BACKGROUND
bread wheat  is one of the most important crops providing food to more than  <dig>  billion people in  <dig> developing countries  <cit> .
it is a huge challenge to ensure global food security through sustainable wheat production for the projected population with the increasing adverse impact of climate change  <cit> .
more scientific and targeted exploitation of wild crop relatives is considered to be a valuable strategy to deal with this challenge  <cit> .
aegilops tauschii, d-genome donor to bread wheat, and their derived shws are major reservoir of favorable alleles for economic traits and have been considered as prioritized genetic resources for wheat genetic improvement  <cit> .
significant variations have been reported in shws including grain weight  <cit> , bread-making quality  <cit> , nutritional quality  <cit> , resistance to biotic stresses  <cit>  and abiotic stresses  <cit> .
while previous use of shws focused on their mining for biotic stresses, there is increasing focus on its potential to contribute favorable genes for grain yield as demonstrated by several shws derived varieties released in china, spain, ecuador and mexico  <cit> .
grain yield in wheat is the most important agronomic trait.
it is underpinned by two numerical components i.e., grain weight and grains per m <dig>  in the past four decades, improvement of grain yield has come from increased grains per m <dig> or larger grain sizes, due to the utilization of rht genes in wheat breeding  <cit> .
improvement of the tkw is considered to be an important approach for further improving yield potential in yellow and huai valleys in china and northwest mexico  <cit> .
shws exhibited significant variation for grain weight compared to bread wheat and tkw of up to 67 g have been reported in mexico  <cit> .
cooper et al.
<cit>  performed two consecutive experiments over two years to examine the yield potential of shws under rain-fed field conditions and concluded that grain weight is the most heritable trait and even some lines with higher number of spikes and higher number of grains per spike maintained their grain size and weight.
grain size and shape in wheat significantly affect grain weight and flour yield  <cit>  and appear to be breeding target dictated by market and industry requirements  <cit> .
theoretical models predict that milling yield could be increased by optimizing grain shape and size with large and spherical grains being the optimum grain morphology  <cit> .
however, accurate characterization of grain size and shape remains a big challenge due to laborious, time consuming techniques and complex nature of wheat grain shape.
recent advances in the photometric techniques provide more concise, potentially cheaper phenotypic information and can better devolve the function of complex traits into individual genetic components  <cit> .
di analysis is proving to be a useful tool and can capture the three dimensional shapes of grains using different image orientations  <cit> .
discovery of qtls for grain weight and their validation are important steps to accelerate the speed of successful deployment of favorable alleles through marker-assisted selection  <cit> .
the relative advantages of association mapping  or linkage disequilibrium  mapping over the linkage mapping for the underlying trait mechanisms have been reported  <cit> .
in wheat, several reports have described the identification of qtls for grain size and weight  <cit> .
however, only few studies targeted qtls for grain shape  <cit> , and only gegas et al.
<cit>  reported these function in wild species of wheat relatives.
further, the development of functional markers and cloning of genes relevant to grain weight have become major research focus in the past few years.
many qtls for grain size and weight in rice have been fine-mapped and cloned in wheat including tacwi-1a  <cit> , tasus2-2b  <cit> , tagw2-6a  <cit> , tackx6-d <dig>  <cit> , tasap1-a <dig>  <cit> , tags1-6d  <cit>  and talsu <dig>  <cit> .
the objectives of current study were i) to characterize shws genotypes for grain size and shape and determine its relationship with grain weight using high-throughput digital imaging phenotyping, ii) to identify the potential genomic regions underlying grain phenotypes using dart markers by genome wide association analysis, and iii) to investigate potential function of qtls identified using sequences of dart markers significantly associated with grain phenotypes.
RESULTS
variation in grain morphology of synthetic hexaploid wheat
phenotypic data for grain morphology descriptors were averaged from two cropping seasons in 2010– <dig> and 2011– <dig>  the basic statistics for grain size and shape traits observed in shws are given as additional file 1: table s <dig> and frequency distributions for these traits are shown as additional file 2: figure s <dig>  broad sense heritability was found to be moderate to high for the  <dig> traits and ranged between  <dig>  and  <dig>  for vertical principal component- <dig>  and vertical area , respectively.
seventeen shws showed mean tkw over 60 g and were mostly derived from different durum and ae.
tauschii accessions.
maximum tkw  was observed in aus <dig> and minimum  in aus <dig>  maximum numbers of shws  were derived from durum wheat variety croc_ <dig> which exhibited greater variation for tkw that ranged between  <dig>  to  <dig>  g. similar trend was observed for other measurements including grain width, length and thickness.
some direct measurements such as grain length, width, thickness and indirect measurements like factor from density  and volume are considered to be very important for determining grain size, shape and weight.
grain length ranged from  <dig>  mm  to  <dig>  mm  with an average of  <dig>  mm.
similarly, grain width ranged from  <dig>  mm  to  <dig>  mm  with an average of  <dig>  mm.
similar trend of variability was found for horizontal area and vertical area of grain which are derivatives of horizontal and vertical major and minor axis, respectively.
grain volume ranged from 25 mm <dig>  to 51 mm <dig>  with an average of  <dig>  mm <dig>  the other very important derived measurement ffd ranged from  <dig>   to  <dig>   with an average of  <dig> .
pearsons’s correlation and path coefficient analysis for grain morphology traits
perason’s coefficient of correlation was calculated for all traits based on the data averaged from two seasons .
the maximum positive correlation  was observed between grain volume and horizontal deviation from ellipse , followed by r =  <dig>  between horizontal area and composite  <dig> .
the maximum negative correlation  was observed between vertical roundness  and vertical principal component  <dig> .
the co-efficient of correlation between grain size direct measurements and grain weight was almost positive and significant.
for example, grain length and grain width had positive correlation with tkw with estimate of r =  <dig>  and r =  <dig> , respectively.
similarly, grain thickness is highly correlated with tkw .
the important derived measurements like volume and ffd were also positively correlated with tkw, with r =  <dig>  and r =  <dig> , respectively.
grain volume has higher value of correlation with vertical area  as compared to horizontal area .
similarly, vertical and horizontal principal components have non-significant mixed trend of correlation with grain weight and therefore not shown in table  <dig> in order to have a clear understanding of the effect of individual measurement on grain weight, path co-efficient analysis was computed by taking tkw as dependent variable.
due to the higher number  of variables of grain size and shape, all the descriptors were partitioned into three groups.
first and second groups consisted of ten variables describing horizontal and vertical aspects of grain size and shapes, respectively.
the third group consisted of nine variables and described some miscellaneous derivative measurements.
a pictorial representation of path analysis of the three descriptor groups is given in figure  <dig>  grain thickness exhibited maximum direct effect on grain weight followed by varea, while horizontal area  has relatively less direct effect on grain weight.
some principal components like hpc <dig>  hpc <dig>  vpc <dig> and vpc <dig> showed direct negative effect on grain weight.
both of the important derivatives such as grain volume and ffd have direct positive effect on grain weight.
horizontal and vertical deviations from the ellipse have indirect positive effect on grain weight and both vertical and horizontal perimeters have direct positive effect on grain weight because these are derivatives of grain length, width and thickness.
*and **represents significance at p <  <dig>  and p <  <dig> , respectively.
harea: horizontal area; hperim: horizontal perimeter; hround: horizontal roundness; hdfe: horizontal deviation from ellipse; varea: verticalarea; vperim: vertical perimeter; vround: vertical roundness; vdfe: vertical deviation from ellipse; ffd: factor from density.
marker coverage and polymorphism in synthetic hexaploid wheats
the  <dig> shws were genotyped with dart markers which are bi-allelic markers.
a consensus genetic map of dart markers based on more than  <dig> mapping populations was used to allocate the chromosomal position  <cit> .
in total,  <dig> polymorphic dart markers were used for final genetic and association analysis.
the marker density in this population was  <dig> markers per chromosome.
dart markers integrated into the framework genetic map covered a total genetic distance of  <dig>  cm, with an average density of one marker per  <dig>  cm.
the number of markers per chromosome ranged between  <dig>  and  <dig> .
however, the marker density for d-genome chromosomes was very low  as compared to a and b genomes.
polymorphic information content  value ranged from  <dig>  to  <dig>  with an average of  <dig> .
population structure
analysis of population structure showed that the logarithm of the data likelihood ) on average continued to increase with increasing numbers of assumed subpopulations  from  <dig> to  <dig> with exception of the depression at k <dig>  k <dig> and k <dig> .
differences between ln p  values at two successive k values became non-significant after k =  <dig>  the ad-hoc quantity based on the second order rate of change in the log probability  showed a clear peak at k =  <dig> , which confirmed that a k value of  <dig> was the most probable prediction for the number of subpopulations.
the number of shws in the five subpopulations ranged from  <dig> to  <dig> genotypes.
maximum numbers of shws were observed in k <dig>  and minimum were observed in k <dig> .
the average distance between sub-populations ranged from  <dig>  to  <dig> .
linkage disequilibrium patterns in germplasm panel
ld was estimated by r <dig> at p ≤  <dig>  from all pairs of the dart markers.
ld patterns along  <dig> wheat chromosomes can be visualized as heatmaps .
on a genome-wide level, almost  <dig> % of all pairs of loci were in significant ld .
the average r <dig> of genome-wide ld was  <dig> .
dart markers assigned to their map position were further used to estimate inter- and intra-chromosomal ld.
about 28% of inter-chromosomal pairs of loci were in significant ld, with an average r <dig> of  <dig> , while 42% of intra-chromosomal pairs of loci were insignificant ld with an average r <dig> of  <dig> .
the extent and distribution of ld were graphically displayed by plotting intra-chromosomal r <dig> values for loci in significant ld at p ≤  <dig>  against the genetic distance in centi-morgans and a second-degree loess curve was fitted .
the critical value for significance of r <dig> was estimated at  <dig>  according to  <cit> , and thus all values of r2 >  <dig>  were estimated to be due to genetic linkage.
the baseline intersection with the loess curve was at 9 cm, which was considered as the estimate of the extent of ld in the shw population, although in a few cases high levels of ld were observed over longer distances .
ld decays to an average r <dig> of  <dig>  from  <dig>  as the genetic distance increased to > 10 cm and the markers in complete ld also reduced to  <dig> from  <dig> .
thus the map coverage of 6 cm was deemed appropriate to perform a genome-wide association analysis on the shws population.
marker-trait associations for grain morphology in synthetic hexaploid wheats
marker-traits associations  for grain size and shape were identified in  <dig> shws by association mapping  analysis using general linear model  and mixed linear model  approaches.
mtas for eight important grain size and shape measurements namely tkw, grain length, width, thickness, volume, varea, harea and ffd are given in table  <dig> while the mtas for remaining  <dig> shapes related characteristics are given as additional file 4: table s <dig>  frequency distribution of mta identified by glm and mlm model over the seven wheat linkage groups and three genomes are presented in table  <dig>  chromosomal linkage groups for significant mtas are shown in figure  <dig> while the manhattan plot of all p values observed in this study is presented in figure  <dig>
p
achr chromosome, bpos the marker position on the linkage map based on detering et al.
<cit> , cmaf minor allele frequency, dqtl/gene the previously reported qtls or genes within the same chromosomal regions with reference.
emqtl refers to meta-qtls for grain yield related traits described in zhang et al.
<cit> .
*qtls without reference are extracted from the consensus maps of individual chromosomes as of june  <dig> .
e
a
b
c
d
aglm mtas identified by general linear model only, bmlm mtas identified by mixed linear model only, cboth mtas identified by both model, dfdr number of mtas passed false discovery rate test, enumber of mtas present in each of the seven wheat homoeologous group, fnumber of mtas present in each of the three wheat genomes.
the glm approach identified  <dig> dart loci on  <dig> chromosomal regions to be associated with grain phenotype traits; this was reduced by 60%  when analyzed using mlm model .
using glm, mtas for grain size and shape were identified on all chromosomes except for chromosomes 1d, 4d and 5a.
maximum number of mtas  were found on chromosome 2b followed by 3b , while only one mta was found on chromosome 6d.
maximum numbers of mtas  were identified on the b genome followed by a genome , with the d genome exhibiting the least mtas .
in total,  <dig> dart markers on  <dig> chromosomal regions were associated with  <dig> grain size and shape traits using mlm approach.
among the significant mtas,  <dig> markers represent direct measurements including tkw, grain area, thickness, width and ffd.
out of  <dig> significant mtas, only  <dig> passed the fdr test out of which only three markers  represented direct grain size measurement i.e.
grain width and vertical area.
these markers are on same chromosomal region  and are in significant ld .
phenotypic variability explained by most of the markers were greater than 5%.
the marker wpt- <dig> on chromosome 3b possessed the maximum phenotypic variation  for vpc <dig>
mta analysis also revealed that  <dig> dart loci were associated with multiple traits.
multiple trait associations ranged from two to five traits per dart locus.
twenty one, six, one, and seven dart loci were associated with two, three, four, and five traits, respectively.
association of markers for known genes controlling grain size and weight like tacwi-2a, tasus-6b, tackx-6d and tagw2-2b were also validated in this study as indicated in table  <dig>  the results confirmed the validity of am approach for alleles of these genes in shws.
alleles for the tacwi-2a gene were significantly associated with tkw, grain width and horizontal area with r <dig> of  <dig> % and  <dig> %, respectively.
similarly, allelic variations for tassus-b <dig> were found to be associated with grain width and horizontal area with r <dig> of  <dig> % and  <dig> % respectively.
allelic variation for gene encoding cytokinin oxidase/reductase, tackx-d <dig>  found to be associated with grain thickness, vertical area of grain and vertical deviation from ellipse .
this strong association for all traits including vertical dimensions revealed the effect of the gene on variability for this dimension of the grain.
similarly, aspect ratio was found to be strongly associated with tagw2-6a gene.
relationship between grain phenotype and number of favored alleles
a linear relationship was observed for grain length, width, thickness and weight, where the addition of every favorable allele in a variety additively contributed to enhance the phenotype .
however, there was only one shw having four favorable alleles for grain thickness which reduced the linear correlation and resulted in negative interaction.
similar trend was observed for grain length, where only  <dig> % of the shws have two favorable alleles.
the number of markers associated with tkw and grain width was relatively high as compared to grain length and thickness.
functional analysis of dart clones associated with grain phenotype
sequences of  <dig> darts were used as a query for similarity search using blastx algorithm.
in many cases, sequences were very short therefore matches were also searched in international wheat genome survey sequence  database.
if a longer genomic clone was identified, it was used as a query in blast2go software.
blast search gave positive result for  <dig> dart clones, which therefore represent putative expressed sequences.
however, putative biological function could be predicted for  <dig> dart loci .
the remaining putatively expressed sequences corresponded to est or protein sequences without functional annotation or known domains.
seven of such darts  had association with a grain shape parameter  which has significant negative effect on grain weight.
for d-genome specific darts,  <dig> out of  <dig> sequences were traced for their corresponding scaffold and putative function of  <dig> dart clones could be determined .
four dart sequences were found in proximity of expressed regions, however protein function was uncharacterized.
putative function of four dart sequences on chromosome 3d associated with relatively important grain phenotypes are very important as the members of receptor like kinase  family.
these results are important because these regions may carry novel alleles for grain phenotype and shws can facilitate their identification and subsequent introgression to bread wheat to enhance grain yield.
go: gene ontology; ucp: uncharacterized protein.
discussions
phenotypic evaluation of grain morphology using digital imaging
seed shape and size are among the most important agronomic traits due to their significant effect on grain weight, milling yield, and market price.
manual measurement methods have limits to the number of data, the quality of measurements, and the variety of shape data that can be gleaned.
by contrast, computational methods using di technology could enable us to automatically measure robust size descriptors  and elliptic fourier descriptors  capturing shape variation such as roughness, asymmetric skewing or other two dimensional aspects not encompassed by axes or distinctions in overall object area  <cit> .
only few studies are available based on di analysis of seed size and shape in wheat  <cit> .
among these studies, gegas et al.
<cit> , williams et al.
<cit>  and williams and sorrells  <cit>  used shape variations as targeted traits influencing grain size and weight and results are comparable to our work.
in this study, low correlations between the major grain dimensions and efds indicate that different aspects of grain morphology were captured by each phenotyping method and likely could be selected independently.
because efds were more highly correlated with tkw and grain length than other traits, therefore, it would be preferred if kernel shape were used in selection to increase length and tkw.
the correlations between efds and tkw suggest that they are able to relate the uniformity and smoothness of the kernel to grain weight because roughness or shriveling would be expected to reduce the ratio of internal volume to surface area of the kernel.
use of efds recorded from kernels imaged on end  also can characterize variation in the depth or angle of a wheat seed’s crease which will impact the volume to surface area relationship of a grain.
a large number of significant correlations were observed for remaining size and shape traits .
for the ease of understanding we only discussed important relationships that give us new insight into the complex composition of grain size and shape components.
in the nutshell: i) grain roundness has significant negative relationship with grain length indicating both traits influencing grain weight independently; ii) horizontal and vertical deviations from optimal ellipse were positively correlated with grain length and width, respectively, indicating deviation from the ellipse enhances grain length and width, and ultimately tkw; iii) grain length and width had slightly significant positive correlation indicating the possibility of finding some shws having wider and lengthy grains simultaneously which may lead to above the average tkw.
this possibility of finding co-localized qtls influencing grain length and breadth is expected and discussed below.
however, grain width had more positive impact on tkw as compared to grain length.
although previous studies reported moderate correlations between grain weight, length, and width with r =  <dig> – <dig>   <cit> , and r =  <dig> – <dig>   <cit> , our results were in agreement with lee et al.
<cit> , who reported strong correlation  between kernel weight and size.
studies have shown that kernel weight was positively correlated with grain yield  <cit>  and kernel growth rate  <cit> ; however, xiao et al.
<cit>  found tkw less correlated with grain yield in 1b.1r × non 1b.1r crosses across environments.
all previous reports described grain size and shapes emerged as independent traits in primitive and improved wheat germplasm  <cit> , similar to the results obtained in this study using the d genome synthetic hexaploids.
however, the significant reduction of phenotypic variation in grain shapes in breeding germplasm pool is probably as a result of relatively recent evolutionary and domestication bottleneck.
as a consequence, the phenotypic variability offered by shws may fill the gap and is a good choice germplasm which can be used to improve grain weight of wheat, hence enhancing grain yield.
the association of grain size and shape descriptors with tkw was further resolved by path coefficient analysis which depicted the phenotypic model with more precision.
this revealed that grain thickness has maximum direct effect on grain weight followed by varea, whereas harea has relatively less direct effect on grain weight.
some principal components like hpc <dig>  hpc <dig>  vpc <dig>  and vpc <dig> have direct negative effect on grain weight and loci harboring their control should undergo negative selection in order to get superior grain weight genotypes.
the efficiency of indirect selection depends on the correlation between a selected trait and a target trait as well as the heritability of the selected trait.
gegas et al.
<cit>  confirmed that kernel size and shape were largely independent traits in a study of six wheat populations.
the results showed that the phenotypic correlations among these traits were caused by closely linked genes or genes with pleiotropic effects.
genetic diversity and population structure in synthetic hexaploid wheats
genetic diversity within ae.
tauschii and synthetic hexaploids have been studied using several marker systems  <cit> .
recently, sohail et al.
<cit>  analyzed the diversity using  <dig>  polymorphic dart markers and found the diversity of ae.
tauschii ssp.
strangulata, the origin of d genome of bread wheat, contains only a limited part of whole diversity of ae.
tauschii.
thus, shws produced by crossing between tetraploid wheat and any subspecies of ae.
tauschii include untapped amount of genetic variation in which useful genes for bread wheat breeding must be present.
our results indicate that five substructures were appropriate in delineating the population structure within the shws used in this study.
the assignment of the shws to the five subgroups was largely in agreement with their ae.
tauschii parent and less so with the durum parent.
recently, mulki et al.
<cit>  studied a wide array of synthetic hexaploids and indicated the presence of seven substructures were appropriate in delineating the population structure.
the minor difference in the results may be attributed to the higher number of accessions used as compared to this study.
the frequency of ae.
tauschii accessions amongst the shws varied from one to a maximum of five while the durum elite lines ranged from  <dig> to  <dig>  an indication of the complexity of the crosses.
it has been suggested that the structure algorithm does not converge to an optimal k when complex genetic structures exist, such as strong relatedness within some germplasm  <cit> .
linkage disequilibrium patterns
linkage disequilibrium is influenced by recombination rate, allele frequency, population structure and selection  <cit> .
in this study, the ld generally decreased with the increase of genetic distance with very strong ld between pairs of loci observed at genetic distances of up to 9 cm, suggestive of ld maintained by genetic linkage.
our results are consistent with those reported by previous studies in wheat.
in a similar study using a subset of  <dig> shws, emebiri et al.
<cit>  reported that the general trend was high ld up to 15 cm, and a decline thereafter.
ld was estimated to extend to about 10 cm among  <dig> united states bread wheat elite varieties and breeding lines  <cit> .
crossa et al.
<cit>  reported that some ld blocks extended up to 87 cm in a set of  <dig> bread wheat breeding lines.
breseghello and sorrells  <cit>  suggested that ld may differ among populations and may need to be evaluated for each population on a case-by-case basis.
nevertheless, it is important to characterize germplasm for examining the extent of ld to study the genetic diversity.
overall the observed ld was low in shws and only ~ <dig> % of the marker pairs reached the threshold of  <dig>  r <dig> value in the collection .
generally self-fertilization leads to a more extensive ld due to the several reduced effective recombination levels  <cit> .
the lower values of ld observed in shws are in concordance with what has been previously reported by chao et al.
<cit>  using the snp marker system.
they reported that cimmyt wheat populations with the lowest ld among completely linked loci and the slowest rate of ld decay was possibly a consequence of an intensive use of synthetic wheat lines.
synthetics wheats and their derivatives have greatly increased genetic diversity in hexaploid wheat, particularly in the d-genome  <cit> .
a similar case is observed in these shws where unusual patterns of ld, rate of ld decay and lower pairwise r2
values are attributed to the genomic constitution of the germplasm.
it is well known that the introduction of new haplotypes from divergent population can increase the extent of ld  <cit> .
marker-trait associations and co-linearity with identified qtls
the mtas identified in this study, can be categorized as those affecting  individual dimensions of the seed and tkw,  multiple dimensions of the seed , and  individual dimensions of the seed but not tkw.
this study is the first report in using association mapping for grain size and shape that employed quantitative photometric measurements.
in total,  <dig> mtas for grain length, width, thickness, and tkw are relatively most important due to their immediate effect on enhancing grain yield.
the co-linearity of mtas of different traits was observed on chromosomes 1a, 2b, 3a, 3d, and 5b and indicated these regions as stable.
a complete region on chromosome 2b from  <dig> to  <dig>  cm harbor  <dig> mtas of important grain phenotypes which is strong evidence of the presence of some functional genes within this proximity affecting grain phenotype.
previously,  <dig> meta-qtls were identified on chromosome 2b  <cit> , but none can be co-localized within this region.
the proximity of tasus-b <dig> on chromosome 2b is within some of the mtas identified in this study .
the co-linearity of some of the important genes and qtls revealed the presence of ppd-b <dig>  q.yld.crc-2b and qtkw.sfr-2b within proximity of this region.
the selection based on these dart markers can result in selection of shws carrying better grain size and shape phenotypes which can be exploited for wheat genetic improvement.
previously, only two association mapping studies are available solely focusing on mapping of grain weight qtls  <cit> .
none of two studies used dart markers, hence, it will be difficult to align and compare qtls detected by these studies.
however, we were able to identify five loci within proximity of qtls identified by williams and sorrells  <cit>  using consensus dart map information  <cit> .
these qtls include q <dig>  on chromosome 3d, q <dig>  on chromosome 2a, q <dig>  on chromosome 1a, q <dig>  on chromosome 5b and q <dig>  on chromosome 2b.
previously, qtls affecting seed size have been identified across all chromosomes of wheat, with varying degrees of effect seen for individual qtl  <cit> , and many of them were found within same regions identified in the present study .
it is expected that  <dig> mtas present on chromosomes 2d, 3d, 5d, 6d, and 7d may have novel allelic variability for measured traits.
horizontal area and ffd were found to be associated with markers present on same genetic region  on chromosome 2d indicating the relative importance of this region underlying grain size and weight.
zhang et al.
<cit>  identified a meta-qtl related to grain weight within the same region.
chromosome 3d appeared to have two genomic regions associated with tkw, grain thickness, width, volume and varea.
additionally, the known wheat grain weight encoding gene, tackx-d <dig>  was found to be associated with varea, grain volume and vdfe indicating the contribution of this locus to grain weight may be through the route to enhance vertical area of grain.
similarly, five very important traits  were found to be clustered on the distal portion of chromosome 3d.
several qtls related to grain weight have been identified on chromosome 3d and available in literatures  <cit> .
haplotype analysis of other known grain weight encoding genes, tacwi-2a, tasus-6b, tagw-2b and tasap-a <dig>  also dissected their potential role to enhance grain weight through different photometric measurements of grain size and shape.
mtas solely for tkw, grain length and width were identified on chromosomes 1a, 2b, 3a, 3b, 3d, 4a, 5b, 7a and 7b.
several qtls were previously reported for kernel width and length on different chromosomes; for example, campbell et al.
<cit>  reported qtls on chromosomes 1a, 2a, 2b, 2dl, and 3dl.
breseghello and sorrells  <cit>  reported qtls on 1b, 2d, and 5b.
sun et al.
<cit>  reported qtls on chromosomes 4a and 6a which were absent in this study.
xiao et al.
<cit>  identified a cluster of qtls for grain length, width and weight on chromosome 6d, which also remained absent in this study.
the justified reason for the absence of these qtls is the very different genetic background of shws having a and b genomes from durum wheats and d genome from wild accessions of ae.
tauschii.
therefore, the identification of several qtls is suggestive to be the novel addition to existing information and in case of co-linearity with existing qtls, shws may carry new alleles.
quantitative analyses of the photometric data revealed that grain size and shape are largely independent traits.
this is unlikely to be the result of artificial selection during breeding since size and shape are also independent variables in primitive wheat.
at the developmental level, this phenomenon may reflect differential modulation in growth  along the main axes of the grain at different developmental stages.
the notion that certain developmental constraints during grain growth could lead to morphological changes is further corroborated by recent studies on grain size/shape genes in rice  <cit> .
the gs <dig> locus was found to have major effects on grain length and weight and smaller effects on grain width  <cit> , and the longer grains can be attributed to relaxed constraints during grain elongation  <cit> .
the gw <dig> gene was shown to alter grain width and weight and to lesser extend grain length owing to changes in the width of the spikelet hull  <cit> .
similarly, the sw <dig> gene has been reported to affect grain width by modulating the size of the outer glume  <cit> .
the results of our study demonstrated the value of genome-wide association mapping for identifying mtas for grain size, shape and weight using genetic resources such as the shws.
given the diversity of mtas identified, the shws possessing potentially novel alleles at different genomic regions could be used as parents in a marker-assisted backcrossing scheme to develop genotypes with higher grain weight, hence high yielding, in elite wheat backgrounds.
for potentially new loci associated with grain phenotype, the development of appropriate genetic stocks using bi-parental populations, backcross families, near-isogenic lines and physical and chemical mutagenesis would enable appropriate delineation of the importance of these loci in enhancing grain weight.
the dart marker clones are almost sequenced and information is available in public domain that can assist geneticists to convert dart into sts markers which would facilitate the incorporation of the favorable loci into elite wheat germplasm.
relationship between number of favorable alleles and grain phenotypes
one of the relative advantages of am is the validation of favored alleles in natural germplasm collection  <cit> .
zhang et al.
<cit>  found that allele xgwm <dig> underwent very strong positive selection during modern breeding.
xgwm <dig> maps between xgwm <dig> and xgwm <dig>  with a genetic distance of  <dig>  cm from xgwm <dig>  similar results were obtained for tasus-b <dig> gene for tkw, where most of the chinese wheat germplasm carried favorable allele indicating the high selection pressure  <cit> .
thus, the identification of favored alleles will help in choosing parents for crossing programs, to ensure maximum levels of favored alleles across sets of loci targeted for selection, and to promote fixation at these loci  <cit> .
whereas linear correlations between major grain phenotypes  and favored alleles indicate the additive effects of qtls or genes, the possibility of other genetic effects should not be discounted.
however, powers to detect allelic effect reduce when numbers of germplasm lines are very few .
one interesting phenomenon in wheat is that genes or markers associated with yield vary across latitudes, such as tasus <dig> on chromosome 2b  <cit> , tagw <dig> on chromosome 6a  <cit>  and gpw <dig>  on chromosome 7b  <cit> .
favored alleles usually occur at relatively lower latitudes.
this might indicate that the functional genes at these loci, including mapped alleles and those linked with markers, might be responsive to sunlight and temperature during the growing season  <cit> .
recently, jones et al.
<cit>  devised a strategy to exploit ae.
tauschii diversity for wheat improvement in relation to climatic and environmental conditions of a specific geography.
this informed and rational strategy can be applied to shws by identifying the ae.
tauschii accessions in the pedigree of shws lines with desirable characteristics.
this will enhance the breeding values of shws and breeders will be able to offer novel diversity tailored to the environment in any regional breeding program.
nevertheless, current results are encouraging and wider options are available to exploit shws to enhance grain yield.
functional analysis of trait associated darts and draft genome sequence of ae.
tauschii
dart markers have been widely used for different studies in many plant species including wheat.
for many years they have been used as anonymous markers, however, the acquisition of sequence knowledge of dart markers made them useful tool for many studies such as co-linearity studies, fine mapping of loci of interest, and identification of candidate genes in association mapping.
the in silico identification of putative function of dart loci associated with grain phenotype is a step forward towards exploitation of these loci for practical wheat improvement.
nevertheless, many of the dart sequences blasted for the similarity search did not show positive results or in some cases identified genes of unknown function.
however, in some cases results are encouraging.
the medium to low positive results through blast analysis in this study are in agreement with tinker et al.
<cit>  where only 40% of the dart sequences showed significant blast similarities to the genes in public databases.
however, results were slightly higher for wheat dart sequences and 64% of them matched with the genes in public databases  <cit> .
in the present study, about 75% of the sequences displayed significant blast similarities and 32% of the sequences were fully annotated.
the cluster of sequences of dart markers on chromosome 2b translated into genes with valid biological functions and may be important candidates for future studies.
similarly, some grain shape parameters  have negative effect on grain trait and the down regulation of predicted biological function of such dart sequences  may be the proper interpretation of the results.
overall, the knowledge of the functional meaning of these widespread markers will provide a very useful tool for the identification of candidate genes for traits under investigation.
the strategy here for the functional analysis of d-genome specific darts was slightly different which ultimately yielded more powerful results.
dart sequences were used as query to blast in draft genome sequence of ae.
taushii  <cit>  to locate the scaffold carrying those sequences and to identify the genes within those scaffolds.
this also identified the position of scaffold on chromosome based on the genetic map provided in the supplementary information of jia et al.
<cit> .
the candidate regions within scaffolds were explored for the flanking genes and almost all queries resulted in positive results.
a summary of the results and the genes present in flanking sequences are depicted in table  <dig>  the strong association of markers wpt- <dig>  wpt- <dig>  wpt- <dig>  and wpt- <dig> with several grain phenotype parameters and presence of some important genes with valid biological functions make them priority candidates for the fine mapping and subsequent cloning of the genes responsible to enhance grain size and weight.
similar is in the case of other d-genome specific dart sequences.
overall, this approach proved to be very useful for targeting sequences that might be orthologous to genes in other cereals.
marone et al.
<cit>  used similar approach to identify the genomic regions having nbs-lrr domain superfamily encoding tolerance to biotic stresses in plants, while more than  <dig> dart sequences showed significant similarity to the gene sequences in the public databases of model species such as brachypodium and rice  <cit> .
similarly, the dart markers associated with insect pest resistance were also searched in different bioinformatics databases to assign the translating function to the sequences found similar  <cit> .
webster et al.
<cit>  used the specific wecpdf domain within cell wall invertase gene  as query to search for its homologues in wheat genome survey sequence database and found five potential isoforms on multiple chromosomes.
conclusively, this approach proved to be very useful and may serve as template for gene cloning and further deployment in wheat breeding.
CONCLUSIONS
the integrated uses of phenomics, genomics and bioinformatics have facilitated the identification of several genomic regions and their putative functions to enhance grain size and weight in shws.
the major loci revealed in this study may be of practical value for further improving wheat grain size as a conduit to enhance productivity.
exploiting the unique genetic diversity of the synthetics has a greater comparative advantage over conventional diversity as the alien d genome accessional novel input so far is minimal in wheat varieties.

 bread wheat is one of the most important crops providing food to more than billion people in developing countries. it is a huge challenge to ensure global food security through sustainable wheat production for the projected population with the increasing adverse impact of climate change. more scientific and targeted exploitation of wild crop relatives is considered to be a valuable strategy to deal with this challenge. aegilops tauschii, d-genome donor to bread wheat, and their derived shws are major reservoir of favorable alleles for economic traits and have been considered as prioritized genetic resources for wheat genetic improvement. significant variations have been reported in shws including grain weight, bread-making quality, nutritional quality, resistance to biotic stresses and abiotic stresses. while previous use of shws focused on their mining for biotic stresses, there is increasing focus on its potential to contribute favorable genes for grain yield as demonstrated by several shws derived varieties released in china, spain, ecuador and mexico. grain yield in wheat is the most important agronomic trait. it is underpinned by two numerical components i.e., grain weight and grains per m in the past four decades, improvement of grain yield has come from increased grains per m or larger grain sizes, due to the utilization of rht genes in wheat breeding. improvement of the tkw is considered to be an important approach for further improving yield potential in yellow and huai valleys in china and northwest mexico. shws exhibited significant variation for grain weight compared to bread wheat and tkw of up to 67 g have been reported in mexico. cooper et al. performed two consecutive experiments over two years to examine the yield potential of shws under rain-fed field conditions and concluded that grain weight is the most heritable trait and even some lines with higher number of spikes and higher number of grains per spike maintained their grain size and weight. grain size and shape in wheat significantly affect grain weight and flour yield and appear to be breeding target dictated by market and industry requirements. theoretical models predict that milling yield could be increased by optimizing grain shape and size with large and spherical grains being the optimum grain morphology. however, accurate characterization of grain size and shape remains a big challenge due to laborious, time consuming techniques and complex nature of wheat grain shape. recent advances in the photometric techniques provide more concise, potentially cheaper phenotypic information and can better devolve the function of complex traits into individual genetic components. di analysis is proving to be a useful tool and can capture the three dimensional shapes of grains using different image orientations. discovery of qtls for grain weight and their validation are important steps to accelerate the speed of successful deployment of favorable alleles through marker-assisted selection. the relative advantages of association mapping or linkage disequilibrium mapping over the linkage mapping for the underlying trait mechanisms have been reported. in wheat, several reports have described the identification of qtls for grain size and weight. however, only few studies targeted qtls for grain shape, and only gegas et al. reported these function in wild species of wheat relatives. further, the development of functional markers and cloning of genes relevant to grain weight have become major research focus in the past few years. many qtls for grain size and weight in rice have been fine-mapped and cloned in wheat including tacwi-1a, tasus2-2b, tagw2-6a, tackx6-d, tasap1-a, tags1-6d and talsu. the objectives of current study were i) to characterize shws genotypes for grain size and shape and determine its relationship with grain weight using high-throughput digital imaging phenotyping, ii) to identify the potential genomic regions underlying grain phenotypes using dart markers by genome wide association analysis, and iii) to investigate potential function of qtls identified using sequences of dart markers significantly associated with grain phenotypes.  variation in grain morphology of synthetic hexaploid wheat phenotypic data for grain morphology descriptors were averaged from two cropping seasons in 2010– and 2011– the basic statistics for grain size and shape traits observed in shws are given as additional file 1: table s and frequency distributions for these traits are shown as additional file 2: figure s broad sense heritability was found to be moderate to high for the traits and ranged between and for vertical principal component- and vertical area, respectively. seventeen shws showed mean tkw over 60 g and were mostly derived from different durum and ae. tauschii accessions. maximum tkw was observed in aus and minimum in aus maximum numbers of shws were derived from durum wheat variety croc_ which exhibited greater variation for tkw that ranged between to  g. similar trend was observed for other measurements including grain width, length and thickness. some direct measurements such as grain length, width, thickness and indirect measurements like factor from density and volume are considered to be very important for determining grain size, shape and weight. grain length ranged from  mm to  mm with an average of  mm. similarly, grain width ranged from  mm to  mm with an average of  mm. similar trend of variability was found for horizontal area and vertical area of grain which are derivatives of horizontal and vertical major and minor axis, respectively. grain volume ranged from 25 mm to 51 mm with an average of  mm the other very important derived measurement ffd ranged from to with an average of. pearsons’s correlation and path coefficient analysis for grain morphology traits perason’s coefficient of correlation was calculated for all traits based on the data averaged from two seasons. the maximum positive correlation was observed between grain volume and horizontal deviation from ellipse, followed by r =  between horizontal area and composite. the maximum negative correlation was observed between vertical roundness and vertical principal component. the co-efficient of correlation between grain size direct measurements and grain weight was almost positive and significant. for example, grain length and grain width had positive correlation with tkw with estimate of r =  and r = , respectively. similarly, grain thickness is highly correlated with tkw. the important derived measurements like volume and ffd were also positively correlated with tkw, with r = and r = , respectively. grain volume has higher value of correlation with vertical area as compared to horizontal area. similarly, vertical and horizontal principal components have non-significant mixed trend of correlation with grain weight and therefore not shown in table  in order to have a clear understanding of the effect of individual measurement on grain weight, path co-efficient analysis was computed by taking tkw as dependent variable. due to the higher number of variables of grain size and shape, all the descriptors were partitioned into three groups. first and second groups consisted of ten variables describing horizontal and vertical aspects of grain size and shapes, respectively. the third group consisted of nine variables and described some miscellaneous derivative measurements. a pictorial representation of path analysis of the three descriptor groups is given in figure  grain thickness exhibited maximum direct effect on grain weight followed by varea, while horizontal area has relatively less direct effect on grain weight. some principal components like hpc hpc vpc and vpc showed direct negative effect on grain weight. both of the important derivatives such as grain volume and ffd have direct positive effect on grain weight. horizontal and vertical deviations from the ellipse have indirect positive effect on grain weight and both vertical and horizontal perimeters have direct positive effect on grain weight because these are derivatives of grain length, width and thickness. *and **represents significance at p <  and p < , respectively. harea: horizontal area; hperim: horizontal perimeter; hround: horizontal roundness; hdfe: horizontal deviation from ellipse; varea: verticalarea; vperim: vertical perimeter; vround: vertical roundness; vdfe: vertical deviation from ellipse; ffd: factor from density. marker coverage and polymorphism in synthetic hexaploid wheats the shws were genotyped with dart markers which are bi-allelic markers. a consensus genetic map of dart markers based on more than mapping populations was used to allocate the chromosomal position. in total, polymorphic dart markers were used for final genetic and association analysis. the marker density in this population was markers per chromosome. dart markers integrated into the framework genetic map covered a total genetic distance of  cm, with an average density of one marker per  cm. the number of markers per chromosome ranged between and. however, the marker density for d-genome chromosomes was very low as compared to a and b genomes. polymorphic information content value ranged from to with an average of. population structure analysis of population structure showed that the logarithm of the data likelihood ) on average continued to increase with increasing numbers of assumed subpopulations from to with exception of the depression at k k and k. differences between ln p values at two successive k values became non-significant after k =  the ad-hoc quantity based on the second order rate of change in the log probability showed a clear peak at k = , which confirmed that a k value of was the most probable prediction for the number of subpopulations. the number of shws in the five subpopulations ranged from to genotypes. maximum numbers of shws were observed in k and minimum were observed in k. the average distance between sub-populations ranged from to. linkage disequilibrium patterns in germplasm panel ld was estimated by r at p ≤  from all pairs of the dart markers. ld patterns along wheat chromosomes can be visualized as heatmaps. on a genome-wide level, almost % of all pairs of loci were in significant ld. the average r of genome-wide ld was. dart markers assigned to their map position were further used to estimate inter- and intra-chromosomal ld. about 28% of inter-chromosomal pairs of loci were in significant ld, with an average r of, while 42% of intra-chromosomal pairs of loci were insignificant ld with an average r of. the extent and distribution of ld were graphically displayed by plotting intra-chromosomal r values for loci in significant ld at p ≤  against the genetic distance in centi-morgans and a second-degree loess curve was fitted. the critical value for significance of r was estimated at according to, and thus all values of r2 >  were estimated to be due to genetic linkage. the baseline intersection with the loess curve was at 9 cm, which was considered as the estimate of the extent of ld in the shw population, although in a few cases high levels of ld were observed over longer distances. ld decays to an average r of from as the genetic distance increased to > 10 cm and the markers in complete ld also reduced to from. thus the map coverage of 6 cm was deemed appropriate to perform a genome-wide association analysis on the shws population. marker-trait associations for grain morphology in synthetic hexaploid wheats marker-traits associations for grain size and shape were identified in shws by association mapping analysis using general linear model and mixed linear model approaches. mtas for eight important grain size and shape measurements namely tkw, grain length, width, thickness, volume, varea, harea and ffd are given in table  while the mtas for remaining shapes related characteristics are given as additional file 4: table s frequency distribution of mta identified by glm and mlm model over the seven wheat linkage groups and three genomes are presented in table  chromosomal linkage groups for significant mtas are shown in figure  while the manhattan plot of all p values observed in this study is presented in figure  p achr chromosome, bpos the marker position on the linkage map based on detering et al., cmaf minor allele frequency, dqtl/gene the previously reported qtls or genes within the same chromosomal regions with reference. emqtl refers to meta-qtls for grain yield related traits described in zhang et al.. *qtls without reference are extracted from the consensus maps of individual chromosomes as of june. e a b c d aglm mtas identified by general linear model only, bmlm mtas identified by mixed linear model only, cboth mtas identified by both model, dfdr number of mtas passed false discovery rate test, enumber of mtas present in each of the seven wheat homoeologous group, fnumber of mtas present in each of the three wheat genomes. the glm approach identified dart loci on chromosomal regions to be associated with grain phenotype traits; this was reduced by 60% when analyzed using mlm model. using glm, mtas for grain size and shape were identified on all chromosomes except for chromosomes 1d, 4d and 5a. maximum number of mtas were found on chromosome 2b followed by 3b, while only one mta was found on chromosome 6d. maximum numbers of mtas were identified on the b genome followed by a genome, with the d genome exhibiting the least mtas. in total, dart markers on chromosomal regions were associated with grain size and shape traits using mlm approach. among the significant mtas, markers represent direct measurements including tkw, grain area, thickness, width and ffd. out of significant mtas, only passed the fdr test out of which only three markers represented direct grain size measurement i.e. grain width and vertical area. these markers are on same chromosomal region and are in significant ld. phenotypic variability explained by most of the markers were greater than 5%. the marker wpt- on chromosome 3b possessed the maximum phenotypic variation for vpc mta analysis also revealed that dart loci were associated with multiple traits. multiple trait associations ranged from two to five traits per dart locus. twenty one, six, one, and seven dart loci were associated with two, three, four, and five traits, respectively. association of markers for known genes controlling grain size and weight like tacwi-2a, tasus-6b, tackx-6d and tagw2-2b were also validated in this study as indicated in table  the results confirmed the validity of am approach for alleles of these genes in shws. alleles for the tacwi-2a gene were significantly associated with tkw, grain width and horizontal area with r of % and %, respectively. similarly, allelic variations for tassus-b were found to be associated with grain width and horizontal area with r of % and % respectively. allelic variation for gene encoding cytokinin oxidase/reductase, tackx-d found to be associated with grain thickness, vertical area of grain and vertical deviation from ellipse. this strong association for all traits including vertical dimensions revealed the effect of the gene on variability for this dimension of the grain. similarly, aspect ratio was found to be strongly associated with tagw2-6a gene. relationship between grain phenotype and number of favored alleles a linear relationship was observed for grain length, width, thickness and weight, where the addition of every favorable allele in a variety additively contributed to enhance the phenotype. however, there was only one shw having four favorable alleles for grain thickness which reduced the linear correlation and resulted in negative interaction. similar trend was observed for grain length, where only % of the shws have two favorable alleles. the number of markers associated with tkw and grain width was relatively high as compared to grain length and thickness. functional analysis of dart clones associated with grain phenotype sequences of darts were used as a query for similarity search using blastx algorithm. in many cases, sequences were very short therefore matches were also searched in international wheat genome survey sequence database. if a longer genomic clone was identified, it was used as a query in blast2go software. blast search gave positive result for dart clones, which therefore represent putative expressed sequences. however, putative biological function could be predicted for dart loci. the remaining putatively expressed sequences corresponded to est or protein sequences without functional annotation or known domains. seven of such darts had association with a grain shape parameter which has significant negative effect on grain weight. for d-genome specific darts, out of sequences were traced for their corresponding scaffold and putative function of dart clones could be determined. four dart sequences were found in proximity of expressed regions, however protein function was uncharacterized. putative function of four dart sequences on chromosome 3d associated with relatively important grain phenotypes are very important as the members of receptor like kinase family. these results are important because these regions may carry novel alleles for grain phenotype and shws can facilitate their identification and subsequent introgression to bread wheat to enhance grain yield. go: gene ontology; ucp: uncharacterized protein. discussions phenotypic evaluation of grain morphology using digital imaging seed shape and size are among the most important agronomic traits due to their significant effect on grain weight, milling yield, and market price. manual measurement methods have limits to the number of data, the quality of measurements, and the variety of shape data that can be gleaned. by contrast, computational methods using di technology could enable us to automatically measure robust size descriptors and elliptic fourier descriptors capturing shape variation such as roughness, asymmetric skewing or other two dimensional aspects not encompassed by axes or distinctions in overall object area. only few studies are available based on di analysis of seed size and shape in wheat. among these studies, gegas et al., williams et al. and williams and sorrells used shape variations as targeted traits influencing grain size and weight and results are comparable to our work. in this study, low correlations between the major grain dimensions and efds indicate that different aspects of grain morphology were captured by each phenotyping method and likely could be selected independently. because efds were more highly correlated with tkw and grain length than other traits, therefore, it would be preferred if kernel shape were used in selection to increase length and tkw. the correlations between efds and tkw suggest that they are able to relate the uniformity and smoothness of the kernel to grain weight because roughness or shriveling would be expected to reduce the ratio of internal volume to surface area of the kernel. use of efds recorded from kernels imaged on end also can characterize variation in the depth or angle of a wheat seed’s crease which will impact the volume to surface area relationship of a grain. a large number of significant correlations were observed for remaining size and shape traits. for the ease of understanding we only discussed important relationships that give us new insight into the complex composition of grain size and shape components. in the nutshell: i) grain roundness has significant negative relationship with grain length indicating both traits influencing grain weight independently; ii) horizontal and vertical deviations from optimal ellipse were positively correlated with grain length and width, respectively, indicating deviation from the ellipse enhances grain length and width, and ultimately tkw; iii) grain length and width had slightly significant positive correlation indicating the possibility of finding some shws having wider and lengthy grains simultaneously which may lead to above the average tkw. this possibility of finding co-localized qtls influencing grain length and breadth is expected and discussed below. however, grain width had more positive impact on tkw as compared to grain length. although previous studies reported moderate correlations between grain weight, length, and width with r =  –, and r =  –, our results were in agreement with lee et al., who reported strong correlation between kernel weight and size. studies have shown that kernel weight was positively correlated with grain yield and kernel growth rate; however, xiao et al. found tkw less correlated with grain yield in 1b.1r × non 1b.1r crosses across environments. all previous reports described grain size and shapes emerged as independent traits in primitive and improved wheat germplasm, similar to the results obtained in this study using the d genome synthetic hexaploids. however, the significant reduction of phenotypic variation in grain shapes in breeding germplasm pool is probably as a result of relatively recent evolutionary and domestication bottleneck. as a consequence, the phenotypic variability offered by shws may fill the gap and is a good choice germplasm which can be used to improve grain weight of wheat, hence enhancing grain yield. the association of grain size and shape descriptors with tkw was further resolved by path coefficient analysis which depicted the phenotypic model with more precision. this revealed that grain thickness has maximum direct effect on grain weight followed by varea, whereas harea has relatively less direct effect on grain weight. some principal components like hpc hpc vpc and vpc have direct negative effect on grain weight and loci harboring their control should undergo negative selection in order to get superior grain weight genotypes. the efficiency of indirect selection depends on the correlation between a selected trait and a target trait as well as the heritability of the selected trait. gegas et al. confirmed that kernel size and shape were largely independent traits in a study of six wheat populations. the results showed that the phenotypic correlations among these traits were caused by closely linked genes or genes with pleiotropic effects. genetic diversity and population structure in synthetic hexaploid wheats genetic diversity within ae. tauschii and synthetic hexaploids have been studied using several marker systems. recently, sohail et al. analyzed the diversity using polymorphic dart markers and found the diversity of ae. tauschii ssp. strangulata, the origin of d genome of bread wheat, contains only a limited part of whole diversity of ae. tauschii. thus, shws produced by crossing between tetraploid wheat and any subspecies of ae. tauschii include untapped amount of genetic variation in which useful genes for bread wheat breeding must be present. our results indicate that five substructures were appropriate in delineating the population structure within the shws used in this study. the assignment of the shws to the five subgroups was largely in agreement with their ae. tauschii parent and less so with the durum parent. recently, mulki et al. studied a wide array of synthetic hexaploids and indicated the presence of seven substructures were appropriate in delineating the population structure. the minor difference in the results may be attributed to the higher number of accessions used as compared to this study. the frequency of ae. tauschii accessions amongst the shws varied from one to a maximum of five while the durum elite lines ranged from to an indication of the complexity of the crosses. it has been suggested that the structure algorithm does not converge to an optimal k when complex genetic structures exist, such as strong relatedness within some germplasm. linkage disequilibrium patterns linkage disequilibrium is influenced by recombination rate, allele frequency, population structure and selection. in this study, the ld generally decreased with the increase of genetic distance with very strong ld between pairs of loci observed at genetic distances of up to 9 cm, suggestive of ld maintained by genetic linkage. our results are consistent with those reported by previous studies in wheat. in a similar study using a subset of shws, emebiri et al. reported that the general trend was high ld up to 15 cm, and a decline thereafter. ld was estimated to extend to about 10 cm among united states bread wheat elite varieties and breeding lines. crossa et al. reported that some ld blocks extended up to 87 cm in a set of bread wheat breeding lines. breseghello and sorrells suggested that ld may differ among populations and may need to be evaluated for each population on a case-by-case basis. nevertheless, it is important to characterize germplasm for examining the extent of ld to study the genetic diversity. overall the observed ld was low in shws and only ~ % of the marker pairs reached the threshold of r value in the collection. generally self-fertilization leads to a more extensive ld due to the several reduced effective recombination levels. the lower values of ld observed in shws are in concordance with what has been previously reported by chao et al. using the snp marker system. they reported that cimmyt wheat populations with the lowest ld among completely linked loci and the slowest rate of ld decay was possibly a consequence of an intensive use of synthetic wheat lines. synthetics wheats and their derivatives have greatly increased genetic diversity in hexaploid wheat, particularly in the d-genome. a similar case is observed in these shws where unusual patterns of ld, rate of ld decay and lower pairwise r2 values are attributed to the genomic constitution of the germplasm. it is well known that the introduction of new haplotypes from divergent population can increase the extent of ld. marker-trait associations and co-linearity with identified qtls the mtas identified in this study, can be categorized as those affecting individual dimensions of the seed and tkw, multiple dimensions of the seed, and individual dimensions of the seed but not tkw. this study is the first report in using association mapping for grain size and shape that employed quantitative photometric measurements. in total, mtas for grain length, width, thickness, and tkw are relatively most important due to their immediate effect on enhancing grain yield. the co-linearity of mtas of different traits was observed on chromosomes 1a, 2b, 3a, 3d, and 5b and indicated these regions as stable. a complete region on chromosome 2b from to  cm harbor mtas of important grain phenotypes which is strong evidence of the presence of some functional genes within this proximity affecting grain phenotype. previously, meta-qtls were identified on chromosome 2b, but none can be co-localized within this region. the proximity of tasus-b on chromosome 2b is within some of the mtas identified in this study. the co-linearity of some of the important genes and qtls revealed the presence of ppd-b q.yld.crc-2b and qtkw.sfr-2b within proximity of this region. the selection based on these dart markers can result in selection of shws carrying better grain size and shape phenotypes which can be exploited for wheat genetic improvement. previously, only two association mapping studies are available solely focusing on mapping of grain weight qtls. none of two studies used dart markers, hence, it will be difficult to align and compare qtls detected by these studies. however, we were able to identify five loci within proximity of qtls identified by williams and sorrells using consensus dart map information. these qtls include q on chromosome 3d, q on chromosome 2a, q on chromosome 1a, q on chromosome 5b and q on chromosome 2b. previously, qtls affecting seed size have been identified across all chromosomes of wheat, with varying degrees of effect seen for individual qtl, and many of them were found within same regions identified in the present study. it is expected that mtas present on chromosomes 2d, 3d, 5d, 6d, and 7d may have novel allelic variability for measured traits. horizontal area and ffd were found to be associated with markers present on same genetic region on chromosome 2d indicating the relative importance of this region underlying grain size and weight. zhang et al. identified a meta-qtl related to grain weight within the same region. chromosome 3d appeared to have two genomic regions associated with tkw, grain thickness, width, volume and varea. additionally, the known wheat grain weight encoding gene, tackx-d was found to be associated with varea, grain volume and vdfe indicating the contribution of this locus to grain weight may be through the route to enhance vertical area of grain. similarly, five very important traits were found to be clustered on the distal portion of chromosome 3d. several qtls related to grain weight have been identified on chromosome 3d and available in literatures. haplotype analysis of other known grain weight encoding genes, tacwi-2a, tasus-6b, tagw-2b and tasap-a also dissected their potential role to enhance grain weight through different photometric measurements of grain size and shape. mtas solely for tkw, grain length and width were identified on chromosomes 1a, 2b, 3a, 3b, 3d, 4a, 5b, 7a and 7b. several qtls were previously reported for kernel width and length on different chromosomes; for example, campbell et al. reported qtls on chromosomes 1a, 2a, 2b, 2dl, and 3dl. breseghello and sorrells reported qtls on 1b, 2d, and 5b. sun et al. reported qtls on chromosomes 4a and 6a which were absent in this study. xiao et al. identified a cluster of qtls for grain length, width and weight on chromosome 6d, which also remained absent in this study. the justified reason for the absence of these qtls is the very different genetic background of shws having a and b genomes from durum wheats and d genome from wild accessions of ae. tauschii. therefore, the identification of several qtls is suggestive to be the novel addition to existing information and in case of co-linearity with existing qtls, shws may carry new alleles. quantitative analyses of the photometric data revealed that grain size and shape are largely independent traits. this is unlikely to be the result of artificial selection during breeding since size and shape are also independent variables in primitive wheat. at the developmental level, this phenomenon may reflect differential modulation in growth along the main axes of the grain at different developmental stages. the notion that certain developmental constraints during grain growth could lead to morphological changes is further corroborated by recent studies on grain size/shape genes in rice. the gs locus was found to have major effects on grain length and weight and smaller effects on grain width, and the longer grains can be attributed to relaxed constraints during grain elongation. the gw gene was shown to alter grain width and weight and to lesser extend grain length owing to changes in the width of the spikelet hull. similarly, the sw gene has been reported to affect grain width by modulating the size of the outer glume. the results of our study demonstrated the value of genome-wide association mapping for identifying mtas for grain size, shape and weight using genetic resources such as the shws. given the diversity of mtas identified, the shws possessing potentially novel alleles at different genomic regions could be used as parents in a marker-assisted backcrossing scheme to develop genotypes with higher grain weight, hence high yielding, in elite wheat backgrounds. for potentially new loci associated with grain phenotype, the development of appropriate genetic stocks using bi-parental populations, backcross families, near-isogenic lines and physical and chemical mutagenesis would enable appropriate delineation of the importance of these loci in enhancing grain weight. the dart marker clones are almost sequenced and information is available in public domain that can assist geneticists to convert dart into sts markers which would facilitate the incorporation of the favorable loci into elite wheat germplasm. relationship between number of favorable alleles and grain phenotypes one of the relative advantages of am is the validation of favored alleles in natural germplasm collection. zhang et al. found that allele xgwm underwent very strong positive selection during modern breeding. xgwm maps between xgwm and xgwm with a genetic distance of  cm from xgwm similar results were obtained for tasus-b gene for tkw, where most of the chinese wheat germplasm carried favorable allele indicating the high selection pressure. thus, the identification of favored alleles will help in choosing parents for crossing programs, to ensure maximum levels of favored alleles across sets of loci targeted for selection, and to promote fixation at these loci. whereas linear correlations between major grain phenotypes and favored alleles indicate the additive effects of qtls or genes, the possibility of other genetic effects should not be discounted. however, powers to detect allelic effect reduce when numbers of germplasm lines are very few. one interesting phenomenon in wheat is that genes or markers associated with yield vary across latitudes, such as tasus on chromosome 2b, tagw on chromosome 6a and gpw on chromosome 7b. favored alleles usually occur at relatively lower latitudes. this might indicate that the functional genes at these loci, including mapped alleles and those linked with markers, might be responsive to sunlight and temperature during the growing season. recently, jones et al. devised a strategy to exploit ae. tauschii diversity for wheat improvement in relation to climatic and environmental conditions of a specific geography. this informed and rational strategy can be applied to shws by identifying the ae. tauschii accessions in the pedigree of shws lines with desirable characteristics. this will enhance the breeding values of shws and breeders will be able to offer novel diversity tailored to the environment in any regional breeding program. nevertheless, current results are encouraging and wider options are available to exploit shws to enhance grain yield. functional analysis of trait associated darts and draft genome sequence of ae. tauschii dart markers have been widely used for different studies in many plant species including wheat. for many years they have been used as anonymous markers, however, the acquisition of sequence knowledge of dart markers made them useful tool for many studies such as co-linearity studies, fine mapping of loci of interest, and identification of candidate genes in association mapping. the in silico identification of putative function of dart loci associated with grain phenotype is a step forward towards exploitation of these loci for practical wheat improvement. nevertheless, many of the dart sequences blasted for the similarity search did not show positive results or in some cases identified genes of unknown function. however, in some cases results are encouraging. the medium to low positive results through blast analysis in this study are in agreement with tinker et al. where only 40% of the dart sequences showed significant blast similarities to the genes in public databases. however, results were slightly higher for wheat dart sequences and 64% of them matched with the genes in public databases. in the present study, about 75% of the sequences displayed significant blast similarities and 32% of the sequences were fully annotated. the cluster of sequences of dart markers on chromosome 2b translated into genes with valid biological functions and may be important candidates for future studies. similarly, some grain shape parameters have negative effect on grain trait and the down regulation of predicted biological function of such dart sequences may be the proper interpretation of the results. overall, the knowledge of the functional meaning of these widespread markers will provide a very useful tool for the identification of candidate genes for traits under investigation. the strategy here for the functional analysis of d-genome specific darts was slightly different which ultimately yielded more powerful results. dart sequences were used as query to blast in draft genome sequence of ae. taushii to locate the scaffold carrying those sequences and to identify the genes within those scaffolds. this also identified the position of scaffold on chromosome based on the genetic map provided in the supplementary information of jia et al.. the candidate regions within scaffolds were explored for the flanking genes and almost all queries resulted in positive results. a summary of the results and the genes present in flanking sequences are depicted in table  the strong association of markers wpt- wpt- wpt- and wpt- with several grain phenotype parameters and presence of some important genes with valid biological functions make them priority candidates for the fine mapping and subsequent cloning of the genes responsible to enhance grain size and weight. similar is in the case of other d-genome specific dart sequences. overall, this approach proved to be very useful for targeting sequences that might be orthologous to genes in other cereals. marone et al. used similar approach to identify the genomic regions having nbs-lrr domain superfamily encoding tolerance to biotic stresses in plants, while more than dart sequences showed significant similarity to the gene sequences in the public databases of model species such as brachypodium and rice. similarly, the dart markers associated with insect pest resistance were also searched in different bioinformatics databases to assign the translating function to the sequences found similar. webster et al. used the specific wecpdf domain within cell wall invertase gene as query to search for its homologues in wheat genome survey sequence database and found five potential isoforms on multiple chromosomes. conclusively, this approach proved to be very useful and may serve as template for gene cloning and further deployment in wheat breeding.  the integrated uses of phenomics, genomics and bioinformatics have facilitated the identification of several genomic regions and their putative functions to enhance grain size and weight in shws. the major loci revealed in this study may be of practical value for further improving wheat grain size as a conduit to enhance productivity. exploiting the unique genetic diversity of the synthetics has a greater comparative advantage over conventional diversity as the alien d genome accessional novel input so far is minimal in wheat varieties. 
statistical simulations showed that favorable alleles for thousand kernel weight, grain length, width and thickness have additive genetic effects. in this study, we report the results from using digital imaging of grain size and shape to understand the relationship among different components of this trait, their contribution to enhance grain weight, and to identify genomic regions controlling grain morphology using genome wide association mapping with high density diversity array technology and allele-specific markers. twenty eight marker-trait associations on the d genome chromosomes 2d, 3d and 6d may carry novel alleles with potential to enhance grain weight due to the use of untapped wild accessions of aegilops tauschii. tacwi-2a, tasus-2b, tackx6-3d and tagw2-6a, were also associated with tkw, grain width and thickness. a total of synthetic hexaploid wheats were grouped into five different sub-clusters by bayesian structure analysis using unlinked dart markers. grain size and shape greatly influence grain weight which ultimately enhances grain yield in wheat. digital imaging based phenomic characterization can capture the three dimensional variation in grain size and shape than has hitherto been possible. significant positive correlations were observed between grain weight and grain size measurements such as grain length, width, thickness and factor from density. allelic variations for known genes controlling grain size and weight, viz. in silico functional analysis predicted a range of biological functions for dart loci and receptor like kinase, known to affect plant development, appeared to be common protein family encoded by several loci responsible for grain size and shape. these approaches provided great opportunity to understand the breeding value of shws for improving grain weight and enhanced our deep understanding on molecular genetics of grain weight in wheat. conclusively, we demonstrated the application and integration of multiple approaches including high throughput phenotyping using di, genome wide association studies and in silico functional analysis of candidate loci to analyze target traits, and identify candidate genomic regions underlying these traits. in total, loci over chromosomal regions and loci over chromosomal regions were associated with grain morphology by genome wide analysis using general linear model and mixed linear model approaches, respectively. linkage disequilibrium decay was observed among dart loci > 10 cm distance and approximately 28% marker pairs were in significant ld.
 grain size and shape greatly influence grain weight which ultimately enhances grain yield in wheat. digital imaging based phenomic characterization can capture the three dimensional variation in grain size and shape than has hitherto been possible. in this study, we report the results from using digital imaging of grain size and shape to understand the relationship among different components of this trait, their contribution to enhance grain weight, and to identify genomic regions controlling grain morphology using genome wide association mapping with high density diversity array technology and allele-specific markers.  significant positive correlations were observed between grain weight and grain size measurements such as grain length, width, thickness and factor from density. a total of synthetic hexaploid wheats were grouped into five different sub-clusters by bayesian structure analysis using unlinked dart markers. linkage disequilibrium decay was observed among dart loci > 10 cm distance and approximately 28% marker pairs were in significant ld. in total, loci over chromosomal regions and loci over chromosomal regions were associated with grain morphology by genome wide analysis using general linear model and mixed linear model approaches, respectively. they were mainly distributed on homoeologous group and chromosomes. twenty eight marker-trait associations on the d genome chromosomes 2d, 3d and 6d may carry novel alleles with potential to enhance grain weight due to the use of untapped wild accessions of aegilops tauschii. statistical simulations showed that favorable alleles for thousand kernel weight, grain length, width and thickness have additive genetic effects. allelic variations for known genes controlling grain size and weight, viz. tacwi-2a, tasus-2b, tackx6-3d and tagw2-6a, were also associated with tkw, grain width and thickness. in silico functional analysis predicted a range of biological functions for dart loci and receptor like kinase, known to affect plant development, appeared to be common protein family encoded by several loci responsible for grain size and shape.  conclusively, we demonstrated the application and integration of multiple approaches including high throughput phenotyping using di, genome wide association studies and in silico functional analysis of candidate loci to analyze target traits, and identify candidate genomic regions underlying these traits. these approaches provided great opportunity to understand the breeding value of shws for improving grain weight and enhanced our deep understanding on molecular genetics of grain weight in wheat. 