On the power of experimental designs for the detection of linkage between marker loci and quantitative loci in crosses between inbred lines

Summary The power of experiments aimed at detecting linkage between a quantitative locus and a marker locus, both segregating in the backross or F₂ generation of a cross between two inbred lines, is examined. Given that the two lines are close to fixation for alternative alleles of both marker locus and quantitative locus, it is concluded that experiments involving a few thousand offspring should be able to detect close linkages involving quantitative loci (or groups of loci) having rather modest effects (i.e., that contribute, say, 1% of the total phenotypic variance in the F₂).     

Mapping quantitative trait loci using molecular marker linkage maps

Summary High-density restriction fragment length polymorphism (RFLP) and allozyme linkage maps have been developed in several plant species. These maps make it technically feasible to map quantitative trait loci (QTL) using methods based on flanking marker genetic models. In this paper, we describe flanking marker models for doubled haploid (DH), recombinant inbred (RI), backcross (BC), F₁ testcross (F₁TC), DH testcross (DHTC), recombinant inbred testcross (RITC), F₂, and F₃ progeny. These models are functions of the means of quantitative trait locus genotypes and recombination frequencies between marker and quantitative trait loci. In addition to the genetic models, we describe maximum likelihood methods for estimating these parameters using linear, nonlinear, and univariate or multivariate normal distribution mixture models. We defined recombination frequency estimators for backcross and F₂ progeny group genetic models using the parameters of linear models. In addition, we found a genetically unbiased estimator of the QTL heterozygote mean using a linear function of marker means. In nonlinear models, recombination frequencies are estimated less efficiently than the means of quantitative trait locus genotypes. Recombination frequency estimation efficiency decreases as the distance between markers decreases, because the number of progeny in recombinant marker classes decreases. Mean estimation efficiency is nearly equal for these methods.     

Marker-based mapping of quantitative trait loci using replicated progenies

Summary When heritability of the trait under investigation is low, replicated progenies can bring about a major reduction in the number of individuals that need to be scored for marker genotype in determining linkage between marker loci and quantitative trait loci (QTL). Savings are greatest when heritability of the trait is low, but are much reduced when heritability of the quantitative trait is moderate to high. Required numbers for recombinant inbred lines will be greater than those required for a simple F₂ population when heritabilities are moderate to high and the proportion of recombination between marker locus and quantitative trait locus is substantial.Contribution No. 2613-E of the Agricultural Research Organization, 1989 series     

On the detection of imprinted quantitative trait loci in line crosses: effect of linkage disequilibrium

Imprinted quantitative trait loci (QTL) are commonly reported in studies using line-cross designs, especially in livestock species. It was previously shown that such parent-of-origin effects might result from the nonfixation of QTL alleles in one or both parental lines, rather than from genuine molecular parental imprinting. We herein demonstrate that if linkage disequilibrium exists between marker loci and nonfixed QTL, spurious detection of pseudo-imprinting is increased by an additional 40–80% in scenarios mimicking typical livestock situations. This is due to the fact that imprinting can be tested only in F₂ offspring whose sire and dam have distinct marker genotypes. In the case of linkage disequilibrium between markers and QTL, such parents have a higher chance to have distinct QTL genotypes as well, thus resulting in distinct padumnal and madumnal allele substitution effects, i.e., QTL pseudo-imprinting.     

The use of replicated progenies in marker-based mapping of QTL's

Summary Seven types of progeny are described which can be used in detection of linkage between marker loci and quantitative trait loci (QTL) in a cross between two inbred lines. Three types of progeny: recombinant inbred lines (RI); doubled haploid lines (DH); and S₁ lines can be used to detect linked main effects, d. DH and RI lines can be used to detect smaller effects than S₁ lines. However, S₁ lines can also be used to detect within-population dominance effects, h. The smallest d detectible is in the range of 1/2 to 1/12 the size of the corresponding LSD_(0.05) for the quantitative trait, using 100 lines and 6 replicates. The smallest h detectible is 3–4 times this size. Four types of progeny can be used to detect differences in the dominance behavior of alleles within the population relative to an allele in another inbred line (P₄: DH lines x P₄; RI lines x P₄; either F₂ x P₄ or S₁ lines x P₄; and progeny generated by crossing (F₁ x P₃) x P₄. Dominance differences in the range of 1 1/4 to 1/6 the size of the corresponding LSD_(0.05) are routinely detectible using 100 lines and 6 replicates. Increasing the numbers of progeny evaluated or the number of replicates allows for the detection of relatively smaller linked effects.Contribution of United AgriSeeds, Inc.     

RAPD linkage mapping in a longleaf pine x slash pine F1 family

Random amplified polymorphic DNAs (RAPDs) were used to construct linkage maps of the parent of a longleaf pine (Pinus palustris Mill.) slash pine (Pinus elliottii Englm.) F₁ family. A total of 247 segregating loci [233 (1∶1), 14 (3∶1)] and 87 polymorphic (between parents), but non-segregating, loci were identified. The 233 loci segregating 1∶1 (testcross configuration) were used to construct parent-specific linkage maps, 132 for the longleaf-pine parent and 101 for the slash-pine parent. The resulting linkage maps consisted of 122 marker loci in 18 groups (three or more loci) and three pairs (1367.5 cM) for longleaf pine, and 91 marker loci in 13 groups and six pairs for slash pine (952.9 cM). Genome size estimates based on two-point linkage data ranged from 2348 to 2392 cM for longleaf pine, and from 2292 to 2372 cM for slash pine. Linkage of 3∶1 loci to testcross loci in each of the parental maps was used to infer further linkages within maps, as well as potentially homologous counterparts between maps. Three of the longleaf-pine linkage groups appear to be potentially homologous counterparts to four different slash-pine linkage groups. The number of heterozygous loci (previously testcross in parents) per F₁ individual, ranged from 96 to 130. With the 87 polymorphic, but non-segregating, loci that should also be heterozygous in the F₁ progeny, a maximum of 183–217 heterozygous loci could be available for mapping early height growth (EHG) loci and for applying genomic selection in backcross populations.     

Comparison of genetic differentiation at marker loci and quantitative traits

The comparison of the degree of differentiation in neutral marker loci and genes coding quantitative traits with standardized and equivalent measures of genetic differentiation (F_ST and Q_ST, respectively) can provide insights into two important but seldom explored questions in evolutionary genetics: (i) what is the relative importance of random genetic drift and directional natural selection as causes of population differentiation in quantitative traits, and (ii) does the degree of divergence in neutral marker loci predict the degree of divergence in genes coding quantitative traits? Examination of data from 18 independent studies of plants and animals using both standard statistical and meta‐analytical methods revealed a number of interesting points. First, the degree of differentiation in quantitative traits (Q_ST) typically exceeds that observed in neutral marker genes (F_ST), suggesting a prominent role for natural selection in accounting for patterns of quantitative trait differentiation among contemporary populations. Second, the F_ST – Q_ST difference is more pronounced for allozyme markers and morphological traits, than for other kinds of molecular markers and life‐history traits. Third, very few studies reveal situations were Q_ST < F_ST, suggesting that selection pressures, and hence optimal phenotypes, in different populations of the same species are unlikely to be often similar. Fourth, there is a strong correlation between Q_ST and F_ST indices across the different studies for allozyme (r=0.81), microsatellite (r=0.87) and combined (r=0.75) marker data, suggesting that the degree of genetic differentiation in neutral marker loci is closely predictive of the degree of differentiation in loci coding quantitative traits. However, these interpretations are subject to a number of assumptions about the data and methods used to derive the estimates of population differentiation in the two sets of traits.     

Mapping quantitative trait loci for binary trait in the F2:3 design

In the analysis of inheritance of quantitative traits with low heritability, an F_2:3 design that genotypes plants in F₂ and phenotypes plants in F_2:3 progeny is often used in plant genetics. Although statistical approaches for mapping quantitative trait loci (QTL) in the F_2:3 design have been well developed, those for binary traits of biological interest and economic importance are seldom addressed. In this study, an attempt was made to map binary trait loci (BTL) in the F_2:3 design. The fundamental idea was: the F₂ plants were genotyped, all phenotypic values of each F_2:3 progeny were measured for binary trait, and these binary trait values and the marker genotype informations were used to detect BTL under the penetrance and liability models. The proposed method was verified by a series of Monte-Carlo simulation experiments. These results showed that maximum likelihood approaches under the penetrance and liability models provide accurate estimates for the effects and the locations of BTL with high statistical power, even under of low heritability. Moreover, the penetrance model is as efficient as the liability model, and the F_2:3 design is more efficient than classical F₂ design, even though only a single progeny is collected from each F_2:3 family. With the maximum likelihood approaches under the penetrance and the liability models developed in this study, we can map binary traits as we can do for quantitative trait in the F_2:3 design.     

An integrated SSR based linkage map for <Emphasis Type="Italic">Zoysia matrella</Emphasis> L. and <Emphasis Type="Italic">Z. japonica</Emphasis> Steud.

Japanese lawngrass (Zoysia japonica) and Manila grass (Z. matrella) are the two most important and commonly used Zoysia species. A consensus based SSR linkage map was developed for the genus by combining maps from each species. This used previously constructed maps for two Z. japonica populations and a new map from Z. matrella. The new SSR linkage map for Z. matrella was based on 86 F₂ individuals and contained 213 loci and covered a map distance of 1,351.2 cM in 32 linkage groups. Comparison of the three linkage maps constructed from populations with different genetic backgrounds indicated that most markers exhibited a consensus order, although some intervals or regions displayed discrepancy in marker orders or positions. The integrated map comprises 507 loci with a mean interval of 4.1 cM, covering a map distance of 2,066.6 cM in 22 linkage groups. The SSR-based map will allow marker-assisted selection and be useful for the mapping and cloning of economically important genes or quantitative trait loci.     

Relationship between heterosis and heterozygosity at marker loci: a theoretical computation

Summary In this paper we have studied the linear correlation between a genetic distance index between two parent lines (based on marker loci information) and the heterosis observed in the F₁ hybrid from the two lines, for a quantitative character (determined by several loci, or QTL). Theoretical computations of the correlation coefficient () between the distance index and the heterosis were made, assuming the biallelic model (defined by Fisher). When the alleles at both marker loci and QTL are equally distributed among the whole population of considered lines, the coefficient is a function of the squares of linkage disequilibria between alleles at marker loci and alleles at QTL. The QTL that are not marked by marker loci and marker loci that do not mark any QTL play symmetrical roles and can decrease greatly. We conclude that the prediction of F₁ hybrid heterosis based on marker loci would be more efficient if these markers were selected for their relationship to the alleles implicated in the heterotic traits considered.     

Analysis of RFLP mapping inaccuracy in Brassica napus L.

 We identified sources of mapping inaccuracy during the construction of RFLP linkage maps from one F₂ population and two F₁ microspore-derived populations from the same cross of oilseed Brassica napus. The genetic maps were compared using a total of 145 RFLP marker loci including 82 loci common to all three populations. In the process, we identified a series of mapping events that could lead to ambigous conclusions. Superimposed restriction fragments could be mistaken as a single dominant restriction fragment in a F₂ population and, when analyzed as such, would yield inaccurate linkage information. Residual heterozygosity in parental lines resulted in complicated allelic assignment and yielded subsequent difficulties in linkage determination. Loose and spurious linkages occurred during mapping and were identified by comparing maps derived from different populations. LOD scores and χ² test of independence were compared for their capacity to detect loose linkages or generate spurious ones. Extreme segregation distortions towards the same parental allele also contributed to an additional source of spurious linkage. Small but significant segregation distortions resulted in reduced estimates of the recombination fraction. The use of the same ‘probe× enzyme’ combinations in doubled haploid populations allowed the identification of the correct allele assignment as well as loose and spurious linkages. A translocation between two homoeologous linkage groups was observed. The consequences of such a chromosomal event as a source of error in mapping applications are discussed. Received: 7 September 1996/Accepted: 25 October 1996     

GENETIC MAPPING OF THE LAMINARIA JAPONICA (LAMINARALES,PHAEOPHYTA) USING AMPLIFIED FRAGMENT LENGTH POLYMORPHISM MARKERS1

To establish a molecular‐marker‐assisted system of breeding and genetic study for Laminaria japonica Aresch., amplified fragment length polymorphism (AFLP) was used to construct a genetic linkage map of L. japonica featuring 230 progeny of F₂ cross population. Eighteen primer combinations produced 370 polymorphic loci and 215 polymorphic loci segregated in a 3:1 Mendelian segregation ratio (P ≤ 0.05). Of the 215 segregated loci, 142 were ordered into 27 linkage groups. The length of the linkage groups ranged from 6.7 to 90.3 centimorgans (cM) with an average length of 49.6 cM, and the total length was 1,085.8 cM, which covered 68.4% of the estimated 1,586.9 cM genome. The number of mapped markers on each linkage group ranged from 2 to 12, averaging 5.3 markers per group. The average density of the markers was 1 per 9.4 cM. Based on the marker density and the resolution of the map, the constructed linkage map can satisfy the need for quantitative trait locus (QTL) location and molecular‐marker‐assisted breeding for Laminaria.     

Genetic linkage map of a wheat×spelt cross

 We constructed a genetic map of a cross between the Swiss winter wheat (Triticum aestivum L.) variety Forno and the Swiss winter spelt (Triticum spelta L.) variety Oberkulmer. For the linkage analysis,176 polymorphic RFLP probes and nine microsatellites were tested on 204 F₅ recombinant inbred lines (RILs) of Forno×Oberkulmer revealing 242 segregating marker loci. Thirty five percent of these loci showed significant (P>0.05) deviation from a 1 : 1 segregation, and the percentage of Forno alleles ranged from 21% to 83% for individual marker loci. Linkage analysis was performed with the program MAPMAKER using the Haldane mapping function. Using a LOD threshold of 10, we obtained 37 linkage groups. After finding the best order of marker loci within linkage groups by multi-point analysis we assembled the linkage groups into 23 larger units by lowering the LOD threshold. All except one of the 23 new linkage groups could be assigned to physical chromosomes or chromosome arms according to hybridisation patterns of nulli-tetrasomic lines of Chinese Spring and published wheat maps. This resulted in a genetic map comprising 230 marker loci and spanning 2469 cM. Since the analysed population is segregating for a wide range of agronomically important traits, this genetic map is an ideal basis for the identification of quantitative trait loci (QTLs) for these traits. Received: 3 August 1998 / Accepted: 28 November 1998     

Genetic analysis of ecological relevant morphological variability in Plantago lanceolata L.

Summary Morphological variability was analysed in an F₂-generation derived from crosses between two ecotypes of Plantago lanceolata L. Six allozyme loci, localised in five linkage groups, were used as markers. For two marker loci, Got-2 and Gpi-1, segregations did not fit monogenic ratios. In the linkage groups to which these two loci belonged, male sterility genes appeared to be present. In these crosses, male sterility (type 3, as described by Van Damme 1983) may be determined by two recessive loci located in the linkage groups of Got-2 and of Gpi-1. Many correlations of morphological and life history characters with allozyme markers were observed. The quantitative trait loci did not appear to be concentrated in major gene complexes. Often many loci were involved, sometimes with effects opposite to those expected from the population values. Main effects of the linkage groups appeared to be more important than interaction effects in determining variability. It also appeared that there is a positive correlation between the number of heterozygous allozyme loci and generative growth.Grassland Species Research Group Publication No. 115     

A Composite Linkage Map from Three Crosses Between Commercial Clones of Cacao, Theobroma cacao L.

In this paper, we report the construction of the first composite map of cacao from linkage data of one F₂ and two F₁ mapping populations with a high number of codominant markers in common. The combination of linkage information from all three maps results in the currently most precise estimates of marker locations and distances between markers, especially in densely marked areas. JoinMap®V4 software was used for all marker quality assessment and mapping. Individual (sub-composite) maps and the composite map contained 10 major linkage groups, corresponding to the number of cacao chromosomes. Homogeneity of marker placement was very high among sub-composite maps, the composite map, and the designated “reference” map. Care was exercised in the re-creation of sub-composite maps and the composite map to include only markers with acceptable mapping quality parameters. The composite map places more markers with higher precision than any individual map. This research clearly demonstrates for the first time a very high level of marker homogeneity among commercial cacao clones compared to other species. The observed homogeneity between different maps, including the composite one, is probably due to a narrow genetic base of commercial cacao clones. Markers linked to identified quantitative trait loci (QTLs) are more likely to retain linkage in other commercial clones, rendering the QTLs in cacao potentially more stable than in other species.     

RFLP mapping of the sugary enhancer1 gene in maize

RFLP marker data from an F₂₃ population derived from a cross between a sugary1 (su1) and a sugary enhancer1 (su1, sel) inbred were used to construct a genetic linkage map of maize. This map includes 93 segregating marker loci distributed throughout the maize genome, providing a saturated linkage map that is suitable for linkage analysis with quantitative trait loci (QTL). This population, which has been immortalized in the form of sibbed F₂₃ families, was derived from each of the 214 F₂ plants and along with probe data are available to the scientific community. QTL analysis for kernel sucrose (the primary form of sugar) concentration at 20 days after pollination (DAP) uncovered the segregation of seven major QTL influencing sucrose concentration; a locus linked to umc36a described the greatest proportion of the variation (24.7%). Since maltose concentration has previously been reported to be associated with the se1 phenotype, an analysis of probe associations with maltose concentration at 40 DAP was also conducted. The highly significant association of umc36a with maltose and sucrose concentrations provided evidence that this probe is linked to se1. Phenotypic evaluation for the se1 genotype in each F₂₃ family enabled us to map the gene 12.1 cM distal to umc36a. In contrast to previous work where se1 was reported to be located on chromosome four, our data strongly suggest that the sugary enhancer1 locus maps on the the distal portion of the long arm of chromosome 2 in the maize genome.     

QTL analysis: unreliability and bias in estimation procedures

Several statistical methods which employ multiple marker data are currently available for the analysis of quantitative trait loci (QTL) in experimental populations. Although comparable estimates of QTL location and effects have been obtained by these methods, using simulated and real data sets, their accuracy and reliability have not been extensively investigated. The present study specifically examines the merit of using F₂ and doubled haploid populations for locating QTL and estimating their effects. Factors which may affect accuracy and reliability of QTL mapping, such as the number and position of the markers available, the accuracy of the marker locations and the size of the experimental population used, are considered. These aspects are evaluated for QTL of differing heritabilities and locations along the chromosome.A population of 300 F₂ individuals and 150 doubled haploid lines gave estimates of QTL position and effect which were comparable, albeit extremely unreliable. Even for a QTL of high heritability (10%), the confidence interval was 35 cM. There was little increase in reliability to be obtained from using 300, rather than 200, F₂ individuals and 100 doubled haploid lines gave similar results to 150. QTL estimates were not significantly improved either by using the expected, rather than the observed, marker positions or by using a dense map of markers rather than a sparse map. A QTL which was asymmetrically located in the linkage group resulted in inaccurate estimates of QTL position which were seriously biassed at low heritability of the QTL. In a population of 300 F₂ individuals the bias increased from 4 cM to 20 cM, for a QTL with 10% and 2% heritability respectively.     

Identification and confirmation of quantitative trait loci controlling resistance to mungbean yellow mosaic disease in mungbean [Vigna radiata (L.) Wilczek]

Mungbean yellow mosaic India virus (MYMIV) is a major constraint on mungbean production in South and Southeast Asia. The virus belongs to the genus Begomovirus, causing yellow mosaic disease and subsequently yield loss up to 75–100 %. The present study employed F₂ and BC₁F₁ populations derived from a cross between susceptible (BARImung 1; BM1) and resistant (BARImung 6; BM6) mungbeans to identify quantitative trait loci (QTLs) associated with resistance to MYMIV. Resistance to the virus was evaluated using F_2:3 and BC₁F_1:2 populations under field conditions in two locations in Bangladesh in 2012. A total of 1,165 simple sequence repeat markers from different legumes were used to detect the polymorphism between BM1 and BM6. Sixty-one polymorphic markers were used to construct a linkage map comprising 11 linkage groups. Composite interval mapping consistently identified two major QTLs, qMYMIV2 on linkage group 2 and qMYMIV7 on linkage group 7, conferring the resistance in both F₂ and BC₁F₁ populations. qMYMIV2 and qMYMIV7 accounted for 31.42–37.60 and 29.07–47.36 %, respectively, of the disease score variation, depending on populations and locations. At both loci, the resistant alleles were contributed by the parent BM6. qMYMIV2 appeared to be common to a major QTL for MYMIV resistance in mungbean reported previously, while qMYMIV7 is a new QTL for the resistance. The markers linked to the QTLs in this study are useful in marker-assisted breeding for development of mungbean varieties resistant to MYMIV.     

RFLP mapping of Brassica napus using doubled haploid lines

The combined use of doubled haploid lines and molecular markers can provide new genetic information for use in breeding programs. An F₁-derived doubled haploid (DH) population of Brassica napus obtained from a cross between an annual canola cultivar (Stellar) and a biennial rapeseed (Major) was used to construct a linkage map of 132 restriction fragment length polymorphism loci. The marker loci were arranged into 22 linkage groups and six pairs of linked loci covering 1016 cM. The DH map was compared to a partial map constructed with a common set of markers for an F₂ population derived from the same F₁ plant, and the overall maps were not significantly different. Comparisons of maps in Brassica species suggest that less recombination occurs in B. napus (n = 19) than expected from the combined map distances of the two hypothesized diploid progenitors, B. oleracea (n = 9) and B. rapa (n=10). A high percentage (32%) of segregating marker loci were duplicated in the DH map, and conserved linkage arrangements of some duplicated loci indicated possible intergenome homoeology in the amphidiploid or intragenome duplications from the diploid progenitors. Deviation from Mendelian segregation ratios (P < 0.05) was observed for 30% of the marker loci in the DH population and for 24% in the F₂ population. Deviation towards each parent occurred at equal frequencies in both populations and marker loci that showed deviation clustered in specific linkage groups. The DH lines and molecular marker map generated for this study can be used to map loci for agronomic traits segregating in this population. Present address Embrapa/Cenargen, C.P. 0.2372, CEP 70.770, Brasilia DF, Brazil     

Mapping of the genomic regions controlling seed storability in soybean (Glycine max L.)

Seed storability is especially important in the tropics due to high temperature and relative humidity of storage environment that cause rapid deterioration of seeds in storage. The objective of this study was to use SSR markers to identify genomic regions associated with quantitative trait loci (QTLs) controlling seed storability based on relative germination rate in the F_2:3 population derived from a cross between vegetable soybean line (MJ0004-6) with poor longevity and landrace cultivar from Myanmar (R18500) with good longevity. The F_2:4 seeds harvested in 2011 and 2012 were used to investigate seed storability. The F₂ population was genotyped with 148 markers and the genetic map consisted of 128 SSR loci which converged into 38 linkage groups covering 1664.3 cM of soybean genome. Single marker analysis revealed that 13 markers from six linkage groups (C1, D2, E, F, J and L) were associated with seed storability. Composite interval mapping identified a total of three QTLs on linkage groups C1, F and L with phenotypic variance explained ranging from 8.79 to 13.43%. The R18500 alleles increased seed storability at all of the detected QTLs. No common QTLs were found for storability of seeds harvested in 2011 and 2012. This study agreed with previous reports in other crops that genotype by environment interaction plays an important role in expression of seed storability.