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In vitro Techniques in Plantation Crops 111 GENETIC MAPPING OF QUANTITATIVE TRAIT LOCI AND MARKER ASSISTED SELECTION IN PLANTATION CROPS K.K.Vinod Indian Agricultural Research Institute, Rice Breeding and Genetics Research Centre, Aduthurai 612101 In many plantation crops, conventional breeding still has much to offer, without the need to bring in new forms of variation. Breeding progress has been particularly slow in most of these crops, mainly due to generation times in tree crop breeding programmes are very long (about 8 years in cocoa and tea, 8-10 years in oil palm, up to 15 years in rubber and coconut). Identifying and cloning good individuals from existing commercial seedling fields offers the illusory prospect of much faster progress than a long-term breeding programme. At present, the application of molecular markers in conventional breeding programmes looks to be the most useful application of biotechnology in plantation crops. There is still much scope for progress by conventional breeding, and marker-assisted selection can help to reduce the time scales. Molecular markers The potential benefits of using markers linked to genes of interest in breeding programmes, thus moving from phenotype based towards genotype-based selection, have been obvious for many decades. In their classic paper, Paterson et al. (1988) showed that with the availability of large numbers of genetic markers, the effects and location of marker-linked genes having an impact on a number of quantitative traits could be estimated using an approach that could be applied to dissect the genetic make-up of any physiological, morphological and behavioural trait in plants and animals. DNA markers fall into two distinct classes: random markers and linked markers. Random markers are relatively easy to develop; they can be used for ‘fingerprinting’, to determine the identity of clones or the legitimacy of progenies (Mayes et al, 1996). They can also be used in studies of genetic diversity and genetic distance (Shah et al, 1994; Mayes et al, 2000), for planning crossing programmes, and in conservation and prospection projects. Linked markers are those linked to useful characters. To develop efficient selection strategy one needs linked markers. In general, linked markers will allow selection for characters which are not expressed, such as disease resistance in an environment where the disease is not present and selection for mature characters in immature plants. The latter possibility, particularly, could significantly accelerate breeding progress. The fundamental aspect of detecting a linked marker is the understanding of the marker-trait association. Dekkers (2004) described three different levels of marker-trait association (a) direct markers, i.e. loci that code for the functional mutation; (b) linkage disequilibrium (LD) markers: loci that are in population-wide LD with the functional mutation; (c) linkage equilibrium (LE) markers: loci that are in population-wide LE with the functional mutation in outbred populations. This article may be cited as, Vinod K K (2009) Genetic mapping of quantitative trait loci and marker assisted selection in plantation crops. In: Proceedings of the training programme on " In vitro Techniques in Plantation Crops", Central Plantation Crops Research Institute, Kasaragod, India. Downloaded from http://kkvinod.webs.com . pp. 111-132.

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Page 1: Genetic mapping of QTL and marker assisted selection in ... · In vitro Techniques in Plantation Crops 111 GENETIC MAPPING OF QUANTITATIVE TRAIT LOCI AND MARKER ASSISTED SELECTION

In vitro Techniques in Plantation Crops

111

GENETIC MAPPING OF QUANTITATIVE TRAIT LOCI AND MARKER ASSISTED SELECTION IN

PLANTATION CROPS

K.K.Vinod

Indian Agricultural Research Institute, Rice Breeding and Genetics Research Centre, Aduthurai 612101

In many plantation crops, conventional breeding still has much to offer, without the need to bring in new forms of variation. Breeding progress has been particularly slow in most of these crops, mainly due to generation times in tree crop breeding programmes are very long (about 8 years in cocoa and tea, 8-10 years in oil palm, up to 15 years in rubber and coconut). Identifying and cloning good individuals from existing commercial seedling fields offers the illusory prospect of much faster progress than a long-term breeding programme. At present, the application of molecular markers in conventional breeding programmes looks to be the most useful application of biotechnology in plantation crops. There is still much scope for progress by conventional breeding, and marker-assisted selection can help to reduce the time scales.

Molecular markers

The potential benefits of using markers linked to genes of interest in breeding programmes, thus moving from phenotype based towards genotype-based selection, have been obvious for many decades. In their classic paper, Paterson et al. (1988) showed that with the availability of large numbers of genetic markers, the effects and location of marker-linked genes having an impact on a number of quantitative traits could be estimated using an approach that could be applied to dissect the genetic make-up of any physiological, morphological and behavioural trait in plants and animals.

DNA markers fall into two distinct classes: random markers and linked markers. Random markers are relatively easy to develop; they can be used for ‘fingerprinting’, to determine the identity of clones or the legitimacy of progenies (Mayes et al, 1996). They can also be used in studies of genetic diversity and genetic distance (Shah et al, 1994; Mayes et al, 2000), for planning crossing programmes, and in conservation and prospection projects. Linked markers are those linked to useful characters. To develop efficient selection strategy one needs linked markers. In general, linked markers will allow selection for characters which are not expressed, such as disease resistance in an environment where the disease is not present and selection for mature characters in immature plants. The latter possibility, particularly, could significantly accelerate breeding progress. The fundamental aspect of detecting a linked marker is the understanding of the marker-trait association. Dekkers (2004) described three different levels of marker-trait association (a) direct markers, i.e. loci that code for the functional mutation; (b) linkage disequilibrium (LD) markers: loci that are in population-wide LD with the functional mutation; (c) linkage equilibrium (LE) markers: loci that are in population-wide LE with the functional mutation in outbred populations. Th

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An important first step towards developing linked markers is the construction of a linkage map. Using the marker map, putative genes affecting traits of interest can then be detected by testing for statistical associations between marker variants and any trait of interest. These traits might be genetically simple like many traits for disease resistance in plants (Young, 1999) or they could be genetically complex quantitative traits, involving many genes (i.e. so-called quantitative trait loci [QTL]) and environmental effects. Mapping in outbreeding heterozygous perennial crops is not as advanced as in annual crops. They require more time and more space, given the long growing cycle and large crop size.

Theory of quantitative trait loci mapping

A quantitative trait locus, popularly known as QTL is a region of the genome that is associated with an effect on a quantitative trait. Conceptually, a QTL can be a single gene, or it may be a cluster of linked genes that affect the trait. Using the methods for QTL detection to be discussed below, it is not possible to resolve the difference, and use the term “locus” to refer to a chromosomal region. QTL can either be structural enzyme genes, or they can code for regulators of gene expression, or may be non-coding regions that affect gene expression.

The major purpose of QTL mapping is primarily to describe the effects of each genomic region on quantitative traits of interest, namely:

1. Detect which regions of the genome that affect the trait

2. Describe the effect of the QTL on the trait

- How much of the variation for the trait is caused by a specific region

- What is the gene action associated with the QTL - additive or dominance

- Which allele is associated with the favourable effect

3. Assign breeding values to lines or families based on their genotypes at one or more QTL.

In this way the information obtained can be used in QTL mapping experiments for applied marker-assisted breeding strategies. Besides, complementary DNAs at QTL positions representing previously uncharacterized or hypothetical genes, whose transcript levels are strongly correlated with those of genes with known functions, may be associated with the same pathway or biological process. Similarly, new functions can tentatively be assigned to previously characterized genes that had not been described in the context of revealing pleiotropic action of these genes.

Basic principles

Mapping is based on the simple genetic principles, namely, linkage and recombination. Let there are two individuals, homozygous for two alleles of a two loci, A and B. The genotype of one individual is AABB and the other is aabb. They each produce only one type of male and female gamete, AB and ab. Crossing between them result in a F1

progeny of constitution AaBb. The F1 can be selfed or intercrossed to produce F2 generation. F1 being heterozygous, throws out segregants in F2, based on the random combination obtained between male and female gametes produced either as AB, ab, Ab or aB. Of these four types of gametes, the first two resembling the gametes produced by the original homozygotic parents, are called parental types. The other two, must have

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been resulted due to a crossing over between the locus A and B in the F1 heterozygote. They are called recombinant types or recombinants (Fig. 1).

Recombination is the process by which new combination of parental genes occur by exchanging the alleles of different loci by exchanging the chromosomal segments between homologous chromosomes carrying them. In a test cross, wherein the F1

heterozygote (AaBb) is crossed with the homozygotic recessive parent (aabb), under normal independent segregation of these loci, with at least a single cross over between them, there would be equal number of parental types and recombinants (50% each). However, if the loci are closely placed enough in such a way that there is only restricted chances of crossing over between them, the proportion of the parental types will be high (>50%) in correspondence to the closeness of the two loci. In such cases we call the loci are linked and the phenomenon is called linkage. The proportion of recombinants in the total progeny, thus provide information about the quantum of cross over took place between the loci, called recombination frequency or cross–over value. This value gives an estimate of the distance between the loci, with the assumption that the amount cross over is proportionate to the distance between the two loci. In simple terms, thus the recombination value can be calculated as,

Recombination frequency (%) = progeny of no. Total

100 x tsrecombiman of No.

One percentage of recombination is equivalent to one arbitrary map unit called as centimorgan or cM. For example, if the recombination frequency between two loci A

 

Fig 1. Genetic basis of marker based mapping

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and B is 5% and the same between B and C is 23%, and that between A and C is 26%, using this values, we can order these loci along a chromosome is given in Fig 2.

Here, it may be noted that the observed distance between the loci A and C is not exactly additive, to the total of the distance between the intervening locus B. This is due to the presence of double or multiple crossovers that take place between the loci, which may not be detectable from the recombination frequency. This warrants mapping with closely placed markers, so that multiple crossover information can be eliminated considerably.

However, estimating the genetic distances between a whole arrays of markers, distributed throughout the genome, and aligning them on linkage groups is a complex problem, which often requires analytical power of a computer. However, at present there are many computer programs available for this purpose. MAPMAKER, QTL cartographer, JoinMap, MapManager etc are some of the widely used programs. The most commonly used procedure in these programs is based on the maximum likelihood method. The output from these programs depicts linear relationship among the markers and the distance between the markers is measured in centimorgans (cM), so that they can be grouped into distinct groups called linkage groups based on the recombination frequency values.

Generations and populations used for mapping

Essentially all that is required to detect QTL is that the QTL and the markers are segregating in the population evaluated, there is some linkage disequilibrium between marker loci and QTL, and that one has a reliable assay or measurements of the phenotypic trait(s). The estimates of QTL effects, and the power and precision of QTL estimates, however, may vary depending on the type of population evaluated. The procedures of genetic mapping are mainly focused on populations developed from crosses between two inbred lines. There are two different types of single-cross populations: F2 and F2-derived populations and recombinant inbred lines (RIL) populations. Other types of populations, such as backcross or random-mating populations can be used for QTL mapping, but the ability to detect QTL or the information contained in such populations is generally lower compared to F2 or RIL populations. Random-mating populations are more difficult for QTL mapping, because, the linkage disequilibrium is a key to detecting QTL with markers. Modification of the genetic model discussed hereunder is necessary to accommodate different types of populations.

These different options have different implications for both genotypic and phenotypic evaluation. Producing recombinant inbred lines (F2-derived lines single seed descended without selection to F6:7 or so generation) allows recombination to occur each generation, so that there are more chances for recombination to occur between two loci in RILs

  A   B  C 

6 23 cM    Fig 2. Diagrammatic representation of markers A,B and C on the molecular linkage

map.

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compared to F2’s. Precise localization of both marker loci and QTL depends upon the number of recombination that occurs between genes. Thus RILs allow higher resolution mapping of QTL because one can distinguish map positions better. On the other hand, the power of detecting QTL depends in part upon association of marker and QTL alleles (to be shown later), so that the additional recombination between QTL and marker loci can reduce the power of tests for QTL. This difficulty can be overcome by use of a sufficiently dense maker linkage map. RILs also differ from F2’s in that the lines are homozygous at nearly all loci, so there is very little power to detect or estimate dominance.

RILs are developed by single seed selections from individual plants of an F2 population. (Because of this procedure, these lines are also called F2-derived lines.) Single seed descent is repeated for several generations. At this point, all of the seed from an individual plant is bulked. For example, a F3:4 RI population underwent single-seed descent through the F3 generation, and was bulked to develop the F4 (Fig 3). This

population of seed can then be grown to obtain a large quantity of seed of each individual line. Importantly, each of the lines is fixed for many recombination events; thereby they contain the segregation adequately fixed to maximum homozygosity (table 1). No selection is exercised in the population.

Table 1. Percentage of homozygosity in RIL generations

RIL inbreeding generations

% within–line homozygosity at each locus

F3:4 75.0 F4:5 87.5 F5:6 92.25 F6:7 96.875 F7:8 98.4375 F8:9 99.21875

Fig 3. Methods of producing recombinant inbred lines

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Because RILs are essentially homozygous, only additive gene action can be measured. F2’s, therefore, may allow mapping of QTL with fewer marker loci, but the precision of the QTL “placements” will be lower. The ability to detect and estimate dominance gene action is also maximized. However, phenotypic evaluation of F2 individuals does not allow for replicated trials (unless with clonally-propagated species), which are critical to obtaining valid phenotypic measurements of quantitative traits. Thus, many prefer to work with F2:3 lines, which can be replicated, although the heterozygosity of each line is halved, so there is less power to detect dominance. If estimating dominance is not of great interest, RILs might be preferred, as greater quantities of seed can often be produced for testing.

BC1F1 populations have the same amount of linkage disequilibrium as do F2 generations, so are equivalent to F2’s in terms of resolution of QTL map positions. Backcross populations have only two genotypic classes at each marker and QTL locus, either AA or AB if A is the recurrent parent. This means that if the QTL allele from the recurrent parent is completely dominant over the allele from the donor parent, then the genotypes QAQA and QAQB are expected to be equal and no QTL will be detected in backcross populations. If backcrosses are made to parent B as well, and both backcross populations are phenotyped and genotyped, then all QTL with complete dominance segregating in the populations may be detected. But evaluating both backcross populations seems to offer little advantage over evaluating F2 populations.

Methods used in mapping

Many different approaches are now available in genetic mapping of QTL. The basis of QTL mapping lies in the fact that the positions of QTL are indirectly estimated. In a population where markers and the QTLs segregate, we only know the marker genotype but not the QTL. In contrary, we do not know the phenotype of the marker, but we do know the phenotype of the QTL. Now with the proximity of the QTL segregation to that of the marker the QTL positions are indirectly estimated. Depending on the number of markers involved in the analysis they are grouped into single marker analysis and multiple marker analysis. Singe marker analysis or single point analysis involves only a marker and its relation to trait segregation vis-à-vis its own. Fundamentally, it does not require a map. Whereas, multiple marker analysis or multi-point analysis require a map, and are generally deal with marker intervals. Since marker intervals can be drawn between any two markers on a linkage group, and precise estimations of the interval points can be made, interval mapping require more complicated computations.

Single-factor analysis of variance - Genetic model

Association between a quantitative trait and genetic markers can be evaluated using single markers or multiple markers. When using one single marker, it is possible to make inference about the segregation of a QTL linked tot that marker. A genetic model that describes the single marker effect on a QTL requires different combinations of marker locus and QTL genotypes to understand how marker genotypes can be used to study QTL indirectly. Arbitrary gene effects are assigned to the QTL in the model, and the corresponding actual effects can be estimated from the data based on the model. Single factor analysis of variance (SF-ANOVA) is the most commonly used procedure.

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Assume that there are two alternate alleles at each QTL that is segregating in the population: Q1 and Q2. For any QTL locus, the following genotypic values for the trait in question are defined:

QTL genotype Value Q1Q1 m+a Q1Q2 m+d Q2Q2 m-a

The notations +a and -a refer to the deviations of the homozygotes from the mid-parent at the QTL locus: these are additive gene effects; d refers to the deviation of the heterozygote from the midparent: this is the dominance deviation. m+a is arbitrarily assigned to the Q1Q1 genotype, as it could also be assigned just as well to the Q2Q2 genotype.

Let the designation of inbred parents as p1 and p2. Consider first a single genomic region, in which the parental genotype can be detected at a DNA marker locus, M. Assuming that there is a QTL, Q, linked to this DNA marker locus with a recombination frequency of r between the marker and the QTL. The parental genotypes at the marker and QTL loci are as follows:

Parent 1 (p1) Parent 2 (p2)

M1 Q1 M2 Q2

M1 r Q1 M2 r Q2

These parents are crossed to produce an F1 genotype:

F1

M1 Q1

M2 r Q2

These identical F1’s can then be selfed or intermated to form an F2 population. Consider the four possible gametes produced by the F1 (Table 2) and the nine different possible genotypes in an F2 generation (Table 3):

Table 2. Gametes produced by an F1 heterozygous at both QTL and marker locus.

Gamete Frequency M1 Q1 ½ (1-r) M1 Q2 ½ (r) M2 Q1 ½ (r) M2 Q2 ½ (1-r)

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Table 3. Genotypic values and frequencies of nine F2 genotypes

Genotype Genotypic value Frequency

M1M1Q1Q1 +a ¼ (1-r)2 M1M1Q1Q2 +d ½ r(1-r) M1M1Q2Q2 -a ¼ r2 M1M2Q1Q1 +a ½ r(1-r) M1M2Q1Q2 +d ½ [(1-r)2+ r2] M1M2Q2Q2 -a ½ r(1-r) M2M2Q1Q1 +a ¼ r2 M2M2Q1Q2 +d ½ r(1-r) M2M2Q2Q2 -a ¼ (1-r)2

The frequency of the different genotypes is based on the frequencies of the gametes that compose the genotypes. For example, the M1M1Q1Q1 genotype can only be formed by the union of a male M1Q1 gamete with a female M1Q1 gamete. The frequency of this occurrence is simply the product of the probabilities of those gametes, in this case, [½ (1-r)]x[½(1-r)] = ¼(1-r)2. The frequency of the M1M1Q1Q2 genotype can be formed in two ways: by the union of a female M1Q1 gamete with a male M1Q2 gamete (an event with frequency ¼r (1-r)) or by the union of a female M1Q2 gamete with a male M1Q1 gamete (also with frequency ¼r(1-r)). The total probability of that genotype, then is the sum of the probabilities of the two ways in which it can be formed, or 2x¼r (1-r) = ½r (1-r). The other genotype frequencies follow similarly. The only exceptional case is the M1M2Q1Q2 genotype, which can be formed in four different ways: by a male M1Q1 combining with female M2Q2 , or by a male M2Q2 combining with a female M1Q1, or by a male M1Q2 combining with a female M2Q1 , or by a male M2Q1 combining with a female M1Q2. The frequency of that genotype is the sum of the probabilities of those four events.

The genotypic values assigned above depend only upon the genotype at the QTL locus, not at the marker locus. While the marker locus has no effect on the genotypic value, only the marker locus genotype is known- not the genotype at the QTL! Thus, the information in the above table is to be used to derive expected genotypic values for each of the three genotypes at a marker locus (Table 3). For example, the expected value of genotypes with marker genotype M1M1 is the weighted average of the three QTL genotypes that compose that marker class, obtained by summing the frequency of the genotypes by their values, then dividing by the sum of the frequencies: [ ¼ (1-r)2a + ½ r(1-r)d + ¼ r2(-a)]/(¼) = a[(1-r)2 - r2] + 2d[r(1-r)].

Table 4. Expected values of F2 marker locus genotypes

Marker Genotype Genotypic Value Frequency Estimated

Phenotypic Mean M1M1 a[(1-r)2-r2] + 2d[r(1-r)] ¼ 11MMY M1M2 d[(1-r)2 + r2] ½ 21MMY M2M2 -a[(1-r)2 - r2] + 2d[r(1-r)] ¼ 22MMY

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In practice, one uses the genotypic data to determine to which class each F2 belongs, and then one computes the mean phenotypic value of each of the three classes from the observed phenotypic data. Based on these expected genotypic values, the expectation of a contrast between the two homozygous genotypic class mean phenotypes can be determined:

)21(2)1(2 22211 rarraYYE r

MMMM

Similarly, the expectation of the difference between the heterozygotes and the mid-parent is:

222221121 )21()441()]1([2])1[())(½( rdrrdrrdrrdYYYE r

MMMMMM

Thus, these contrasts can be used to detect the presence of QTL and estimate their additive and dominant effects. If the marker is not linked to the QTL, then r = ½ and the expected contrasts are:

02211 MMMM YYE

0)(½)( 2222112111 MMMMMMMMMM YYYYYE

Thus, the test indicates correctly that the marker is not associated with the trait.

It is important to note that performing these “single-factor” ANOVA-based estimates confounds the effects of the QTL with the recombination frequency between the maker and the QTL (Edwards et al. 1987). If the difference between the two homozygous marker classes is, for example, 20 units, it could be because the marker is extremely tightly linked r ~ 0) to the QTL with a 10 units additive effect [(M1M1 - M2M2) = 2 × 10 units], or because the QTL has a 20 units additive effect and the marker is located 25 recombination units away [E(M1M1 - M2M2)] = 2 × 20 units [1-2 (0.25)] = 20 units].

Furthermore, single-factor analyses give no indication as to which side of the marker the QTL is located. This difficulty can be overcome to some extent by use of a reasonably dense linkage map. For example, if marker loci were located every 10 cM throughout the genome, then the marker effects on the trait at 10 cM intervals on each chromosome could be tested. It would be possible to determine which marker on a chromosome arm was associated with the largest effect, which would suggest that the QTL is located 5 cM on either side of the locus. By determining which flanking marker had the next largest effect, it was also possible to determine which side of the marker the QTL was located on.

Interval mapping – Genetic model

In the case of single markers it is not possible to distinguish between size of a QTL effect and its position (relative to the marker). Also, single marker analyses have less power if the markers are far apart. If two (or more) markers are jointly used in an analysis, there is a lot less confounding between the position and size of QTL effect, and there is more power in detecting a QTL, even if the markers are far apart. Inference about the QTL

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effect as well as the recombination rate between QTL and markers (i.e. position of QTL) is possible. The recombination rate between markers is usually assumed known. Therefore mapping of a QTL therefore requires the use of multiple marker genotypes in the analysis. Depending on the complexity of computations in the interval mapping it can be simple interval mapping, composite interval mapping or mixed model mapping. Mixed models involve fixed and random factors in the model, like QTL x environment interactions.

Parent 1 Parent 2

M1 Q M2 m1 q m2

M1 r1 Q r2 M2 m1 q m2

These parents are crossed to produce an F1 genotype:

F1

M1 Q M2

m1 q m2

Maximum likelihood

The term ‘interval mapping’ is used for estimating the position of a QTL within two markers (often indicated as ‘marker-bracket’). Interval mapping is originally based on the maximum likelihood but there are also very good approximations possible with simple regression. The principle involve is:

1) The Likelihood can be calculated for a given set of parameters (particularly QTL effect and QTL position) given the observed data on phenotypes and marker genotypes.

2) The estimates for the parameters are those were the likelihood are highest.

3) The significance can be tested with a likelihood ratio test:

)(_

)(_ln2LR

fullLikelihoodMax

reducedLikelihoodMax

The reduced model refers to the null-hypothesis, e.g. "there is no QTL effect". Using the log-likelihood, )lnln(ln2LR LLr , where lnL is the loge of the maximum likelihood.

Regression methods

Regression analysis is easier and usually much quicker than maximum likelihood, and in many cases, it is very similar. The basic idea is given here in the context of interval mapping

For a given haplotype that was inherited from male parent, we can calculate the probability for having inherited the Q or the q allele. It seems therefore natural to regress phenotype on Q-probability. The model is, a.xμy , where y is the observed

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phenotype, and x is the probability of having inherited a paternal Q, given the observed marker genotype.

The coefficient in x is obtained as P(Q|Mi Mj) for a given QTL position. There are only four different x-values, one for each haplotype as given in Table 5.

Table 5. Gametic probabilities when QTL is flanked between two markers

Parental genotype M1 Q M2

m1 q m2

Possible gametes Recombination Gamete probability

M1 Q M2 no (1-r1)(1-r2)/2

M1 q M2 double: M1-q, q-M2 r1.r2/2

M1 Q m2 yes: Q-m2 (1-r1)r2/2

M1 q m2 yes: M1-q r1(1-r2)/2

m1 Q M2 yes: m1-Q r1(1-r2)/2

m1 q M2 yes: q-M2 (1-r1)r2

m1 Q m2 double: m1-Q, Q-m2 r1.r2/2

m1 q m2 no (1-r1)(1-r2)/2

The probabilities for the paternal Q-allele of different marker haplotypes Prob(Q|M1M2)

)1(½

)1)(1(½

2.1

21

r

rr

)1(1

2.1

21

r

rr

Prob(Q|M1m2)

2.1

21

½

)1(½

r

rr 2.1

212

r

rrr

Prob(Q|m1M2)

2.1

21

½

)1(½

r

rr 2.1

211

r

rrr

Prob(Q|m1m2) )1(½

½

2.1

21

r

rr

)1( 2.1

21

r

rr

For each recorded individual, we can then give a predicted phenotype with this “QTLmodel” which is equal to ii .xaμy , where the “hats” refer to estimated (predicted) values.

A model ignoring a QTL would predict each observation as 0μy , where 0μ is typically

the general progeny mean.

Now let the total sum of squares (SST) be the sum (over progenies) of 20 )μy( and let

the residual sum of squares (SSE) be the sum (over animals) of 2i0i ).xaμy(

Each map position will yield an SSE and the position with the lowest SSE is the most likely position.

A test statistic for this method is for an experiment with n observations is

)ln(LRSSE

SSTn ,

where n is equal to the number of observations.

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The LR stands for “Likelihood Ratio”, as this test statistic is approximately similar to the LR from maximum likelihood. Haley and Knott (1992) have shown that this similarity. If there are more fixed effects in the model, the test statistic is calculated as

)ln(LRfull

reduced

SSE

SSEn

Which is ratio of the residual sums of squares in a model with the QTL (‘full’) and a model without it (‘reduced’).

The information about a QTL is only dependent on the flanking markers. If the QTL lies outside the bracket, it will only depend on the nearest marker. Likelihood maps can be constructed for neighbouring marker brackets and they should exactly match up at each marker, and a map of multiple intervals M1-M2-M3....-Mk can be made smooth.

Methods to improve precision

Permutation tests (Churchill and Doerge, 1994) offer one alternative. These tests work by first randomly assigning the observed phenotypes to the observed genotypes in the study. Then, QTL detection tests are performed at each locus. Since the phenotypes were randomly assigned to the genotypes, one should not detect any QTLs. However, simply due to random chance, some of the tests might indicate significance. The highest F-value (for example) among all of the loci for this random assignment is recorded. Then, the phenotypes are reshuffled and randomly assigned to genotypes again. Significance tests are performed at all loci again, and the highest value is recorded again. This process of reshuffling phenotypes and recording the highest test statistic among all loci is repeated 1,000 times. After this, the highest 5% of the 1,000 F-values recorded from each permutation are selected and their lowest value is used as the threshold level that indicates an F-test significant at the 5% level. Permutation tests are available as part of the “QTL Cartographer” software available from North Carolina State University.

A somewhat liberal ad hoc alternative is to adjust the error rate for the number of known independent tests made. For example, if markers on all 20 arms of the 10 chromosomes of maize were used in the study, and each arm is considered to be independent, then one might use p=0.05/20 = 0.0025 as a liberal, but reasonable threshold level.

If one has QTL mapping data from several environments, one can select QTLs that were important on average over environments. On the other hand, one can perform QTL analyses for each environment separately, and then declare as “significant” only those loci that were significant in more than one or two environments. This method selects for “stable” QTLs, and will most likely to miss QTLs that are truly important only in specific environments. Whether this is a good or a bad thing depends on the objectives of the QTL study.

Multiple regression or multiple locus ANOVA models can be developed in some systematic fashion as a method of “selection” of important QTLs.

Principles of marker aided selection

Twenty years have passed since the first demonstrations that QTL for major effects could be mapped with molecular markers (Stuber et al. 1980; Paterson et al. 1988; Lander and Botstein, 1989), and several reviews have described the potential benefits and caveats of MAS in the plant genetics literature (e.g. Tanksley, 1993; Beavis, 1998; Young, 1999;

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Mauricio, 2001; Dekkers and Hospital, 2002). Having identified markers physically located beside or even within genes of interest, in the next step it is now possible to carry out marker assisted (aided) selection (MAS), i.e. to select identifiable marker variants (alleles) in order to select for non-identifiable favourable variants of the genes of interest. For example, consider a hypothetical situation where a molecular marker M (with two alleles M1 and M2), identified using a DNA assay, is known to be located on a chromosome close to a gene of interest Q (with a variant Q1 that increases yield and a variant Q2 that decreases yield), that is, as yet, unknown. If a given individual in the population has the alleles M1 and Q1 on one chromosome and M2 and Q2 on the other chromosome, then any of its progeny receiving the M1 allele will have a high probability (how high depends on how close M and Q are to each other on the chromosome) of also carrying the favourable Q1 allele, and thus would be preferred for selection purposes. On the other hand, those that inherit the M2 allele will tend to have inherited the unfavourable Q2 allele, and so would not be preferred for selection. With conventional selection which relies on phenotypic values, it is not possible to use this kind of information.

Once markers have been detected that are associated with major genes or QTL they can be employed to practical plant breeding in the following broad fields.

For genotype identification and genetic diversity

In selection and breeding for resistance to diseases and pests

In selection of lines for male fertility restoration

Selection for high performing genotypes based on QTL compositing

Purity analysis of seeds of varieties and hybrids

It may assist breeders is in breaking linkages between negatively correlated traits

MAS in a breeding context involves scoring indirectly for the presence or absence of a desired phenotype or phenotypic component based on the sequences or banding patterns of molecular markers located in or near the genes controlling the phenotype. The sequence polymorphism or banding pattern of the molecular marker is indicative of the presence or absence of a specific gene or chromosomal segment that is known to carry a desired allele. DNA markers can increase screening efficiency in breeding programmes in a number of ways. For example, they provide:

The ability to screen in the juvenile stage for traits that are expressed late in the life of the organism (i.e. grain or fruit quality, male sterility, photoperiod sensitivity);

The ability to screen for traits that are extremely difficult, expensive or time consuming to score phenotypically (i.e. quantitatively inherited or environmentally sensitive traits such as root morphology, resistance to quarantined pests or to specific races or biotypes of diseases or insects, tolerance to certain abiotic stresses such as drought, salt and mineral deficiencies or toxicities);

The ability to distinguish the homozygous from the heterozygous condition of many loci in a single generation without the need for progeny testing (as molecular markers are co-dominant);

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The ability to perform simultaneous MAS for several characters at one time (or to combine MAS with phenotypic or biochemical evaluation).

Once markers have been detected that are associated with QTL, the logical next step is to perform selection on lines within a population. The obvious method would be to only advance those lines which contain those alleles with a positive effect on the quantitative trait, the selection criterion being the summation index showing maximum accumulation

of the desired QTL (fig 4). A collateral advantage of such an approach is that it offers a true validation of the putative genes (QTL) for the traits of interest. The associated response to marker selection namely indicates the presence of true genes; in particular in the vicinity of markers strongly affected by the selection imposed.

MAS strategies

Before molecular markers can be used for selection purposes, their association with genes or traits of interest must be firmly established. MAS can be applied to support existing conventional breeding programmes such as:

Recurrent selection (i.e. using within-breed or within-line selection, important in livestock);

Development of crossbreds or hybrids (by crossing several improved lines or breeds)

Introgression (where a target gene is introduced from, for example, a low-productive line or breed (donor) into a productive line (recipient) that lacks the target gene (a strategy especially important in plants).

Marker assisted selection is effective when the genetic base of the participating genotypes is broad. This will facilitate identification of specific QTL related to target traits (Fig 5). Keeping this as the starting point, by precise MAS we can go up in pyramiding the beneficial QTLs culminating into development of elite cultivars.

The success of MAS is influenced by the relationship between the markers and the genes of interest. Dekkers (2004) distinguished three kinds of relationship:

 Fig 4. Marker assisted selection by employing summation index of plus QTL

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The molecular marker is located within the gene of interest (i.e. within the gene Q, using the example above). In this situation, one can refer to gene-assisted selection (GAS). This is the most favourable situation for MAS since, by following inheritance of the M alleles, inheritance of the Q alleles is followed directly. On the other hand, these kinds of markers are the most uncommon and are thus the most difficult to find.

The marker is in linkage disequilibrium (LD) with Q throughout the whole population. LD is the tendency of certain combinations of alleles (e.g. M1 and Q1) to be inherited together. Population wide LD can be found when markers and genes of interest are physically very close to each other and/or when lines or breeds have been crossed in recent generations. Selection using these markers can be called LD-MAS.

The marker is not in linkage disequilibrium (i.e. it is in linkage equilibrium [LE]) with Q throughout the whole population. Selection using these markers can be called LE-MAS. This is the most difficult situation for applying MAS.

In a breeding context, understanding the genetic basis of genotype by genotype interaction (G x G) and genotype by environment interaction (G x E) is critical as the basis for predicting how QTL are likely to behave. QTL x environment interaction (QEI) makes MAS more difficult.

Fig 5. Marker assisted selction under varying genetic base

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QTL mapping in plantation crops

Linkage map construction

On plantation crops, maps have been published for cocoa (Lanaud et al, 1995, Risterucci et al 2000), coffee (Paillard et al, 1996), oil palm (Mayes et al, 1997) and rubber (Lespinasse et al, 2000a) and tea (Unilever, unpublished). Later, linkage maps of 16 linkage groups each for the two coconut types Laguna Tall (LAGT), an ecotype indigenous to the Philippines, and Malayan Yellow Dwarf (MYD), have been reported (Herrán et al 2000). A map allows the selection of markers which are evenly distributed over the genome, thus enhancing the probability of finding markers linked to quantitative traits.

Mapping strategies

Except for particular situations (Lanaud et al. 1995; Plomion et al. 1995; Tulsieram et al. 1992) only progeny issued from the cross between two heterozygous parents (F1 cross) are usually available. In this case, up to four alleles per locus may segregate. Data can be analysed as a double pseudo-testcross (Grattapaglia and Sederoff 1994) and a map constructed separately for each parent. New algorithms for recombination rate estimates can also be used, taking advantages of meioses occurring in both parents (Maliepaard et al. 1997; Ritter et al. 1990; Ritter and Salamini 1996; Stam 1993; Stam and van Ooijen 1995). In these F1 crosses, marker phase (coupling or repulsion) can not always be deduced from parent and grandparent banding patterns (Carlson et al. 1991), which adds one source of complexity. With several common markers of the same order present in chromosomes of both parents (bridge markers), it is possible to combine the information of markers from different individuals as described by Ritter and Salamini (1996). In this way the number of markers available per chromosome can be increased. Bridge markers are required to merge the parental genetic maps and the more bridges used, the better the synthetic map will be. It is necessary, before considering a locus as a bridge, to check the consistancy of the map position in both parental maps. Finally, it is necessary to compare parental recombination rates before merging the maps. Therefore, more codominant markers are needed to combine marker information from different parents. The mapping of recently developed coconut microsatellites (SSRs, Rivera et al. 1999; Perera et al. 1999) and of single nucleotide polymorphisms (SNPs) established during a sequencing programme of coconut genes belonging to homeotic gene families (Rohde, unpublished) offers one possibility to achieve this goal.

Detection of QTLs

In plantation crops, QTL analysis is performed generally by single marker ttests and interval regression. The single marker approach, however, is less sensitive, particularly with a small sample size, and does not allow an estimation of the recombination frequency between the marker and the QTL (Lander and Botstein 1989).

Coconut

In coconut, genetic mapping using different DNA marker types (including amplified fragment length polymorphisms (AFLPs), ISTRs, random amplified polymorphic DNA (RAPD), and inter-SSRs (ISSRs)), and several quantitative trait loci (QTLs) for early germination were detected (Herrán et al. 2000). In addition, QTLs for other traits, including leaf production and girth height, were identified for the same mapping

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population (Ritter et al. 2000). QTLs are now available for the traits early germination (Herrán et al. 2000), girth height, and leaf production (Ritter et al. 2000) and for the yield characters (Lebrun et al 2001).

Rubber

Genetic resistance to Microcyclus ulei causing South American leaf blight (SALB) disease was identified to rely on 1–5 QTLs, among which two have a major effect. Except for the major QTL on linkage group 13 which was found for all strains, other QTLs were strain-specific, even QTLs associated with quantitative variation of LD (Lespinasse et al 2000b).

Oil palm

Mayes et al (1997) found a marker linked to the shell thickness gene in oil palm; this will allow selection of specific fruit types in the nursery, before fruiting starts.

Cocoa

In cocoa, markers associated with growth and flowering characteristics have been identified (Crouzillat et al, 1996). Besides, QTLs were identified for Phytophthora resistance using composite interval mapping. One of these was detected with five strains belonging to the three Phytophthora species. Two other regions were detected with two or three strains of two different species. Three additional QTLs were detected for only one species of Phytophthora (Risterucci et al. 2003).

Eucalyptus

QTL mapping experiments in Eucalyptus have, found a few major QTL for all traits considered in spite of the limited experimental precision, the lack of pre-designed pedigree to maximize phenotypic segregation, and the relatively small segregating populations evaluated. QTL for juvenile traits such as seedling height, leaf area and seedling frost tolerance have been mapped (Vaillancourt et al. 1995; Byrne et al. 1997a, b), while traits related to vegetative propagation ability such as adventitious rooting, stump sprouting and in vitro shoot multiplication have also been detected (Grattapaglia et al 1995; Marques et al. 1999), as has a major QTL for early flowering (Missiaggia et al. 2005). In addition, QTL for insect resistance and essential oil traits were mapped (Shepherd et al. 1999) and recently a major QTL for Puccinia psidii rust resistance with quasi Mendelian inheritance was found and mapped in E. grandis (Junghans et al. 2003). Major QTL were also found for rotation age traits such as volume growth, wood specific gravity, bark thickness and stem form (Grattapaglia et al. 1996; Verhaegen et al. 1997; Thamarus et al. 2004; Kirst et al. 2004, 2005).

Thamarus et al. (2004) identified QTLs for wood density, pulp yield and microfibril angle (MFA), including three QTL in common genetic regions on both crosses for wood density, one for pulp yield and one for MFA. Recently QTL analysis of transcript levels of lignin-related genes showed that their mRNA abundance is regulated by two genetic loci co-localized with QTL for growth, suggesting that the same genomic regions are regulating growth, lignin content and composition (Kirst et al. 2004).

Marker assisted selection in plantation crops

In most of tree breeding in general, the application of molecular markers for directional selection is still an unfulfilled promise. This is largely due to:

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The recent domestication of tree crops and hence the wide genetic heterogeneity of breeding populations;

The inability to develop inbred lines at least on a short-term basis to allow a more precise understanding of genetic architecture of quantitative traits;

The absence of simply inherited traits that could be immediately and more easily targeted;

The very limited number of scientists actually working on forest trees.

Quantitative theory as well as common sense suggests that MAS in perennial trees should help, particularly in situations where trait heritability is low and selection occurs at the level of the individual tree. However, implementing MAS for such traits is a challenging task as extremely precise QTL mapping information is required and this can only be derived from experiments with large progeny sizes (in the order of several hundred individuals), clonal replicates for increased precision, representative and multiple genetic backgrounds and environments.

QTL linked markers could be used to carry out early selection thus reducing the time necessary to carry out the first selection especially for traits related to wood properties, and at the same time reducing the number of trees to be selected, propagated and advanced all the way to clonal trials (Fig. 6).

Fig 6. Scheme for early marker assisted selection in clonally propagated species

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Very large progeny sizes would have to be deployed to have a reasonable probability of recovering genotypes with a combination of favourable alleles at many QTL for many traits. When using MAS, priorities will have to be established not only for traits but also for specific QTL. This will require a very good understanding of the relative magnitude of each QTL, potential QTL x background interactions and pleiotropic effects of QTL.

Theoretically, when the total proportion of the additive genetic variance explained by the marker loci exceeds the heritability of the character, selection on the basis of the markers alone is more efficient than selection on the individual phenotype.

For the exploitation of MAS in coconut breeding, it will be necessary to establish additional mapping populations segregating for important traits such as early flowering, tolerance to biotic and abiotic stress, copra yield and quality, and other characters of interest. Furthermore, these analyses should be performed in several different crosses, to establish QTLs in different genetic backgrounds. This will facilitate comparative QTL analyses in terms of the location of QTLs and the effects of quantitative trait alleles and their possible interaction.

Challenges of MAS in plantation crops

The challenge of applying MAS is difficult and complex for perennial trees because it requires:

(i) Manipulation of polygenic traits with variable heritabilities in breeding populations with a heterogeneous genetic base and in linkage equilibrium;

(ii) Its incorporation in breeding schemes that involve altering the frequencies of favourable alleles through recurrent selection in large populations; and

(iii) Dealing with age x age trait correlations, and late expressing phenotypes (Grattapaglia, 2000).

(iv) In most of the experiments in plantation crops, the relatively small progeny sizes used for QTL detection (around 100 to 200 individuals), the estimated magnitude of the effects were largely overestimated commonly well known as “Beavis effect” (Beavis, 1998).

(v) The large majority of mapped QTL have been localized on RAPD or AFLP maps. Consequently, it is impossible to compare positions of QTL for the same or correlated traits, seriously limiting the long-term value of such mapping for MAS.

(vi) The location of QTL is imprecise as they can only be mapped to 5–10 cM. This may translate into a physical distance of several megabases, which may contain several hundred genes.

(vii) The effect of a QTL is also likely to vary over time in perennial plants with changing biotic and abiotic factors (Brown et al. 2003).

(viii) The cost of assembling and integrating the necessary infrastructure and personnel is soaring high.

New approaches in marker-assisted breeding

Linkage disequilibrium (LD) mapping is another marker-assisted approach that provides important information that is immediately relevant to breeding programmes (Remington et al. 2001; Flint-Garcia et al. 2003). Using collections of distantly related germplasm

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accessions rather than populations derived from bi-parental crosses allows researchers to explore the relationship between phenotype and genotype in materials that have been amply tested over years and environments, often as part of an applied breeding programme. This provides critical information about how specific combinations of genes and alleles interact in relevant varietal backgrounds and allows breeders to compare the phenotypic effect of genes or chromosomal segments that have been inherited from a common ancestor and selected in multiple-cross combinations.

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