161 research outputs found

    The strong thirteen spheres problem

    Full text link
    The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

    Linkage Mapping and Comparative Genomics Using Next-Generation RAD Sequencing of a Non-Model Organism

    Get PDF
    Restriction-site associated DNA (RAD) sequencing is a powerful new method for targeted sequencing across the genomes of many individuals. This approach has broad potential for genetic analysis of non-model organisms including genotype-phenotype association mapping, phylogeography, population genetics and scaffolding genome assemblies through linkage mapping. We constructed a RAD library using genomic DNA from a Plutella xylostella (diamondback moth) backcross that segregated for resistance to the insecticide spinosad. Sequencing of 24 individuals was performed on a single Illumina GAIIx lane (51 base paired-end reads). Taking advantage of the lack of crossing over in homologous chromosomes in female Lepidoptera, 3,177 maternally inherited RAD alleles were assigned to the 31 chromosomes, enabling identification of the spinosad resistance and W/Z sex chromosomes. Paired-end reads for each RAD allele were assembled into contigs and compared to the genome of Bombyx mori (n = 28) using BLAST, revealing 28 homologous matches plus 3 expected fusion/breakage events which account for the difference in chromosome number. A genome-wide linkage map (1292 cM) was inferred with 2,878 segregating RAD alleles inherited from the backcross father, producing chromosome and location specific sequenced RAD markers. Here we have used RAD sequencing to construct a genetic linkage map de novo for an organism that has no previous genome data. Comparative analysis of P. xyloxtella linkage groups with B. mori chromosomes shows for the first time, genetic synteny appears common beyond the Macrolepidoptera. RAD sequencing is a powerful system capable of rapidly generating chromosome specific data for non-model organisms

    Genetic dissection of fruit quality traits in the octoploid cultivated strawberry highlights the role of homoeo-QTL in their control

    Get PDF
    Fruit quality traits are major breeding targets in the Rosaceae. Several of the major Rosaceae species are current or ancient polyploids. To dissect the inheritance of fruit quality traits in polyploid fleshy fruit species, we used a cultivated strawberry segregating population comprising a 213 full-sibling F1 progeny from a cross between the variety ‘Capitola’ and the genotype ‘CF1116’. We previously developed the most comprehensive strawberry linkage map, which displays seven homoeology groups (HG), including each four homoeology linkage groups (Genetics 179:2045–2060, 2008). The map was used to identify quantitative trait loci (QTL) for 19 fruit traits related to fruit development, texture, colour, anthocyanin, sugar and organic acid contents. Analyses were carried out over two or three successive years on field-grown plants. QTL were detected for all the analysed traits. Because strawberry is an octopolyploid species, QTL controlling a given trait and located at orthologous positions on different homoeologous linkage groups within one HG are considered as homoeo-QTL. We found that, for various traits, about one-fourth of QTL were putative homoeo-QTL and were localised on two linkage groups. Several homoeo-QTL could be detected the same year, suggesting that several copies of the gene underlying the QTL are functional. The detection of some other homoeo-QTL was year-dependent. Therefore, changes in allelic expression could take place in response to environmental changes. We believe that, in strawberry as in other polyploid fruit species, the mechanisms unravelled in the present study may play a crucial role in the variations of fruit quality
    • 

    corecore