BACKGROUND
until the end of the 20th century, the lack of high throughput genotyping techniques and the limited development of high-density snp arrays have hindered the advancement of genome-based breeding strategies for crop improvement.
during the last  <dig> years, the genome sequences of about  <dig> plant species, including some from the rosaceae family, were made publicly available  <cit> , which offers opportunities for transforming breeding strategies to improve the yield and quality of major crops.
genome-wide association studies  and genomic selection  are among some new breeding tools proposed for crop improvement  <cit> .
the underlying philosophy of both these strategies is to genotype enough markers across the genome so that at least one of the genotyped markers is likely in ld with the quantitative trait locus  alleles  <cit> .
both gs and gwas can be conducted using the same genotypic and phenotypic data, but their objectives are different  <cit> .
gs is used to predict phenotype from marker profiles alone, to reduce dramatically the length of the breeding cycle and the costs involved in phenotyping  <cit> .
the objective of gwas is to identify novel functional variation that can be deployed in cultivar development through marker-assisted selection  <cit> .
gwas studies in humans have used two fundamentally different designs  <cit> : family-based and population-based .
the power of a gwas of a quantitative phenotype using related individuals was shown to be slightly lower than that for a sample of unrelated individuals in a human study  <cit> , but in crops and livestock controlled mating could make family designs more powerful than a population sample  <cit> .
both population-based  <cit>  and family-based  <cit>  designs have been used for gwas in crops.
the advantages of using relatives are manifold, including greater quality control, the ability to perform within-family tests of association that are robust to population stratification, and joint linkage and association analysis.
a nested association mapping  population  <cit> , which consists of multiple families derived from multiple inbred lines crossed to one or more reference inbred line, has been used for gwas of different traits in maize.
multi-parent advanced generation inter-cross  population was first used in arabidopsis <cit> .
other family-based designs, such as parent-offspring, multi-generational pedigrees and multi-parent crosses, have historically been used in quantitative genetic studies.
thus, for plant populations, it is reasonable to consider large number of progenies derived from controlled crosses in various mating schemes for gwas  <cit> .
population stratification and cryptic relatedness among studied individuals, when not taken into account, could lead to spurious genotype-phenotype associations in gwas.
population stratification refers to the inclusion of individuals from different populations, while cryptic  relatedness refers to the presence of varying degree of genetic relationships between individuals within the study sample.
gwas methods based on the unified mixed linear model  were developed by  <cit>  to account for population-level membership  and individual-level relationships .
a realized individual-level kinship matrix  calculated using molecular markers is more efficient than the pedigree-based kinship matrix  as it can account for mendelian sampling and segregation distortion  <cit> .
as family sizes in plant populations are much larger than those in other species, implementation of mlm was computationally very intensive.
therefore, the efficient mixed model association expedited  algorithm was developed to reduce this computational burden by re-parameterizing the mlm likelihood function  <cit> .
further, a computationally more efficient and powerful compressed mlm  that uses a group kinship matrix calculated from clustered individuals was developed recently  <cit> .
development of these methods has now made it much easier to analyze large amounts of data for gwas.
unlike fitting each snp in turn, which is a typical feature of gwas, simultaneously fitting high density genome-wide snps could avoid the need to fit population and pedigree effects in mlm specifically  <cit> .
in  <dig>  an international consortium published the first draft of the apple  genome sequence using dna from a popular apple variety ‘golden delicious’  <cit> , which led to re-sequencing of  <dig> apple cultivars that are the founders in global apple breeding programs.
these efforts produced a huge reservoir of dna markers, which helped the development of the first-generation apple infinium snp chip, comprising nearly  <dig>  markers  <cit> .
in the present study, we used this 8k snp chip for gwa analysis of various fruit quality traits in a family-based design.
traits considered in this study relate to eating quality: fruit firmness  and titratable acidity ; visual quality: red-flesh coverage ; see methods); and susceptibility to physiological disorders: internal flesh browning , bitter pit  and fruit splitting  .
to elucidate the relative contributions of different genomic regions, we implemented single-snp analysis models, with and without accounting for population structure, and compared these with a model fitting all markers simultaneously.
the statistical power of detecting snp-trait associations was calculated using an expression derived in this study.
the relative advantage of using realized relationships compared with pedigree-based expected relationships was also investigated.
to our knowledge, this is the first large snp array-based gwas study to unravel the genetic architecture of quantitative traits for any major fruit crop.
RESULTS
realized relationships and population structure
a plot of the first two principal components of the snp genotypes data matrix grouped seedlings largely according to their familial relationships .
some individuals did not cluster within their pedigree-assigned full-sib family groupings.
for example, individuals in two families, namely a <dig> and a <dig>  which have the same maternal parent, were clustered less tightly than the other five families.
a break-away group of individuals from families a <dig> and a <dig>  having the same maternal parent, apparently formed a separate cluster away from their respective full-sibs .
these patterns of clustering suggested some pollen contamination, so the actual number of pollen parents should be higher than that suggested by the mating design.
overall, a product–moment correlation of  <dig>  was observed between pedigree-based  and snp-based estimates of pair-wise coefficient of relationships.
the average pair-wise coefficient of relationships among all study individuals, obtained from the a and g matrices, were  <dig>  and  <dig>  respectively, reflecting that there are many more relationships not captured by the known pedigree records.
the proportion of phenotypic variation explained rlr <dig> using the g matrix  was higher than that using the a matrix for all traits .
results obtained after removing apparent contaminant seedlings, identified from pca analysis  and also by using plink software , suggested that the magnitude of differences in rlr <dig> values were almost identical  to those in figure  <dig>  information presented in figures  <dig> and  <dig> would suggest that using g would better account for population stratification than a, so only gwas results  using g are presented here.
linkage disequilibrium
the pattern of ld  decay in our gwas population of  <dig> individuals  was compared with that observed in the successive generation .
results showed a high degree of ld even at longer distances between markers; for example, in the second generation the average r <dig> for snps separated by  <dig>  mbp,  <dig>  mbp , and  <dig>  mbp was  <dig> ,  <dig> , and  <dig> , respectively .
this is somewhat lower compared to ld in the first generation , but the pattern of ld decay was quite similar in both generations .
genome-wide associations
goodness-of-fit of ‘q+k’  and ‘k’  models were compared to understand whether population structure could bias results.
different numbers of pcs of the snp genotypes matrix constituted the q matrix.
the rlr <dig> values of the ‘q+k’ and ‘k’ models were identical for wci, ta and bp, but were higher for ‘q+k’ for the other three traits.
thus, the optimum number, as determined using the bayesian information criterion , of pcs varied for different traits:  <dig> for wci, ta and bp;  <dig> for ib; and  <dig> for ff and cr.
however, results with or without incorporating q in equation  <dig> were not materially different, suggesting that accounting only for cryptic relatedness was sufficient to account for population stratification.
the profiles of p-values ) for all tested snps for each trait are illustrated in figure  <dig>  uncorrected p-values of p <  <dig> × 10- <dig>  which roughly equates to a genome-wide p-value of  <dig>   as we tested a total of  <dig>  snps, was used as a significance threshold for individual snp testing.
the numbers of genome-wide significant snps detected for fruit firmness , weighted cortical intensity , internal browning , titratable acidity , fruit cracking  and bitter pit  were  <dig>   <dig>   <dig>   <dig>   <dig> and  <dig> respectively.
most of the significant snps for any trait were clustered within a small genomic region, suggesting the presence of large-effect qtl at those positions.
snp-trait association signals for ff were identified on linkage groups  lg <dig> and lg10; for wci and ib on lg <dig> and lg16; for ta on lg8; for cr and bp on lg <dig> .
the snp with the largest effect on ff was located on lg <dig>  and this snp is a t/g variant located within the first exon of the polygalacturonase  gene ,  <dig>  kb from the top of lg <dig> .
a snp with a massive effect  on wci was located on lg <dig> .
this snp on lg <dig> is a t/c variant and is located within the second exon of the mdmyb <dig> gene ,  <dig>  kb from the bottom of lg <dig>  a cluster of snps with large effects on cr and bp, and moderate effects on wci and ib, resides within the leucoanthocyanidin reductase  gene  that is located between  <dig>  kb and  <dig>  kb on the top of lg <dig>  the most significant snps described here are probably not the causative ones for our study traits due to extensive ld.
for all traits except ff, the q-q plots  showed a close adherence of the observed and expected –log <dig> values over most of the range, implying that the significant snps  identified by the unified mma are unlikely to be biased by population stratification.
the majority of snps individually explained only a small proportion of phenotypic variation , while the largest-effect snp explained  <dig>   <dig>   <dig>   <dig>   <dig> and 11% of the phenotypic variation for ff, wci, ib, ta, cr and bp respectively .
the joint contribution of genome-wide significantly associated snps was also investigated.
because of ld, there were many significant snps within a small genomic region, so only the snps with the largest test statistics within  <dig> mb regions were chosen.
the joint rlr <dig> calculated by fitting the chosen snps together in equation  <dig>  for ff, wci, ib, ta, cr and bp were  <dig> ,  <dig> ,  <dig> ,  <dig> ,  <dig>  and  <dig>  respectively , suggesting some improvement over single-snp analysis.
fitting all  <dig>  markers simultaneously  captured nearly all genetic variance  for most of the traits .
correlation coefficients between snp allele substitution effects  obtained from single-snp analysis and all-snp analysis were about  <dig>  for all traits, and largest-effect snps were generally common to both methods .
1estimates of narrow-sense heritability  obtained using pedigree-based relationships matrix .
approximate standard errors of ha <dig> estimates varied from  <dig>   to  <dig>  .
2proportion of the phenotypic variance explained jointly by genome-wide significant snps.
3simultaneously using all  <dig>  markers in the form of the g matrix.
approximate standard errors of hg <dig> estimates varied from  <dig>   to  <dig>  .
genomic regions with significant effects on the two pairs of traits  were further investigated by comparing lg-level estimated genetic correlations  for these two pairs of traits.
results suggested that rg values for the lgs harboring common significant regions were relatively higher than those for other lgs.
some of these lg-level correlations were quite different in magnitude as well as direction from the whole-genome correlation .
power of the gwas
the power of detecting marker-trait association for various qtl allele frequencies and trait heritabilities is shown in figure  <dig>  a ld value of  <dig>  between a marker and qtl allele was assumed.
for an unrelated sample size of  <dig> individuals , the power of detection of an association with a locus explaining 2% of the phenotypic variation was  <dig> , when marker and qtl allele frequency were  <dig> .
the power increased with reductions in marker and qtl allele frequencies.
for a fixed sample size, the power of detecting snp-trait associations declined with increasing relatedness among study individuals, but loss of power was minimal.
the effect of trait heritability became more evident as the degree of relatedness increased .
discussion
realized coefficient of relationships
the availability of genome sequence, the abundance of dna markers, and high throughput genotyping platforms are providing a range of applications of molecular markers, including pedigree reconstruction, estimation of genetic parameters, and understanding relationships between genotype and phenotype in various species  <cit> .
using a likelihood ratio based parameter rlr <dig>  our study showed that using snp-based realized relationships in mlm could provide a better goodness-of-fit than using pedigree-based expected relationships.
our results also showed that for all traits, except ib, fitting all markers simultaneously could explain most or all the trait heritability.
similar results have been reported in studies on humans  <cit>  and animals  <cit> .
also, approximate standard errors of g-based estimates of h <dig> were considerably less than those for a-based because the former captured genetic relationships that are not accessible from pedigree records.
similar to studies on animals  <cit> , our results suggest that the accuracy of artificial selection in plants species can also be increased by using more precise marker-derived estimates of genetic parameters.
snp-trait genome-wide associations
with only a little loss of power, family-based designs in association studies offer various advantages compared with population-based designs  <cit> .
the average snp-derived pair-wise coefficient of relationship in our study was about  <dig> , but the loss of power to detect snp-trait association was small  compared with that for an unrelated sample of the same size.
various factors such as sample size, high ld, minimal effect of population structure, and the presence of some large-effect qtl provide high confidence in the snp-trait associations identified in this study.
the snp array used in this study was designed to encompass snps in the coding region of predicted gene models and some candidate genes such as mdmyb <dig>  mdpg, and mdlar <cit> .
peak association signals for ff, wci and ta were located close to genomic regions that have been previously identified in bi-parental qtl mapping studies.
the snps showing the largest effect on ff on lg <dig>  reside in the polygalacturonase  gene, which depolymerizes cell wall pectin, and the involvement of this gene in the fruit softening process has been previously demonstrated in apple  <cit> .
red color in apple flesh results from a high concentration of anthocyanins.
the role of the mdmyb <dig> gene on anthocyanin biosynthesis in red-fleshed apple was demonstrated using various approaches  <cit> , and this gene has been mapped to lg <dig>  <cit> .
the snp marker associated with weighted cortical intensity  in our experiment is located in the second exon of mdmyb <dig>  which is physically close to the motif in the mdmyb <dig> promoter that causally regulates transcription of mdmyb <dig> itself and thereby anthocyanin synthesis in apple flesh  <cit> .
a cluster of snps at lg <dig> commonly associated with wci and ib resides in the mdlar <dig> candidate gene.
lar <dig> is a key enzyme in the flavonoid biosynthetic pathway, reducing leucoanthocyanidin into the flavanol compound catechin, a monomer of condensed tannins .
perhaps condensed tannins  act as co-pigments of cyanidin to create more intense red coloration in the fruit and hence the effect on wci.
common genomic regions  found associated with wci and ib are supported by results showing high genetic correlation  between these two traits  <cit> .
also, cold-stored fruit from all mdmyb <dig> transgenic lines of cultivar ‘royal gala’ showed varying degrees of symptoms of ib  <cit> , suggesting a pleiotropic effect of mdmyb <dig> on wci and ib.
in our study, the estimated genetic correlation differed in degree as well as direction across different lgs, suggesting some possibility of breaking this undesirable correlation by means of carefully designed breeding and selection strategies, but further work on elucidating the genetic architecture of wci and ib is required first.
the distribution of snp effects for ta  suggests one major qtl on lg <dig>  supporting similar results from bi-parental qtl mapping studies  <cit> .
however, there is no published report of candidate genes for ta on apple lg <dig>  segregation analysis approaches showed that inheritance of ta in a large apple population was better described by a mixed genetic architecture .
our results appeared to be in agreement with  <cit>  in the sense that the largest-effect snp accounted for about half the genetic variation, while the other half was accounted for by small-effect genes.
cr, which is a pre-harvest physiological disorder of apple, can be a serious economic problem for some cultivars  <cit> .
however, little is known about the genetic architecture of this trait.
similarly to our results, estimate of h <dig> from a previous study  <cit>  indicated moderate genetic control of cr.
while little is known on the physiological causes of genetic variability in cr susceptibility, it may be linked to the internal properties of the fruit during growth and differences in the elasticity of the peel when under particular stresses and strains caused by the developing parenchyma cells beneath it  <cit> .
to our knowledge, there is no published report on marker-trait association for cr.
a cluster of snps with a large effect on cr resides within the mdlar <dig> candidate gene on lg <dig>  which was previously reported to influence some other fruit quality traits such as astringency  <cit>  and polyphenolic compounds  <cit> .
bp is also a serious physiological disorder whose expression is generally observed in fruit after storage, but symptoms can also be observed on the fruit surface at harvest , and in our study they were classified as the same disorder.
genetic predisposition, calcium nutrition of the fruit, and environmental factors influence incidence of bp  <cit> .
based on the segregation ratio of resistant to susceptible seedlings, it was hypothesized that resistance to bp is controlled by two major dominant genes, named bp- <dig> and bp- <dig> <cit> .
different segregation ratios  of resistance to susceptible seedlings were observed in various families in our study, suggesting a complex nature to this trait, which is further supported by our results showing that gwa-significant snps explained only about half the observed genetic variation .
interestingly, the same cluster of snps on lg <dig> showed association with expression of bp and cr, and the direction and magnitude of lg-level genetic correlations were similar.
molecular, physiological and biochemical pathways that commonly contribute to the expression of these two traits are poorly understood, but our study provides a genomic hotspot for further investigations.
mlm that concurrently fits all available snps has been adapted in recent gwas in animals  <cit>  following an earlier study  <cit>  that showed that provided high-density snps are fitted simultaneously, admixed populations can be used to obtain reliable snp effects even if pedigree structure and population structure have not been explicitly modeled.
high correlations between snp ases obtained from the ‘q+k’ model  and all-marker analysis  for all six traits in this study  reinforces the findings of  <cit> .
application of snp-trait associations
in our study population, the average ld between snps separated by  <dig> kb was high  largely because of relatedness  among seedlings and small effective population size.
it is not uncommon to find different ld structures in different types of plant populations within a species.
for example, in maize, ld decays within  <dig> kb in land races, within  <dig> kb in diverse inbred lines, and can extend up to  <dig> kb in commercial elite inbred lines .
preliminary results  from an unrelated set of  <dig> individuals from a diverse apple germplasm collection showed that for a given distance  between markers, the extent of ld was almost one-third  of that in this study.
one practical implication of these results is that marker-trait associations identified in advanced-generation crosses may not be repeated in relatively less improved breeding material .
one of the key goals of gwas is to identify large-effect marker-trait associations that can be deployed through marker-assisted selection  in subsequent generations of cultivar development populations.
however, in order to conduct mas using these snps in successive generations, strong ld between marker and qtl must persist across generations.
generally, only a selected set of individuals from the current generation are used as parents for the subsequent generation.
selection will lead to changes in allele frequencies at marker and trait loci, potentially reducing the ld between two loci, similar to that observed in the second generation of our study material .
as a result, the efficiency of gwas-associated snps could be lower in the following generations.
nevertheless, except for wci, the significant snps jointly explained less than 50% of the trait heritability in this study, which raises a question of how much variation in a quantitative trait needs to be accounted by a marker  so that it would be worthwhile for mas to be applied.
such a mas scheme is generally viewed as cost effective compared with the genome selection, but this scheme does not bypass the phenotypic evaluation stage because there could be some quantitative traits for which no significant snps are identified.
on the other hand however, a small snp assay comprising gwa-significant snps for the key breeding traits could be used for pre-screening of seedlings before further field evaluation.
such an approach will not reduce the length of the breeding/selection cycle, but will shift the mean of the selection population.
in order to keep the accuracy of mas similar to that in the generation where snps were identified, periodical recalibration of snp effects would be necessary  <cit> .
CONCLUSIONS
the use of realized relationship matrix will provide higher accuracy of estimated genetic parameters, resulting in increased accuracy of artificial selection.
there are apparently major differences in the genetic architecture of various traits in this study, i.e.
for traits with similar heritability the distributions of snps effect were very different.
the majority of snps individually explained only a small proportion of trait variation, but fitting all markers simultaneously captured most of the trait heritability for majority apple fruit traits.
these findings suggest that genome-based methods could potentially replace the traditional apple cultivar breeding methods.

 until the end of the 20th century, the lack of high throughput genotyping techniques and the limited development of high-density snp arrays have hindered the advancement of genome-based breeding strategies for crop improvement. during the last years, the genome sequences of about plant species, including some from the rosaceae family, were made publicly available, which offers opportunities for transforming breeding strategies to improve the yield and quality of major crops. genome-wide association studies and genomic selection are among some new breeding tools proposed for crop improvement. the underlying philosophy of both these strategies is to genotype enough markers across the genome so that at least one of the genotyped markers is likely in ld with the quantitative trait locus alleles. both gs and gwas can be conducted using the same genotypic and phenotypic data, but their objectives are different. gs is used to predict phenotype from marker profiles alone, to reduce dramatically the length of the breeding cycle and the costs involved in phenotyping. the objective of gwas is to identify novel functional variation that can be deployed in cultivar development through marker-assisted selection. gwas studies in humans have used two fundamentally different designs: family-based and population-based. the power of a gwas of a quantitative phenotype using related individuals was shown to be slightly lower than that for a sample of unrelated individuals in a human study, but in crops and livestock controlled mating could make family designs more powerful than a population sample. both population-based and family-based designs have been used for gwas in crops. the advantages of using relatives are manifold, including greater quality control, the ability to perform within-family tests of association that are robust to population stratification, and joint linkage and association analysis. a nested association mapping population, which consists of multiple families derived from multiple inbred lines crossed to one or more reference inbred line, has been used for gwas of different traits in maize. multi-parent advanced generation inter-cross population was first used in arabidopsis. other family-based designs, such as parent-offspring, multi-generational pedigrees and multi-parent crosses, have historically been used in quantitative genetic studies. thus, for plant populations, it is reasonable to consider large number of progenies derived from controlled crosses in various mating schemes for gwas. population stratification and cryptic relatedness among studied individuals, when not taken into account, could lead to spurious genotype-phenotype associations in gwas. population stratification refers to the inclusion of individuals from different populations, while cryptic relatedness refers to the presence of varying degree of genetic relationships between individuals within the study sample. gwas methods based on the unified mixed linear model were developed by to account for population-level membership and individual-level relationships. a realized individual-level kinship matrix calculated using molecular markers is more efficient than the pedigree-based kinship matrix as it can account for mendelian sampling and segregation distortion. as family sizes in plant populations are much larger than those in other species, implementation of mlm was computationally very intensive. therefore, the efficient mixed model association expedited algorithm was developed to reduce this computational burden by re-parameterizing the mlm likelihood function. further, a computationally more efficient and powerful compressed mlm that uses a group kinship matrix calculated from clustered individuals was developed recently. development of these methods has now made it much easier to analyze large amounts of data for gwas. unlike fitting each snp in turn, which is a typical feature of gwas, simultaneously fitting high density genome-wide snps could avoid the need to fit population and pedigree effects in mlm specifically. in an international consortium published the first draft of the apple genome sequence using dna from a popular apple variety ‘golden delicious’, which led to re-sequencing of apple cultivars that are the founders in global apple breeding programs. these efforts produced a huge reservoir of dna markers, which helped the development of the first-generation apple infinium snp chip, comprising nearly markers. in the present study, we used this 8k snp chip for gwa analysis of various fruit quality traits in a family-based design. traits considered in this study relate to eating quality: fruit firmness and titratable acidity; visual quality: red-flesh coverage; see methods); and susceptibility to physiological disorders: internal flesh browning, bitter pit and fruit splitting. to elucidate the relative contributions of different genomic regions, we implemented single-snp analysis models, with and without accounting for population structure, and compared these with a model fitting all markers simultaneously. the statistical power of detecting snp-trait associations was calculated using an expression derived in this study. the relative advantage of using realized relationships compared with pedigree-based expected relationships was also investigated. to our knowledge, this is the first large snp array-based gwas study to unravel the genetic architecture of quantitative traits for any major fruit crop.  realized relationships and population structure a plot of the first two principal components of the snp genotypes data matrix grouped seedlings largely according to their familial relationships. some individuals did not cluster within their pedigree-assigned full-sib family groupings. for example, individuals in two families, namely a and a which have the same maternal parent, were clustered less tightly than the other five families. a break-away group of individuals from families a and a having the same maternal parent, apparently formed a separate cluster away from their respective full-sibs. these patterns of clustering suggested some pollen contamination, so the actual number of pollen parents should be higher than that suggested by the mating design. overall, a product–moment correlation of was observed between pedigree-based and snp-based estimates of pair-wise coefficient of relationships. the average pair-wise coefficient of relationships among all study individuals, obtained from the a and g matrices, were and respectively, reflecting that there are many more relationships not captured by the known pedigree records. the proportion of phenotypic variation explained rlr using the g matrix was higher than that using the a matrix for all traits. results obtained after removing apparent contaminant seedlings, identified from pca analysis and also by using plink software, suggested that the magnitude of differences in rlr values were almost identical to those in figure  information presented in figures  and would suggest that using g would better account for population stratification than a, so only gwas results using g are presented here. linkage disequilibrium the pattern of ld decay in our gwas population of individuals was compared with that observed in the successive generation. results showed a high degree of ld even at longer distances between markers; for example, in the second generation the average r for snps separated by mbp, mbp, and mbp was,, and, respectively. this is somewhat lower compared to ld in the first generation, but the pattern of ld decay was quite similar in both generations. genome-wide associations goodness-of-fit of ‘q+k’ and ‘k’ models were compared to understand whether population structure could bias results. different numbers of pcs of the snp genotypes matrix constituted the q matrix. the rlr values of the ‘q+k’ and ‘k’ models were identical for wci, ta and bp, but were higher for ‘q+k’ for the other three traits. thus, the optimum number, as determined using the bayesian information criterion, of pcs varied for different traits: for wci, ta and bp; for ib; and for ff and cr. however, results with or without incorporating q in equation were not materially different, suggesting that accounting only for cryptic relatedness was sufficient to account for population stratification. the profiles of p-values ) for all tested snps for each trait are illustrated in figure  uncorrected p-values of p < × 10- which roughly equates to a genome-wide p-value of as we tested a total of snps, was used as a significance threshold for individual snp testing. the numbers of genome-wide significant snps detected for fruit firmness, weighted cortical intensity, internal browning, titratable acidity, fruit cracking and bitter pit were and respectively. most of the significant snps for any trait were clustered within a small genomic region, suggesting the presence of large-effect qtl at those positions. snp-trait association signals for ff were identified on linkage groups lg and lg10; for wci and ib on lg and lg16; for ta on lg8; for cr and bp on lg. the snp with the largest effect on ff was located on lg and this snp is a t/g variant located within the first exon of the polygalacturonase gene, kb from the top of lg. a snp with a massive effect on wci was located on lg. this snp on lg is a t/c variant and is located within the second exon of the mdmyb gene, kb from the bottom of lg a cluster of snps with large effects on cr and bp, and moderate effects on wci and ib, resides within the leucoanthocyanidin reductase gene that is located between kb and kb on the top of lg the most significant snps described here are probably not the causative ones for our study traits due to extensive ld. for all traits except ff, the q-q plots showed a close adherence of the observed and expected –log values over most of the range, implying that the significant snps identified by the unified mma are unlikely to be biased by population stratification. the majority of snps individually explained only a small proportion of phenotypic variation, while the largest-effect snp explained and 11% of the phenotypic variation for ff, wci, ib, ta, cr and bp respectively. the joint contribution of genome-wide significantly associated snps was also investigated. because of ld, there were many significant snps within a small genomic region, so only the snps with the largest test statistics within mb regions were chosen. the joint rlr calculated by fitting the chosen snps together in equation for ff, wci, ib, ta, cr and bp were,,,, and respectively, suggesting some improvement over single-snp analysis. fitting all markers simultaneously captured nearly all genetic variance for most of the traits. correlation coefficients between snp allele substitution effects obtained from single-snp analysis and all-snp analysis were about for all traits, and largest-effect snps were generally common to both methods. 1estimates of narrow-sense heritability obtained using pedigree-based relationships matrix. approximate standard errors of ha estimates varied from to. 2proportion of the phenotypic variance explained jointly by genome-wide significant snps. 3simultaneously using all markers in the form of the g matrix. approximate standard errors of hg estimates varied from to. genomic regions with significant effects on the two pairs of traits were further investigated by comparing lg-level estimated genetic correlations for these two pairs of traits. results suggested that rg values for the lgs harboring common significant regions were relatively higher than those for other lgs. some of these lg-level correlations were quite different in magnitude as well as direction from the whole-genome correlation. power of the gwas the power of detecting marker-trait association for various qtl allele frequencies and trait heritabilities is shown in figure  a ld value of between a marker and qtl allele was assumed. for an unrelated sample size of individuals, the power of detection of an association with a locus explaining 2% of the phenotypic variation was, when marker and qtl allele frequency were. the power increased with reductions in marker and qtl allele frequencies. for a fixed sample size, the power of detecting snp-trait associations declined with increasing relatedness among study individuals, but loss of power was minimal. the effect of trait heritability became more evident as the degree of relatedness increased. discussion realized coefficient of relationships the availability of genome sequence, the abundance of dna markers, and high throughput genotyping platforms are providing a range of applications of molecular markers, including pedigree reconstruction, estimation of genetic parameters, and understanding relationships between genotype and phenotype in various species. using a likelihood ratio based parameter rlr our study showed that using snp-based realized relationships in mlm could provide a better goodness-of-fit than using pedigree-based expected relationships. our results also showed that for all traits, except ib, fitting all markers simultaneously could explain most or all the trait heritability. similar results have been reported in studies on humans and animals. also, approximate standard errors of g-based estimates of h were considerably less than those for a-based because the former captured genetic relationships that are not accessible from pedigree records. similar to studies on animals, our results suggest that the accuracy of artificial selection in plants species can also be increased by using more precise marker-derived estimates of genetic parameters. snp-trait genome-wide associations with only a little loss of power, family-based designs in association studies offer various advantages compared with population-based designs. the average snp-derived pair-wise coefficient of relationship in our study was about, but the loss of power to detect snp-trait association was small compared with that for an unrelated sample of the same size. various factors such as sample size, high ld, minimal effect of population structure, and the presence of some large-effect qtl provide high confidence in the snp-trait associations identified in this study. the snp array used in this study was designed to encompass snps in the coding region of predicted gene models and some candidate genes such as mdmyb mdpg, and mdlar. peak association signals for ff, wci and ta were located close to genomic regions that have been previously identified in bi-parental qtl mapping studies. the snps showing the largest effect on ff on lg reside in the polygalacturonase gene, which depolymerizes cell wall pectin, and the involvement of this gene in the fruit softening process has been previously demonstrated in apple. red color in apple flesh results from a high concentration of anthocyanins. the role of the mdmyb gene on anthocyanin biosynthesis in red-fleshed apple was demonstrated using various approaches, and this gene has been mapped to lg. the snp marker associated with weighted cortical intensity in our experiment is located in the second exon of mdmyb which is physically close to the motif in the mdmyb promoter that causally regulates transcription of mdmyb itself and thereby anthocyanin synthesis in apple flesh. a cluster of snps at lg commonly associated with wci and ib resides in the mdlar candidate gene. lar is a key enzyme in the flavonoid biosynthetic pathway, reducing leucoanthocyanidin into the flavanol compound catechin, a monomer of condensed tannins. perhaps condensed tannins act as co-pigments of cyanidin to create more intense red coloration in the fruit and hence the effect on wci. common genomic regions found associated with wci and ib are supported by results showing high genetic correlation between these two traits. also, cold-stored fruit from all mdmyb transgenic lines of cultivar ‘royal gala’ showed varying degrees of symptoms of ib, suggesting a pleiotropic effect of mdmyb on wci and ib. in our study, the estimated genetic correlation differed in degree as well as direction across different lgs, suggesting some possibility of breaking this undesirable correlation by means of carefully designed breeding and selection strategies, but further work on elucidating the genetic architecture of wci and ib is required first. the distribution of snp effects for ta suggests one major qtl on lg supporting similar results from bi-parental qtl mapping studies. however, there is no published report of candidate genes for ta on apple lg segregation analysis approaches showed that inheritance of ta in a large apple population was better described by a mixed genetic architecture. our results appeared to be in agreement with in the sense that the largest-effect snp accounted for about half the genetic variation, while the other half was accounted for by small-effect genes. cr, which is a pre-harvest physiological disorder of apple, can be a serious economic problem for some cultivars. however, little is known about the genetic architecture of this trait. similarly to our results, estimate of h from a previous study indicated moderate genetic control of cr. while little is known on the physiological causes of genetic variability in cr susceptibility, it may be linked to the internal properties of the fruit during growth and differences in the elasticity of the peel when under particular stresses and strains caused by the developing parenchyma cells beneath it. to our knowledge, there is no published report on marker-trait association for cr. a cluster of snps with a large effect on cr resides within the mdlar candidate gene on lg which was previously reported to influence some other fruit quality traits such as astringency and polyphenolic compounds. bp is also a serious physiological disorder whose expression is generally observed in fruit after storage, but symptoms can also be observed on the fruit surface at harvest, and in our study they were classified as the same disorder. genetic predisposition, calcium nutrition of the fruit, and environmental factors influence incidence of bp. based on the segregation ratio of resistant to susceptible seedlings, it was hypothesized that resistance to bp is controlled by two major dominant genes, named bp- and bp-. different segregation ratios of resistance to susceptible seedlings were observed in various families in our study, suggesting a complex nature to this trait, which is further supported by our results showing that gwa-significant snps explained only about half the observed genetic variation. interestingly, the same cluster of snps on lg showed association with expression of bp and cr, and the direction and magnitude of lg-level genetic correlations were similar. molecular, physiological and biochemical pathways that commonly contribute to the expression of these two traits are poorly understood, but our study provides a genomic hotspot for further investigations. mlm that concurrently fits all available snps has been adapted in recent gwas in animals following an earlier study that showed that provided high-density snps are fitted simultaneously, admixed populations can be used to obtain reliable snp effects even if pedigree structure and population structure have not been explicitly modeled. high correlations between snp ases obtained from the ‘q+k’ model and all-marker analysis for all six traits in this study reinforces the findings of. application of snp-trait associations in our study population, the average ld between snps separated by kb was high largely because of relatedness among seedlings and small effective population size. it is not uncommon to find different ld structures in different types of plant populations within a species. for example, in maize, ld decays within kb in land races, within kb in diverse inbred lines, and can extend up to kb in commercial elite inbred lines. preliminary results from an unrelated set of individuals from a diverse apple germplasm collection showed that for a given distance between markers, the extent of ld was almost one-third of that in this study. one practical implication of these results is that marker-trait associations identified in advanced-generation crosses may not be repeated in relatively less improved breeding material. one of the key goals of gwas is to identify large-effect marker-trait associations that can be deployed through marker-assisted selection in subsequent generations of cultivar development populations. however, in order to conduct mas using these snps in successive generations, strong ld between marker and qtl must persist across generations. generally, only a selected set of individuals from the current generation are used as parents for the subsequent generation. selection will lead to changes in allele frequencies at marker and trait loci, potentially reducing the ld between two loci, similar to that observed in the second generation of our study material. as a result, the efficiency of gwas-associated snps could be lower in the following generations. nevertheless, except for wci, the significant snps jointly explained less than 50% of the trait heritability in this study, which raises a question of how much variation in a quantitative trait needs to be accounted by a marker so that it would be worthwhile for mas to be applied. such a mas scheme is generally viewed as cost effective compared with the genome selection, but this scheme does not bypass the phenotypic evaluation stage because there could be some quantitative traits for which no significant snps are identified. on the other hand however, a small snp assay comprising gwa-significant snps for the key breeding traits could be used for pre-screening of seedlings before further field evaluation. such an approach will not reduce the length of the breeding/selection cycle, but will shift the mean of the selection population. in order to keep the accuracy of mas similar to that in the generation where snps were identified, periodical recalibration of snp effects would be necessary.  the use of realized relationship matrix will provide higher accuracy of estimated genetic parameters, resulting in increased accuracy of artificial selection. there are apparently major differences in the genetic architecture of various traits in this study, i.e. for traits with similar heritability the distributions of snps effect were very different. the majority of snps individually explained only a small proportion of trait variation, but fitting all markers simultaneously captured most of the trait heritability for majority apple fruit traits. these findings suggest that genome-based methods could potentially replace the traditional apple cultivar breeding methods. 
the accuracy of artificial selection in plants species can be increased by using more precise marker-derived estimates of realized coefficients of relationships. results from ‘q+k’ and ‘k’ models were very similar, suggesting that the snp-based kinship matrix captures most of the underlying population structure. the patterns of linkage disequilibrium were also investigated. gwaslinkage disequilibriumgenetic architectureallele substitution effectpleiotropymalus × domestica a high degree of ld even at longer distances between markers was observed, and the patterns of ld decay were similar across successive generations. this study revealed large differences in the genetic architecture of apple fruit traits, and the marker-trait associations identified here will help develop genome-based breeding methods for apple cultivar development. understanding the genetic architecture of quantitative traits is important for developing genome-based crop improvement methods. phenotypic variation explained by the loci identified through a whole-genome scan ranged from 3% to 25% across different traits, while fitting all markers simultaneously generally provided heritability estimates close to those from pedigree-based analysis. all-marker analyses that indirectly account for population- and pedigree structure will be a credible alternative to single-snp analyses in gwas. using a family-based design involving apple seedlings genotyped for an 8k snp array, we report the first systematic evaluation of the relative contributions of different genomic regions to various traits related to eating quality and susceptibility to some physiological disorders. single-snp analyses models that accounted for population structure, or not, were compared with models fitting all markers simultaneously. genomic regions were identified, some of which coincided with known candidate genes, with significant effects on various traits. genomic regions with probable pleiotropic effects were supported by the corresponding higher linkage group level estimated genetic correlations.
 understanding the genetic architecture of quantitative traits is important for developing genome-based crop improvement methods. genome-wide association study is a powerful technique for mining novel functional variants. using a family-based design involving apple seedlings genotyped for an 8k snp array, we report the first systematic evaluation of the relative contributions of different genomic regions to various traits related to eating quality and susceptibility to some physiological disorders. single-snp analyses models that accounted for population structure, or not, were compared with models fitting all markers simultaneously. the patterns of linkage disequilibrium were also investigated.  a high degree of ld even at longer distances between markers was observed, and the patterns of ld decay were similar across successive generations. genomic regions were identified, some of which coincided with known candidate genes, with significant effects on various traits. phenotypic variation explained by the loci identified through a whole-genome scan ranged from 3% to 25% across different traits, while fitting all markers simultaneously generally provided heritability estimates close to those from pedigree-based analysis. results from ‘q+k’ and ‘k’ models were very similar, suggesting that the snp-based kinship matrix captures most of the underlying population structure. correlations between allele substitution effects obtained from single-marker and all-marker analyses were about for all traits. use of snp-derived realized relationships in linear mixed models provided a better goodness-of-fit than pedigree-based expected relationships. genomic regions with probable pleiotropic effects were supported by the corresponding higher linkage group level estimated genetic correlations.  the accuracy of artificial selection in plants species can be increased by using more precise marker-derived estimates of realized coefficients of relationships. all-marker analyses that indirectly account for population- and pedigree structure will be a credible alternative to single-snp analyses in gwas. this study revealed large differences in the genetic architecture of apple fruit traits, and the marker-trait associations identified here will help develop genome-based breeding methods for apple cultivar development. gwaslinkage disequilibriumgenetic architectureallele substitution effectpleiotropymalus × domestica 