A pseudo-spectral scheme for systems of two-point boundary value problems with left and right sided fractional derivatives and related integral equations

We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left- and right-sided fractional derivatives. The main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral equations. Then, a Legendre-based spectral collocation method is developed for solving the transformed system. Therefore, we can make good use of the advantages of the Gauss quadrature rule. We present the construction and analysis of the collocation method. These results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler-Lagrange equations. Two numerical examples are given to confirm the convergence analysis and robustness of the scheme. © 2021 Tech Science Press. All rights reserved.Russian Foundation for Basic Research, РФФИ: 19-01-00019The Russian Foundation for Basic Research (RFBR) Grant No. 19-01-00019

Origin and evolution of the bread wheat D genome

Bread wheat (Triticum aestivum) is a globally dominant crop and major source of calories and proteins for the human diet. Compared with its wild ancestors, modern bread wheat shows lower genetic diversity, caused by polyploidisation, domestication and breeding bottlenecks1,2. Wild wheat relatives represent genetic reservoirs, and harbour diversity and beneficial alleles that have not been incorporated into bread wheat. Here we establish and analyse extensive genome resources for Tausch’s goatgrass (Aegilops tauschii), the donor of the bread wheat D genome. Our analysis of 46 Ae. tauschii genomes enabled us to clone a disease resistance gene and perform haplotype analysis across a complex disease resistance locus, allowing us to discern alleles from paralogous gene copies. We also reveal the complex genetic composition and history of the bread wheat D genome, which involves contributions from genetically and geographically discrete Ae. tauschii subpopulations. Together, our results reveal the complex history of the bread wheat D genome and demonstrate the potential of wild relatives in crop improvement

Origin and evolution of the bread wheat D genome

Bread wheat (Triticum aestivum) is a globally dominant crop and major source of calories and proteins for the human diet. Compared with its wild ancestors, modern bread wheat shows lower genetic diversity, caused by polyploidisation, domestication and breeding bottlenecks. Wild wheat relatives represent genetic reservoirs, and harbour diversity and beneficial alleles that have not been incorporated into bread wheat. Here we establish and analyse extensive genome resources for Tausch’s goatgrass (Aegilops tauschii), the donor of the bread wheat D genome. Our analysis of 46 Ae. tauschii genomes enabled us to clone a disease resistance gene and perform haplotype analysis across a complex disease resistance locus, allowing us to discern alleles from paralogous gene copies. We also reveal the complex genetic composition and history of the bread wheat D genome, which involves contributions from genetically and geographically discrete Ae. tauschii subpopulations. Together, our results reveal the complex history of the bread wheat D genome and demonstrate the potential of wild relatives in crop improvement

Harnessing landrace diversity empowers wheat breeding

Harnessing genetic diversity in major staple crops through the development of new breeding capabilities is essential to ensure food security1. Here we examined the genetic and phenotypic diversity of the A. E. Watkins landrace collection2 of bread wheat (Triticum aestivum), a major global cereal, by whole-genome re-sequencing of 827 Watkins landraces and 208 modern cultivars and in-depth field evaluation spanning a decade. We found that modern cultivars are derived from two of the seven ancestral groups of wheat and maintain very long-range haplotype integrity. The remaining five groups represent untapped genetic sources, providing access to landrace-specific alleles and haplotypes for breeding. Linkage disequilibrium-based haplotypes and association genetics analyses link Watkins genomes to the thousands of identified high-resolution quantitative trait loci and significant marker–trait associations. Using these structured germplasm, genotyping and informatics resources, we revealed many Watkins-unique beneficial haplotypes that can confer superior traits in modern wheat. Furthermore, we assessed the phenotypic effects of 44,338 Watkins-unique haplotypes, introgressed from 143 prioritized quantitative trait loci in the context of modern cultivars, bridging the gap between landrace diversity and current breeding. This study establishes a framework for systematically utilizing genetic diversity in crop improvement to achieve sustainable food security