Representations of (2,n)(2,n)-semigroups by multiplace functions

We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs.Comment: 17 page

Molecular Inversion Probes for targeted resequencing in non-model organisms

Applications that require resequencing of hundreds or thousands of predefined genomic regions in numerous samples are common in studies of non-model organisms. However few approaches at the scale intermediate between multiplex PCR and sequence capture methods are available. Here we explored the utility of Molecular Inversion Probes (MIPs) for the medium-scale targeted resequencing in a non-model system. Markers targeting 112 bp of exonic sequence were designed from transcriptome of Lissotriton newts. We assessed performance of 248 MIP markers in a sample of 85 individuals. Among the 234 (94.4%) successfully amplified markers 80% had median coverage within one order of magnitude, indicating relatively uniform performance; coverage uniformity across individuals was also high. In the analysis of polymorphism and segregation within family, 77% of 248 tested MIPs were confirmed as single copy Mendelian markers. Genotyping concordance assessed using replicate samples exceeded 99%. MIP markers for targeted resequencing have a number of advantages: high specificity, high multiplexing level, low sample requirement, straightforward laboratory protocol, no need for preparation of genomic libraries and no ascertainment bias. We conclude that MIP markers provide an effective solution for resequencing targets of tens or hundreds of kb in any organism and in a large number of samples

Single nucleotide polymorphisms reveal genetic structuring of the Carpathian newt and provide evidence of interspecific gene flow in the nuclear genome

Genetic variation within species is commonly structured in a hierarchical manner which may result from superimposition of processes acting at different spatial and temporal scales. In organisms of limited dispersal ability, signatures of past subdivision are detectable for a long time. Studies of contemporary genetic structure in such taxa inform about the history of isolation, range changes and local admixture resulting from geographically restricted hybridization with related species. Here we use a set of 139 transcriptome-derived, unlinked nuclear single nucleotide polymorphisms (SNP) to assess the genetic structure of the Carpathian newt (Lissotriton montandoni, Lm) and introgression from its congener, the smooth newt (L. vulgaris, Lv). Two substantially differentiated groups of Lm populations likely originated from separate refugia, both located in the Eastern Carpathians. The colonization of the present range in north-western and south-western directions was accompanied by a modest loss of variation; admixture between the two groups has occurred in the middle of the Eastern Carpathians. Local, apparently recent introgression of Lv alleles into several Lm populations was detected, demonstrating increased power for admixture detection in comparison to a previous study based on a limited number of microsatellite markers. The level of introgression was higher in Lm populations classified as admixed than in syntopic populations. We discuss the possible causes and propose further tests to distinguish between alternatives. Several outlier loci were identified in tests of interspecific differentiation, suggesting genomic heterogeneity of gene flow between species

Linkage map of Lissotriton newts provides insight into the genetic basis of reproductive isolation

Linkage maps are widely used to investigate structure, function, and evolution of genomes. In speciation research, maps facilitate the study of the genetic architecture of reproductive isolation by allowing identification of genomic regions underlying reduced fitness of hybrids. Here we present a linkage map for European newts of the Lissotriton vulgaris species complex, constructed using two families of F2 L. montandoni × L. vulgaris hybrids. The map consists of 1146 protein-coding genes on 12 linkage groups, equal to the haploid chromosome number, with a total length of 1484 cM (1.29 cM per marker). It is notably shorter than two other maps available for salamanders, but the differences in map length are consistent with cytogenetic estimates of the number of chiasmata per chromosomal arm. Thus, large salamander genomes do not necessarily translate into long linkage maps, as previously suggested. Consequently, salamanders are an excellent model to study evolutionary consequences of recombination rate variation in taxa with large genomes and a similar number of chromosomes. A complex pattern of transmission ratio distortion (TRD) was detected: TRD occurred mostly in one family, in one breeding season, and was clustered in two genomic segments. This is consistent with environment-dependent mortality of individuals carrying L. montandoni alleles in these two segments and suggests a role of TRD blocks in reproductive isolation. The reported linkage map will empower studies on the genomic architecture of divergence and interactions between the genomes of hybridizing newts

Around the Hossz\'u-Gluskin theorem for nn-ary groups

We survey results related to the important Hossz\'u-Gluskin Theorem on $n$-ary groups adding also several new results and comments. The aim of this paper is to write all such results in uniform and compressive forms. Therefore some proofs of new results are only sketched or omitted if their completing seems to be not too difficult for readers. In particular, we show as the Hossz\'u-Gluskin Theorem can be used for evaluation how many different $n$-ary groups (up to isomorphism) exist on some small sets. Moreover, we sketch as the mentioned theorem can be also used for investigation of $\mathcal{Q}$-independent subsets of semiabelian $n$-ary groups for some special families $\mathcal{Q}$ of mappings