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a Dep. of Agronomy and Plant Genetics, Univ. of Minnesota, 411 Borlaug Hall, 1991 Upper Buford Cir., St. Paul, MN 55108
b Institut National de la Recherche Agronomique, Station de génétique végétale, Ferme du Moulon, 91190 Gif-sur-Yvette, France
* Corresponding author (bernardo{at}umn.edu)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Abbreviations: cM, centimorgan • MARS, marker-assisted recurrent selection • QTL, quantitative trait loci
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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The MARS procedures used to date have relied on ad hoc significance tests (i) to identify markers associated with the trait and, subsequently, (ii) to estimate the effect associated with each marker. These ad hoc significance tests are done separately for each population undergoing MARS. Advances in genomics and post-genomics sciences, however, are expected to uncover most, if not all, of the genes for important traits in crops. Such gene discovery is expected through different approaches including candidate gene analysis, sequence homology comparisons, gene expression profiles, proteomics, metabolomics, and phenomics (Bowen and Luedtke, 1997; Somerville and Somerville, 1999; Thiellement et al., 2002; Fiehn, 2002; Gerlai, 2002). If the genes underlying a quantitative trait become known, then their locations would no longer need to be determined by ad hoc significance tests in MARS. Only the quantitative effects associated with the actual QTL would need to be estimated. In this manuscript we define known QTL as QTL whose genomic locations are known a priori but whose effects in terms of the quantitative trait need to be estimated in the breeding population. The known QTL may be identified through markers for the QTL themselves, or through functionally neutral markers linked to the actual QTL.
Results from a previous study (Bernardo, 2001) suggest that having known QTL would enhance MARS. Bernardo (2001) investigated the usefulness of known QTL in inbred and hybrid development. He found that best linear unbiased prediction based on pedigree information was highly effective for predicting hybrid performance. Due to this high effectiveness, having known QTL did not substantially enhance hybrid development. In contrast, best linear unbiased prediction based on pedigree information is ineffective in selection within an F2 or backcross population because all individuals within the population have the same degree of relatedness based on pedigree (Bernardo, 2002, p. 234). This ineffectiveness of pedigree information in selection led to greater room for improvement, through markers linked to the QTL or markers for the QTL themselves, in inbred development than in hybrid development. Bernardo (2001) did not investigate the usefulness of known QTL in MARS. Because populations undergoing MARS lack pedigree relationships that can be exploited in best linear unbiased prediction, we surmise that having known QTL would enhance MARS in the same manner that it enhances inbred development.
In a preliminary study, Charcosset and Moreau (2004) found that having known QTL increased the expected efficiency of marker-assisted selection. This preliminary study involved a simple genetic model of 10 unlinked QTL with equal effects. In the current study, we examined the usefulness of having known QTL under genetic models that included different numbers of QTL, different levels of heritability, unequal gene effects, linkage, and epistasis. Our first objective was to determine whether knowing some or all of the QTL, as opposed to detecting unknown QTL through ad hoc significance tests, is advantageous in MARS. Our second objective was to determine whether knowing the QTL themselves, as opposed to knowing QTL through functionally neutral linked markers, is advantageous in MARS.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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We considered a trait controlled by l = 10, 40, or 100 QTL in a linear metabolic pathway, which is described in the next section. The first QTL had the largest effect, the second QTL had the second largest effect, the third QTL had the third largest effect, and so on. For both the Flanking Marker and QTL Per Se models, the percentage of known QTL was P = 0%, 10%, 20%, 30%, ... , 100%. We assumed that the QTL with the largest effects were known first and that the QTL with the smallest effects were known last. For example, for l = 100 QTL, the first 10 QTL (i.e., the 10 QTL with the largest effects) were known for P = 10%, and the first 20 QTL were known for P = 20%. This assumption was for simplicity and was based on the argument that the QTL with large effects are likely to be discovered first. The percentage of the genetic variance (VG) accounted for by the known QTL was 20% (l = 10) to 24% (l = 100) for P = 10%; 39% (l = 10) to 41% (l = 100) for P = 20%; and 53% (l = 10) to 55% (l = 100) for P = 30%. For P > 30%, values at a given P were similar regardless of the number of QTL: 66% for P = 40%; 75% for P = 50%; 82% for P = 60%; 88% for P = 70%; 93% for P = 80%; 97% for P = 90%; and 100% for P = 100%.
When none of the QTL were known (P = 0%), markers with significant effects were detected by ad hoc statistical tests at significance levels of 
= 0.20, 0.30, or 0.40. These levels were consistent with previous studies indicating MARS is most efficient at relaxed significance levels (Hospital et al., 1997; Moreau et al., 1998).
Mapping Population, Genotypic and Phenotypic Values, and QTL Detection
Details of the procedures we used to simulate MARS were described in a previous article (Bernardo, 2004). We conducted 500 repeats of each simulation experiment and averaged the results across the repeats. Each repeat differed in the genetic map, the genotypes of the individuals sampled, and the phenotypic values.
A simulated F1 generation, formed by crossing two parental inbreds, was selfed to form an F2 population of N = 100, 200, or 400 plants. The F2 population was segregating at 100 codominant marker loci. The sizes of the chromosomes (ranging from 128 to 241 cM) and of the entire genome (1749 cM) corresponded to those in a published maize linkage map (Senior et al., 1996). The genome was divided into 100 bins of 1749/100 
17 cM. A marker was assumed randomly located within ±5 cM of the midpoint of each bin. In the Flanking Marker model, the l QTL were randomly located among the 10 chromosomes. In the QTL Per Se model, the position of a QTL corresponded to the exact position of a random marker. The first parent had the favorable allele at even-numbered QTL and the less-favorable allele at odd-numbered QTL. This procedure led to random coupling and repulsion linkages between QTL.
In each simulated cycle of selection, F2 (in cycle 0) or S0 individuals (in cycles 1–4) were selfed and the resulting F3 or S1 families were crossed to an unrelated inbred tester. Testcross genotypic values were simulated according to metabolic control theory (Bost et al., 1999). For the ith QTL, the enzyme activity for the favorable allele was mi + bi whereas the enzyme activity for the less favorable allele was mi – bi. The midparent enzyme activity was mi = a–i/2, where the value of a for an effective number of loci equal to l was calculated using Eq. 11 of Lande and Thompson (1990). The value of bi, assuming a coefficient of variation of 0.15 relative to mi, was calculated as (0.15)mi
2 (Bost et al., 1999). The enzyme activity of the heterozygote was equal to mi. The metabolic flux, which depended on the enzyme activities according to metabolic control theory (Kacser and Burns, 1981), was considered as the testcross genotypic value (Bost et al., 1999):
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Under metabolic control theory, genes show physiological epistasis (Kacser and Burns, 1981; Cheverud and Routman, 1995) but additive variance accounts for a high percentage of VG (about 98% in this study, and 95 to 99% in Bost et al., 1999). Justification for the use of metabolic control theory is given in the Discussion.
Random nongenetic effects were added to the genotypic values to obtain testcross phenotypic values. The random nongenetic effects had a normal distribution with a mean of zero and were scaled so that broad-sense heritability among testcrosses was H = 0.20, 0.50, or 0.80 in the initial F2 population. The amount of nongenetic variance, for each level of H, was constant across cycles of selection.
For both the Flanking Marker model and QTL Per Se model, the effects associated with markers were estimated only in the initial F2 population (i.e., cycle 0). When none of the QTL were known (P = 0%), markers associated with the trait at a given level were identified using a two-step process (Bernardo, 2004). First, multiple regression of phenotypic value on the number of marker alleles (0, 1, or 2) from the first parental inbred was performed on a chromosome-by-chromosome basis. Significant markers on each chromosome were identified by backward elimination. Second, multiple regression coefficients were obtained by jointly analyzing all the markers found significant in the per-chromosome analysis. When QTL were known (P > 0%), the pairs of markers that flanked the known QTL were included in multiple regression (without testing for their significance) in the Flanking Marker model. Likewise, the markers that corresponded to the known QTL themselves were included in multiple regression (without testing for their significance) in the QTL Per Se model. Standard procedures were used to handle any singularities encountered in multiple regression analysis (Press et al., 1992, p. 56).
When none of the QTL were known (P = 0%), the average power to detect QTL, false discovery rate, and ratio between the variance explained by the significant markers (VM; Lande and Thompson, 1990; Hospital et al., 1997) and VG were calculated (Bernardo, 2004).
Simulation of MARS
In phenotypic selection, the 10% of families with the highest testcross performance were random-mated to form the next cycle of selection. The following procedures were used in MARS. In cycle 0, a marker score (Mi; Lande and Thompson, 1990) for the ith family was calculated from the multiple regression coefficients for the markers with significant effects (for P = 0%) or for the known QTL (for P = 10 to 100%). This marker score was then combined with the family's testcross phenotypic value in a least-squares selection index (Ii) as outlined by Lande and Thompson (1990), but with the restriction that the weight for the phenotypic value was always positive (Hospital et al., 1997). The 10% of cycle 0 families with the highest Ii values (i.e., marker-assisted selection) were random-mated to form cycle 1. The cycle 1 families were then ranked according to Mi only (i.e., marker-based selection) and the best 10% of families were random-mated to form the next cycle 2. This marker-based selection procedure was repeated in cycles 2 and 3 of MARS. Selection responses, expressed in terms of units of the genetic standard deviation (
G) in cycle 0, were calculated for each cycle of phenotypic selection and MARS. Frequencies of the favorable allele at each QTL were calculated.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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When none of the QTL were known (P = 0%), the significance level for detecting QTL that led to the largest response to MARS was usually Max = 0.20 when 10 QTL controlled the trait and Max = 0.40 when 100 QTL controlled the trait (Table 1). However, the differences in the response to MARS at = 0.20, 0.30, or 0.40 were generally small (results not shown). The number of QTL, heritability, and population size affected the ability to detect QTL. Consider a trait controlled by 10 QTL, a high heritability (H = 0.80), and a large population (N = 400) for detecting the unknown QTL. For the QTL Per Se model and a significance level of Max = 0.20, the average power to detect QTL was 0.98; the average number of significant markers was 31 (out of 100); the average false discovery rate was 0.63 (i.e., about 20 of the 31 significant markers did not correspond to a QTL); and the average VM/VG ratio was 0.98. On the other hand, consider a complex trait controlled by 100 QTL, a low heritability (H = 0.20), and a small population (N = 100) for detecting the unknown QTL. For the Flanking Marker model and a significance level of Max = 0.30, the average power was 0.40; the average number of significant markers was 37; the average false discovery rate was 0.15; and the average VM/VG ratio was 2.00.
Known QTL versus Ad Hoc Significance Tests to Detect QTL
The response obtained when some or all of the QTL were known (P > 0%) was not always greater than the response obtained when none of the QTL were known (P = 0%). Consider a trait controlled by 10 QTL, a heritability of H = 0.80, and a population size of N = 100. For the Flanking Marker model, the response to MARS for P > 0% was greater than the response for P = 0% only when the percentage of known QTL was ranged from P = 70 to 100% (i.e., RP > RMax = 70–100 in Table 1). The RP > RMax values in Table 1 indicated the bounds for which having known QTL was advantageous over having unknown QTL in MARS. Outside such bounds, the response to MARS was greater when QTL were unknown and, subsequently, QTL were detected using the appropriate Max significance level. When 10 QTL controlled the trait, the lower bound of the RP > RMax values, for both the Flanking Marker and QTL Per Se model, was smallest when the population size and heritability were both low (N = 100 and H = 0.20, Table 1). In this case, P was equal to 0.40 (i.e., RP > RMax = 40–100), so that at least four out of the 10 QTL had to be known for prior knowledge of QTL locations to be useful. These four QTL accounted for 66% of the genetic variation for the trait (see Materials and Methods). When 40 or 100 QTL controlled the trait, the smallest lower bound of the RP > RMax values was P = 0.30 (Table 1). For P = 0.30, the known QTL accounted for about 55% of the genetic variation for the trait. The lower bounds increased as both the population size and heritability increased regardless of the number of QTL controlling a trait.
The largest upper bound of RP > RMax was always P = 100% when 10 or 40 QTL controlled the trait. But when 100 QTL controlled the trait, the upper bound of RP > RMax was often less than P = 100%, particularly when QTL effects were estimated from smaller populations (N = 100 or 200) and heritability was low (H = 0.20; Table 1). Consider a complex trait controlled by 100 QTL and with a low heritability (H = 0.20). When effects of the QTL were estimated with a population size of N = 100, having known QTL under the Flanking Marker model was advantageous only within the bounds of RP > RMax = 30–40 (Table 1). When less than P = 30% or more than P = 40% of the QTL were known, it was more advantageous (in terms of the response to MARS) to completely ignore the prior information on all known QTL and detect the QTL by ad hoc significance tests at Max = 0.30. When all 100 QTL were known (P = 100%), MARS led to a negative response after cycle 1 under the QTL Per Se model (Fig. 1b). Under the Flanking Marker model, the responses to MARS after cycle 1 were small across a wide range of percentages of known QTL (Fig. 1c).
The advantage of having known QTL in MARS was quantified by the difference between the selection response at PMax (for P > 0%; solid circles in Fig. 2
) and the selection response at Max (for P = 0%; open circles in Fig. 2). Consider a simple trait controlled by few QTL (10) and with a high heritability (H = 0.80); a trait controlled by 40 QTL and with a heritability of H = 0.50; and a complex trait controlled by many QTL (100) and with a low heritability (H = 0.20). For population sizes typically used in a maize breeding program (N = 100), such advantage was greatest when a trait with a heritability of H = 0.50 was controlled by 40 QTL under the QTL Per Se model (Fig. 2). In this situation, the responses (in G) at cycle 4 in MARS were 3.86 at PMax = 80% and 2.64 at Max = 0.40. Knowing the exact locations of 32 out of the 40 QTL therefore led to an added response of 3.86 – 2.64 = 1.22, or (3.86 – 2.64)/2.64 = 46%. These gains were substantially higher than those for the Flanking Marker model. Knowing the flanking markers for 24 out of the 40 QTL (PMax = 60%, N = 100, H = 0.50; Table 1) led to an added response of only 0.37 G or 17% (Fig. 2).
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Max = 0.30 (Fig. 2). Knowing the flanking markers for 30 out of the 100 QTL therefore led to an added response of only 1.07 – 1.00 = 0.07, or (1.07 – 1.00)/1.00 = 7%. Increasing the population size to N = 400 failed to increase the advantage of having known QTL. In this situation, the selection responses were 2.52 at PMax = 50% and 2.38 at Max = 0.40; the added response was 2.52 – 2.38 = 0.14, or (2.52 – 2.38)/2.38 = 6%.
Phenotypic Selection versus MARS under the Flanking Marker and QTL Per Se Models
In maize, four cycles of phenotypic selection would require 8 yr whereas MARS would require 3 yr. If the amount of time required is considered, MARS (requiring 3 yr) should be compared to one or two cycles of phenotypic selection (requiring 2 to 4 yr) rather than to four cycles of phenotypic selection. Nevertheless, per-cycle comparisons indicated that the maximum response to MARS (at cycle 4) under the QTL Per Se model was usually greater than the response to phenotypic selection (at cycle 4). Specifically, MARS under the QTL Per Se model was superior to phenotypic selection in 18 out of the 27 combinations of number of QTL, heritability, and population size (MARS > PS in Table 1). This frequency of MARS > PS was greater than that for the Flanking Marker model, where MARS was superior to phenotypic selection in only 4 out of the 27 combinations. Phenotypic selection became superior to MARS as the number of QTL controlling the trait increased and as the population size decreased. Consider a trait controlled by 100 QTL, a heritability of H = 0.20, and a population size of N = 100. The response at cycle 4 to MARS assuming PMax known QTL (solid circles in Fig. 2) was only about 50 to 60% of the response to phenotypic selection (triangles in Fig. 2) under the Flanking Marker and QTL Per Se models.
For the three combinations of number of QTL and heritability in Fig. 2 (N = 100), the advantage of having markers for the QTL themselves over having markers linked to the QTL was greatest when 40 QTL controlled the trait (H = 0.50). In this situation, the responses at cycle 4 were 3.86 at PMax = 80% for the QTL Per Se model versus 2.57 at PMax = 60% for the Flanking Marker model (Fig. 2). The added response due to having markers for the QTL themselves was therefore 3.86 – 2.57 = 1.29, or (3.86 – 2.57)/2.57 = 50%. Underlying this 50% added response were higher frequencies of favorable alleles (at the known QTL) under the QTL Per Se model (average allele frequency of 0.76, PMax = 70%) than under the Flanking Marker model (average allele frequency of 0.69, PMax = 60%). The added response in terms of unit gain was smallest (0.32 G) when 100 QTL controlled the trait (H = 0.20). The added response in terms of percentage of gain was smallest (20%) when 10 QTL controlled the trait (H = 0.80).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Genetic Model
To do so, we conducted simulations of MARS under a genetic model that aimed to integrate current knowledge of the genetics of quantitative traits. These models were consistent with the empirical evidence of a few QTL with large effects and many QTL with small effects for complex traits (Kearsey and Farquhar, 1998; Bernardo, 2002, p. 310). The models included linkage and comprised different combinations of number of QTL and level of entry-mean heritability, which accounted for both within-environment error and genotype x environment interaction. The metabolic flux model we used is well known for modeling physiological epistasis (Cheverud and Routman, 1995) for a quantitative trait (Kacser and Burns, 1981; Keightley, 1989; Bost et al., 1999). Empirical data on gluconeogenesis in rat (Rattus sp.) liver cells (Groen et al., 1986), succinate oxidation in cucumber (Cucumis sativus L.) cotyledon mitochondria (Hill et al., 1993), and the TCA cycle in Dictyostelium discoideum (Albe and Wright, 1992) have been found consistent with metabolic control theory (Bost et al., 1999). We simulated a linear metabolic pathway only, although the general properties for a linear pathway can be extended to branched pathways (Kacser and Burns, 1981). Despite the presence of physiological epistasis, the genetic variation was mainly additive in the models we considered, with additive variance accounting for about 98% of VG. This result was comparable to those of Bost et al. (1999), who found that additive variance for a metabolic flux accounted for >95% of VG. Having largely additive variance even in the presence of physiological epistasis is expected when many loci control a trait (Crow, 1999), and summaries of empirical studies have shown that genetic variance for quantitative traits is primarily additive in self-pollinated crops (Moll and Stuber, 1974). We considered maize, which is a cross-pollinated crop for which estimates of epistatic variance are largely insignificant but for which dominance variance is significant (Moll and Stuber, 1974; Hallauer and Miranda, 1988, p. 119; Lamkey and Edwards, 1999). Dominance does not affect testcross genotypic values, which we simulated (Hallauer and Miranda, 1988, p. 24; Bernardo, 2002, p. 79). In summary, although we did not simulate any known pathway for the expression of a quantitative trait, the genetic models we considered encompassed key factors (i.e., number of QTL, size of gene effects, linkage, heritability, and epistasis) that underlie the genetic control complex traits.
Benefits and Possible Pitfalls of Having Known QTL in Recurrent Selection
We found that the response to MARS was larger when QTL are known a priori than when QTL are unknown, provided that the available information on known QTL is used judiciously. Our results indicated that prior knowledge of QTL locations is consistently useful in MARS when few QTL (e.g., 10) control the trait. When 10 QTL controlled the trait, the response to MARS was largest when all QTL were known, and the response decreased when fewer QTL were known. This result agreed with the preliminary findings of Charcosset and Moreau (2004). At least 40% (for N = 100 and H = 0.20) of the QTL (those with the largest effects) had to be known for the selection response to be greater than that when unknown QTL are detected by ad hoc significance tests. A higher percentage of the QTL need to be known when heritability and the population size increase, due to a higher power of QTL detection when QTL were unknown a priori.
When 40 or 100 QTL controlled the trait, at least 30% of the QTL (those with the largest effects) had to be known for prior information on QTL locations to be useful. Some of the gains were large, e.g., 1.22 G or 46% when 32 out of the 40 QTL were known, heritability was H = 0.50, and QTL effects were estimated with a population size (N = 100) typically used in MARS (Johnson and Mumm, 1996; Johnson, 2001). However, contrary to when only 10 QTL controlled the trait, selection efficiency did not necessarily increase as the number of known QTL included in the model increased. When 100 QTL controlled the trait, heritability was low (H = 0.20), and the population size was N = 100, knowing all the QTL reduced the response to MARS. Knowing all the QTL was detrimental to the point that it was more advantageous to completely ignore all prior information on QTL locations and detect QTL by ad hoc significance tests.
The problem, as Bernardo (2001) and Johnson (2004) pointed out, is statistical: it is difficult to get good estimates of 100 QTL effects with a population size of N = 100. Consistently, the percentage of known QTL that maximized the response to MARS (PMax) was less than 100%. In other words it was often advantageous to exploit only the QTL with the largest effects (i.e., major QTL) and ignore those with small effects (i.e., minor QTL), even if the locations of the minor QTL were known. Exploiting only the major QTL also reduces the cost of marker genotyping. The PMax values were consistently highest when the population size was N = 400. This result indicated that that minor QTL can be exploited to a greater extent in MARS if the population size is increased. Breeders practice selection in several F2 or backcross populations at a time (Hallauer, 1990). If field resources and marker-genotyping resources are kept constant, an increase in the size of each population would require a decrease in the total number of F2 or backcross populations. Maize breeders generally prefer to select in several F2 or backcross populations, each with relatively few families, than in only a few F2 or backcross populations, each with many families (Hallauer, 1990; Bernardo, 2002, p. 13). Breeders need to overcome this preference and use larger population sizes for MARS to be most effective. If fewer populations, each with many families, are used in MARS, then the choice of parents of the F2 or backcross populations becomes crucial. In practice this implies that MARS would be used mainly for crosses among elite, proven inbreds rather than for speculative crosses.
The objective in MARS is to explain as much of the genetic variance as possible with a set of markers, while keeping within a reasonable level the noise due to false positives (i.e., when QTL are unknown) and/or poor estimation of QTL effects. This difference in primary objectives relative to detecting individual QTL explains why the conditions that maximize the efficiency of MARS when QTL are unknown a priori (i.e., relaxed significance levels of 0.20 to 0.40; Hospital et al., 1997) are different from those for mapping QTL (i.e., stringent significance levels). Having known QTL obviously eliminates the need to detect QTL in MARS and limits the statistical issue to the estimation of QTL effects. Here we simulated QTL that differed in the size of their effects and, in the Flanking Marker model, markers tightly linked to a minor QTL could have explained as much variation as markers loosely linked to a major QTL. Our results show that this uncertainty in estimating the effects of QTL has limited detriment in MARS when compared with the benefits of including the right markers in the model.
As previously mentioned in the Introduction, Bernardo (2001) investigated the usefulness of having known QTL in the context of (i) predicting the performance of untested single-crosses and (ii) marker-based selection among recombinant inbreds (without MARS) within an F2 population. He found that QTL effects estimated from the performance of single crosses among many inbreds were useful for identifying the best recombinant inbreds derived from an F2 population between two inbreds. Specifically, when the heritability among single crosses was H = 0.20, exploiting only the 30 QTL with the largest effects (out of 100) led to the highest efficiency relative to phenotypic selection among recombinant inbreds. Our current results therefore complement those of Bernardo (2001), as we have shown that having known QTL is useful also for improving an F2 population before selfing.
Benefits from Having Markers for the QTL Themselves
Our results showed that knowing markers that flank the QTL (Flanking Marker model) increases the response to MARS, and knowing markers for the QTL themselves (QTL Per Se model) increases the response further. We found that knowing markers for the QTL themselves was most beneficial for traits controlled by a moderately large number of QTL (e.g., 40). For a trait controlled by 40 QTL, knowing the QTL through flanking markers led to an added response of 0.37G or 17% (PMax = 60%, H = 0.50, and N = 100). Having markers for the QTL themselves increased these gains to 1.29G or 50% (PMax = 80%, H = 0.50, and N = 100). We observed clear and consistent increases in the frequency of favorable alleles. Recombination between a QTL and linked markers has been cited as a potential problem in MARS (Hospital et al., 1997). Knowledge from genomics and post-genomics sciences of the actual QTL will eliminate the loss, through recombination, of QTL information during the later cycles in MARS.
When few QTL (e.g., 10) control the trait, knowing the QTL through linked markers (Flanking Marker model) rapidly leads to a high frequency of favorable alleles in MARS. This leaves little room for further increases in the frequency of favorable alleles through the use of markers for the QTL themselves (QTL Per Se model). On the other hand, estimating the effects of many QTL (e.g., 100) with population sizes typically used in maize (N = 100) is problematic, not only because of the number of QTL whose effects are estimated but also because of the increased probability of having linked QTL as the total number of QTL increases. Even if markers are available for the QTL themselves, linkage causes the effect of a known QTL to be difficult to separate from the effects of other linked QTL.
Finally, we speculate that a combination of approaches for exploiting known QTL would be necessary. With continuing advances in genomics and post-genomics sciences, some QTL might be known through markers for the QTL themselves, some QTL might be known through linked markers, and some QTL might remain unknown. Known QTL could be directly accounted for in MARS while unknown QTL could be detected and accounted for by ad hoc significance tests using relaxed significance levels. Studies on jointly exploiting both the known QTL and unknown QTL are needed.
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ACKNOWLEDGMENTS |
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Received for publication May 26, 2005.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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), MARS when the percentage of known QTL was PMax (•), and MARS when QTL were unknown and were detected by tests at the 
). Effects of the QTL were estimated with a population size of N = 100.