Evaluation of Reciprocal Cross Design on Detection and Characterization of Non-Mendelian QTL in F 2 Outbred Populations : I . Parent-of-origin Effect

A simulation study was conducted to evaluate the effect of reciprocal cross on the detection and characterization of parent-of-origin (POE) QTL in F2 QTL populations. Data were simulated under two different mating designs. In the one-way cross design, six F0 grand sires of one breed and 30 F0 grand dams of another breed generated 10 F1 offspring per dam. Sixteen F1 sires and 64 F1 dams were randomly chosen to produce a total of 640 F2 offspring. In the reciprocal design, three F0 grand sires of A breed and 15 F0 grand dams of B breed were mated to generate 10 F1 offspring per dam. Eight F1 sires and 32 F1 dams were randomly chosen to produce 10 F2 offspring per F1 dam, totaling 320 F2 offspring. Another mating set comprised three F0 grand sires of B breed and 15 F0 grand dams of A breed to produce the same number of F1 and F2 offspring. A chromosome of 100 cM was simulated with large, medium or small QTL with fixed or different allele frequencies in parental breeds. A series of tests between Mendelian and POE models were applied to characterize QTL as Mendelian, paternal, maternal or partial expression QTL. The overall detection powers were similar between the two mating designs. However, the proportions of paternally expressed QTL that were declared as paternal QTL type were greater in the reciprocal cross design than in the one-way cross, and vice versa for Mendelian QTL. When QTL alleles were segregating in parental breeds, a significant proportion of Mendelian QTL were spuriously declared POE QTL, suggesting that care must be taken to characterize imprinting QTL in a QTL mapping population with a small number of F1 parents. (


INTRODUCTION
Genetic improvement schemes and quantitative trait loci (QTL) mapping experiments in livestock usually assume Mendelian inheritance, in which parents contribute equally to progeny.Genomic imprinting, a non-Mendelian effect where only one of the two parental copies of a gene is expressed, has been an interesting research area in mammalian genetics due to its unique expression and inheritance mechanisms, and its important role in growth, development, and behavior (Tycko and Morison, 2002;Wilkens and Haig, 2003).One typical imprinted gene, insulin-like growth factor 2 (IGF2), influences body composition in swine (Jeon et al., 1999;Nezer et al., 1999), and a causative SNP in the IGF2 gene was identified (Nezer et al., 2003;van Laere et al., 2003).Genomic regions with imprinting or parent-of-origin (POE) effects can be detected using QTL interval mapping in F 2 crosses between lines or breeds that segregate for marker alleles because of the ability to follow parental origin.Development and application of statistical methods to detect chromosomal regions or QTL with imprinting effects in a breed-cross design were implemented for F 2 crosses of swine breeds (de Koning et al., 2000;Thomsen et al., 2004;Kim et al., 2005a), and there have been several reports suggesting that non-Mendelian or POE effects on quantitative traits in swine exist (de Koning et al., 2001;Kim et al., 2007).
Most F 2 mating designs in pig QTL populations are based on one-way cross, i.e., all grandsires are from one breed and all grand-dams from anther breed (Kim et al., 2005c;Shulin et al., 2005;Choi et al., 2006).The one-way mating design can generate progeny with phenotypic differences due to breed-specific maternal environmental effects, mitochondrial inheritance, genomic imprinting, or sex chromosome-linked effects (Thallman et al., 1992).Recently, reciprocal cross designs have been used for QTL detection in swine, in which individuals of two breeds were used as both grand-sires and grand-dams (Rohrer et al., 2006).However, characterization of imprinting QTL due to the reciprocal cross is unknown in F 2 outbred populations.
The purpose of this study was to evaluate the effect of reciprocal mating designs on detection and characterization of POE QTL using a series of Mendelian and non-Mendelian QTL mapping models.

QTL analysis models
Least squares interval mapping models that are based on a breed-cross F 2 design were used for Mendelian and POE QTL detection (Haley et al., 1994;de Koning et al., 2000).The models assume that alternate breed alleles are fixed in grand-parental breeds, and the Mendelian (Mend) model is: where Y is a vector of phenotypes of F 2 individuals; X is a design matrix; b is a vector of fixed and covariate effects; a is the additive QTL effect, modeled as half of the difference between two breed homozygotes; d is dominance effect, modeled as the difference between the average of two breed heterozygotes and the homozygote midpoint; P a and P d are vectors containing functions for genotype probabilities for each animal at the chromosomal position of the putative QTL conditional on flanking marker genotypes.The second model was the full (partial) expression model (Full): Full model: Y = Xb+a pat P pat +a mat P mat +dP d +e where Y, X, b, and e are as previously defined and a pat , a mat , and d are the paternally inherited, maternally inherited, and dominance QTL coefficients, respectively.Vector P pat contains probabilities of inheriting one breed allele, Q, vs. the other breed allele, q, from its sire, P mat probabilities of inheriting one breed allele, Q vs. the other breed allele, q from its dam, and P d probabilities of being heterozygous.
The next models are the paternal (Pat) and maternal (Mat) expression models, and the null model: where all terms are as previously defined.All models were tested at each 1 cM position along the chromosomes.
To define a QTL as a Mendelian, paternal, maternal, or partial expression QTL, the following decision tree, based on trees already described as used previously (Thomsen et al., 2004;Kim et al., 2005a;McElroy et al., 2006), was used with some minor modifications for the specific tests: If the Mend model vs. the null model was significant: The Full model was tested against the Mend model at the most likely position under the full model around the region where QTL was detected in the Mend model.If this F-test was not significant, then the QTL was classified as a Mend QTL.
If the Full model vs. the Mend model was significant, then the Full model was tested against the Pat and Mat models.
If the Full model vs. the Pat model was not significant and the Full model vs. the Mat model was significant at the most likely position under the Pat model, then the QTL was classified as a paternally expressed QTL.
If the Full model vs. the Pat model was significant and the Full model vs. the Mat model was not significant at the most likely position under the Mat model, then the QTL was classified as a maternally expressed QTL.
If the Full model vs. the Pat model and the Full model vs. the Mat model were both significant or both not significant, then the QTL was classified as a partially expressed QTL.
If the Mend model vs. the null model was not significant: The Full model was tested against the null model.If this test was significant, then the Full model was tested against the Mat model and Pat model as described above.
If the Full model vs. the null model was not significant, then the Pat model and Mat model was tested against the null model.If the Pat model vs. the null model was significant, then the QTL was classified as a paternally expressed QTL.If the Mat model vs. the null model was significant, then the QTL was classified as a maternally expressed QTL.
A paternally (maternally) expressed QTL is one that shows a significant allelic effect when inherited from the sires (dams) of progeny without showing a significant allelic effect when inherited from the dams (sires) of progeny.A partially expressed QTL is one that shows an allelic effect when inherited from the sires and dams of progeny, but the effect is different depending on the sex of the parents from which it was inherited.
For QTL detection, i.e., Full, Mend, Pat, or Mat model vs. null model, empirically derived 5% chromosome-wise significance thresholds were used for each model.Lack-offit tests, i.e., Full model vs. Mend, Pat or Mat model, were performed at a 5% comparison-wise level using standard F statistic thresholds.

Simulation
To compare the power and ability to distinguish alternative Mendelian or POE QTL types, F 2 populations were simulated based on two designs: one-way cross and reciprocal cross.The one-way cross design comprised six F 0 grandsires of one breed and 30 F 0 grand-dams of another breed, to generate 10 F 1 offspring per dam.Sixteen F 1 sires and 64 F 1 dams were randomly chosen to produce a total of 640 progeny.In the reciprocal cross design, three F 0 grand sires of breed A were mated to 15 F 0 grand-dams of breed B to generate 10 F 1 offspring per dam.Eight F 1 sires and 32 F 1 dams were randomly chosen to produce 10 F 2 offspring per dam, for a total of 320 F 2 offspring.Also, using three F 0 grand sires of breed B and 15 F 0 grand-dams of breed A, the same number of F 1 s were generated and chosen to produce a total of 320 F 2 offspring.
A chromosome of 100 cM was simulated with 11 markers at 10 cM intervals.Markers were simulated with four alleles with frequencies of 0.5, 0.3, 0.1, 0.1 in one breed and 0.1, 0.1, 0.3, 0.5 in the other breed.This simulation was based on the marker information content in an experimental QTL population using F 0 s of Korean Native Pig and Yorkshire (data not shown).A series of biallelic additive, dominant, paternally, and maternally expressed QTL were simulated at position 75 cM on the chromosome with large, medium and small effects, which explain 32%, 12.5% and 5.1% of phenotypic variances, respectively.Table 1 explains the expected QTL effects and genetic variances for various levels of QTL size and alternate allele frequencies.The QTL genotypes for the F 0 parents were drawn from two alternative sets of frequencies of the favorable QTL allele in the two parental breeds: 1.0:0.0 and 0.8:0.2.Three-hundred replicate data sets were simulated for each set.Thresholds at the 5% chromosomewise level for QTL detection for the three models were derived from three-thousand replicates with QTL effects set to zero.

Power to detect QTL and their characterization
Table 2 presents the power to detect Mendelian and POE QTL and proportions of declared QTL types in oneway and reciprocal mating designs.Nearly all QTL were detected when alternate QTL alleles were fixed in parental breeds across all QTL types, sizes and mating designs.However, the power to detect QTL decreased when alternate alleles were not fixed in parental breeds; this was more pronounced for small QTL.Additive QTL had a greater detection power than dominance QTL, e.g., 10% difference for small QTL with segregating alleles in parental breeds in the one-way cross design (Table 2).Also, the proportions of detected QTL were greater for maternally expressed QTL compared to paternally expressed QTL, e.g., 97% vs. 94% for medium QTL with segregating alleles in grand parental breeds in the reciprocal design.This result was consistent with the simulation results of de Koning et al. (2002), in which maternally expressed QTL had a greater power to detect QTL than paternally expressed QTL when a small number of F 1 sires were used.Generally, the overall detection powers were similar in the two mating designs across all QTL types, sizes, and allele frequency difference (FD) (Table 2).Detected QTL were well defined as their corresponding QTL types under alternate allele fixation in parental breeds, e.g., more than 90% of Mendelian, paternally, and maternally expressed QTL were classified as Mend, Pat and Mat QTL, respectively, for a given QTL size and mating design.However, when QTL alleles were segregating in parental breeds, the proportion of QTL that were declared as their respective QTL types decreased.Also, a significant proportion of Mendelian QTL were spuriously declared as POE QTL, and vice versa, e.g., for the dominance QTL in the one-way cross design, only 52.3% of the small QTL were classified as Mend QTL and 16% of the QTL as paternal, maternal or partially expressed QTL (Table 2).
The proportion of additive or dominant QTL that were declared as Mend QTL was marginally greater in the one- way cross compared to the reciprocal cross design for all QTL sizes and FD, e.g., 84.3% vs. 80% for large dominant QTL when alternate alleles segregated in parental breeds.However, for paternally expressed QTL, the proportion of QTL declared as Pat QTL was consistently greater in the reciprocal cross design, e.g., 97% vs. 93.7%for large QTL under alternate allele fixation in parental breeds in the reciprocal and the one-way cross, respectively.There was no consistent difference between the two mating designs in the proportion of maternal expression QTL that were classified as Mat QTL for a given QTL size and FD (Table 2).

Estimates of QTL effects
Table 3 lists the means of estimates of QTL effects by QTL that were declared Pat, Mat or Mend QTL.Mean estimates of effects of the QTL declared as their corresponding QTL types were generally similar to their expectation under alternate allele fixation in parental breeds, but estimates were biased upward when alternate alleles segregated, which was more pronounced for small QTL.
Estimates for detected QTL that were not classified as their corresponding QTL types were significantly downward biased, e.g., for the large additive QTL with FD In the one-way cross design, six F 0 grand sires of one breed and 30 F 0 grand dams of another breed generate 10 F 1 offspring per dam.Sixteen F 1 sires and 64 F 1 dams are randomly chosen to produce 10 F 2 offspring per F 1 dam, for a total of 640 F 2 offspring.In the reciprocal design, one mating set comprised three F 0 grand sires of A breed and 15 F 0 grand dams of B breed to generate 10 F 1 offspring per dam.Eight F 1 sires and 32 F 1 dams are randomly chosen to produce 10 F 2 offspring per F 1 dam, for a total of 320 F 2 offspring.Another mating set used three F 0 grand sires of B breed and 15 F 0 grand dams of A breed to produce the same number of F 1 and F 2 offspring as the previous mating set.b Large, medium and small indicate QTL effects, such that QTL effects explain 32%, 12.5% and 5.1% of phenotypic variance, respectively, under the condition that alternate alleles are fixed within F 0 grandparents from the two breeds.c Proportion of replicates in which QTL were detected at 5% chromosome-wise level in at least one of the paternal, maternal, Mendelian, or partial expression models.d Relative proportion of declared QTL type for the detected QTL. Paternal (maternal) QTL: shows a significant allelic effect when inherited from the sires (dams) of progeny without showing a significant allelic effect when inherited from the dams (sires) of progeny.Mend QTL: shows additive and/or dominant effects.Partial QTL: shows an allelic effect when inherited from the sires and dams of progeny, but the effect is different depending on the sex of the parents from which it was inherited.
= 0.6 that were declared Pat QTL in the one-way cross, the estimate of paternal expression effect was 0.20 (expectation was 0.34).The exceptions to this were the paternally (maternally) expressed QTL that were falsely declared partially expressed, for which the estimates of paternal (maternal) QTL effects in the Full model were similar to those of the respective effects of Pat (Mat) type QTL (results not shown).
For Mendelian QTL that were declared Mend QTL, the estimates of QTL effects were more biased and slightly greater in the one-way cross than in the reciprocal cross when alternate alleles were not fixed in the parental breeds, e.g., 0.51 vs. 0.49 and 0.29 vs. 0.27 for additive and dominant effects of large additive and dominance QTL, respectively (Table 3).However, there were no significant differences between the two mating designs in estimates of QTL effect for paternally or maternally expressed QTL that were declared as their corresponding types.

Estimates of QTL position
Position estimates of the detected QTL that were declared as their corresponding types were close to unbiased (75 cM) and had high precision (low standard deviation) when alternate alleles were fixed in parental breeds across all QTL types, sizes, and mating designs.However, position estimates tended to be biased and less precise when alternate allele frequencies differed or detected QTL were not classified as their corresponding QTL types, which was more pronounced when QTL effects were small (results not shown).There were no significant differences between the two mating designs in position estimates of the detected QTL that were declared as their corresponding QTL types across all QTL types and sizes (results not shown).2. c For paternally or maternally expressed QTL, expected QTL effects (a) are 0.566, 0.354, and 0.226 with allele frequency (1.0/0.0), and 0.34, 0.21, and 0.14 with allele frequency (0.8/0.2), for large, medium and small QTL, respectively.d For additive QTL (d = 0), expected additive (dominant) QTL effects are 0.8 (0.0), 0.5 (0.0), and 0.32 (0.0) with allele frequency (1.0/0.0), and 0.48 (0.0), 0.30 (0.0), and 0.19 (0.0) with allele frequency (0.8/0.2), respectively.For dominance QTL (a = d), expected additive (dominant) QTL effects are 0.65 (0.65), 0.41 (0.41) and 0.26 (0.26) with allele frequency (1.0/0.0), and 0.39 (0.24), 0.25 (0.15) and 0.16 (0.09) with allele frequency (0.8/0.2), respectively.

DISCUSSION
The results of our simulation confirmed previous reports (Alfonso and Haley, 1998;de Koning et al., 2002), in which the power to detect Mendelian or POE QTL decreased in the breed-cross QTL model when alternate breed-specific QTL alleles were not fixed in grand-parental breeds, because QTL effects that were based on the differences between breed-origin alleles were diluted when some of the breed-specific alleles were not inherited to F 2 s from their corresponding F 0 grand-parental breeds.The decreased proportion of QTL detection differed depending on QTL mode, i.e., dominance QTL had smaller power to detect QTL compared to additive, paternally or maternally expressed QTL (Table 2).However, these results were not surprising, because the decreasing magnitudes of QTL effect are much greater for dominant QTL.That is, expected values of additive and dominance effects are ∆f×a and ∆f 2 ×d, respectively (de Koning et al., 2002), where ∆f is allele frequency difference (FD) in grand-parental breeds, such that for the large complete dominant QTL with FD (0.8/0.2), ∆f = 0.8-0.2= 0.6, ∆f×a = 0.6×0.654= 0.392, and ∆f 2 ×d = 0.6 2 ×0.654 = 0.235, which explains the smaller proportion of F 2 phenotype variance compared to the large additive or POE QTL (Table 1).
Generally, overall detection powers were similar between the two mating designs for a given QTL type, size, and FD.However, the proportions of detected QTL that were declared as their corresponding QTL differed between the two crosses.For example, paternally expressed QTL had a greater proportion of detected QTL that were classified as Pat QTL in the reciprocal cross design compared to the one-way cross, while there were no consistent differences between the two mating designs in the proportion of maternally expressed QTL that were declared as Mat QTL (Table 2).As described in our previous simulation study about combined line-cross and half-sib analysis (Lee et al., 2007), the use of a small number of F 1 sires, which is a common practice in most porcine QTL mapping populations, may cause biased selection of F 1 sires, i.e., genetic materials of parental breeds are not randomly transmitted to F 2 progeny due to sampling effects of F 1 sires.This would cause QTL alternate alleles to be distributed in unexpected patterns (e.g., homozygous F 1 sires for the QTL), causing a smaller proportion of paternally expressed QTL to be classified as Pat QTL when QTL alleles segregate within parental breeds.However, the reciprocal cross, in which F 1 sires are sired or dammed by both breeds, can offset non-random transmissions of alternate alleles to F 1 sires, resulting in a greater proportion of paternally expressed QTL to be declared Pat QTL under the different allele frequencies in the parental breeds.However, for maternally expressed QTL, a much larger number (64) of F 1 dams were used (compared to 16 F 1 sires in each cross design), such that the chance of selecting large proportions of homozygous F 1 dams would not occur non-randomly.
Dominance QTL had a marginally greater proportion of QTL with Mend QTL type in the one-way cross than in the reciprocal cross, especially when QTL effects were large or medium with segregating alternate alleles within parental breeds (Table 2).However, the method of classifying Mend QTL in this study is not the best strategy when QTL have Mendelian inheritance with segregating alternate alleles in the parental breeds.In this case, we proposed an alternate strategy to better characterize Mendelian QTL type in terms of allele frequency in parental breeds (Kim et al., 2005b;Lee et al., 2007).
When QTL alleles were segregating in parental breeds, a significant proportion of Mendelian QTL were spuriously declared Pat, Mat, or partially expressed QTL across all QTL sizes, and this spurious QTL declaration rate did not diminish even when both breeds were used as grand-sires or grand-dams in the reciprocal cross design (Table 2).This result was consistent with the previous report by de Koning et al. (2002), in which more than 10% of large or medium Mendelian QTL were spuriously detected as imprinting QTL when few F 1 sires were used to detect QTL with segregating alleles within parental breeds.As de Koning et al. (2002) indicated, use of a few F 1 parents is not a good option for the generation of F 2 breed-cross populations to detect imprinting QTL.Also, a significant proportion of POE QTL were spuriously declared Mendelian QTL in both mating designs when the QTL were small and the alternate alleles were not fixed in parental breeds (Table 2).These simulation results suggest that great care must be taken to characterize QTL inheritance mode, i.e., POE vs. Mendelian expression, especially when QTL magnitude is small in a QTL mapping population with a small number of F 1 parents.
paternal expression model: Y = Xb+a pat P pat +e maternal expression model: Y = Xb+a mat P mat +e null model: Y = Xb+e

Table 1 .
Koning et al., 2002) and proportion of F 2 phenotypic variances due to the QTL used to simulate large, medium, and small QTL with Mendelian and parent-of-origin inheritance patterns in an F 2 breed cross Upper and lower values for each QTL inheritance mode are expectation under the condition that alternate QTL alleles are fixed (1.0/0.0) or differently distributed (0.8/0.2) within parental breeds, respectively.bDifferentQTL effects under varying genetic models were set such that large, medium and small QTL explained 32%, 12.5% and 5.1% of the phenotypic variance, respectively.Error variances were set equal to 0.680, 0.875 and 0.949 for the large, medium and small QTL, respectively, such that overall phenotypic variances were 1, when alternate breed alleles are fixed in parental breeds.When the allele frequencies differ, expected values of additive and dominant effects are ∆f×a and ∆f 2 ×d (deKoning et al., 2002), where ∆f is allele frequency difference (FD) in grand-parental breeds, e.g., for large complete dominant QTL with FD (0.8/0.2), ∆f = 0.8-0.2= 0.6, and ∆f×a = 0.6×0.654= 0.392, and ∆f 2 ×d = 0.6 2 ×0.654 = 0.235.c Expected values of proportion of phenotypic variance due to QTL are obtained using the formulae of genetic variance by functions of QTL effects for the given QTL inheritance modes. a

Table 2 .
Power to detect QTL under different genetic models and proportion of detected QTL declared as Mendelian, paternally, maternally, or partially expressed QTL in different inheritance modes, sizes, and mating designs One-way cross a

Table 3 .
Mean and standard deviation (in parentheses) of estimates of QTL effects for paternally, maternally or Mendelian expressed QTL, depending on the difference in QTL modes, sizes, and mating designs for an F 2 breed cross under two alternate mating designs One-way cross a a, b Described in Table