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ANIMAL GENETICS |
* Department of Primary Industries Victoria, Attwood, Victoria 3049, Australia; and
Land and Food Resources, University of Melbourne, Parkville, Victoria 3010, Australia
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Abstract |
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 Top Abstract INTRODUCTIONMETHODSRESULTS AND DISCUSSIONLITERATURE CITED |
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Key Words: breeding values • marker-derived relationship matrix
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INTRODUCTION |
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TopAbstractINTRODUCTIONMETHODSRESULTS AND DISCUSSIONLITERATURE CITED |
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). If pedigree information has been collected over multiple generations, the additive relationship matrix can be constructed from this information. However, in many livestock populations, this information may be unavailable, incomplete, or contain errors. In beef or sheep breeding schemes, accurate pedigree information may be difficult to collect due to the practice of multiple sire matings (more than one sire per paddock). Error rates in pedigrees, even where they are collected, can be considerable. For example, Visscher et al. (2002) estimated the error rate in the UK dairy herd to be approximately 10%. Even minimal error rates in pedigrees can significantly reduce the accuracy of breeding values, and, therefore, the rate of genetic gain (Sanders et al., 2006).
An alternative to constructing the additive relationship matrix from pedigrees is to use marker information to infer relationships. Attempting to do this from a limited number of markers can result in bias and inaccurate estimates of genetic parameters (Wilson et al., 2003). However, if the markers are sufficiently dense, such an approach could potentially be more accurate than using pedigree information. The marker information should capture past relationships not contained in the pedigree and should not be subject to pedigree errors. In several livestock species including cattle, chicken, and pig, tens of thousands of SNP markers are now available.
The aim of this paper was to demonstrate that additive relationship matrices can be constructed from dense SNP data, and these matrices can be used to accurately predict breeding values and estimate additive variances. A data set of 9,323 SNP genotyped in an Angus cattle population, as well as simulated data, was used.
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METHODS |
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TopAbstractINTRODUCTIONMETHODSRESULTS AND DISCUSSIONLITERATURE CITED |
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). Simulated Data Set
The simulation approach is fully described in Hayes and Goddard (2003). Briefly, a diploid population of n = Ne = 1,000 was simulated for 1,000 generations. Each individual in the population contained 29 pairs of chromosomes, and was either male or female (probability 0.5). Each chromosome was 100 cM long, and had 301 marker loci and 300 QTL loci. To create an offspring, a pair of parents of different sex was randomly chosen from the population. For each parent in a mating pair, a gamete was formed from its chromosome pairs by sampling the number of crossovers for each chromosome pair from a Poisson distribution, with mean of 1. Crossover points were randomly positioned along chromosome pairs. The haploid gametes were mutated at a rate of 1.7 x 10–4 per locus per gamete per generation at the markers and 6 x 10–6 at the QTL. If a locus was mutated, a new allele was added. If the locus was a QTL, the effect of the new QTL allele on the quantitative trait following mutation was sampled from a gamma distribution, scale parameter 5.4 and shape parameter 0.42, and with an equal probability of favorable or unfavorable effect, as described by Hayes and Goddard (2001). The marker mutation rate was chosen to give an average marker heterozygosity at mutation-drift balance of
The QTL mutation rate was chosen to give approximately 200 segregating QTL across the genome, with allele frequencies following the distribution f(p) = K/p(1 – p), where K is a constant and p is the frequency of one allele, where 1/2Ne < p < (1 – 1/2Ne). The observed values of Hmarkers, number of QTL, and distribution of QTL allele frequencies closely matched their expectations.
The genetic value of individual i was
where pi,j is the effect of the paternal allele inherited by progeny i at QTL j, and qi,j is the effect of the maternal allele inherited by progeny i at QTL j. No dominance effect was simulated. Allele frequencies at the QTL were the result of mutation-selection-drift balance, with an average heterozygosity of
After generation 1,000, 50 males and 200 females were selected for 5 generations on phenotype, and 1,000 offspring were produced each generation. In generation 1,005 of the simulation, phenotypes of individuals were generated by adding a random residual to their genetic value. These phenotypes were used in the prediction of breeding values and estimation of heritability. The genetic variance among individuals was determined in generation 1,000. Then a residual was sampled for individuals in generation 1,005 from N(0,
), where
). Either pedigree or markers were used to build the average additive relationship matrix. The additive relationship was constructed from the markers among individuals in generation 1,005 as follows. For a given single locus, a similarity index Sxy between 2 individuals x and y is calculated, where Sxy = 1 when genotype x = kk (i.e., both alleles at locus l are identical) and genotype y = kk. Sxy = 0.5 when x = kk and y = kl, or vice versa, or when x = kl and y = kl, Sxy = 0.25 when x = kl and y = km, and Sxy = 0 when the 2 individuals have no alleles in common at the locus (Eding and Meuwissen, 2001). The similarity index was averaged over loci. Each element of the matrix was transformed as S xy = (S xy – min) /(1 –min) , where min is the minimum relationship in the matrix. Ten replicate populations were simulated. Angus Data Set
Three hundred seventy-nine Angus animals were selected from a research project based at Trangie Agricultural Research Centre in New South Wales, Australia. All animals were of Angus breed with sire and dam pedigree records, and animals born from 1993 to 2000 had been selected for high or low postweaning residual feed intake, a measure of feed efficiency. The original project design has been reported by Arthur et al. (2001). Approximately equal numbers of the extreme highest and lowest residual feed intake animals were selected for SNP genotyping. A set of 9,323 SNP randomly distributed across the genome was genotyped in the Angus animals. Genotyping was performed by Parallele or Affymetrix (San Diego, CA). These SNP were largely discovered as a result of the bovine genome sequencing project (http://www.ncbi.nlm.nih.gov/projects/genome/guide/cow/); other SNP were discovered as the result of assembly of expressed sequence tags (Hawken et al., 2004).
An additive model was fitted to the trait fat thickness at the P8 site (mm):
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where fatp8ij is the record of animal j in the ith contemporary group [herd| |sex| |test group| |management group (Arthur et al., 2001)], µ is the mean, aj is a polygenic breeding value for animal j, and aj ~ N(0,Ar
A2), with Ar a matrix of additive relationships among the animals from either pedigree or markers, and 
A2 is the additive genetic variance.
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RESULTS AND DISCUSSION |
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TopAbstractINTRODUCTIONMETHODSRESULTS AND DISCUSSIONLITERATURE CITED |
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). Accuracy of the heritability estimates from pedigree declined as fewer generations of pedigree were used. One partial explanation for the results may be that the average relationship matrix derived from pedigree cannot capture Mendelian sampling effects. That is, the relationship coefficient between 2 full sib individuals will always be 0.5 when estimated from pedigree. However, due to sampling during meiosis, 2 full sib individuals may actually share more or less than 50% of their chromosomes. The marker-derived relationship matrix will capture these Mendelian sampling effects (Visscher et al., 2006).
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The relationship coefficient estimated from markers was plotted against the relationship coefficient estimated from pedigree for the Angus data set (Figure 1). The correlation between marker and pedigree additive average relationship coefficients was high, 0.69. One way to assess the accuracy of our marker-estimated relationships is to compare the variability of relationship for the full sibs in the Angus data set with the variability expected due to Mendelian sampling. If the variability of marker-estimated relationship for full sibs is within the expected value, we can be confident the marker estimated relationships are accurate. For a genome of length 30 Morgan, the expected standard deviation of genome-wide IBD sharing between full sibs is approximately 0.04 (Visscher et al., 2006). The standard deviation of relationship of full sibs estimated by the markers was 0.02, well within the range expected by Mendelian sampling, although the number of full sibs in both data sets was limited.
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In conclusion, there are several situations in which marker-derived relationship matrices will be valuable. When there is limited or no pedigree recorded in a population, marker genotypes may be the only source of information available to build relationship matrices. For example, in livestock, there are many traits that can only be recorded in animals that are not candidates for selection, such as meat quality. If there is no recorded pedigree linking selection candidates and commercial animals on which the trait is recorded, marker-derived relationship matrices could be used in estimation of breeding values for selection candidates. Another example is livestock populations where multiple sires are used in the same paddock of dams, such that recording of pedigree is impossible. In this situation marker-derived relationship matrices could be used in the prediction of breeding values for progeny resulting from multiple sire matings. Another valuable application of marker-derived relationships will be to avoid spurious associations in genome-wide association or QTL mapping experiments where relationships between animals are poorly identified.
1 Corresponding author: ben.hayes{at}dpi.vic.gov.au
Received for publication November 15, 2007. Accepted for publication April 3, 2008.
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LITERATURE CITED |
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TopAbstractINTRODUCTIONMETHODSRESULTS AND DISCUSSIONLITERATURE CITED |
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This article has been cited by other articles:
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  B. J. Hayes, P. J. Bowman, A. J. Chamberlain, and M. E. Goddard Invited review: Genomic selection in dairy cattle: Progress and challenges J Dairy Sci, February 1, 2009; 92(2): 433 - 443. [Abstract] [Full Text] [PDF]
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