# Application of Association Mapping to Understanding the Genetic Diversity of Plant Germplasm Resources

Authors: Ibrokhim Y. Abdurakhmonov; Abdusattor Abdukarimov
Journal: International Journal of Plant Genomics
 (2008)

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## Abstract

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.


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## Body

## 1. Introduction

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 [1]. Presently, out of 150 plant species cultivated in agriculture, twelve
provide about 75% of human food and four produce 50% of human diet [2].
According to Food and Health Organization report, ~800 million people in the
developing countries are suffering from food
deficiency [3] that underlies an attention to improve agricultural production
to eliminate or, at least, reduce the feedingproblems.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
[4]. 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.


## 2. Genetic Mapping of Causative Variants

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]: (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. [6], and further basic description of the approach here would be
a redundant. For detailed concept, models and methodologies, problems, and
perspectives of linkage analysis, readers are suggested refer to Liu [7] and Wu
et al. [8]. 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
[6–8],
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. This is accomplished through assessing of recombination
rates between the marker loci. 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 [6]. 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 [10] 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 [11].


## 3. Association Mapping as an Alternative Approach

These
limitations, however, can be reduced with the use of “association mapping” [1].
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 [12]. 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 [13–16].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 [17–19].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 Figure1): (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].Figure 1
The scheme of association mapping for tagging a gene of interest using germplasm accessions. Note that the outlined scheme may vary based on population characteristics and methodology chosen for association study.


## 4. Linkage Disequilibrium (LD)

### 4.1. Concept of LD

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, 22–24] that will be
discussed in below sections. Linkage disequilibrium also referred as “gametic
phase disequilibrium” (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)
[26]. Besides D, a various different measures of LD (D′,
r2,
D2,
D*, F, X (2), and δ) have been developed to quantify LD [25, 27–29]. 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. [25].
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 r2 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 r2 before using for quantification of the extent of LD [26]. The r2,
the square of the correlation coefficient between the two loci have more
reliable sampling properties than D′ with the cases of low allele frequencies
[26]. The r2 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 r2 that is also an indicative of marker-trait
correlations [25, 26, 32]. The r2 value varies from 0 to 1, and it
will be equal to 1 when only two haplotypes are present. The r2 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 [33].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 [34] 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 [36], and the results of GLD
and ZLD are mostly in agreement, yet ZLD detects more extensive LD than determined
by GLD [37]. 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 [35–37].


### 4.2. Calculation and Visualization of LD: LD Triangle and Decay Plots

LD can be calculated using available haplotyping
algorithms [26]. One of such efficient methodology is the maximum likelihood
estimate (MLE) using an expectation maximization algorithm [38]. 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. [25].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 (Figure2) based on significant pairwise
LD level (r2, 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) [39],
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 [41] 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 [42]. 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.Figure 2
The TASSEL generated triangle plot for pairwise
LD between marker sites in a hypothetical genome fragment, where pairwise LD
values of polymorphic sites are plotted on both theX- and Y-axis; above the
diagonal displays r2 values and below the diagonal displays the
corresponding p-values from rapid 1000 shuffle permutation test. Each cell
represents the comparison of two pairs of marker sites with the color codes for
the presence of significant LD. Colored bar code for the significance threshold
levels in both diagonals is shown. The genetic distance scale for a hypothetical
genome fragment was manually drawn. Note: this is for demonstration purposes
only and does not have any real impact or correspond to any genomic fragment of
an organism.To
estimate the size of these LD blocks, ther2 values (alternatively,
D′ can also be used) usually plotted against the genetic (cM) or weighted (bp)
distance referred to as a “LD decay plot” (Figure 3). 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 (r2) 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 (r2 ≥ 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].Figure 3
Linkage disequilibrium (LD) decay plot depicted from the LD values of a hypothetical marker data to demonstrate a measure of an average genome-wide LD block sizes. A pairwise LD values (r2) are plotted against a genetic distance. Inner fitted trend line is a nonlinear logarithmic regression curve of r2 on genetic distance. LD decay is considered below r2=0.1 threshold and based on trend line it is around 38–40 cM in above plot. A pairwise LD between unlinked marker loci is assigned to 100 cM distance point. Note: this is for demonstration purposes only and does not have any real impact or correspond to any genomic fragment of an organism.


### 4.3. Factors Affecting LD and Association Mapping

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 [24], 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].LD conserved with linkage is very useful for
association mapping. 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) [45], and epistatic selection or the so-called coadapted genes
[46] that is the result of coselection of loci during breeding for multiple
traits [26], 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 [22]. 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
[22–24], which is evidenced
by nonuniform distribution of LD in chromosomes [24].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.
[25]. 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, 48–50]. The r2 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 5–10% (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]).


### 4.4. Estimation of LD Using Dominant versus Codominant Markers

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, 27–30]).
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 [54].
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. Misassignment
of allelic relationships of loci is the concern in association analysis [55]. 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., [57]).
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., [17–19, 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 [63].Recently,
Li et al. [54] 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 [54].


### 4.5. LD Quantification in Plants

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.Nordborg et al. [20] sequenced
0.5–1 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. They determined that LD decays within a 1 cM distance or 250 kb.
Later, investigation of the same authors [21] 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 50–250 kb. LD blocks
extended up to 50–100 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. [64] reported
much smaller LD block size, extended up to only 10 kb. Likewise, LD quickly
decays within 10–50 kb distance
around the CLAVATA 2 region of
Arabidopsis [65]. Recently, Ehrenreich et al. [66] 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. [67] 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. [68]
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 r2=0.2
and extended up to 1000 bp (~1 kb) in a group of US inbred lines. Later,
Remington et al. [43] also reported a very rapid decline of LD in their survey
of 6 genes (1.2–10 kb long) in
102 inbred lines, including tropical and semitropical lines with a wide genetic
diversity. For these surveyed genes, LD declined generally within 200–2000 bp with r2=0.1
except sugary1 (su1) loci, where LD remained significant (r2=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. [43] 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.Long stretches of LD for maize
also were reported. Thornsberry et al. [69] measured LD in and around the Dwarf8 locus. They found “localized LD”
(i.e., restricted to particular regions, meaning that high LD stretches
interspersed with regions of low LD) extended up to 3 kb. Jung et al. [70]
reported the extent of LD within 500 kb in surveying adh1 locus. Stich et al. [22] 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 [43] was explained due to using (1) much higher marker density, and (2)
both related and unrelated inbred lines. In another study, the same authors [9]
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. [71] reported that LD is
persisted over entire 3.5 kb phenylalanine
ammonia lyase (PAL) gene with the
r2>0.2 in a survey of 32 European maize inbred lines.In the selfing tetraploid
wheat (Triticum durum Desf.), Maccaferri et al. [50] 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 [52]. Recently, Chao et al. [72] 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 [72]. Tommasini et al. [56] 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. [73] examined the LD surrounding disease
resistance locus Xa5 using 21 SSRs in
a survey of 114 rice accessions. They determined the strong LD within 100 kb
with r2=0.1. Agrama and Eizenga [74] 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” rice collections. 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]. There is evidence that the
LD is remarkably different in other rice species. Rakshit et al. [75] reported
that LD in O. rufipogon decays within 5 kb, while it declines at 50 kb in O. sativa ssp. indica accessions. Mather et al. [76] 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 [76].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]. Caldwell et al. [51] 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. [78] 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) [10], 10–50 cM in soybean
(Glycine max) [79, 80], 3 cM in sugar
beet (Beta vulgaris L) [81], 50 cM in sorghum (Sorghum bicolor) [44], 5–10 cM in grape (Vitis vinifera L) [53], 16–34 kb in poplar (Populus trichocarpa) [82], <500 bp in
European aspen (Poplus termula) [83],
2000 bp in loblolly pine (Pinus taeda)
[84], 1000 bp in Douglas-fir (Pseudostuga
menziensii) [85], 100–200 bp in Norway Spruce (Picea abies) [86], 200-1, 200 bp in silage maize (Zea mays L) [87, 88], and 500–2000 bp in
ryegrass (Lolium perenne) [89–91]. 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) [92]. 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 r2>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. unpublished,
submitted elsewhere for publication).


### 4.6. Implications for Association Mapping Gained from LD Quantification Studies in Plants

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 [56]; (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 [12]. 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 [86]; 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.


## 4.1. Concept of LD

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, 22–24] that will be
discussed in below sections. Linkage disequilibrium also referred as “gametic
phase disequilibrium” (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)
[26]. Besides D, a various different measures of LD (D′,
r2,
D2,
D*, F, X (2), and δ) have been developed to quantify LD [25, 27–29]. 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. [25].
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 r2 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 r2 before using for quantification of the extent of LD [26]. The r2,
the square of the correlation coefficient between the two loci have more
reliable sampling properties than D′ with the cases of low allele frequencies
[26]. The r2 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 r2 that is also an indicative of marker-trait
correlations [25, 26, 32]. The r2 value varies from 0 to 1, and it
will be equal to 1 when only two haplotypes are present. The r2 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 [33].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 [34] 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 [36], and the results of GLD
and ZLD are mostly in agreement, yet ZLD detects more extensive LD than determined
by GLD [37]. 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 [35–37].


## 4.2. Calculation and Visualization of LD: LD Triangle and Decay Plots

LD can be calculated using available haplotyping
algorithms [26]. One of such efficient methodology is the maximum likelihood
estimate (MLE) using an expectation maximization algorithm [38]. 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. [25].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 (Figure2) based on significant pairwise
LD level (r2, 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) [39],
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 [41] 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 [42]. 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.Figure 2
The TASSEL generated triangle plot for pairwise
LD between marker sites in a hypothetical genome fragment, where pairwise LD
values of polymorphic sites are plotted on both theX- and Y-axis; above the
diagonal displays r2 values and below the diagonal displays the
corresponding p-values from rapid 1000 shuffle permutation test. Each cell
represents the comparison of two pairs of marker sites with the color codes for
the presence of significant LD. Colored bar code for the significance threshold
levels in both diagonals is shown. The genetic distance scale for a hypothetical
genome fragment was manually drawn. Note: this is for demonstration purposes
only and does not have any real impact or correspond to any genomic fragment of
an organism.To
estimate the size of these LD blocks, ther2 values (alternatively,
D′ can also be used) usually plotted against the genetic (cM) or weighted (bp)
distance referred to as a “LD decay plot” (Figure 3). 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 (r2) 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 (r2 ≥ 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].Figure 3
Linkage disequilibrium (LD) decay plot depicted from the LD values of a hypothetical marker data to demonstrate a measure of an average genome-wide LD block sizes. A pairwise LD values (r2) are plotted against a genetic distance. Inner fitted trend line is a nonlinear logarithmic regression curve of r2 on genetic distance. LD decay is considered below r2=0.1 threshold and based on trend line it is around 38–40 cM in above plot. A pairwise LD between unlinked marker loci is assigned to 100 cM distance point. Note: this is for demonstration purposes only and does not have any real impact or correspond to any genomic fragment of an organism.


## 4.3. Factors Affecting LD and Association Mapping

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 [24], 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].LD conserved with linkage is very useful for
association mapping. 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) [45], and epistatic selection or the so-called coadapted genes
[46] that is the result of coselection of loci during breeding for multiple
traits [26], 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 [22]. 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
[22–24], which is evidenced
by nonuniform distribution of LD in chromosomes [24].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.
[25]. 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, 48–50]. The r2 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 5–10% (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]).


## 4.4. Estimation of LD Using Dominant versus Codominant Markers

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, 27–30]).
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 [54].
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. Misassignment
of allelic relationships of loci is the concern in association analysis [55]. 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., [57]).
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., [17–19, 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 [63].Recently,
Li et al. [54] 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 [54].


## 4.5. LD Quantification in Plants

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.Nordborg et al. [20] sequenced
0.5–1 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. They determined that LD decays within a 1 cM distance or 250 kb.
Later, investigation of the same authors [21] 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 50–250 kb. LD blocks
extended up to 50–100 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. [64] reported
much smaller LD block size, extended up to only 10 kb. Likewise, LD quickly
decays within 10–50 kb distance
around the CLAVATA 2 region of
Arabidopsis [65]. Recently, Ehrenreich et al. [66] 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. [67] 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. [68]
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 r2=0.2
and extended up to 1000 bp (~1 kb) in a group of US inbred lines. Later,
Remington et al. [43] also reported a very rapid decline of LD in their survey
of 6 genes (1.2–10 kb long) in
102 inbred lines, including tropical and semitropical lines with a wide genetic
diversity. For these surveyed genes, LD declined generally within 200–2000 bp with r2=0.1
except sugary1 (su1) loci, where LD remained significant (r2=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. [43] 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.Long stretches of LD for maize
also were reported. Thornsberry et al. [69] measured LD in and around the Dwarf8 locus. They found “localized LD”
(i.e., restricted to particular regions, meaning that high LD stretches
interspersed with regions of low LD) extended up to 3 kb. Jung et al. [70]
reported the extent of LD within 500 kb in surveying adh1 locus. Stich et al. [22] 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 [43] was explained due to using (1) much higher marker density, and (2)
both related and unrelated inbred lines. In another study, the same authors [9]
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. [71] reported that LD is
persisted over entire 3.5 kb phenylalanine
ammonia lyase (PAL) gene with the
r2>0.2 in a survey of 32 European maize inbred lines.In the selfing tetraploid
wheat (Triticum durum Desf.), Maccaferri et al. [50] 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 [52]. Recently, Chao et al. [72] 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 [72]. Tommasini et al. [56] 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. [73] examined the LD surrounding disease
resistance locus Xa5 using 21 SSRs in
a survey of 114 rice accessions. They determined the strong LD within 100 kb
with r2=0.1. Agrama and Eizenga [74] 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” rice collections. 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]. There is evidence that the
LD is remarkably different in other rice species. Rakshit et al. [75] reported
that LD in O. rufipogon decays within 5 kb, while it declines at 50 kb in O. sativa ssp. indica accessions. Mather et al. [76] 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 [76].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]. Caldwell et al. [51] 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. [78] 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) [10], 10–50 cM in soybean
(Glycine max) [79, 80], 3 cM in sugar
beet (Beta vulgaris L) [81], 50 cM in sorghum (Sorghum bicolor) [44], 5–10 cM in grape (Vitis vinifera L) [53], 16–34 kb in poplar (Populus trichocarpa) [82], <500 bp in
European aspen (Poplus termula) [83],
2000 bp in loblolly pine (Pinus taeda)
[84], 1000 bp in Douglas-fir (Pseudostuga
menziensii) [85], 100–200 bp in Norway Spruce (Picea abies) [86], 200-1, 200 bp in silage maize (Zea mays L) [87, 88], and 500–2000 bp in
ryegrass (Lolium perenne) [89–91]. 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) [92]. 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 r2>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. unpublished,
submitted elsewhere for publication).


## 4.6. Implications for Association Mapping Gained from LD Quantification Studies in Plants

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 [56]; (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 [12]. 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 [86]; 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.


## 5. Association Studies in Plants

### 5.1. The Methodology Overview

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 [93]), 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
[93]. Falk and Rubinstein [95] developed a haplotype relative risk (HRR)
approach that minimizes, but not eliminates population stratification issues in
association mapping [96]. 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 [93].To
efficiently eliminate the confounding effects coming from population structure
and stratification, Spielman et al. [97] developed transmission disequilibrium test
(TDT) method that compares transmission versus nontransmission of marker
alleles to affected offspring by using chi-square test [93], 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 [93]. To
address these issues, a variety of extensions of TDT approach were developed and
applied for multiallelic markers (i.e., GTDT,
ETDT, MC-Tm) [98–102], multiple
markers [103–105], missing
parental information (Curtis-test, S-TDT, SDT, 1-TDT, C-TDT or RC-TDT) [96, 106–110], which were
reviewed by Schulze and McMahon [93] 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 [111]. 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 [93].
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) [117–119].
The unified family-based association test package (FBAT) incorporating some of
TDT is also developed [120–122] to deal with
wide types of experimental designs. The next generation of association mapping
approaches in both “case and control” and family-based designs, referred to as
identity by decent (IBD) mapping [123], haplotypes-sharing analysis (HSA) [124],
and decay of haplotypes sharing (DHS) [125], 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 [93].Although
family-based association mapping methodology is effective to control
confounding effects of a sample and remove spurious associations, it is less
powerful design [126] and have its disadvantageous sides compared to
case-control [93] 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 [128], it will not remove spurious associations in highly structured
populations. Zhao et al. [129] 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.”To
better deal with highly structured populations, Pritchard et al. [47, 62]
developed approach of structured association (SA). 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 [130]. 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.Hence,
recently, Yu et al. [133] developed new methodology, a mixed linear model (MLM)
that combines both population structure information (Q-matrix) and level of
pairwise relatedness coefficients—“kinship” (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) [134] measured using SpaGedi software [135], 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 [133].Later
Zhao et al. [129] extensively tested the MLM approach of Yu et al. [133] 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) [130] with P-matrix (from more robust principal
component analysis) [136] performed similarly to MLM of Yu et al. [133], 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 [129].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 [140].However,
as stated by Malosetti et al. [59] and others [140] 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 cannot 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. This approach was used for association mapping in highly
selfing rice germplasm [58]. 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. This increases the power and precision of the
trait-marker correlations [142].


### 5.2. Power of Association Mapping

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 [143]
or false discovery rate (FDR) [144].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 [142]. Ball [142] 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
[142]. 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 [142]. 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 [142]. Bayes factor
can be calculated using R function of ld.design from ldDesign package [140].


### 5.3. Examples from Reports

The pioneer association studies in plants were performed by
Beer et al. [166] in oat, and by Virk et al. [167] in rice. Beer et al. [166]
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 [11].
Virk et al. [167] 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. Hansen et al. [19]
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, 149–153].In wheat, Breseghello and Sorrells [52] 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 [159] and blotch resistance [56] 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. [156] successfully used
association mapping for multiple agronomic traits using discriminant analysis
(DA) with SSR and AFLP markers. Recently, Iwata et al. [58] 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 [138], bacterial blight [60], Phytophtora [59] that utilized a
pedigree-based mixed model.To date association mapping has also been extended to long
lifespan plant species, forest tree populations [163], where associations of
polymorphisms in cinnamoil CoA reductase (CCR) with earlywood microfibril angle trait [141], and polymorphisms a
putative stress response gene with wood density and wood growth rate [163] 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].Table 1
Linkage disequilibrium and association mapping studies in plants.
SpeciesMating
systemLD
extentMapped
traits*Approach
usedArabidopsisSelfing10–250 kb and 50–100 cM [20, 21, 64, 66, 67]Flowering time, growth response, pathogen resistance, and branching
architecture [66, 129, 145–148]One way ANOVA, simple regression, SA, MLMMaizeOutcrossing200–2000 bp [43, 68], 3–500 kb [43, 69–71], 4–41 cM [9, 22]Plant height, flowering time, endosperm color, starch production,
maysin and chlorogenic acid accumulation, cell wall digestibility, forage
quality, and oleic acid level [43, 69, 71, 87, 88, 149–154]GLM, SA, MLM, WGARice (indica, japonica and rufipogon)Selfing5–500 kb [73, 75, 76]
50–225 cM [74], 20–30 cM [155]Multiple agronomic traits such as plant height, heading date, flag leaf length and width, tiller number, steam diameter, panicle length, grain length and width, grain length/width ratio, grain thickness, 1000-grain weight, width and length of milled rice grains [58, 155, 156]DA, MLM, mixed model with multiple QTL effectBarleySelfing10–50 cM [16, 77], 98–500 kb [51],
300 bp [78]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]Pearson correlation; regression, ANOVATetraaploid wheatSelfing10 and 20 cM [50]N/AN/AHexaploid wheatSelfing<1–10 cM [52, 56, 72]Kernel size and milling, a high molecular weight glutenin and blotch
resistance [52, 56, 159]GLM-Q, LMMPotatoSelfing0.3–1 cM [25, 60],
3 cM [160]Resistance to wilt disease, bacterial blight,Phytophtora, and potato quality (tuber shape, flesh color, under
water weight, maturity, and etc.)[59, 60, 138, 160]Nonparametric Mann-Whitney U test, standard two samplet-test,
GMMSoybeanSelfing10–50 cM [79, 80],Seed protein content [80]WGASorghumOutcrossing50 cM [44]N/AN/AGrapeVegetative propagation5–10 cM [53]N/AN/ASugarcaneOutcrossing/Vegetative propagation10 cM [10]N/AN/ASugar beetOutcrossing3 cM [81]N/AN/AForage grasses (silage maize and ryegrass)Outcrossing200–2000 bp [87–91]Cold tolerance, flowering time and forage quality, water-soluble
carbohydrate content [87, 88, 161, 162]Multiple linear regression; ANOVAForest trees (Norway spruce, Loblolly pine, poplar,
European aspen, Douglas-fir)Outcrossing100–200 bp [86],
~500–2000 bp [83–85]Early-wood microfibril angle trait, wood density and wood growth rate
[141, 163]ANOVA; combination of LD and QTL mapping* MLM: mixed linear model
[133]; GLM: general linear model without population structure [71]; GLM-Q:
general linear model using population structure matrix (Q) or the least square
solution to the fixed effects GLM [56]; DA: discriminant analysis [156];
SA-structured association [47]; LMM: linear mixed model [52]; WGA: whole
genome association [154, 164, 165]; GMM:
general mixed model [59]; ANOVA: analysis of variance test; N/A—not available
(search of known major online library database as of December 2007).Association mapping of
traits in Arabidopsis also has been reported and overall suitability of the
approach well documented. Associations ofCRY2 with flowering time were reported [145, 146]. Balasubramanian et al. [147]
reported the association of PHYC with
flowering and growth response in Arabidopsis. Later Zhao et al. [129] 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 “standard
linear methods without correcting population structure.” 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 [129]. Flowering time (in FRI gene) and pathogen resistance (in Rpm1, Rps5, and Rps2 genes) associated polymorphisms were also reported [148].
Recently, Ehrenreich et al. [66] 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.


### 5.4. Choice of the Appropriate Approach

Table1 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 [59]; however, MLM considering both relatedness and
population structure [133] and pedigree-based mixed model [59] or multiple QTL
model [58] 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. [23], 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. [23] suggested use of family based association approach [168] 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 [169].


## 5.1. The Methodology Overview

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 [93]), 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
[93]. Falk and Rubinstein [95] developed a haplotype relative risk (HRR)
approach that minimizes, but not eliminates population stratification issues in
association mapping [96]. 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 [93].To
efficiently eliminate the confounding effects coming from population structure
and stratification, Spielman et al. [97] developed transmission disequilibrium test
(TDT) method that compares transmission versus nontransmission of marker
alleles to affected offspring by using chi-square test [93], 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 [93]. To
address these issues, a variety of extensions of TDT approach were developed and
applied for multiallelic markers (i.e., GTDT,
ETDT, MC-Tm) [98–102], multiple
markers [103–105], missing
parental information (Curtis-test, S-TDT, SDT, 1-TDT, C-TDT or RC-TDT) [96, 106–110], which were
reviewed by Schulze and McMahon [93] 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 [111]. 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 [93].
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) [117–119].
The unified family-based association test package (FBAT) incorporating some of
TDT is also developed [120–122] to deal with
wide types of experimental designs. The next generation of association mapping
approaches in both “case and control” and family-based designs, referred to as
identity by decent (IBD) mapping [123], haplotypes-sharing analysis (HSA) [124],
and decay of haplotypes sharing (DHS) [125], 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 [93].Although
family-based association mapping methodology is effective to control
confounding effects of a sample and remove spurious associations, it is less
powerful design [126] and have its disadvantageous sides compared to
case-control [93] 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 [128], it will not remove spurious associations in highly structured
populations. Zhao et al. [129] 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.”To
better deal with highly structured populations, Pritchard et al. [47, 62]
developed approach of structured association (SA). 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 [130]. 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.Hence,
recently, Yu et al. [133] developed new methodology, a mixed linear model (MLM)
that combines both population structure information (Q-matrix) and level of
pairwise relatedness coefficients—“kinship” (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) [134] measured using SpaGedi software [135], 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 [133].Later
Zhao et al. [129] extensively tested the MLM approach of Yu et al. [133] 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) [130] with P-matrix (from more robust principal
component analysis) [136] performed similarly to MLM of Yu et al. [133], 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 [129].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 [140].However,
as stated by Malosetti et al. [59] and others [140] 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 cannot 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. This approach was used for association mapping in highly
selfing rice germplasm [58]. 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. This increases the power and precision of the
trait-marker correlations [142].


## 5.2. Power of Association Mapping

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 [143]
or false discovery rate (FDR) [144].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 [142]. Ball [142] 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
[142]. 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 [142]. 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 [142]. Bayes factor
can be calculated using R function of ld.design from ldDesign package [140].


## 5.3. Examples from Reports

The pioneer association studies in plants were performed by
Beer et al. [166] in oat, and by Virk et al. [167] in rice. Beer et al. [166]
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 [11].
Virk et al. [167] 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. Hansen et al. [19]
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, 149–153].In wheat, Breseghello and Sorrells [52] 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 [159] and blotch resistance [56] 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. [156] successfully used
association mapping for multiple agronomic traits using discriminant analysis
(DA) with SSR and AFLP markers. Recently, Iwata et al. [58] 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 [138], bacterial blight [60], Phytophtora [59] that utilized a
pedigree-based mixed model.To date association mapping has also been extended to long
lifespan plant species, forest tree populations [163], where associations of
polymorphisms in cinnamoil CoA reductase (CCR) with earlywood microfibril angle trait [141], and polymorphisms a
putative stress response gene with wood density and wood growth rate [163] 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].Table 1
Linkage disequilibrium and association mapping studies in plants.
SpeciesMating
systemLD
extentMapped
traits*Approach
usedArabidopsisSelfing10–250 kb and 50–100 cM [20, 21, 64, 66, 67]Flowering time, growth response, pathogen resistance, and branching
architecture [66, 129, 145–148]One way ANOVA, simple regression, SA, MLMMaizeOutcrossing200–2000 bp [43, 68], 3–500 kb [43, 69–71], 4–41 cM [9, 22]Plant height, flowering time, endosperm color, starch production,
maysin and chlorogenic acid accumulation, cell wall digestibility, forage
quality, and oleic acid level [43, 69, 71, 87, 88, 149–154]GLM, SA, MLM, WGARice (indica, japonica and rufipogon)Selfing5–500 kb [73, 75, 76]
50–225 cM [74], 20–30 cM [155]Multiple agronomic traits such as plant height, heading date, flag leaf length and width, tiller number, steam diameter, panicle length, grain length and width, grain length/width ratio, grain thickness, 1000-grain weight, width and length of milled rice grains [58, 155, 156]DA, MLM, mixed model with multiple QTL effectBarleySelfing10–50 cM [16, 77], 98–500 kb [51],
300 bp [78]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]Pearson correlation; regression, ANOVATetraaploid wheatSelfing10 and 20 cM [50]N/AN/AHexaploid wheatSelfing<1–10 cM [52, 56, 72]Kernel size and milling, a high molecular weight glutenin and blotch
resistance [52, 56, 159]GLM-Q, LMMPotatoSelfing0.3–1 cM [25, 60],
3 cM [160]Resistance to wilt disease, bacterial blight,Phytophtora, and potato quality (tuber shape, flesh color, under
water weight, maturity, and etc.)[59, 60, 138, 160]Nonparametric Mann-Whitney U test, standard two samplet-test,
GMMSoybeanSelfing10–50 cM [79, 80],Seed protein content [80]WGASorghumOutcrossing50 cM [44]N/AN/AGrapeVegetative propagation5–10 cM [53]N/AN/ASugarcaneOutcrossing/Vegetative propagation10 cM [10]N/AN/ASugar beetOutcrossing3 cM [81]N/AN/AForage grasses (silage maize and ryegrass)Outcrossing200–2000 bp [87–91]Cold tolerance, flowering time and forage quality, water-soluble
carbohydrate content [87, 88, 161, 162]Multiple linear regression; ANOVAForest trees (Norway spruce, Loblolly pine, poplar,
European aspen, Douglas-fir)Outcrossing100–200 bp [86],
~500–2000 bp [83–85]Early-wood microfibril angle trait, wood density and wood growth rate
[141, 163]ANOVA; combination of LD and QTL mapping* MLM: mixed linear model
[133]; GLM: general linear model without population structure [71]; GLM-Q:
general linear model using population structure matrix (Q) or the least square
solution to the fixed effects GLM [56]; DA: discriminant analysis [156];
SA-structured association [47]; LMM: linear mixed model [52]; WGA: whole
genome association [154, 164, 165]; GMM:
general mixed model [59]; ANOVA: analysis of variance test; N/A—not available
(search of known major online library database as of December 2007).Association mapping of
traits in Arabidopsis also has been reported and overall suitability of the
approach well documented. Associations ofCRY2 with flowering time were reported [145, 146]. Balasubramanian et al. [147]
reported the association of PHYC with
flowering and growth response in Arabidopsis. Later Zhao et al. [129] 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 “standard
linear methods without correcting population structure.” 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 [129]. Flowering time (in FRI gene) and pathogen resistance (in Rpm1, Rps5, and Rps2 genes) associated polymorphisms were also reported [148].
Recently, Ehrenreich et al. [66] 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.


## 5.4. Choice of the Appropriate Approach

Table1 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 [59]; however, MLM considering both relatedness and
population structure [133] and pedigree-based mixed model [59] or multiple QTL
model [58] 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. [23], 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. [23] suggested use of family based association approach [168] 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 [169].


## 6. Conclusions

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 [164], accounting for rare
and common copy number variants (CNV) (for review see, e.g., [165]) 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.



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*Source: 574927-2008-06-08.xml*