (edaphic environment and climate) in the Caatinga, a SDTF in Brazil. Caatinga is characterized by semiarid climate and three distinct edaphic environments – sedimentary, crystalline, and inselberg –representing a decreasing gradient in soil water availability. We used two measures of phylogenetic diversity: Net Relatedness Index based on the entire phylogeny among species present in a site, reflecting long-term diversification; and Nearest Taxon Index based on the tips of the phylogeny, reflecting more recent diversification. We also evaluated woody species in contrast to herbaceous species. The main climatic variable influencing phylogenetic pattern was precipitation in the driest quarter, particularly for herbaceous species, suggesting that environmental filtering related to minimal periods of precipitation is an important driver of Caatinga biodiversity, as one might expect for a SDTF. Woody species tended to show phylogenetic clustering whereas herbaceous species tended towards phylogenetic overdispersion. We also found phylogenetic clustering in two edaphic environments (sedimentary and crystalline) in contrast to phylogenetic overdispersion in the third (inselberg). We conclude that while niche conservatism is evident in phylogenetic clustering in the Caatinga, this is not a universal pattern likely due to heterogeneity in the degree of realized environmental filtering across edaphic environments. Thus, SDTF, in spite of a strong shared environmental filter, are potentially heterogeneous in phylogenetic structuring. Our results support the need for scientifically informed conservation strategies in the Caatinga and other SDTF regions that have not previously been prioritized for conservation in order to take into account this heterogeneity.Publisher PDFPeer reviewe

Resolving sets for Johnson and Kneser graphs

A set of vertices $S$ in a graph $G$ is a {\em resolving set} for $G$ if, for any two vertices $u,v$, there exists $x\in S$ such that the distances $d(u,x) \neq d(v,x)$. In this paper, we consider the Johnson graphs $J(n,k)$ and Kneser graphs $K(n,k)$, and obtain various constructions of resolving sets for these graphs. As well as general constructions, we show that various interesting combinatorial objects can be used to obtain resolving sets in these graphs, including (for Johnson graphs) projective planes and symmetric designs, as well as (for Kneser graphs) partial geometries, Hadamard matrices, Steiner systems and toroidal grids.Comment: 23 pages, 2 figures, 1 tabl

Haplotype Profile Comparisons Between Spodoptera frugiperda (Lepidoptera: Noctuidae) Populations From Mexico With Those From Puerto Rico, South America, and the United States and Their Implications to Migratory Behavior

Fall armyworm [Spodoptera frugiperda (J. E. Smith)] is a major economic pest throughout the Western Hemisphere of maize, cotton, sorghum, and a variety of agricultural grasses and vegetable crops. Previous studies demonstrated extensive annual migrations occurring as far north as Canada from overwintering locations in southern Florida and Texas. In contrast, migratory behavior in the rest of the hemisphere is largely uncharacterized. Understanding the migration patterns of fall armyworm will facilitate efforts to predict the spread of pesticide resistance traits that repeatedly arise in this species and assess the consequences of changing climatic trends on the infestation range. Four independent fall armyworm colonies derived from widely separated populations in Mexico and two field collections were examined for their mitochondrial cytochrome oxidase I (COI) gene haplotypes and compared with other locations. The Mexico populations were most similar in their haplotype profile to those from Texas and South America, but also displayed some distinctive features. The data extend the haplotype distribution map in the Western Hemisphere and confirm that the previously observed regional differences in haplotype frequencies are stable over time. The Mexico collections were associated with haplotypes rarely found elsewhere, suggesting limited migratory interactions with foreign populations, including those in neighboring Texas