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

On the rate of convergence of the Legendre spectral collocation method for multi-dimensional nonlinear Volterra–Fredholm integral equations

Abstract While the approximate solutions of one-dimensional nonlinear Volterra–Fredholm integral equations with smooth kernels are now well understood, no systematic studies of the numerical solutions of their multi-dimensional counterparts exist. In this paper, we provide an efficient numerical approach for the multi-dimensional nonlinear Volterra–Fredholm integral equations based on the multi-variate Legendre-collocation approach. Spectral collocation methods for multi-dimensional nonlinear integral equations are known to cause major difficulties from a convergence analysis point of view. Consequently, rigorous error estimates are provided in the weighted Sobolev space showing the exponential decay of the numerical errors. The existence and uniqueness of the numerical solution are established. Numerical experiments are provided to support the theoretical convergence analysis. The results indicate that our spectral collocation method is more flexible with better accuracy than the existing ones.</jats:p

A wheat kinase and immune receptor form the host-specificity barrier against the blast fungus

AbstractSince emerging in Brazil in 1985, wheat blast has spread throughout South America and recently appeared in Bangladesh and Zambia. We show that two wheat resistance genes, Rwt3 and Rwt4, acting as host-specificity barriers against non-Triticum blast pathotypes encode a nucleotide-binding leucine-rich repeat immune receptor and a tandem kinase, respectively. Molecular isolation of these genes allowed us to develop assays that will ensure the inclusion of these two genes in the wheat cultivars to forestall the recurrence of blast host jumps.</jats:p

A wheat kinase and immune receptor form host-specificity barriers against the blast fungus

AbstractSince emerging in Brazil in 1985, wheat blast has spread throughout South America and recently appeared in Bangladesh and Zambia. Here we show that two wheat resistance genes, Rwt3 and Rwt4, acting as host-specificity barriers against non-Triticum blast pathotypes encode a nucleotide-binding leucine-rich repeat immune receptor and a tandem kinase, respectively. Molecular isolation of these genes will enable study of the molecular interaction between pathogen effector and host resistance genes.</jats:p