MATERIALS AND METHODS

Development of plant material: All parents used in this study were from oilseed B. napus cultivars having canola quality (i.e., oil with <2% erucic acid and <30 μmol of aliphatic glucosinolates per gram of meal). The cultivars belong to different germplasm groups (Diers and Osborn 1994) and are adapted to different environments. The donor parent was from the German winter-type cultivar “Ceres” and the spring recurrent parents were from the spring-type cultivars “Marnoo” (Australian) and “Westar” (Canadian).

Four inbred backcross populations were developed using one or two backcrosses to the recurrent parent (Figure 1). A total of 128 BC₁S₃-BC₂S₂ pairs were planned (64 backcross pairs to Marnoo and 64 to Westar), but 5 had one of its members missing and 11 had one of its members with one selfing generation less than planned. All plants were selfed a final time to create BC₁S₄ and BC₂S₃ families for field testing. These four populations of backcross inbred lines were named “MBC₁S₃,” “MBC₂S₂,” “WBC₁S₃,” and “WBC₂S₂.” These plants also served as pollen donors to produce hybrid seed using “Topas,” a European spring canola, as a “tester.” Topas and its sister line “Karat” (Sernyk 1990; Diers and Osborn 1994) are known to combine well with Marnoo and Westar (Brandle and McVetty 1990; Banks and Beversdorf 1994). For each hybrid, only one female was used, and each female was hand-emasculated in the greenhouse prior to controlled pollination. The four resulting hybrid populations were named “Tp × MBC₁S₃,” “Tp × MBC₂S₂,” “Tp × WBC₁S₃,” and “Tp × WBC₂S₂.”

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Figure 1.

—Pedigree used to create two populations (WBC₁S₃ and WBC₂S₂) of inbred backcross lines (IBLs). A single plant from each cultivar was used as founder; however, a subpopulation structure was created by using two different F₁ hybrids and two different Westar S₁ plants to derive two sets of 32 BC₁S₃-BC₂S₂ pairs each. Two additional populations of IBLs (MBC₁S₃ and MBC₂S₂) were created by using the same pedigree structure, but using Marnoo instead of Westar as the recurrent parent.

Trait measurements: Yield trials: Yield trials were conducted at the Arlington Agricultural Research Station (Columbia County, WI) during 1996 and 1997. The experiment was arranged in a split-plot design, where main plots were the eight populations (four populations of IBLs and four populations of hybrids), and subplots were individual families within each population. Subplots within main plots and main plots within year were completely randomized. Main plots were replicated three times each year (only twice for IBLs of WBC₂S₂ and MBC₂S₂ in 1997, due to insufficient seeds). Several checks were also used, including the recurrent parents (Westar and Marnoo), the tester (Topas), other commercial open-pollinated and hybrid cultivars, and all possible F₁s among Westar, Marnoo, Topas, and Ceres. Ceres was not included because it would fail to flower under our conditions. Standard field practices were used, including incorporation of herbicide (Trifluralin at 2 liters/ha) and fertilizer (100 kg of N/ha) prior to planting and additional hand weeding when necessary. No other pesticide application was needed.

In 1996, each subplot consisted of two rows, 3 m long and 0.30 m apart and separated from the next plot by a guard row (at 0.30 m) sown with bulked seed from the same population. The seeding rate was 110 seeds/m². In 1997, each subplot was seven rows wide (0.15 m between rows) and 2.40 m long, adjacent subplots were 0.30 m apart and the seeding rate was 87 seeds/m². For each plot, the date when half of the plants had at least one open flower was recorded. Before harvest in 1996, we measured plant height in each plot. When seeds started to turn color, the plots were hand harvested, dried, and threshed. The center 1.8 m of all plot rows (two rows in 1996, seven in 1997) was harvested. We measured the seed yield and 1000-seed weight for each plot. The oil content of the inbred families was determined by David Syme, PGS Canada, from a composite sample of all the replicates of each entry within each year using the NMR method in which percentage oil is calculated by weight on a whole seed basis at 0% moisture.

Trait analysis: Statistical analyses were conducted using the MIXED procedure of SAS (Littellet al. 1996). Year, recurrent parent, backcross level, and hybridity were treated as fixed effects while entries within population and blocks within year and population were treated as random effects to study differences at the population level. In 1997, an unplanned systematic pattern appeared in the field due to staggering of subplots at planting, combined with lodging and white mold infection (Sclerotinia sclerotiorum). This effect was included in the model by using an indicator variable to describe the position of every subplot in the field relative to other subplots. Broad sense heritability estimates were obtained for each population and each trait by using the estimates of the variance component parameters calculated with the MIXED procedure as h^2=σ^entry2∕(σ^residual2+σ^entry2). Data were also analyzed considering individual entries within the population as fixed effects to derive least-squares estimates for the biometrical and QTL analyses. Subpopulation, as defined by which F₁ and S₁ within each pedigree were used in the backcrossing steps (legend of Figure 1), was included as an effect in the linear model prior to biometrical analysis. Least-squares estimates for the checks were obtained for the biometrical analysis.

IBLs were originally proposed to estimate the minimum number of genes controlling a trait (Wehrhahn and Allard 1965). To calculate this number, we determined what was the proportion of lines (or hybrids) significantly different from the parents (or parental hybrids; Mulitze and Baker 1985). Those were lines (or hybrids) with a mean value outside of the confidence interval, [μ^parent−1.96σ^error parent2+σ^errorIBL2,μ^parent+1.96σ^error parent2+σ^errorIBL2]. The value of σ^error parent2 was obtained for each parent (or parent × Topas), and σ^errorIBL2 was obtained for each IBL (or IBL × Topas) using the MIXED procedure of SAS. These error variances generally correspond to MSE_subplot/n_replicates but depart from this value for entries with missing data. From this separation of the population, we calculated the observed proportion of nonparental lines, dˆ, and the estimated number of loci, kˆ, as k^=ln(1−d^)∕ln[1−12b+1], where b is the number of backcrosses, and the 95% confidence interval for kˆ is (ln[1−d^+1.96d^(1−d^)∕m]∕ln[1−12b+1],ln[1−d^−1.96d^(1−d^)∕m]∕ln[1−12b+1]), where m is the sample size.

Two types of analyses of covariance were conducted using the least-squares estimates of the means of the traits studied. The first one tried to assess the impact of the paired structure (BC₁S₃-BC₂S₂) in the pedigree. Means of the BC₂S₂ lines were used as covariates in a model where the means of the paired BC₁S₃ lines were the dependent variables. This was also done for hybrids. Other effects in this model were parents and subpopulation within parents. In the second type of analysis of covariance, performed to detect possible pleiotropic effects, yield was the dependent variable and the other traits were used as covariates. It was done within the IBL and within the IBL test-crossed onto Topas. Inbred yield was also used as a covariate for hybrid yield.

Molecular markers: The DNAs for restriction fragment length polymorphism (RFLP) genotyping of the inbred lines, parents, original F₁s, and tester were extracted from bulked tissue of 24 seedlings from each entry. We otherwise proceeded as described in Ferreira et al. (1994). Most probes (genomic and cDNA probes) were previously used by Ferreira et al. (1994) and by Thormann et al. (1996). Two Arabidopsis thaliana genomic probes, mi193 and mi259, were also used (Liuet al. 1996; obtained from the Arabidopsis Biological Resource Center, Ohio State University). Restriction endonucleases used were EcoRI and HindIII. Because B. napus is an amphidiploid derived from two diploid species (B. rapa and B. olearacea), which themselves have some degree of genome duplication, the polymorphisms detected did not always correspond to the same loci mapped previously. Loci in the present populations were considered identical to the one previously mapped when RFLP alleles had identical molecular weights. RFLP alleles at some loci behaved as dominant markers, but most were codominant. We scored both types of loci using the following system (“D” represents the allele from the donor parent and “R” the recurrent parent allele): C={DD}homozygous codominant or recessive donor allele;W(orM)={RR}homozygous codominant or recessive recurrent allele;H={DR}heterozygous codominant alleles;B={DD,DR}homozygous or heterozygous dominant donor allele;V={DR,RR}homozygous or heterozygous dominant recurrent allele;X={DD,DR,RR}no information.

Autoradiographs were scored at least three times to reduce possibilities of misscoring. For some loci, the original parent was heterozygous (1 of 122 loci for Westar and 18 of 122 loci for Marnoo), and phase had to be assessed in a recursive fashion by first mapping the locus in both phases and then choosing the phase that resulted in the most likely configuration [reduced recombination and highest logarithm of the odds (LOD) score].

Linkage analysis: To our knowledge, none of the genetic mapping software commonly used would perform multipoint analysis and mapping on this pedigree. However, several mapping procedures accept two-point information to build genetic maps (two-point information consists of an estimated recombination frequency and a corresponding LOD score). Thus, we chose to perform the exact two-point analysis and use the resulting information to enrich a previous map built in a population of 105 F₁-derived doubled-haploid lines (DH lines; Ferreiraet al. 1994). Several programs with which to build composite maps are available, including MAP+ (Collinset al. 1996), a software package developed to build composite genetic maps based on multiple pairwise information. This software requires that an approximate order of loci be known and uses all the pairwise information that can be obtained. MAP+ allowed us to test for heterogeneity of the recombination fraction between populations, and we used this to identify regions where merging was likely to give erroneous marker orders. Because this software requires a reasonably accurate starting order, we added new loci sequentially, beginning with the loci that had been mapped previously in a population of DH lines (Ferreiraet al. 1994; Thormannet al. 1996; Osbornet al. 1997) using MAPMAKER (Landeret al. 1987) and data for 200 RFLP and 260 amplified fragment length polymorphisms (AFLP; Voset al. 1995) loci. For this study, we used all of the RFLP loci plus 10 AFLP loci that gave expanded genome coverage, and we determined the pairwise recombination values for the population of DH lines by simply counting the recombinant (r) and nonrecombinant gametes (s) and then calculating the recombination frequency as θ = r/(r + s) and the LOD score as LOD=(r+s)[log(2)+θlog(θ)+(1−θ)log(1−θ)]ifr>0 and LOD=s[log(2)]ifr=0.

For the populations of IBLs, we built tables of joint-probability distributions of the BC₁S₃ and the BC₂S₂ members of each pair. The joint probability distribution formulas are given as a function of the recombination fraction in a BC₁S₃-BC₂S₂ pair when both loci were homozygous in the parents (appendix a, A1). Failure of one of the loci to be homozygous in the parents or one of the lines to be selfed one time less required construction of additional tables (appendix a, A2). To reduce computing time, “grid searches” were conducted using successively more refined steps: in the first step we assumed that all loci were homozygous in the parents and that all lines were at the intended selfing level. The table was constructed at 1% increments (selection of the recombination fraction that gave the highest LOD score after scanning in 1% steps from 0 to 50%). The second step, still at 1% increments, was used to recalculate the values for loci that were heterozygous in the recurrent parent and corrected for the actual selfing level of each line. The third step served to refine the precision of the table from 1 to 0.1% (appendix b).

To compare the informativeness of each population (the DH lines, the WBC₁S₃/WBC₂S₂ IBLs, and MBC₁S₃/MBC₂S₂ IBLs), we used the recombination frequency and the LOD score of each pair of loci belonging to the same linkage group and estimated the equivalent number of fully informative F₁ gametes (n_eq) needed to obtain the same information: neq=LOD∕[log(2)+θlog(θ)+(1−θ)log(1−θ)]when0<θ<0.5;neq=LOD∕log(2)whenθ=0.

The values obtained were then averaged within intervals of 2% recombination (i.e., 0-2%; 2-4%;...; 48-50%) so that the loss of information in the IBLs due to additional meioses could be documented. The use of the actual data, instead of expectations, allowed us to examine the overall quality of the information (considering missing data, dominant markers, heterozygous parents, etc.). The final map was drawn assuming an interference parameter of 0.5, for which the Rao mapping function is identical to the Kosambi mapping function.

QTL analysis: Assigning genotypic probabilities at loci: Once a composite genetic map was in hand (i.e., locus orders and distances), an additional computer program was written to assign to every locus in each individual a probability of being either RR, DR, or DD [P(RR), P(DR), or P(DD), respectively, as described in appendix c]. If complete marker information was available at this locus for this individual, the probability would be 1 that it is the genotype scored and 0 for the remaining two. Otherwise, these probabilities were calculated using the partial information available for this locus (e.g., dominant allele present) in this individual and in the other member of the backcross pair, as well as the information available from up to three partially or completely informative flanking loci (within a distance of 43 cM, which corresponds to 35% recombination with the Kosambi mapping function) on each side of this locus in both members of the pair. When local marker information was not available the resulting probabilities were calculated on the basis of the pedigree structure alone. Probabilities at positions within intervals can be calculated as for loci with missing data. As a simplifying assumption, when a locus was heterozygous in the recurrent parent, we assumed that a QTL at or near it would still be homozygous. For this reason, the IBL marker data at this locus were recoded (M or W remained as such, but H was converted to V, and C and B were both converted to X) prior to calculating the genotypic probabilities of a coincident QTL.

Backward elimination of main effects: The least-squares estimates of each quantitative trait were used as dependent variables in a linear model that was simplified by backward elimination. The full model included “parent” (Westar or Marnoo), “backcross” (one or two), “parent by backcross” interaction, “subpopulation” (within parent), “subpopulation by backcross” (within parent) interaction, and “translocation.” This last parameter was included to account for the effects of a reciprocal translocation present in Marnoo and Westar with respect to Ceres (our unpublished data). Segregating progeny from a cross between Marnoo or Westar and Ceres could lose either the B. rapa or the B. oleracea homeologous fragment involved in the translocation, resulting in five states for the translocation in this model: 0, 1, 2, 3, and 4 doses of the B. rapa homeolog, and simultaneously 4, 3, 2, 1, and 0 doses of the B. oleracea homeolog. Five RFLP probes (WG5A1, EC3E12, WG7F5, TG5D9, and WG2A3) that hybridize to loci on the translocation were used to determine the status of each IBL with respect to this translocation.

The pairing of IBL between the two populations due to a common BC₁ ancestor was not considered in this model. Although this might have resulted in a slight overestimation of the effects of QTL, the possibility that a marker-trait association is the result of the marker indicating a good family instead of indicating physical linkage is much smaller than with advanced-backcross QTL when all advanced lines are derived from a few BC₁ or BC₂ ancestors. To obtain more information on the potential bias, an analysis of covariance was done for each trait using the value of the BC₁S₃ line as a dependent variable and the value of the associated BC₂S₂ lines as a covariate.

Forward selection of marker loci: Marker loci were added to the reduced model using forward selection. For the inbred populations the marker information was divided into additive (a) and dominance (d) components: Pa=P(DD)−P(RR);Pd=P(DR).

For traits measured in the hybrid populations only an additive component could be estimated. In this case, P_a actually represents P(DT) - P(RT), where T indicates the tester allele. When a locus is heterozygous in the IBL parent (DR), half of its testcrossed progeny is RT and half is DT.

At each cycle of testing the most significant marker locus was added to the multilocus model until no other loci with a significant effect could be added. Loci that were segregating only in the DH population were not included in the model. Loci that segregated only in the Westar or in the Marnoo background were included if flanking loci segregated in the other background; otherwise, these loci were included when each background was analyzed separately. The addition of each locus required the testing of several hypotheses to choose the best model, such as the presence of an average additive effect, an average dominance effect, and a difference of effects between the Westar- and the Marnoo-derived populations. A significance threshold of P < 0.002 (i.e., LOD of 2.7) was chosen for adding a new locus into the model. The percentage of the variance explained by a given multilocus model was calculated as Variance explained=100×(SSmain effect+all loci selected−SSmain effects)∕SSTotal, where SS is the sum of squares obtained from the analysis of variance table. The formula to calculate the additional variance explained by incorporating a new locus in the model was Var.expl.=100×(SSmain effects+all loci selected−SSmain effects+all loci selected but the last one)∕SSTotal.

Estimating the effects of allele substitution on a trait: We equated the expected mean performance of the selfed progeny of an IBL to μ+aPa+dPd.

The effect of substituting RR by DD at the locus under consideration was thus estimated to be 2a, and the actual dominance deviation was twice the value estimated by d because only half the selfed progeny of a heterozygous IBL was expected to be heterozygous.

The expected mean performance of the testcrossed progeny of an IBL can then be written as μ+a[P(DT)−P(RT)]. The value 2a then becomes the estimated effect of substituting RT by DT in the hybrid.