J. Anim. Sci. 2005. 83:2471-2481
© 2005 American Society of Animal Science
Evaluation of approaches to detect quantitative trait loci for growth, carcass, and meat quality on swine chromosomes 2, 6, 13, and 18. II. Multivariate and principal component analyses1
T. M. Stearns,
J. E. Beever,
B. R. Southey,
M. Ellis,
F. K. McKeith and
S. L. Rodriguez-Zas2
Department of Animal Sciences, University of Illinois at Urbana-Champaign, Urbana 61801
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Abstract
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The merits of complementary multivariate techniques to identify QTL associated with multiple traits were evaluated. Records from 806 F2 pigs pertaining to a Berkshire x Duroc three-generation population were available. Six multitrait groups on SSC 2, 6, 13, and 18 with information on 30 markers were studied. Multivariate techniques studied included multivariate models and principal components analysis of each multitrait group. All models included, in addition to systematic effects, additive, dominance, and imprinting coefficients corresponding to a one-QTL model and a random family effect. Multivariate analysis identified QTL associated with genomewise significant variation in four of the multitrait groups. The majority of the multivariate analysis provided greater precision of parameter estimates and higher statistical significance in some cases than univariate approaches, because of the greater parameterization of the multivariate models and moderate information content of the data. Principal component analysis results were consistent with univariate and multivariate analyses and recovered the levels of statistical significance observed in univariate analyses on the original data. In addition, principal component analysis was able to provide a location associated with LM area not detected by other analyses. The relative advantage of multivariate over the univariate approaches varied with the level of genetic covariance between traits because of the modeled QTL effect and information contained in the data; however, multivariate approaches have the unique capability to identify pleiotropic effects or multiple linked QTL.
Key Words: Growth Interval Mapping Meat Quality Multivariate Principal Components
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Introduction
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Several studies have reported QTL associated with growth, carcass, and meat quality in swine (Dekkers et al., 2003
; Sato et al., 2003
; Thomsen et al., 2004
). The majority of QTL mapping studies use univariate approaches to detect QTL on a trait-by-trait basis, although multiple correlated traits are under study, and results often suggest that several traits are influenced by the same or linked loci. The univariate approach does not allow for the formal testing of the hypothesis of pleiotropic or linked QTL effects. In addition, most genetic improvement programs aim to improve several traits simultaneously; thus, the identification of genomic regions influencing multiple traits is critical for effective genetic progress.
In outbred F2 swine populations, the least squares interval mapping approach proposed by Haley et al. (1994)
is commonly used to detect QTL on a univariate trait-by-trait basis. Knott and Haley (2000)
expanded on the approach by creating a multiple-trait QTL mapping method. Weller et al. (1996)
proposed an alternative method to detect QTL influencing multiple traits by analyzing linear combinations of traits or principal components (PC). No study has applied multivariate models and PC analysis to detect QTL influencing swine carcass and meat quality in field data. The objectives of this study were to evaluate multivariate and univariate approaches to detect QTL on a new Illinois Meat Quality Pedigree reference population and to characterize QTL influencing carcass and meat quality traits segregating in a cross between commercial lines.
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Materials and Methods
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Population
Three purebred Berkshire sires were mated to 18 purebred Duroc dams to produce six F1 males and 56 F1 females. The F1 sows were multiple mated to F1 sires and farrowed one to four times between July 2000 and August 2001. Phenotypic data were available on 806 F2 pigs (approximately one-half males and one-half females), and detailed information on diet and management can be found in Stearns et al. (2005)
.
Molecular Markers and Linkage Analysis
Sex-averaged linkage maps were constructed using CRI-MAP (Green et al., 1990
), and the microsatellite markers were distributed into linkage groups of eight, nine, nine, and four markers on SSC 2, 6, 13, and 18, respectively (Stearns et al., 2005
). The markers had an average spacing of 16 cM (Table 1
), and the minimum information content calculated using the method described by Knott et al. (1998)
was 0.3, 0.4, 0.5, and 0.4 for SSC 2, 6, 13, and 18, respectively.
Phenotype Measurements
Forty traits were recorded following the guidelines of the NPB (2000)
. The 11 traits selected for multivariate analyses were LM area; backfat thickness at the first, tenth, and last ribs and at the last lumbar vertebra; percentages of moisture, drip loss, and intramuscular fat; marbling score; shear force; and tenderness. The selection was based on results from univariate QTL analyses (Stearns et al., 2005
) and phenotypic correlations suggesting potential pleiotropic or linked QTL detectable with multivariate techniques. The LM area was measured at the tenth rib, and the area was determined by tracing with acetate paper. Midline backfat measurements were obtained opposite the first rib, last rib, last lumbar vertebra, and one-half the distance from the midline of the tenth rib with a ruler (Hemann et al., 2000
). External fat and connective tissue were removed from a 2.5-cm-thick portion of the LM, and the sample was homogenized, placed in a Whirl-pak bag (NASCO, Modesto, CA), and subsequently frozen. The sample was used to determine fat and moisture percentages following the procedures described by Novakofski et al. (1989)
and Hamilton et al. (2003)
. Drip loss percentage was determined using a 2.5-cm-thick chop of the LM stored in a Whirl-pak bag in a 4°C cooler for 48 h. Marbling was scored by a trained individual on an integer scale of 1 (low) to 10 (high). A panel of six independent testers scored tenderness using an integer scale ranging from 1 (tough) to 15 (tender). Shear force was measured with a Universal Testing Machine (Instron, Canton, MA) using a Warner-Bratzler shear attachment following the procedure described by Hamilton et al. (2003)
.
Estimates of narrow sense heritabilities for all traits were obtained using a univariate model including the fixed effects of sex, birth year and month, the covariate live weight at slaughter, and the random effects of sire, dam, and sire x dam that were evaluated using ASREML (Gilmour et al., 2002
). All pairwise correlations between traits were computed using PROC CORR (SAS Inst., Inc., Cary, NC). The estimates of genetic and phenotypic correlation between the traits were obtained in ASREML (Gilmour et al., 2002
) using a dam model with the same fixed effects used in univariate estimation of narrow sense heritabilities.
The 11 traits were divided into six groups determined by the chromosome in which univariate analysis had identified putative QTL influencing multiple traits (Stearns et al., 2005
) and by the correlation between the traits. The SSC 2 A group included last lumbar vertebra, last rib, and tenth rib backfat thicknesses, as well as LM area. The SSC 2 B group consisted of shear force and tenderness. The SSC 2 C group included fat and moisture percentage measurements. The SSC 6 group consisted of last lumbar vertebra, last rib, and tenth rib backfat thicknesses and LM area. The SSC 13 group included marbling score and percentages of drip loss, intramuscular fat, and moisture and was based on the pairwise correlation estimates. The SSC 18 group consisted of first and tenth rib backfat thicknesses and percentages of fat and moisture. The multitrait groups studied offered a complete representation of possible genotypic-environmental correlation scenarios and permitted evaluation of the relative advantages of multivariate analysis.
Multivariate Analysis
Multivariate QTL mapping allows the detection of possible pleiotropic effects and linked QTL, while exploiting the information from genetic and phenotypic correlations between traits (Korol et al., 1995
; Knott and Haley, 2000
; Gilbert and Le Roy, 2003
). The multivariate model used was
 | [1] |
where Y is a dependent variable matrix consisting of the number of observations for each trait (n) and the number of traits within the subgroup analyzed (k). The design matrix, X, related the n observations to m fixed-effect explanatory variables. In this study, the fixed effects were sex (two levels: male and female), birth year and month (13 levels; months from July 2000 to August 2001), covariate live weight at slaughter, and additive, dominance, and imprinting coefficients computed at every 1 cM using the method of Haley et al. (1994)
and described by Stearns et al. (2005)
. The m x k matrix B includes the coefficients corresponding to the fixed effect levels. The Z design matrix relates the n observations to the l (i.e., family with 90 levels) random effect levels, and the l x k matrix U includes the coefficients corresponding to the random effect levels for each trait. The matrix
is a matrix of residuals corresponding to n observations and k traits. Analysis was performed using PROC GLM in SAS (SAS Inst., Inc., Cary, NC). The residuals are assumed to be multivariate normal, with a mean of zero and a variance-covariance matrix, V, representing independence of residuals within trait and correlation among traits.
The null hypothesis of no QTL was tested using Wilks criterion:
 | [2] |
where
max denotes the maximum eigenvalue of E1H, H represents the sums of squares and cross-products of the QTL genetic effect, and E represents the sums of squares and cross-products of the errors (Littell et al., 1991
; Khattree and Naik, 1999
). Rejection of the null hypothesis would provide supporting evidence for the existence of QTL that could display pleiotropic effects or multiple linked QTL (Jiang and Zeng, 1995
; Knott and Haley, 2000
).
Principal Component Analysis
Principal component analysis is a multivariate technique that transforms a number of correlated quantitative variables into fewer uncorrelated (orthogonal) variables termed PC (Chatterjee and Price, 1991
). Each PC is a linear combination of the original variables, with coefficients equal to the eigenvectors of the correlation or covariance matrix. Consequently, univariate and multivariate methods are equivalent to the two extremes of model complexity and computational requirements in the analysis of multiple correlated traits, and PC analysis is an intermediate compromising approach.
The percentage of the variation of the original traits explained by each PC is equal to the associated eigenvalue, and the weights of the traits in each PC are the terms in the associated eigenvectors. The relationship among the variance-covariance matrix of the traits (A), any one eigenvalue (
), and corresponding eigenvectors (x) is
 | [3] |
Principal components for each multitrait group were obtained using PROC PRINCOMP of SAS on the original trait records. The same explanatory variables used in the multivariate model were used to detect QTL associated with the PC using a univariate model in PROC GLM of SAS.
Evidence of QTL at every 1 cM was summarized in an F-test statistic in the PC analysis and in a pseudo-F statistic (Wilks criterion) in the multivariate analysis. The chromosome locations with local F-test statistic maxima that surpassed the significance threshold were reported as putative QTL with the associated estimates of mode of action. A chromosomewise permutation test provided the distribution of the F-test under the null hypothesis of no QTL residing on the chromosome based on 1,000 permutations and the associated P-value of 0.05 and 0.01 thresholds (Churchill and Doerge, 1994
). The genomewise F-threshold was obtained from the average chromosomewise F-thresholds across traits using a Bonferroni adjustment to account for the 18 chromosome pairs in the pig genome. The critical values of the F-test statistic were 6.33 and 7.86 for the 0.05 and 0.01 P-values, respectively. This Bonferroni adjustment is conservative for this study because only four chromosomes were studied.
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Results and Discussion
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The number of F2 pigs measured, the associated mean and SD, and narrow sense heritability estimates of the 11 traits analyzed using multivariate techniques are given in Table 2
. All pairwise correlations between traits and the number of records in common are provided in Table 3
. Traits within multitrait group had moderate to high Pearson correlation (Table 3
), and the univariate analyses resulted in significant evidence of a QTL for at least one trait (Stearns et al., 2005
). The backfat thickness measurements in the SSC 2 A group were moderately to highly correlated (>0.6), whereas tenth rib backfat thickness had the highest correlation (0.49) with LM area. Fat and moisture percentage (SSC 2 C group) had a correlation equal to 0.83. In the SSC 13 group, high positive pairwise correlations were found between fat and moisture percentages and marbling score (>0.50), and a moderate and negative correlation (0.35) was found between marbling score and drip loss percentage.
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Table 2. Number of records, average, SD, and narrow-sense heritability (h2) estimate and SE of the growth, carcass, and meat quality traits studied
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Table 3. Phenotypic correlations between the tenth rib, last rib, and last lumbar vertebra backfat thicknesses; LM area; percentages of drip loss, fat, and moisture; marbling score; shear force; and taste panel tendernessa
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A summary of the genetic and phenotypic correlations between traits is provided in Table 4
. The absolute values of the genetic correlations ranged from 0.02 to 0.88, and the absolute phenotypic correlations ranged from 0.01 to 0.69. The genetic correlations suggested that the putative QTL regions are shared by the traits within a group and may be present on the chromosomes under study. The multitrait groups included consistent phenotypic and genetic correlations between traits (e.g., last lumbar and last rib backfat), opposite genetic and environmental correlations (e.g., fat and moisture percentage), and virtually no environmental correlation (e.g., marbling score and moisture percentage) between traits. The multivariate analyses of the groups permitted the evaluation of these techniques in different scenarios.
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Table 4. Genetic (above diagonal) and phenotypic (below diagonal) correlations and SE for traits constituting multitrait groups
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Table 5
provides the composition of all PC corresponding to each multitrait group. The first two PC explain approximately 86% of the variation of the four-trait groups, and the first PC explained between 77 and 83% of the variation of the two-trait groups. The weights for backfat measurements tend to be similar within multitrait groups, reflecting the positive and strong bivariate correlation among them. The slight differences in backfat weights across groups may be caused by the different traits in each group and the different number of individuals with available genotype across chromosomes. In the two-trait groups, the positive correlation between marbling score and intramuscular fat percentage and the negative correlation between shear force and tenderness are responsible for the opposite weight pattern across PC observed in both groups.
Chromosome 2
Group A.
Univariate analysis (Stearns et al., 2005
) provided significant evidence for QTL with maternal imprinting at 0 cM for last lumbar vertebra, last rib, and tenth rib backfat thicknesses and LM area (Figure 1
). The multivariate analysis provided significant evidence for QTL at 0 cM with maternal imprinting effect (Tables 6
and 7
). The profile of the multivariate Wilks test statistic across SSC 2 (Figure 2
) had a lower maximum than the test statistics from all univariate tests, except for last rib backfat thickness (Table 6
). These results were consistent with those of Knott et al. (1998)
, de Koning et al. (1999)
, and Dekkers et al. (2003)
, who identified QTL at 0 cM connected with several fatness traits. The Insulin-like Growth Factor 2 (IGF2) is a strong candidate gene because it is located at the proximal end of SSC 2 (0 cM) and has an imprinting mode of action (Jeon et al., 1999
; Nezer et al., 1999
; Van Laere et al., 2003
).

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Figure 1. The P-values [pval = log10(P-value)] for the QTL effect of the traits constituting the multitrait group (LM area [LMA], and last rib, tenth rib, and last lumbar vertebra backfat thicknesses) in the multivariate analysis of SSC 2. Marker positions are indicated by upward-pointing arrows ( ) on the abscissa. Horizontal lines indicate threshold values for genomewise 1% level (dashed line) and genomewise 5% level (solid line).
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Table 6. Summary of locations, F-ratios, and comparisonwise P-values of QTL for the multitrait groups on SSC 2, 6, 13, and 18
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Table 7. Estimates of additive, dominance, and imprinting effects, SE, and comparisonwise P-values of QTL for the multitrait groups on SSC 2, 6, 13, and 18a
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Figure 2. The P-values [pval = log10(P-value)] for the QTL effect in the multivariate analysis of SSC 2. Marker positions are indicated by upward-pointing arrows ( ) on the abscissa. Horizontal lines indicate threshold values for genomewise 1% level (dashed line) and genomewise 5% level (solid line).
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Principal component analysis performed on the A subgroup identified two significant QTL associated with the first and second PC (Table 8
). A QTL related to PC 1 had a significant maternal imprinting effect and was located at 0 cM (Table 9
). Principal Component 1 had approximately equal weights for backfat measurements and slightly less weight for LM area; thus, additional supporting evidence that both traits were associated with QTL at 0 cM was found in this study (Figure 3
). The second QTL with an additive effect was related to PC 2 at 28 cM (Figure 4
). This PC had high weight for LM area compared with the other traits, and therefore, this QTL is primarily associated with LM area. The QTL for PC 2 is located in the second highest peak of the multitrait analysis; thus, the two analyses provide supporting evidence for the presence of a QTL at 28 cM. The second largest peak graphed in the univariate analysis of LM area was at 28 cM found in the univariate analysis.
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Table 8. Summary of locations, F-ratios, and comparisonwise P-values of QTL for principal components (PC) on SSC 2, 6, 13, and 18
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Table 9. Estimates of additive, dominance, and imprinting effects; SE; and comparisonwise P-values of QTL for principal components (PC) on SSC 2, 6, 13, and 18a
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Figure 3. The P-values [pval = log10(P-value)] for the QTL effect of PC 1 in the multivariate analysis of SSC 2. Marker positions are indicated by upward-pointing arrows ( ) on the abscissa. Horizontal lines indicate threshold values for genomewise 1% level (dashed line) and genomewise 5% level (solid line).
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Figure 4. The P-values [pval = log10(P-value)] for the QTL effect of PC 2 in the multivariate analysis of SSC 2. Marker positions are indicated by upward-pointing arrows ( ) on the abscissa. Horizontal lines indicate threshold values for genomewise 1% level (dashed line) and genomewise 5% level (solid line).
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Group B.
The multivariate analysis identified the same chromosome region (Table 6
) found in the univariate models for both shear force and tenderness (Stearns et al., 2005
). The maximum Wilks statistic was more significant at the same location (39 cM) than the univariate analysis (Table 6
). Similarly, the additive mode of action detected by multivariate analysis was consistent with that detected by univariate analysis (Table 7
). The similarity between the univariate and multivariate analyses suggests the same QTL because of the high genetic and phenotypic correlations between shear force and tenderness (Tables 3
and 4
).
Results of PC analyses yielded significant evidence for a QTL associated with the first PC that accounted for 77% of the total variation of tenderness and shear force (Table 5
). The QTL was detected at 39 cM (Table 8
) and had an additive effect (Table 9
), which agrees with the multivariate model and univariate analysis on the original traits. The estimates from PC analysis indicated the presence of a QTL with cis-acting effect on tenderness and shear force that is consistent with the negative correlation and opposite scales of both traits.
Group C.
Significant evidence of QTL influencing both fat percentage and marbling score in the telomeric region, although 30 cM apart (Table 6
), was identified using univariate models (Stearns et al., 2005
). The test statistic of the multivariate analysis peaked at 30 cM (Table 6
) and was more significant than the univariate analysis (Stearns et al., 2005
), although both approaches suggested a QTL with additive effect (Table 7
). A significant QTL associated with PC 1 with an additive effect was detected at 28 cM (Tables 8
and 9
). Principal Component 1 explained 83% of the variation of the traits (Table 5
) and had equal and positive weights for marbling score and intramuscular fat percentage. The results from PC analysis suggested that the same QTL region is cis-acting on both fat-related traits.
Chromosome 6 Group
The multivariate techniques were applied to the last lumbar vertebra, last rib, and tenth rib backfat thicknesses and to LM area. Univariate analysis detected a QTL with a paternal imprinting effect for last lumbar vertebra, last rib, and tenth rib backfat thicknesses at 72, 62, and 105 cM, respectively, and a QTL with an additive effect associated with LM area was located at 95 cM (Stearns et al., 2005
). The test statistic of the multivariate analysis was higher than the univariate test maxima (Table 6
). The multivariate model with more parameters provided more significant results and increased precision in estimating parameters than did univariate analyses for this multitrait scenario. In addition, the multivariate analysis accommodated potential pleiotropic effects or multiple linked QTL, with an additive effect at 100 cM (Table 7
). Gerbens et al. (2001)
, Grindfleck et al. (2001)
, and Ovilo et al. (2002)
postulated that heart-fatty acid binding protein located at 84 cM influences backfat thickness. The span of the QTL detected (70 to 120 cM) suggests that >1 QTL is present in the region, one possibly being heart-fatty acid binding protein.
The PC analysis provided evidence of several QTL associated with the traits in the SSC 6 group (Table 8
) that had significance levels similar to the univariate analyses (Stearns et al., 2005
). A QTL with an additive effect was associated with PC 2 at 98 cM (Table 9
). The second PC accounted for 20% of the variation in the traits, and LM area had the highest weight (Table 5
). The relatively close location of the QTL to the location of the univariate and multivariate QTL affiliated with the LM area and the similarity in mode of action indicate that the QTL identified by PC 2 might be the same QTL identified by univariate and multivariate analyses. Significant evidence of a QTL with a paternal imprinting effect was identified for PC 1 at 71 cM (Tables 8
and 9
). Principal Component 1 accounted for approximately equal weights for all backfat measurements and slightly less weight for the LM area. The QTL identified by PC 1 may be associated with last lumbar vertebra backfat thickness because of similar locations of QTL identified by PC analysis and univariate analyses reported by Stearns et al. (2005)
. The location of QTL for last and tenth rib backfat thicknesses lies beyond the marker interval flanking the QTL identified by PC 1; thus, the QTL identified by PC 1 might not be related to those two traits.
Chromosome 13 Group
Marbling score and percentages of moisture, intramuscular fat, and drip loss were studied using multivariate techniques because univariate analysis had detected significant QTL for fat and moisture percentages at 88 and 86 cM, respectively (Stearns et al., 2005
). The multivariate test statistic (Table 6
) was lower than the two highest univariate test statistics for fat and moisture percentages (Stearns et al., 2005
). de Koning et al. (1999)
identified a QTL at 115 cM related to shear force; however, our univariate analysis did not detect a QTL near this location for tenderness or shear force (Stearns et al., 2005
). The inability of the multivariate analysis to identify significant QTL in this group suggests that the univariate results are false positives or that the low information content in this multitrait data set could not compensate for the greater parameterization of the multivariate model.
Principal component analysis identified evidence (borderline genomewise P-value <0.05) of QTL with an additive effect for PC 1 at 86 cM (Tables 8
and 9
). Principal Component 1 accounted for >60% of the variation and had approximately equal weights for marbling score, fat, and moisture percentages and lower weight for drip loss percentage (Table 5
). The similarity in statistical significance, location, and mode of action of the QTL identified for fat and moisture percentages and marbling in the univariate analyses reported by Stearns et al. (2004) and the QTL identified for PC 1 suggest that PC analysis has a relative advantage over multivariate and univariate models. This advantage occurs because PC analysis can model pleiotropic effects or multiple-linked QTL while providing statistically significant evidence. No significant evidence for QTL was obtained from the analysis of PC 2 that had a high weight for drip loss percentage. This result is consistent with univariate and multivariate models on the original traits.
Chromosome 18 Group
First and tenth rib backfat thickness and percentages of fat and moisture were studied using multivariate techniques based on univariate analyses that provided significant evidence of QTL with an additive effect related to these traits between 64 and 69 cM (Stearns et al., 2005
). The multivariate Wilks test provided weak evidence of a QTL at 67 cM (Table 6
); however, the multivariate test statistic was lower (nonsignificant at genomewise P-value <0.05) than three of the univariate test statistics.
Principal component analysis of the SSC 18 group identified a significant (genomewise P-value <0.01) QTL with an additive effect on PC 1 at 67 cM (Tables 8
and 9
). The first PC accounted for >58% of the variation in the traits and had high and similar weights for fat and moisture percentages and tenth rib backfat thickness and slightly lower weight for first rib backfat thickness. Based on the similar statistical levels, location, and mode of action of the QTL identified in the univariate analysis (Stearns et al., 2005
), PC analysis might have identified QTL a with pleiotropic effect or multiple-linked QTL influencing these traits. The QTL position identified by PC analysis is consistent with multivariate analysis although the evidence is more significant in the former analysis.
Evaluation of Multivariate Approaches
Multivariate approaches can increase the power of the test, increase the precision of parameter estimates, and allow testing of hypotheses involving multiple traits (Jiang and Zeng, 1995
; Korol et al., 1995
; Gilbert and Le Roy, 2004
). The study of the multitrait groups aided in the understanding of the scenarios in which multivariate techniques are more beneficial than univariate techniques. Results from our study suggest that the realization of these benefits depends on the phenotypic and genotypic data studied, which agrees with Jiang and Zeng (1995)
, who postulated that if residual and pleiotropic effects are positively correlated, the test statistic of the joint tests will be smaller than the sum of the test statistics under the separate tests because of the inability of the model to differentiate between effects. In addition, a set of parameters is estimated for each trait in the multivariate analysis. As the number of traits added to the model increases, so does the number of parameters to be estimated, although the variation explained by the model might not be decreased in similar fashion, and as a result, precision may decrease.
Principal component analysis allows for multiple traits to be analyzed without an increase in the number of parameters to be estimated because traits are combined into single and orthogonal PC that can be analyzed with univariate methods. Despite the ability of PC analysis to identify QTL, results might be difficult to interpret because PC are composed of a specific partition of the phenotypic covariance that might not reflect the associated QTL covariance (Gilbert and Le Roy, 2003
).
There is a clear gain of power with PC techniques over univariate models on the original traits when the traits are influenced by QTL in a manner consistent with the linear combination in the PC as in Group C. The multivariate techniques did not offer substantial gain over the univariate models in Group B because of the moderate to low correlation between traits, evidence of distant QTL influencing both traits, and greater parameterization of the multivariate model compared with the univariate model.
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Implications
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Evidence of quantitative trait loci influencing carcass and meat quality traits segregating among current commercial swine lines was found. Multivariate and principal component analyses offered insights into the genetic factors (including pleiotropic and linked loci) that influence multiple traits and are complementary to univariate analyses. The additional information provided by the multivariate analyses depends on the genetic and environmental correlations among traits and on the information content necessary to overcome the greater parameterization of these models. The power of principal component analysis to detect loci is greater than that of univariate analysis of the original traits when the traits are influenced by loci in a manner consistent with the principal component function. These conditions can seldom be completely anticipated, and therefore, univariate, multivariate, and principal component approaches should be considered when mapping loci.
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Footnotes
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1 This study was funded by the USDA-IFAS, Grant #00-52100-9610 and C-FAR, Grant #01I-121-1-UIUC. 
2 Correspondence: 1207 W. Gregory Dr. (phone: 217-333-8810; fax: 217-333-8286; e-mail: rodrgzzs{at}uiuc.edu).
Received for publication September 30, 2004.
Accepted for publication August 8, 2005.
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