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ANIMAL GENETICS |
* Scottish Agricultural College, Edinburgh EH9 3JG, U.K.;
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Roslin Institute (Edinburgh), Roslin, Midlothian EH25 9PS, U.K.; and
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INIA, 28040 Madrid, Spain
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Abstract |
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 Top Abstract IntroductionMethodsResultsDiscussionImplicationsLiterature Cited |
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Key Words: BLUP Genetic Evaluation • Additive Relationship Matrix • Marker-Assisted Selection
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionImplicationsLiterature Cited |
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; Goddard and Hayes, 2002; Villanueva et al., 2002). These studies have assumed mixed inheritance models, where an identified or mapped QTL of significant effect is segregating together with polygenes.
Marker information also could offer benefits in selection programs when no QTL has been mapped or when the underlying genetic model can be considered the infinitesimal model, where no QTL has a significant large effect. The benefits can be expected through an increased accuracy when estimating genetic relationships in BLUP genetic evaluations. The additive relationship matrix (matrix A) used in BLUP is normally calculated exclusively from pedigree information, and it therefore gives only expectations of the proportion of genes that two particular individuals have in common (Christensen et al., 1996). Markers can be used to estimate the exact proportions with a high degree of precision.
Ideally, the matrix A to be used in BLUP should describe the additive genetic relationships due to those QTL affecting the trait under selection. Nejati-Javaremi et al. (1997) found substantial increases in accuracy and selection response when using this relationship matrix in BLUP evaluation; however, the computation of this matrix assumes implicitly that genotypes for all loci affecting the trait are known, and this is unrealistic. A more realistic scenario is to have genotypes for markers linked to QTL rather than the QTL genotypes themselves.
The objective of this study was to quantify the benefits from using marker information in the calculations of the relationship matrix used in genetic evaluations when the inheritance of the trait of interest follows an infinitesimal genetic model with linkage.
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionImplicationsLiterature Cited |
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) was used to obtain the relationship of the distance between two loci and their recombination frequency. All individuals were assumed to be genotyped for the marker loci each generation. The genetic value for each individual was the sum of its genotypic values for the 2,000 separate QTL. All QTL had an equal effect (a), defined as half the difference between the two homozygotes, and the value of a was chosen for giving an initial additive genetic variance of 0.2 (i.e., a = 0.0141). The phenotypic value for each individual was obtained by adding a normally distributed environmental component with mean zero and variance 0.8 to the genetic value; thus, the initial heritability was 0.2.
Population Model
The base population (t = 0) was composed of 100 unrelated individuals (50 males and 50 females). Markers and QTL were in linkage equilibrium at this initial generation. Ten males and 10 females were selected and mated at t = 0 to produce Generation 1 (t = 1). Ten discrete generations of selection were simulated. The individuals chosen to produce the next generation were those with the highest EBV (i.e., truncation selection). The number of selection candidates (100) and the number of individuals selected (10 males and 10 females) were constant across generations. Thus, each mating generated 10 progeny.
Evaluation Methods
Two methods for obtaining EBV were considered. The methods differed in the additive relationship matrix (A) used in the BLUP evaluation.
Standard BLUP (BLUPs).
Genetic evaluations were based entirely on phenotypic and pedigree information. Estimated breeding values were obtained from BLUPs, whereas the relationship matrix was calculated using only pedigree information (Ap).
Marker BLUP (BLUPm).
The EBV were obtained from BLUP using an A matrix based on all available information (i.e., both pedigree and marker information). This matrix (Apm) was an identical-by-descent (IBD) matrix whose elements, gij, are the expectation of the number of alleles carried by individual j that are IBD with a randomly sampled allele from individual i, conditional on the marker and pedigree information (Sørensen et al., 2002). The IBD matrices were computed at different evenly spaced positions in each chromosome following the approach of Pong-Wong et al. (2001), and were averaged across positions and chromosomes to obtain Apm. Different number of markers were considered to compute the IBD matrices.
The accuracy of evaluation was computed as the correlation between the true and the estimated breeding values. Results from different scenarios were averaged over 300 replicates.
Inbreeding Coefficients
Average inbreeding coefficients were computed: 1) from the pedigree (Fp); and 2) at the QTL (Fq). The inbreeding coefficient Fp was obtained from the diagonal elements of matrix Ap. The inbreeding coefficient Fq at each generation was obtained as the frequency of homozygotes genotypes corrected for the frequency of homozygotes in the base population. The correction (Toro et al., 2002) takes into account the fact that at t = 0, there are alleles identical in state. Thus, the average Fq for individuals born at generation t was computed as follows:
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where q is the number of QTL (i.e., 2,000), n is the number of alleles per QTL (i.e., 2), pij is the initial frequency of allele j for QTL i (i.e., 0.5), and Hoi is the frequency of homozygotes for QTL i.
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Results |
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shows the extra gain obtained by using Apm (relative to the gain by using Ap) in the BLUP evaluation when IBD matrices were computed at different numbers of positions per chromosome (x). As expected, the benefit of using markers increased with x, but the extra gain obtained by increasing x from 10 to 20 was very small, and that obtained by increasing x from 20 to 40 was practically nil. Given these results, comparisons of genetic gains from BLUPm and BLUPs were carried out with Apm matrices when the IBD was computed at 10 positions per chromosome. This was considered a good compromise because gains were very similar to those with higher x, but the computation time was decreased considerably.
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shows the benefits from using marker information in BLUP genetic evaluation for genomes of different sizes. With BLUPs, schemes simulating different numbers of chromosomes produced very similar responses; thus, the average values over BLUPs schemes are presented. To estimate IBD matrices with high accuracy, the number of markers used in BLUPm was very large (i.e., 40 per chromosome). The smaller the genome, the larger the benefit of using markers. The benefit of using marker information was practically nil in the initial generations of selection, but it increased over generations both in percent and in absolute values. After 10 generations, BLUP selection using Apm gave 11, 9, 7, and 5% greater response than BLUPs selection for genomes with c = 5, 10, 20, and 30 chromosomes, respectively.
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. Standard errors ranged from 0.0041 (at t = 0) to 0.0101 (at t = 9). With BLUPs, the accuracy decreased over generations (after t = 1) because of changes in genetic variance (which decreased from 0.20 in t = 0 to around 0.08 in t = 10) due to the Bulmer effect (Bulmer, 1971) and to inbreeding. When using markers, accuracies were kept more or less constant from t = 1 to 5 (with the exception of c = 5, where there was a slight increase from t = 1 to 4) and decreased afterward as markers became less informative and genetic variance was decreased because of inbreeding. In all cases, the accuracy with BLUPm was higher than with BLUPs across all generations. The larger the genome, the closer the accuracy from BLUPm to that from BLUPs.
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. The highest Fq was observed for the smallest genome (i.e., c = 5). At t = 10, Fq was 0.58, 0.55, 0.55, and 0.53 for c = 5, 10, 20, and 30, respectively. In these scenarios, where the number of markers was high (40 per chromosome), the inbreeding coefficients computed at the marker loci were very similar to those computed at the QTL. Standard errors for Fq ranged from 0.0021 (at t = 2) to 0.0053 (at t = 10).
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). In all schemes, the inbreeding computed from the pedigree underestimated the true inbreeding. This underestimation was greater for BLUPm than for BLUPs schemes, and greater for smaller rather than larger genomes. With BLUPs, Fq was approximately 8, 4, 3, and 2% greater than Fp for c = 5, 10, 20 and 30, respectively, at t = 10. Equivalent figures for BLUPm were 35, 17, 9, and 6%.
Effect of Number of Markers on the Benefit of BLUPm
The effect of the number of markers used to compute genetic relationships for a genome of small size (c = 5) is shown in Figure 4. The SE for the average genetic values presented ranged from 0.0061 (at t = 1) to 0.0387 (at t = 10). As expected, the higher the number of markers, the greater the benefit of using Apm rather than Ap, which was particularly clear in later generations of selection. In early generations, differences between schemes were small, and variation across replicates was high. As t increased, the benefit of using markers accumulated and trends became clearer. At t = 2, benefits from BLUPm over BLUPs ranged from 0.2 (m = 1) to 1.7% (m = 20). By t = 5, benefits ranged from 1.6 (m = 1) to 8.4% (m 
20). At the end of the selection period (t = 10), the extra gains from BLUPm were only 2 and 4% with m = 1 and 2, respectively, but increased to approximately 11% with m 10. Very little improvement was observed by increasing the number of markers further than m =10 (i.e., approximately one marker every 10 cM).
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. Standard errors for the average genetic values ranged from 0.0026 (at t = 1) to 0.0207 (at t = 10). Trends were very similar to those observed for c = 5, although gains from BLUPm were substantially less with c = 20 (see also Figure 4). Benefits from BLUPm over BLUPs ranged from 0.0 (m = 10) to 0.5% (m = 40) at t = 2, from 2.3 (m = 2) to 4.0% (m = 40) at t = 5, and from 2.4 (m = 1) to 7.3% (m 10) at t = 10. As with c = 5, there were practically no further extra gains by increasing the number of markers beyond m = 10.
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Discussion |
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TopAbstractIntroductionMethodsResultsDiscussionImplicationsLiterature Cited |
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). Benefits of using marker data came in the form of increased accuracy when computing the numerator relationship matrix used in BLUP evaluations, thereby improving the accuracy of overall effects of genes with small effect (polygenes). This result differs from most studies on marker-assisted selection (MAS) that considered mixed inheritance models and where markers were used to better estimate the effect of specific QTL of large effect (Fernando and Grossman, 1989; Kennedy et al., 1992; Villanueva et al., 2002). The extra gains obtained by using information from markers depended greatly on genome size. The smaller the genome, the larger the benefits from MAS. Extra gains increased over generations as information accumulated, and at t = 10, the response from BLUPm using 40 markers per chromosome was 11, 9, 7, and 5% greater than with BLUPs for genomes with 5, 10, 20, and 30 chromosomes, respectively.
Most species of agricultural interest under artificial breeding programs have genome sizes larger than c = 10, although there are some cultivars with small c (e.g., c = 7 in barley and rye, c = 10 in corn, and c = 12 in tomato and rice). For genome sizes typical of livestock species (i.e., c = 19 in pigs, c = 27 in sheep, and c = 30 in cattle and goats), extra gains from using markers were still detectable.
The extra gains obtained by using marker information were due to an increase in the accuracy of selection, which was clearly higher for small vs. large genomes (Figure 2). Variation around the mean IBD for a particular group of relatives with the same pedigree is higher with small than with large genomes. As a consequence, with small genomes, the differences between Apm and Ap are greater, and the scope for additional progress with molecular data is larger. Hill (1993) predicted the variance of genetic identity for different types of relatives. For instance, for full-sibs (for which the average proportion of the genome shared is 50%), the SD for genome sizes considered here were 9.7, 6.9, 4.9, and 4.0% for c = 5, 10, 20, and 30, respectively. Thus, expected variances are small unless genomes are small. This decrease in variance of the IBD with increased genome sizes consequently leads to decreased benefits from using markers (Goddard, 2001). Consideration of variances for all types of relationships in complex pedigrees as those considered here would increase the extra gains from markers. In fact, the benefit from using marker information increased over generations.
For small genomes (c 
10), the expected benefits from markers were of the same order of magnitude as those expected from including information of relatives in the genetic evaluation (i.e., BLUPs vs. phenotypic or mass selection). Genetic gain from BLUPs after 10 generations of selection was 10% higher than that obtained from mass selection for schemes simulated with the same parameters (i.e., heritability, selection intensities, number of chromosomes, and number of QTL per chromosome) used here to compare BLUPm with BLUPs.
The extra gains from marker BLUP also depended on the number of markers per chromosome (m) used to estimate relationships (i.e., Apm). As expected, increasing the number of markers increased gains; however, our results show that increasing m beyond 10 did not increase gains any further. Thus, maps of markers with intervals of 10 cM would be dense enough to achieve the greatest benefits. In the present study, markers were assumed to be very informative (10 alleles per marker). In cases where the informativeness of markers is less, the marker density would need to be increased to obtain equivalent gains.
The true inbreeding (i.e., inbreeding computed at the QTL or Fq) decreased as the genome length increased. For a given genome size, BLUP incorporating marker information led to small increases in true inbreeding (i.e., inbreeding computed at the QTL or Fq) compared with standard BLUP, although these increases were only detectable for the smallest genomes.
It is of interest to investigate how the inbreeding computed from the pedigree (Fp) estimated the true inbreeding. The inbreeding computed from the pedigree is expected to provide accurate estimates of the true inbreeding but only for neutral, unlinked loci. In BLUPs schemes, Fp provided good estimates of the true inbreeding except for the smallest genomes considered, for which Fp clearly underestimated Fq. This underestimation was much more important with BLUPm schemes for all genome sizes and in particular for c = 5. Our results follow the same trends as those observed by Fernández et al. (2000). They investigated the efficiency of two methods for controlling the rate of inbreeding (i.e., selection based on minimizing the average coancestry of selected individuals and compensatory matings) using the relationship matrix computed from marker (Am) or from pedigree information (i.e., Ap). Both methods for controlling inbreeding only benefited from the use of Am (rather than Ap) when the genome size was small (5 M). For larger genome sizes, the rate of increase in the true inbreeding was successfully controlled by using Ap.
Inbreeding coefficients calculated from the pedigree were higher for BLUPs than for BLUPm. In addition, with BLUPm, Fp followed a clear trend for different genome sizes, and this trend was opposite to that followed by Fq; the smaller the genome, the lower the Fp. Extra within-family information given by using Apm decreases the correlation between EBV of relatives and thereby decreases the probability of selecting relatives (Meuwissen and Van Arendonk, 1992). With large genomes, Apm approaches Ap, BLUPm approaches BLUPs and Fp approaches true inbreeding (Fq).
The extra gains expected from MAS for an infinitesimal genetic model were far from the upper limit represented by direct selection on the QTL. Simulations were run with the same parameters as those used herein, but assumed that genotypes for all QTL affecting the traits were known for all individuals (i.e., there was no need for a genetic evaluation). At t = 10, the gains obtained from selecting directly on the QTL were approximately 85% greater than those from standard BLUP. The extra gains obtained here from MAS also were far from those described in Nejati-Javaremi et al. (1997), who used the actual allelic identity between individuals for loci controlling the trait under selection (Aq). These loci were assumed to be segregating independently. With 100 QTL affecting the trait and heritabilities of 0.1 and 0.3, they found responses from BLUP using Aq approximately 35% greater than responses from standard BLUP using Ap. With more realistic assumptions (i.e., availability of marker rather than QTL genotypes and linked rather than independent QTL), the benefits from markers are smaller, but they are nonetheless detectable, even for large genomes.
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Implications |
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TopAbstractIntroductionMethodsResultsDiscussionImplicationsLiterature Cited |
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Footnotes |
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2 Correspondence: Sustainable Livestock Systems Group, SAC, Bush Estate, Penicuik, Midlothian EH26 0PH, Scotland, U.K. (phone: +44-131-535-3224; fax: +44-131-535 3121; e-mail: beatriz.villanueva{at}sac.ac.uk).
Received for publication January 31, 2005. Accepted for publication April 18, 2005.
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Literature Cited |
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TopAbstractIntroductionMethodsResultsDiscussionImplicationsLiterature Cited |
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