Isoclinism of skew braces Letourmy, T.; Vendramin, L.
The Bulletin of the London Mathematical Society,
12/2023, Letnik:
55, Številka:
6
Journal Article
Recenzirano
Odprti dostop
Abstract
We define isoclinism of skew braces and present several applications. We study some properties of skew braces that are invariant under isoclinism. For example, we prove that right nilpotency ...is an isoclinism invariant. This result has application in the theory of set‐theoretic solutions to the Yang–Baxter equation. We define isoclinic solutions and study multipermutation solutions under isoclinism.
Plants offer excellent models to investigate how gene flow shapes the organization of genetic diversity. Their three genomes can have different modes of transmission and will hence experience varying ...levels of gene flow. We have compiled studies of genetic structure based on chloroplast DNA (cpDNA), mitochondrial DNA (mtDNA) and nuclear markers in seed plants. Based on a data set of 183 species belonging to 103 genera and 52 families, we show that the precision of estimates of genetic differentiation (G(ST)) used to infer gene flow is mostly constrained by the sampling of populations. Mode of inheritance appears to have a major effect on G(ST). Maternally inherited genomes experience considerably more subdivision (median value of 0.67) than paternally or biparentally inherited genomes (approximately 0.10). G(ST) at cpDNA and mtDNA markers covary narrowly when both genomes are maternally inherited, whereas G(ST) at paternally and biparentally inherited markers also covary positively but more loosely and G(ST) at maternally inherited markers are largely independent of values based on nuclear markers. A model-based gross estimate suggests that, at the rangewide scale, historical levels of pollen flow are generally at least an order of magnitude larger than levels of seed flow (median of the pollen-to-seed migration ratio: 17) and that pollen and seed gene flow vary independently across species. Finally, we show that measures of subdivision that take into account the degree of similarity between haplotypes (N(ST) or R(ST)) make better use of the information inherent in haplotype data than standard measures based on allele frequencies only.
Given a right-non-degenerate set-theoretic solution (X,r) to the Yang–Baxter equation, we construct a whole family of YBE solutions r(k) on X indexed by its reflections k (i.e., solutions to the ...reflection equation for r). This family includes the original solution and the classical derived solution. All these solutions induce isomorphic actions of the braid group/monoid on Xn. The structure monoids of r and r(k) are related by an explicit bijective 1-cocycle-like map. We thus turn reflections into a tool for studying YBE solutions, rather than a side object of study. In a different direction, we study the reflection equation for non-degenerate involutive YBE solutions, show it to be equivalent to (any of the) three simpler relations, and deduce from the latter systematic ways of constructing new reflections.
Abstract
Motivated by the proof of Rump of a conjecture of Gateva–Ivanova on the decomposability of square-free solutions to the Yang–Baxter equation, we present several other decomposability ...theorems based on the cycle structure of a certain permutation associated with the solution.
High genetic variation and extensive gene flow may help forest trees with adapting to ongoing climate change, yet the genetic bases underlying their adaptive potential remain largely unknown. We ...investigated range‐wide patterns of potentially adaptive genetic variation in 64 populations of European beech (Fagus sylvatica L.) using 270 SNPs from 139 candidate genes involved either in phenology or in stress responses. We inferred neutral genetic structure and processes (drift and gene flow) and performed differentiation outlier analyses and gene‐environment association (GEA) analyses to detect signatures of divergent selection. Beech range‐wide genetic structure was consistent with the species’ previously identified postglacial expansion scenario and recolonization routes. Populations showed high diversity and low differentiation along the major expansion routes. A total of 52 loci were found to be putatively under selection and 15 of them turned up in multiple GEA analyses. Temperature and precipitation related variables were equally represented in significant genotype‐climate associations. Signatures of divergent selection were detected in the same proportion for stress response and phenology‐related genes. The range‐wide adaptive genetic structure of beech appears highly integrated, suggesting a balanced contribution of phenology and stress‐related genes to local adaptation, and of temperature and precipitation regimes to genetic clines. Our results imply a best‐case scenario for the maintenance of high genetic diversity during range shifts in beech (and putatively other forest trees) with a combination of gene flow maintaining within‐population neutral diversity and selection maintaining between‐population adaptive differentiation.
Glacial refuge areas are expected to harbor a large fraction of the intraspecific biodiversity of the temperate biota. To test this hypothesis, we studied chloroplast DNA variation in 22 widespread ...European trees and shrubs sampled in the same forests. Most species had genetically divergent populations in Mediterranean regions, especially those with low seed dispersal abilities. However, the genetically most diverse populations were not located in the south but at intermediate latitudes, a likely consequence of the admixture of divergent lineages colonizing the continent from separate refugia.
Understanding local adaptation in forest trees is currently a key research and societal priority. Geographically and ecologically marginal populations provide ideal case studies, because ...environmental stress along with reduced gene flow can facilitate the establishment of locally adapted populations. We sampled European silver fir (Abies alba Mill.) trees in the French Mediterranean Alps, along the margin of its distribution range, from pairs of high‐ and low‐elevation plots on four different mountains situated along a 170‐km east–west transect. The analysis of 267 SNP loci from 175 candidate genes suggested a neutral pattern of east–west isolation by distance among mountain sites. FST outlier tests revealed 16 SNPs that showed patterns of divergent selection. Plot climate was characterized using both in situ measurements and gridded data that revealed marked differences between and within mountains with different trends depending on the season. Association between allelic frequencies and bioclimatic variables revealed eight genes that contained candidate SNPs, of which two were also detected using FST outlier methods. All SNPs were associated with winter drought, and one of them showed strong evidence of selection with respect to elevation. QST–FST tests for fitness‐related traits measured in a common garden suggested adaptive divergence for the date of bud flush and for growth rate. Overall, our results suggest a complex adaptive picture for A. alba in the southern French Alps where, during the east‐to‐west Holocene recolonization, locally advantageous genetic variants established at both the landscape and local scales.
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