Breeding design in wheat by combining the QTL information in a GWAS panel with a general genetic map and computer simulation

A large amount of genome-wide association study(GWAS)panels together with quantitative-trait locus(QTL)information associated with breeding-targeted traits have been described in wheat(Triticum aestivum L.).However,the application of mapping results from a GWAS panel to conventional wheat breeding remains a challenge.In this study,we first report a general genetic map which was constructed from 44 published linkage maps.It permits the estimation of genetic distances between any two genetic loci with physical map positions,thereby unifying the linkage relationships between QTL,genes,and genomic markers from multiple genetic populations.Second,we describe QTL mapping in a wheat GWAS panel of 688 accessions,identifying 77 QTL associated with 12 yield and grain-quality traits.Because these QTL have known physical map positions,they could be mapped onto the general map.Finally,we present a design approach to wheat breeding by using known QTL information and computer simulation.Potential crosses between parents in the GWAS panel may be evaluated by the relative frequency of the target genotype,trait correlations in simulated progeny populations,and genetic gain of selected progenies.It is possible to simultaneously improve yield and grain quality by suitable parental selection,progeny population size,and progeny selection scheme.Applying the design approach will allow identifying the most promising crosses and selection schemes in advance of the field experiment,increasing predictability and efficiency in wheat breeding.

Formula for calculating spatial similarity degrees between point clouds on multi-scale maps taking map scale change as the only independent variable

The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.

CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES

Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces.

A progressive method for the collapse of river representation considering geographical characteristics

During map generalization,the collapse of geometry,which is also called geometric dimension reduction,is a basic generalization operation.When the map scale decreases,rivers with long,shallow polygonal shapes,usually require their dual-line representation to be collapsed to a single line.This study presents a new algorithm called superpixel river collapse(SURC)to convert dual-line rivers to single-line rivers based on raster data.In this method,dual-line rivers are first segmented at different levels of detail using a superpixel method called simple linear iterative clustering.Then,by connecting the edge midpoints and centre of mass of each superpixel,single-line rivers are preliminarily generated from dual-line rivers.Finally,an interpolation algorithm called polynomial approximation with an exponential kernel is applied to maintain the uniform distribution of the feature points of single-line rivers at different levels of detail(LOD).The presented method can progressively collapse the river during scale transformation to support the LOD representation in a highly sensitive way.The results show that compared with three typical thinning algorithms,the SURC method can generate smooth single-line rivers from dual-line rivers considering different river widths while effectively avoiding burrs and fractured intersections.

A raster-based typification method for multiscale visualization of building features considering distribution patterns

In map multiscale visualization,typification is the process of replacing original objects,such as buildings,using a smaller number of objects while maintaining initial geometrical and distribution characteristics.During the past few decades,many vector-based methods for building typification have been developed,whereas raster-based methods have received less attention.In this paper,a new method for the typification of buildings with different distribution patterns called superpixel building typification(SUBT)is developed based on raster data.Using this method,buildings with different distribution patterns,such as linear,grid and irregular patterns,are first grouped by image connected component detection and superpixel analysis.Then,the new positions for building typification are determined by superpixel resegmentation.Finally,a new representation of the buildings is determined through analysis of the orientation and shape of the buildings in each superpixel.To test the proposed SUBT method,buildings from both cities and countrysides in China are applied to perform typification.The experimental results show that the proposed SUBT method can realize typification for buildings with linear,grid and irregular distributions while effectively maintaining the original distribution characteristics of the buildings.