the level of the genetic diversity is pivotal for world food security 
 and survival of human civilization on earth .
historically , humans exploited 
 plant species for their livelihoods that resulted in domestication of many of 
 them as improved cultivars to produce food for the better supply of the human 
 diet . presently , out of 150 plant species cultivated in agriculture , twelve 
 provide about 75% of human food and four produce 50% of human diet . 
 according to food and health organization report
, ~800 million people in the 
 developing countries are suffering from food 
 deficiency   that underlies an attention to improve agricultural production 
 to eliminate or , at least , reduce the feeding problems .
the narrow genetic base of modern crop cultivars is the serious obstacle 
 to sustain and improve crop productivity due to rapid vulnerability of 
 genetically uniform cultivars by potentially new biotic and abiotic stresses 
 .
however , plant germplasm resources worldwide , comprising of wild plant 
 species , modern cultivars , and their crop wild relatives , are the important 
 reservoirs of natural genetic variations , originated from a number of 
 historical genetic events as a respond to environmental stresses and selection 
 through crop domestication [ 1 , 5 ] .
the efficient exploiting these ex situ conserved genetic diversities 
 is vital to overcome future problems associated with narrowness of genetic base 
 of modern cultivars .
however , many agriculturally important variations such as 
 productivity and quality , tolerance to environmental stresses , and some of 
 forms of disease resistance are controlled by polygenes and  multifactorial  
 that greatly depends on genetic  
 environmental ( g  e ) interactions [ 1 , 6 ] . these complex traits are 
 referred to as quantitative trait loci ( qtls ) , and it is challenging to 
 identify qtls based on only traditional phenotypic evaluation .
identification 
 of qtls of agronomic importance and its utilization in a crop improvement 
 further requires mapping of these qtls in a genome of crop species using 
 molecular markers [ 1 , 6 ] .
this was the major breakthrough and accomplishment in 
 many crops in  genomics era  since the end of the 20th century , and now 
 extended to flourish in the 21st century . in this review , we provide a brief description for the concept of 
 genetic mapping ; then , as a flourish of the crop genomics era , we thoroughly 
 review one of the powerful genetic mapping tools for crops , linkage 
 disequilibrium ( ld)-based association study , as a high - resolution , broader 
 allele coverage , and cost effective gene tagging approach in plant germplasm 
 resources .
this provides an opportunity to widely dissect and exploit existing 
 natural variations for crop improvement .
the 
 main goal of genetic mapping is to detect neutrally inherited markers in close 
 proximity to the genetic causatives or genes controlling the complex 
 quantitative traits .
genetic mapping can be done mostly in two ways : ( 1 ) 
 using the experimental populations ( also referred to as  biparental 
mapping 
 populations ) that is called qtl - mapping as well as  genetic mapping  or  gene 
 tagging ,  and ( 2 ) using the diverse lines from the natural populations or 
 germplasm collections that is called ld - mapping or  association mapping .  the 
 details of the traditional qtl - mapping approach has recently been reviewed by 
 collard et al . , and further basic description of the approach here would be 
 a redundant . for detailed concept , models and methodologies , problems , and 
 perspectives of linkage analysis ,
here , we briefly outline linkage mapping procedure for the sake of 
 highlighting the merits of the alternative approach - association mapping .
so 
 that such a linkage analysis can be done [ 68 ] , firstly , the 
 experimental populations such as f2 , back cross ( bc ) , double haploid 
 ( dh ) , recombinant inbred line ( ril ) , and near isogenic line ( nil ) populations , 
 derived from the genetic hybridization of two parental genotypes with an 
 alternative trait of interest , need to be developed .
secondly , these 
 experimental populations including a large number of progenies or lines are 
 measured for the segregation of a trait of interest in the different 
 environmental conditions .
thirdly , a set of polymorphic dna markers , 
 differentiating the parental genotypes and segregating in a mapping population , 
 need to be identified and genotyped .
for that , usual practice is that , first , 
 the parental genotypes are screened , and if markers are polymorphic over the 
 parents , then , all individuals of a mapping population are genotyped with these 
 polymorphic molecular markers .
once genotypic data of a mapping population is 
 ready , marker data is used to construct the framework linkage maps , 
 representing the order ( position ) and linkage ( a relative genetic distance in 
 cm ) of used molecular markers along the linkage groups or segments of 
 particular chromosomes .
consequently , these markers ordered along the 
 linkage map are statistically correlated with phenotypic characteristics of 
 individuals of a mapping population , and qtl regions affecting a trait of 
 interest , along with closely positioned marker tags to that qtl , are 
 identified .
one 
 can imagine these linkage marker maps as a  road map ,  marker tags as the 
 labels directing to specific places , and qtls to a community / neighborhood ( with 
 specific function ) on the map .
the precision of qtl - mapping largely depends 
 on the genetic variation ( or genetic background ) covered by a mapping 
 population , the size of a mapping population , and a number of marker loci used . 

once qtls affecting a trait of interest accurately tagged using above - outlined 
 approach , marker tags are the most effective tools in a crop improvement that 
 allows the mobilization of the genes of interest from donor lines to the 
 breeding material through marker - assisted selection ( mas ) .
although traditional 
 qtl - mapping will continue being an important tool in gene tagging of crops , it 
 is a  now classical approach  and overall is very costly [ 1 , 9 ] , and has low 
 resolution with simultaneous evaluation of only a few alleles   in a longer 
 research time scale . in linkage mapping , the major limitation , hampering the 
 fine mapping , is associated with the availability of only a few meiotic events 
 to be used that occurred since experimental hybridization in a recent past .
these 
 limitations , however , can be reduced with the use of  association mapping  . 

turning the gene - tagging efforts from biparental crosses to natural population 
 of lines ( or germplasm collections ) , and from traditional qtl - mapping to 
 linkage disequilibrium ( ld)-based association study became a powerful tool in 
 mapping of the genes of interest .
this leads to the most effective 
 utilization of ex situ 
 conserved natural genetic diversity of worldwide crop germplasm resources .
ld 
 refers to a historically reduced ( nonequilibrium ) level of the recombination of 
 specific alleles at different loci controlling particular genetic variations in 
 a population .
this ld can be detected statistically , and has been widely 
 applied to map and eventually clone a number of genes underlying the complex 
 genetic traits in humans [ 1316 ] .
the 
 advantages of population - based association study , utilizing a sample of 
 individuals from the germplasm collections or a natural population , over 
 traditional qtl - mapping in biparental crosses primarily are due to ( 1 ) 
 availability of broader genetic variations with wider background for 
 marker - trait correlations ( i.e. , many alleles evaluated simultaneously ) , ( 2 ) 
 likelihood for a higher resolution mapping because of the utilization of 
 majority recombination events from a large number of meiosis throughout the 
 germplasm development history , ( 3 ) possibility of exploiting historically 
 measured trait data for association , and ( 4 ) no need for the development of 
 expensive and tedious biparental populations that makes approach timesaving and 
 cost - effective [ 1719 ] .
although 
 the overall approach of population - based association mapping in plants varies 
 based on the methodology chosen ( see below sections ) , assuming structured 
 population samples , the performance of association mapping includes the 
 following steps ( see figure 1 ) : ( 1 ) selection of a group of individuals from a 
 natural population or germplasm collection with wide coverage of genetic 
 diversity ; ( 2 ) recording or measuring the phenotypic characteristics ( yield , 
 quality , tolerance , or resistance ) of selected population groups , preferably , 
 in different environments and multiple replication / trial design ; ( 3 ) genotyping 
 a mapping population individuals with available molecular markers ; ( 4 ) 
 quantification of the extent of ld of a chosen population genome using a 
 molecular marker data ; ( 5 ) assessment of the population structure ( the level of 
 genetic differentiation among groups within a sampled population individuals ) 
 and kinship ( coefficient of relatedness between pairs of each individuals 
 within a sample ) ; and ( 6 ) based on information gained through quantification of 
 ld and population structure , correlation of phenotypic and genotypic / haplotypic 
 data with the application of an appropriate statistical approach that reveals  marker 
 tags  positioned within close proximity of targeted trait of interest .
consequently , 
 a specific gene(s ) controlling a qtl of interest can be cloned using the marker 
 tags and annotated for an exact biological function ( figure 1 ) . as a starting 
 point for association mapping , it is important to gain knowledge of the patterns of ld for genomic regions of the  target  organisms and the specificity of the 
 extent of ld among different populations or groups to design and conduct unbiased 
 association mapping [ 20 , 21 ]
genetic 
 linkage generally refers to coinheritance of different loci within a genetic 
 distance on the chromosome .
there are two terms used in population genetics , 
 linkage equilibrium ( le ) , and linkage disequilibrium ( ld ) to describe linkage 
 relationships ( co - occurrence ) of alleles at different loci in a population .
le 
 is a random association of alleles at different loci and equals the product of allele frequencies within haplotypes , 
 meaning that at random combination of alleles at each locus its haplotypes ( combination of alleles ) frequency 
 has equal value in a population . in contrast , ld is a nonrandom association of 
 alleles at different loci , describing the condition with nonequal ( increased or 
 reduced ) frequency of the haplotypes in a population at random combination of 
 alleles at different loci .
ld is not the same as linkage , although tight 
 linkage may generate high levels of ld between alleles .
usually , there is 
 significant ld between more distant sites or sites located in different 
 chromosomes , caused by some specific genetic factors [ 9 , 2224 ] that will be 
 discussed in below sections .
( gpd ) or  gametic disequilibrium  ( gld ) [ 11 , 25 ] in the 
 literature that describes the same nonrandom association of haplotypes within 
 unrelated populations with a distantly shared ancestry , assuming hardy - weinberg 
 equilibrium ( hwe ) .
the concept of ld was first described by jennings in 1917 , and its 
 quantification ( d ) was developed by lewtonin in 1964 .
the simplified 
 explanation of the commonly used ld measure , d or d ( standardized version of 
 d ) , is the difference between the observed gametic frequencies of haplotypes 
 and the expected gametic haplotype frequencies under linkage equilibrium ( d = pab  papb = pabpab  pabpab ) 
 . besides d , a various different measures of ld ( d , r , d , 
 d * ,
f , x ( 2 ) , and  ) have been developed to quantify ld [ 25 , 2729 ] .
the detail 
 formulae and description of ld quantification was well explained by a number of 
 review papers [ 10 , 25 , 26 ] with a number of hypothetical scenarios for ld and 
 le .
the merits , sensitivity , comparison , appropriate statistical tests , and 
 calculation methodology for these ld measures with the utilization of biallelic 
 or multiallelic loci have been extensively described in the literature in 
 detail [ 10 , 26 , 30 , 31 ] , and have recently been reviewed by gupta et al . . 

hence here we highlight only some of key utility properties of ld measures to 
 provide a brief understanding the merits of ld in association mapping . choosing the appropriate ld measures
really depends on 
 the objective of the study , and one performs better than other in particular 
 situations and cases ; however , d and r is the most commonly used measures 
 of ld [ 25 , 26 ] .
d is informative for the comparisons of different allele 
 frequencies across loci and strongly inflated in a small sample size and low - allele 
 frequencies ; therefore , intermediate values of d is dangerous for comparative 
 analyses of different ld studies and should be verified with the r before using for quantification of the extent of ld .
the r , 
 the square of the correlation coefficient between the two loci have more 
 reliable sampling properties than d with the cases of low allele frequencies 
 .
the r is affected by both mutation and recombination while d 
 is affected by more mutational histories ( it might indicate minimal historic 
 recombination when high d values used ) [ 10 , 25 , 26 , 31 ] . considering the 
 objective ,
the most appropriate ld quantification measure needed for 
 association mapping is r that is also an indicative of marker - trait 
 correlations [ 25 , 26 , 32 ] .
the r value varies from 0 to 1 , and it 
 will be equal to 1 when only two haplotypes are present .
the r value 
 of equal to 0.1 ( 10% ) or above considered the significant threshold for the 
 rough estimates of ld to reveal association between pairs of loci .
it is noteworthy to briefly mention here that the 
 estimation of above described gld ( commonly used in association mapping ) 
 between different loci ordered within gametes assumes that a targeted 
 population or sampled germplasm is randomly mating and under hwe .
nevertheless , 
 many natural populations violate hwe due to different genetic events 
 ( bottleneck , mutation , admixture , artificial selection , population structure , etc . ) 
 occurred in history of a population , and are under hardy - weinberg disequilibrium 
 ( hwd ) .
a concept of  zygotic disequilibrium ( zld )  was introduced for such a 
 nonequilibrium population   that measures ld between different loci of 
 gametes .
zld , being defined as a deviation of joint zygotic frequencies from 
 the expected values of zero zygotic associations [ 35 , 36 ] , has a power to 
 measure nonrandom associations at both gametic and zygotic level [ 34 , 37 ] .
it 
 shares the most of statistical properties of gld , and the results of gld 
 and zld are mostly in agreement , yet zld detects more extensive ld than determined 
 by gld .
the statistical models of zld measures for biallelic and 
 multilocus data , its application for natural populations , and inference the 
 genetic and demographic events from the comparisons of gld and zld results as 
 well as implication for whole genome association studies ( wgas ) were 
 excellently addressed and described by a number of studies [ 3537 ] .
one of such efficient methodology is the maximum likelihood 
 estimate ( mle ) using an expectation maximization algorithm .
several 
 computer software packages are available and can be utilized for calculation of 
 ld using variety type of molecular markers .
these software packages were 
 extensively listed and described in the review by gupta et al . .
graphical 
 display of pairwise ld between two loci is very useful to estimate the ld 
 patterns measured using a large number of molecular markers .
pairwise ld can be 
 depicted as a color - code triangle plot ( figure 2 ) based on significant pairwise 
 ld level ( r , and p - value as well as d ) that helps to visualize the 
 block of loci ( red blocks ) in significant ld .
the large red blocks of 
 haplotypes along the diagonal of the triangle plot indicate the high level of 
 ld between the loci in the blocks , meaning that there has been a limited or no 
 recombination since ld block formations .
there is freely available specific 
 computer software ,  graphical overview of linkage disequilibrium  ( gold ) , 
 to depict the structure and pattern of ld . 

some other software packages measuring ld such as  trait analysis by association , evolution and linkage  ( tassel ) 
 [ 33 , 40 ] and powermarker   have also similar graphical display features . 

the strong block - like ld structures are of a great interest in association 
 mapping which simplifies ld mapping efforts of complex traits .
ld blocks 
 are very useful in association mapping when sizes are calculated , which suggest 
 the needs for the minimum number of markers to efficiently cover the 
 genome - wide haplotype blocks in association mapping . to 
 estimate the size of these ld blocks , the r values (
alternatively , 
 d can also be used ) usually plotted against the genetic ( cm ) or weighted ( bp ) 
 distance referred to as a  ld decay plot 
one can estimate an average genome - wide 
 decay of ld by plotting ld values obtained from a data set covering an entire 
 genome ( i.e. , with more or less evenly spaced markers across all chromosomes in 
 a genome ) against distance .
alternatively , the extent of ld for particular 
 region ( gene or chromosome ) can be estimated from an ld decay plot 
 generated using dataset obtained from a region of interest . when such a ld 
 decay plot generated , usual practice is to look for distance point where ld 
 value ( r ) decreases below 0.1 or half strength of d ( d = 0.5 ) based 
 on curve of nonlinear logarithmic trend line ( see , e.g. , [ 33 , 43 , 44 ] ) .
this 
 gives the rough estimates of the extent of ld for association study , but for 
 more accurate estimates , highly significant threshold ld values ( r  0.2 ) 
 are also used as a cutoff point .
the decrease of the ld within the genetic distance indicates that the 
 portion of ld is conserved with linkage and proportional to recombination [ 22 , 25 ] .
there are many genetic and demographic factors that 
 play a role in the shaping of the haplotypic ld blocks in a genome [ 9 , 22 , 23 , 25 , 26 ] .
although mutation and recombination are one of the strong impact factors 
 influencing ld , generally , factors affecting ld can be grouped into two 
 categories : ( 1 ) factors that increasing ld , and ( 2 ) factors that decreasing ld . 

the increase of ld is observed with new mutation , mating system ( self - pollination ) , 
 genetic isolation , population structure , relatedness ( kinship ) , small founder 
 population size or genetic drift , admixture , selection ( natural , artificial , 
 and balancing ) , epistasis , and genomic rearrangements [ 25 , 26 ] .
the decrease of 
 ld is observed with high recombination and mutation rate , recurrent mutations , 
 outcrossing , and gene conversions [ 25 , 26 ] .
however , more often there is a significant ld between 
 pairs of loci located far from each other or even in different chromosomes that 
 might cause spurious correlations in association mapping .
these long stretched 
 ld or ld between unlinked loci indicate the existence of other ld generating 
 factors than linkage itself in a genome [ 9 , 22 , 23 ] .
one 
 of those factors is selection that generate ld between unlinked loci through  a 
 hitchhiking  effect ( high - frequency sweeping and fixation of alleles flanking a 
 favored variant ) , and epistatic selection or the so - called coadapted genes 
  that is the result of coselection of loci during breeding for multiple 
 traits , common in traditional crop breeding programs worldwide .
the 
 population structure ( existences of distinctly clustered subdivisions in a 
 population ) and population admixture are the main factors to create such an ld 
 between unlinked loci .
this primarily happens due to the occurrence of distinct 
 allele frequencies with different ancestry in an admixed or structured 
 population .
theoretically , relatedness generates ld between linked loci , yet it 
 might also generate ld between unlinked loci pairs when predominant parents 
 exist in germplasm groups . there is evidence that relatedness caused ld between 
 linked and unlinked loci in an equal proportion in maize germplasm .
the 
 high ratio value of linked to unlinked loci in ld is good indicative to draw 
 conclusion about the role of ld generating factor(s ) such as selection or 
 population stratification ( cryptic relatedness ) [ 9 , 22 , 23 ] .
the other factors 
 such as genetic drift or bottlenecks might have also generated ld in a genome 
 [ 2224 ] , which is evidenced 
 by nonuniform distribution of ld in chromosomes .
knowing these factors that are increasing or 
 decreasing ld in a genome , obvious question one might ask is whether increased or 
 decreased level of ld is favored in association mapping ?
very extensive level of 
 ld ( means ld persists within a long distance ) , theoretically , reduces a number 
 of markers needed for association mapping , but makes resolution lower ( coarse 
 mapping ) .
in contrast , less extensive level of ld ( means that ld quickly decays 
 within a short distance ) requires many markers to tag a gene of interest , but 
 in high resolution ( fine mapping ) .
hence , choosing a population with low or 
 high level of ld depends on the objective of association mapping study . 
 furthermore , increased ld level due to ld between unlinked loci is not salutary 
 in association mapping since it tends to cause spurious marker - trait 
 associations .
ld generated by selection , population structure , relatedness , and 
 genetic drift might be theoretically useful for association mapping 
 in specific situations and population groups that reduces number of markers needed 
 for association mapping [ 9 , 22 ] , but requires serious attention to control 
 factors affecting ld ( e.g. , population structure and relatedness ) to perform 
 unbiased population - based association mapping in plants [ 41 , 47 ] ( see next sections ) .
there 
 are other factors affecting ld referred to as a whole  ascertainment bias  that 
 are associated with an assayed sample and data characteristics .
some of these 
 factors leading to inaccurate estimate of ld were well reviewed by gupta et al . 
 .
one of such factors largely affecting the ld and leading inaccurate 
 estimates is the presence of minor alleles ( also referred as to rare alleles 
 that are present in only 5 to 10% individuals of the sample ) in a dataset . 

minor alleles are problematic in ld quantification as they largely inflate ld 
 values ( in particular the d and p - values ) [ 43 , 4850 ] .
the r is 
 also very sensitive and has a large variance with rare alleles [ 43 , 51 ] .
hence 
 in the quantification of ld and association mapping , markers with minor allele 
 frequency of 510% ( varied from 
 study to study ) are ( 1 ) removed before analysis ( see , e.g. , [ 17 , 18 , 43 , 44 , 51 ] ) , ( 2 ) pooled into common allelic class ( see , e.g.,[44 , 46 ] ) , and ( 3 ) replaced 
 with missing values ( see , e.g. , [ 52 , 53 ] ) .
the 
 quantification methodology of ld , perfectly suitable for biallelic codominant 
 type of markers ( majorly , single nucleotide polymorphisms ( snps ) and now 
 largely extended to multiallelic simple sequence repeats - ssrs ) , has been well 
 developed and used in human , animal , and plant populations ( for reviews see [ 25 , 2730 ] ) . 

ld quantification using dominant markers ( such as random amplified polymorphic 
 dnas - rapd , and amplified fragment length polymorphisms - aflps ) is poorly explored and usually subject 
 to wrong perception and interpretation
. however , many underrepresented plant 
 species , like forest trees , or other crops with limited genomic information 
 largely rely on dominant type of markers such as rapds and aflps . 

furthermore , even with codominant , and multiallelic ssr markers , there is a 
 great challenge with assigning correct allelic relationships ( identity by 
 decent ) of multiple band amplicons when diverse , reticulated , and polyploid 
 germplasm resources , lacking historical pedigree information , are genotyped .
to 
 avoid such a challenging cases , ( 1 ) one might select only single band ssr loci 
 and code a dataset as a codominant marker type , yet such a single band ssrs are 
 usually not many in polyploid crop genomes and yield also multiple bands when 
 very diverse germplasm resources are genotyped ; ( 2 ) alternatively , multiple - band 
 ssrs with unknown allelic relationship may be scored as a dominant marker 
 taking each band as an independent marker locus ( uniquely ) with a clear size 
 band separation ( see , e.g. , [ 52 , 56 ] ) .
could 
 a dominant marker data be used for ld quantification ? there are some reports 
 where ld level of natural forest tree populations has been measured using 
 dominant markers ( aflps ) and commonly used statistical approach ( see , e.g. , ) . 

there are also a number of reports where dominantly coded ( present versus 
 absent ) marker data of rapd , rflp , aflp ,  candidate gene  ( caps ) , and ssrs were 
 successfully used in genome - wide ld analyses and ld - based association mapping 
 in plants ( see , e.g. , [ 1719 , 56 , 58 , 59 , 60 ] ) , 
 demonstrating the feasibility of dominantly coded molecular data in revealing 
 of haplotypic associations .
although a dominant type of coding has limited 
 statistical power compared to codominant markers in population - based analyses 
 because of missing heterozygote information , previous studies suggested that it 
 can be successfully applied to the clustering of individuals and grouping of 
 populations using a bayesian approach when a large number of loci are genotyped 
 [ 61 , 62 ] .
dominant - type markers can be a useful tool to estimate the kinship 
 coefficients between individuals .
recently , 
 li et al .   investigated the use of dominant markers in estimation of ld in 
 diploid species and developed appropriate em algorithm . based on their 
 conclusion from the comparative data simulation of dominant versus codominant 
 markers ,
the dominant - type markers could effectively be used in ld analysis 
 with preferentially large number of marker loci and population sample sizes of 200 for high heterozygous ( proportion of 
 alternative alleles ( present versus absent ) in a data set , i.e. , 0.5 versus 
 0.5 ) marker data or with even larger sample size 400 for low - heterozygous 
 ( i.e. , 0.9 versus 0.1 ) dominant markers .
it is also recommended that a mixture 
 of codominant and dominant markers should be used to better characterization of 
 a genetic structure of a population . 

ld quantification and ld - based association mapping have been a research objective in plants 
 beginning with the model organism as arabidopsis , and now extended to crops as 
 maize , barley , durum wheat , spring wheat , rice , sorghum , sugarcane , sugar beet , 
 soybean , and grape , as well as in forest tree species , and forage grasses .
sequenced 
 0.51 kb long 13 fragments from a 250 kb region surrounding the flowering time fri gene in a 20 global sample of a. thaliana , highly selfing model plant 
 species .
later , investigation of the same authors   with markers surrounding the 
 disease resistance locus rpm1 in a 
 globally - derived set of 96 arabidopsis accessions revealed that a genome - wide 
 ld extended up to 50250 kb .
ld blocks 
 extended up to 50100 cm in local 
 michigan arabidopsis populations . 

these long - stretched lds in local arabidopsis 
 population were explained as a genetic bottleneck or founder effect through 
 introduction a. thaliana into north america in recent past ( 200 years ago ) .
in contrast , 
 in other study that targeted the region surrounding another disease resistance 
 gene rps5 , tian et al .  
likewise , ld quickly 
 decays within 1050 kb distance 
 around the clavata 2 region of 
 arabidopsis .
recently , ehrenreich et al .   reported the ld decay within ~10 kb in extensive sequence analysis of 600-bp 
 fragments of the regions more axillary 
 growth 2 ( max2 ) and more axillary 
 growth 3 ( max3 ) in a panel of 96 accessions from a restricted geographic 
 range in central europe . in their genome - wide 
 survey of 1347 fragments of 600-bp lengths , plagnol et al
.   reported that 
 ld completely disappears after ~100 kb , which is comparable to that observed in 
 human . in maize ( zea mays l. ) , a highly outcrossing crop species , very rapid 
 genome - wide ld decay was determined .
tenaillon et al .  
 first reported the extent of ld for maize , genotyping of 21 loci of chromosome 1 over the 25 
 individuals of the exotic landrace and united states maize germplasm .
an 
 average ld decay was determined to occur within 400 bp with r = 0.2 
 and extended up to 1000 bp ( ~1 kb ) in a group of us inbred lines .
later , 
 remington et al .   also reported a very rapid decline of ld in their survey 
 of 6 genes ( 1.210 kb long ) in 
 102 inbred lines , including tropical and semitropical lines with a wide genetic 
 diversity .
for these surveyed genes , ld declined generally within 2002000 bp with r = 0.1 
 except sugary1 ( su1 ) loci , where ld remained significant ( r = 0.3  0.4 ) 
 for 10 kb distance .
this was explained by strong selective episodes in su1 gene . in the same study , remington 
 et al
.   found higher level of ld with 47 ssr markers compared to those 
 obtained from snp data .
this result was explained by different mutation rate of 
 these two marker systems that tends to capture different historic information .
( i.e. , restricted to particular regions , meaning that high ld stretches 
 interspersed with regions of low ld ) extended up to 3 kb .
examined the genetic diversity and ld 
 in a cross section of 147 european and united states 
  elite inbred material 
 with 100 ssrs .
they reported an average significant ( p < .5 ) ld block 
 size of 26 cm for flint group , or 41 cm for dent group with nonuniform 
 distribution of ld among 10 chromosomes .
they showed a very long stretched ld 
 blocks up to 105 cm in chromosome 2 and up to 103 cm in chromosome 7 in flint 
 and dent groups , respectively .
obtaining of different result from earlier 
 studies   was explained due to using ( 1 ) much higher marker density , and ( 2 ) 
 both related and unrelated inbred lines . in another study ,
the same authors 
 examined 72 european elite inbred lines with 452 aflp and 93 ssr markers and 
 reported much shorter average ld block sizes for aflp ( 4 cm ) , but extensive ld 
 for ssr ( 30 - 31 cm ) in both flint 
 and dent germplasm groups .
this suggested a potential for exploiting both 
 markers in association mapping , but with the favor of ssrs over aflps because 
 of power of detecting ld .
recently , andersen et al .   reported that ld is 
 persisted over entire 3.5 kb phenylalanine 
 ammonia lyase ( pal ) gene with the 
 r > 0.2 in a survey of 32 european maize inbred lines . in the selfing tetraploid 
 wheat ( triticum durum desf . ) , maccaferri et al .  
quantified ld in a 134 durum 
 wheat accessions that extended up to 10 and 20 cm with d = 0.67 and 0.43 , 
 respectively .
in hexaploid wheat ( triticum 
 aestivum l ) , almost 
 completely self - pollinating species , strong ld was determined to occur 
 on average within < 1 and ~5 cm for region on chromosome 2d and centromeric 
 region 5a that was surveyed with 36 ssr markers in a 95 cultivars of winter 
 wheat .
investigated the genome - wide ld among 43 us wheat elite cultivars 
 and breeding lines representing seven us wheat market classes using 242 ssrs 
 distributed throughout the wheat genome .
for this germplasm collection , a 
 genome - wide ld estimates were generally less than 1 cm for the 
 genetically linked loci pairs .
most of the ld regions observed were 
 between loci less than 10 cm apart , suggesting ld is likely to vary 
 widely among wheat populations .
tommasini et al .   reported that ld on 
 chromosome 3b extended up to 0.5 cm in 44 varieties or 30 cm in 240 ril populations 
 of winter wheat , surveyed with 91 ssr and sts markers .
this suggested 
 usefulness of cultivar germplasm over biparental mapping population in 
 association mapping . in rice ( oryza staiva l ) , a 
 selfing species , garris et al .  
examined the ld surrounding disease 
 resistance locus xa5 using 21 ssrs in 
 a survey of 114 rice accessions .
agrama and eizenga   investigated ld patterns in a 
 worldwide collection of oryza staiva , and its wild relatives using 176 ssr markers . although it was not specifically 
 indicated , ld decay plot suggests a long range ld declining ~50 cm with d = 0.5 
 in the  international  and  us 
interestingly , ld persisted 
 over an average of 225 cm distance with significant d > 0.5 in a wild 
 accessions .
in contrast , many other studies reported a less extent of ld in 
 wild and landrace ( broad - based ) germplasm and high extent of ld in cultivar 
 ( narrow - based ) germplasm resources in plants [ 9 , 43 ] .
reported 
 that ld in o. rufipogon decays within 5 kb , while it declines at 50 kb in o. sativa ssp .
observed that the extent of ld is greatest in temperate japonica ( > 500 kb ) , followed by tropical japonica ( ~150 kb ) and indica ( ~75 kb ) that was revealed by using unlinked snps .
ld extends over a shorter 
 distance in o. rufipogon ( 40 kb ) than in any of the o. sativa groups assayed in their study .
ld also has been extensively quantified another highly self - pollinated 
 crop , barley ( hordeum vulgare l ) , where 
 the extent of ld varied from 10 cm to 50 cm range depending on assayed set of a 
 germplasm [ 17 , 77 ] .
measured ld in four genes surrounding 
 hardness locus ( ha ) in three 
 different gene pools and reported a long stretched ld extended up to at least 
 212 kb in inbred barley and 98 kb in landrace barley germplasm .
in contrast to 
 these long range lds observed in barley germplasm , morrell et al .   reported 
 a rapid decay of ld detected within 300 bp in their study of 18 nuclear genes 
 ( average length of 1 361.1 bp ) in 25 diverse wild barley accessions . in that , ld 
 completely disappeared within a 1200 bp distance .
this demonstrates another 
 example of variability of ld quantification across germplasm resources , 
 breeding material , and regions tested .
furthermore , genome - wide ld 
 has been quantified for many other plant species that extended up to 10 cm in 
 sugar cane ( saccharum ) , 1050 cm in soybean 
 ( glycine max ) [ 79 , 80 ] , 3 cm in sugar 
 beet ( beta vulgaris l ) , 50 cm in sorghum ( sorghum bicolor ) , 510 cm in grape ( vitis vinifera l ) , 1634 kb in poplar ( populus trichocarpa ) , < 500 bp in 
 european aspen ( poplus termula ) , 
 2000 bp in loblolly pine ( pinus taeda ) 
 , 1000 bp in douglas - fir ( pseudostuga 
 menziensii ) , 100200 bp in norway spruce ( picea abies ) , 200 - 1 , 200 bp in silage maize ( zea mays l ) [ 87 , 88 ] , and 5002000 bp in 
 ryegrass ( lolium perenne ) [ 8991 ] . also , ld 
 quantification for other important crops , perhaps , is in progress . in this 
 context , recently , we have quantified ld level for improved varieties and 
 landrace stock germplasm of cotton ( gossypium 
 hirsutum l ) .
survey of 200 microsatellite markers in 335 g. 
 hirsutum variety germplasm demonstrated that a genome - wide 
 averages of ld extended up to genetic distance of 25 cm with r > 0.1 . 
 likewise , our another companion study using 95 core set microsatellite markers 
 in a total of 286  exotic
 g. hirsutum revealed 
 that a genome - wide averages of ld decays within the genetic distance at < 10 cm in the landrace stocks germplasm and > 30 cm in photoperiodic variety 
 germplasm , providing evidence of the potential for association mapping of 
 agronomically important traits in cotton ( abdurakhmonov et al .
important 
 information and implication for association mapping gained from above studies 
 are that : ( 1 ) ld more quickly declines in outcrossing plant species than highly 
 self - pollinating plants , enabling high resolution mapping of a trait of 
 interest in outbreeder plant germplasm . at the same time , ld rapidly declines 
 in crop variety groups ( even in selfing species ) compared to populations 
 derived from biparental crosses , which provides an advantage of discovery more 
 polymorphisms in the variety germplasms than biparental populations of 
 self - pollinated crops ; ( 2 ) the extent of ld varies across the genomic 
 regions , among population samples and between species with the examples of 
localized 
 ld  ; ( 3 ) ld measures differ per marker systems used as a reflection of 
 capturing of different historic information in a genome due to different mutation 
 rate ( e.g. , snp versus ssr or aflp versus ssr ) ; ( 4 ) an estimate of genome - wide 
 averages for the extent of ld in plant germplasm may not adequately reflect ld 
 patterns of specific regions or specific population groups .
each of these 
 specific regions or population groups should additionally be explored for the 
 extent of ld in order to conduct successful association mapping of variants 
 within regions or populations of interest ; ( 5 ) ld blocks in narrow - based 
 germplasm groups are longer than broad - based germplasm groups in plants [ 9 , 43 ] . 

this suggests an opportunity perform coarse mapping with less number of markers 
 in narrow - based plant germplasm and then fine mapping in broad - based plant 
 germplasm , assuming that genetic causations is sufficiently similar across 
 germplasm groups .
this also suggest an opportunity develop a set of 
 mapping populations with the required amount of ld and diversity for high - resolution 
 mapping through directed crossing between selected broad- and narrow - based 
 germplasm groups ; and ( 6 ) confounding population characteristics and 
 biological behavior have serious impact on pattern and structure of ld in plant 
 germplasm resources that need to be taken into consideration in conducting 
 unbiased association mapping .
there 
 are many types of different methodologies that have been developed and initially are 
 widely used for association mapping studies in human ( comprehensively reviewed 
 by schulze and mcmahon ) , yet perfectly applicable without change or 
 case - to - case modifications for wide range of organisms , including plants . 
 lately
, some considerably successful achievements have been made to develop 
 powerful , more precise , and unbiased population - based association - mapping 
 methodology for plants . here , we provide a brief overview for a basic concept 
 and ideology of widely used pioneer methodologies for association mapping , and 
 then highlight the latest developments in the methodology and experimental 
 design of association mapping in plant population with the examples of 
 association mapping of useful traits in crop species .
the 
 classical methodology and design of association mapping is  case and control  
 ( also referred to as  case - control  ) approach that identifies the causative 
 gene tags in the comparison of allele frequencies in a sample of unrelated 
 affected ( referred to as  cases  ) individuals and a sample of uninfected or 
 healthy individuals ( referred to as  controls  ) [ 93 , 94 ] .
this design requires 
 an equal numbers of unrelated and unstructured  case - control 
samples for 
 accurate mapping . the pearson chi - square test , fisher 's exact test , or yates 
 continuity correction can be used for a comparison of allele frequencies and 
 detection of an association between a disease phenotype and marker .
although 
 favored , the random sampling individuals from a population do not provide the 
 equal representation of case and controls in the mapping population since cases 
 in the population are usually low , thus requires special efforts to collect the 
 cases .
case and control approach is seriously affected by the existence of 
 population structure and stratification that caught the attention of scientist 
 . falk and rubinstein   developed a haplotype relative risk ( hrr ) 
 approach that minimizes , but not eliminates population stratification issues in 
 association mapping . in that , first , a  pseudocontrol  group ( containing 
 combination of two alleles that are not transmitted to affected offspring ) is 
 created ; then , the marker allele frequencies in case and  pseudocontrol  groups 
 are correlated . to 
 efficiently eliminate the confounding effects coming from population structure 
 and stratification , spielman et al .   developed transmission disequilibrium test 
 ( tdt ) method that compares transmission versus nontransmission of marker 
 alleles to affected offspring by using chi - square test , assuming a linkage 
 between marker and trait .
the tdt design requires genotyping of markers from 
 three individuals : one heterozygous parent , one homozygous parent , and one 
 affected offspring . although hrr performs better with unstructured sample than 
 tdt because of its power to completely eliminate spurious association with good 
 experimental design , later is widely used as a tool for unbiased fine mapping 
 of traits in the presence of linkage with a biallelic , one marker model that 
 can accommodate pedigree structure [ 30 , 93 ] . nonetheless , 
 initial tdt approach had issues with the use of multiallelic markers , multiple 
 markers , missing parental information , extended ( larger ) pedigrees , and complex 
 quantitative traits . to 
 address these issues ,
a variety of extensions of tdt approach were developed and 
 applied for multiallelic markers ( i.e. , gtdt , 
 etdt , mc - tm ) [ 98102 ] , multiple 
 markers [ 103105 ] , missing 
 parental information ( curtis - test , s - tdt , sdt , 1-tdt , c - tdt or rc - tdt ) [ 96 , 106110 ] , which were 
 reviewed by schulze and mcmahon   in detail .
shortly after publication of 
 various extensions of tdt to multiallelic and multiple markers , the extensions 
 for x - linked genes , 
 such as xs - tdt or xrc - tdt were developed and applied .
tdt approach was 
 also extended to pedigrees of any size as a pdt approach [ 112 , 113 ] that was 
 demonstrated more powerful than tdt , and s - tdt or sdt under the assumption of 
 high disease prevalence [ 93 , 114 ] .
further , 
 there were many studies to extend the tdt approaches to qtl and covariates . 

one of the comprehensive approaches , qtdt was developed with its three 
 different extensions for quantitative traits for any pedigree structure [ 115 , 116 ] . 

these family - based association - mapping approaches have their other improvements 
 using more powerful statistical and robust algorithmic procedures , such as 
 likelihood - base statistics and em algorithm ( tdtlike , lrt , em - lrt ) [ 117119 ] . 

the unified family - based association test package ( fbat ) incorporating some of 
 tdt is also developed [ 120122 ] to deal with 
 wide types of experimental designs .
control  and family - based designs , referred to as 
 identity by decent ( ibd ) mapping , haplotypes - sharing analysis ( hsa ) , 
 and decay of haplotypes sharing ( dhs ) , involves the analysis of 
 haplotypes by testing the length of haplotypes in the data sample , assuming 
 affected individuals will have a longer haplotypes than controls . although 
 family - based association mapping methodology is effective to control 
 confounding effects of a sample and remove spurious associations , it is less 
 powerful design   and have its disadvantageous sides compared to 
 case - control   that led to develop the methodologies with better controlling 
 of population structure and stratification .
such an improved methodology for a 
 case and control design or random samples from a population involves the use of 
 additional markers that have neutral effect ( null loci ) to the trait of 
 interest in the analysis .
this approach is referred to as the genomic control 
 ( gc ) that finds confounding effects of a population and corrects it , thus 
 enabling to remove spurious associations [ 127 , 128 ] .
although gc is powerful 
 then tdt , it will not remove spurious associations in highly structured 
 populations .
put it as    methods 
 like  genomic control ,  which simply rescale p - values without changing the ranking of loci are not likely to be useful in genome - wide scans where the 
 existence of true positives is not in doubt .
sa first searches a 
 population for closely related clusters / subdivisions using bayesian approach , and 
 then uses the clustering matrices ( q ) in association mapping ( by a logistic 
 regression ) to correct the false associations .
population structure and shared 
 coancestry coefficients between individuals of subdivisions of a population can 
 be effectively estimated with structure program using several models for linked and unlinked markers .
similar 
 type of methodology measuring and using the population subdivisions ( k ) in 
 association mapping referred to as  mixture model  was proposed by several 
 other studies [ 131 , 132 ] .
however , sa incorporating only population structure 
 information in the analysis is not good enough itself when highly structured 
 population with some degree of related individuals used in the association 
 mapping .
developed new methodology , a mixed linear model ( mlm ) 
 that combines both population structure information ( q - matrix ) and level of 
 pairwise relatedness coefficientskinship 
( k - matrix ) in the analysis . to 
 perform mlm : ( 1 ) q - matrix is generated using structure , ( 2 ) the pairwise relatedness coefficients between 
 individuals of a mapping population ( k - matrix )   measured using spagedi software , and ( 3 ) then 
 both q- and k - matrices are used in association mapping to control spurious 
 associations . although computationally intensive , mlm approach found to be 
 effective in removing the confounding effects of the population in association 
 mapping .
extensively tested the mlm approach of yu et al .   in 
 their global set of
95 highly structured arabidopsis population and came to 
 overall agreement with better performance of q + k mlm model than any of the 
 other tests that used k- or q - matrix alone .
however , they also noted that ( 1 ) k 
 matrix would alone be good enough if a kinship estimated as a proportion of 
 shared haplotypes for each pair of individuals ( as denoted k * ) ; ( 2 ) the 
 replacement of q - matrix ( from the computational intensive structure analysis )   with p - matrix ( from more robust principal 
 component analysis )   performed similarly to mlm of yu et al .
, thus 
 suggesting a potential for future replacements ; ( 3 ) removing of the confounding 
 effects will also subject to remove true associations with biological effect , 
 which is strongly correlated with population structure that requires a caution ; 
 and ( 4 ) in a small and highly structured population , the causations with major 
 effect should be expected to be found and , perhaps , larger samples and adequate 
 marker densities are needed for genome - wide dissection of the most traits of 
 interest segregating in an association mapping population .
there 
 are other types of mixed models for association mapping that have its own 
 advantages to control population confounding effects and tag a genetic 
 causative of a trait of interest .
one of such mixed models utilizes a sample 
 with pedigree information to measure a pedigree - based relatedness and 
 incorporates it directly in qtl - mapping and association mapping [ 59 , 137 , 138 ] . 

this type of mixed model for known pedigree population combines haplotype 
 effects with pedigree - based structure of variance - covariance relatedness matrix 
 and random polygenic effect that control the population structure [ 59 , 139 ] . 

the efficiency of pedigree population for association mapping depends on the 
 population size of pedigree founders ( i.e. , pedigree population obtained from 
 just two parents will not provide significant level of ld ) and the level of 
 relatedness of the founders .
latter is very important and may still lead to 
 spurious association due to initial population structure ( mostly unknown ) 
 coming from founders that needs to be analyzed also by using structure .
however , 
 as stated by malosetti et al .   and others   the pedigree - based mixed 
 model is highly appropriate in association mapping in crops due to ( 1 ) plant 
 breeding programs have already generated many useful pedigree populations that 
 contain ld useful for association studies but can not be used as an independent 
 ld - mapping population , and ( 2 ) many historical trait data sets in plant 
 breeding are unbalanced that have been collected over multiple - years , and multienvironmental 
 trials .
at the same time , issues with obtaining the fine - grained pedigree 
 information and difficulty of finding population structure of narrow - based 
 elite cultivars are the concern in pedigree - based mixed model .
there is another 
 mixed model that combines the bayesian variable selection for mapping multiple 
 qtls and ld mapping method , incorporating estimates of population structure , 
 but not relatedness .
authors stated that incorporation of multiple qtl 
 effects and population structure efficiently reduces spurious association and 
 useful for future whole genome associations , with the development of more 
 complex models dealing with differences of ld and effect of qtl alleles between 
 populations .
the 
 other mixed model approach combines qtl and ld analyses of distinct studies . in 
 that , qtls or candidate genes with already annotated biological function(s )
are 
 used as a priori information in 
 association mapping [ 140 , 141 ] .
this is one of the effective alternative 
 strategies in association mapping that allow reducing the total amount of 
 marker genotyping ( because of preselecting of markers restricted to qtl region ) 
 in less number of individuals .
the power of association mapping is the probability of 
 detecting the true associations within the mapping population size that really 
 depends on ( 1 ) the extent and evolution of the ld in a population , ( 2 ) the 
 complexity and mode of gene action of the trait of interest , ( 3 ) sample size 
 and experimental design .
the power can be increased utilizing the better data 
 ( knowledgeable experimental design and accurate measurements ) and increasing 
 the sample size . in qtl mapping studies ,
there are specific statistical 
 approaches to estimate the false - positive level of the obtained strong 
 ( p - value ) associations ( control for type i error ) such as a permutation test 
 or false discovery rate ( fdr ) .
a statistical approach within the bayesian framework is used 
 test the reliability of obtained significance ( p - values ) in association mapping 
 because of possibility of getting unreliable values due to ( 1 ) overestimation 
 of effects ( selection bias ) , ( 2 ) association coming from neglecting confounding 
 effects of a sample , ( 3 ) poor experimental design , and ( 4 ) instability of 
 genetic effects across different environments .
ball   developed a 
 methodology , combining the bayesian and non - bayesian approaches , that 
 determines the bayes factors guiding to 
 properly design the experiments with given power to detect reliable effects .
to 
 detect the reliable effects in association mapping , experiments should be 
 designed at least with the bayes factor of 20 that may require much larger sample sizes .
bayes factor provides stronger evidence than conventional p - values 
 . if given bayes factor value 
 ( say b = 20 ) reached with larger sample than the original experimental design , 
 then
, the original results indicate a very weak evidence to provide the real 
 effects . at this point ,
requirement for larger sample size might make 
 association mapping disadvantageous over a traditional qtl - mapping .
however , 
 the sample size for association mapping can be decreased keeping the high power 
 with ( 1 ) preselecting a priori 
 known qtl regions or candidate genes ( from qtl - mapping and expression 
 analyses ) , ( 2 ) using the large populations with samples longer ld block that 
 require a less number of markers to find useful associations , ( 3 ) an 
 alternative experimental design ( i.e. , tdt ) , and ( 4 ) choosing the single marker 
 from the haplotypes of interest that would cut also marker number and so 
 genotyping cost . bayes factor 
 can be calculated using r function of ld.design from lddesign package   the pioneer association studies in plants were performed by 
 beer et al .   in oat , and by virk et al .   in rice .
associated 13 qtl with rflp loci using 64 oat varieties and landraces , yet 
 without considering the population structure that resulted in more increased 
 associations than what were obtained in separate analysis of subpopulations . 

virk et al .   predicted 6 trait values using rapd markers in rice 
 germplasm .
later , association mapping was extended to sea beet , barley , maize , 
 wheat , potato , more examples in rice , and arabidopsis that have utilized 
 population level of ld considering a population structure .
reported association of alfp markers with bolting gene in sea beat . in barley , 
 various traits such as yield , yield stability , heading date , flowering time , 
 plant height , rachilla length , resistance to mildew and leaf rust were 
 associated with many different types of molecular markers [ 17 , 18 , 157 , 158 ] . 
 in maize , flowering time and plant height [ 43 , 69 ] were associated using snp 
 and ssrs .
following these pioneer studies of association mapping in maize , 
 several other traits such as phenotypic variation in flowering time , endosperm 
 color , starch production , maysin and chlorogenic acid accumulation , cell wall 
 digestibility , and forage quality were associated using snp markers of 
 candidate genes [ 71 , 87 , 88 , 149153 ] . in wheat , breseghello and
sorrells   reported first 
 association mapping of kernel size and milling quality in a collection of usa 
  winter 
 wheat using ssrs . following this work , association mapping of a high 
 molecular - weight glutenin   and blotch resistance  
were reported that 
 utilized snps , ssrs , and sts markers . in rice , association mapping has not 
 widely been applied yet due to highly structured population of rice ( due to 
 high selfing ) [ 58 , 133 ] .
however , zhang et al .   successfully used 
 association mapping for multiple agronomic traits using discriminant analysis 
 ( da ) with ssr and aflp markers . recently ,
iwata et al .   associated rflp 
 markers with width and length of milled rice grains in a set of 332 rice 
 germplasm using their multiple qtl model considering the population structure . 

association mapping approach was also successfully applied in tetraploid potato 
 where resistance to wilt disease , bacterial blight , phytophtora   that utilized a 
 pedigree - based mixed model . to date
association mapping has also been extended to long 
 lifespan plant species , forest tree populations , where associations of 
 polymorphisms in cinnamoil coa reductase ( ccr ) with earlywood microfibril angle trait , and polymorphisms a 
 putative stress response gene with wood density and wood growth rate   were 
 reported .
there are also the examples of association mapping successes for cold 
 tolerance , flowering time , water - soluble 
 carbohydrate content , and forage quality in forges species that have recently been reviewed by 
 dobrowolski and forster ( table 1 ) [ 87 , 88 , 161 ] .
association mapping of 
 traits in arabidopsis also has been reported and overall suitability of the 
 approach well documented .
later zhao et al .   revisited 
 to these association results with their mixed model approach and reproved some 
 of previously reported associations ( with phyc ) , 
 but challenged the power of these associations detected by using 
 they put it as  clearly , none of these polymorphisms would 
 have been picked up in a genome - wide scan  while noting the use of 
 different sample and trait measurements in the original studies .
they also 
 reported one of the significant flowering time associated polymorphisms in clf gene in their genome - wide analysis 
 using mlm . flowering time ( in fri gene ) and pathogen resistance ( in rpm1 , rps5 , and rps2 genes ) associated polymorphisms were also reported . 

recently , ehrenreich et al .   reported polymorphisms of candidate genes ( sps1 , max2 , and max3 ) 
 associated with branching architecture in a survey of 36 genes involved in 
 branch development that were genotyped in a panel of 96 arabidopsis accessions 
 from central europe . 

table 1 summarizes the ld and association mapping efforts in 
 plants including some of very recent whole genome association mapping studies . 

as one can see , within the frame of above highlighted association studies in 
 plants , various association mapping methodologies ( table 1 ) , molecular markers 
 ( both dominant and co - dominant markers ) , and plant germplasm resources 
 ( including landrace stocks , elite germplasm , and experimental populations  e.g . , 
 rils ) have been utilized .
identifying of the most appropriate approach and 
 marker systems , therefore , is challenging and might be irrelevant case - to - case 
 basis . choosing the appropriate association mapping depends on ( 1 ) 
 the extent and evolution of the linkage disequilibrium in a population , ( 2 ) the 
 level of population structure and stratification , ( 3 ) availability of pedigree 
 information , ( 4 ) complexity of the trait of interest under study , and ( 5 ) 
 availability of the genomic information and resources .
based on reported 
 studies , gc is favored approach when population structure is suspected , but 
 failed to be detected ; however , mlm considering both relatedness and 
 population structure   and pedigree - based mixed model   or multiple qtl 
 model   performs well in most cases with highly structured and stratified 
 population although one still might argue based on his own experience , knowledge , 
 and type of gemplasm used .
according to stich et al . , sa and mlm models do 
 not  explicitly correct  for ld caused by selection and genetic drift , the major 
 factors causing ld in plant germplasm and breeding materials . hence stich et 
 al .   suggested use of family based association approach   with breeding 
 materials . however , again the choice of methodology greatly depends on the 
 germplasm used for mapping .
the germplasm materials used for association 
 mapping were comprehensively discussed by breseghello and sorrells .
thus the association mapping methodology , initially developed 
 by the human geneticists , has found its successive application in plant 
 germplasm resources , in particular after recent improvements in minimization of 
 spurious associations .
the examples of association mapping studies performed in 
 various plant germplasm resources including model plant arabidopsis and extended 
 to various crop germplasm largely demonstrate the flourish of crop genomics era 
 with the utilization of powerful ld - based association mapping tool .
this is 
 also a good indicative of the potential utilization of this technology with the 
 other crops and plant species in the future .
currently , a number of such 
 studies are , perhaps , in progress in many laboratories worldwide .
the 
 near - future completion of genome sequencing projects of crop species , powered 
 with more cost - effective sequencing technologies , will certainly create a basis 
 for application of whole genome - association studies , accounting for rare 
 and common copy number variants ( cnv ) ( for review see , e.g. , ) and 
 epigenomics details of the trait of interest in plants , which is widely being 
 applied in human genetics with great success .
this will provide with more 
 powerful association mapping tool(s ) for crop breeding and genomics programs 
 in tagging true functional associations conditioning genetic diversities , and 
 consequently , its effective utilization .
 compared to the conventional linkage mapping , linkage disequilibrium ( ld)-mapping , using the nonrandom associations of loci in haplotypes , is a powerful high - resolution mapping tool for complex quantitative traits . 
 the recent advances in the development of unbiased association mapping approaches for plant population with their successful applications in dissecting a number of simple to complex traits in many crop species demonstrate a flourish of the approach as a  
 powerful gene tagging  
 tool for crops in the plant genomics era of 21st century . 
 the goal of this review is to provide nonexpert readers of crop breeding community with ( 1 ) the basic concept , merits , and simple description of existing methodologies for an association mapping with the recent improvements for plant populations , and ( 2 ) the details of some of pioneer and recent studies on association mapping in various crop species to demonstrate the feasibility , success , problems , and future perspectives of the efforts in plants . 
 this should be helpful for interested readers of international plant research community as a guideline for the basic understanding , choosing the appropriate methods , and its application . 
1. INTRODUCTION
2. GENETIC MAPPING OF CAUSATIVE VARIANTS
3. ASSOCIATION MAPPING AS
AN ALTERNATIVE APPROACH
4. LINKAGE DISEQUILIBRIUM (LD)
5. ASSOCIATION STUDIES IN PLANTS
6. CONCLUSIONS