J. Anim. Breed. Genet. ISSN 0931-2668
`
`O R I G I N A L A R T I C L E
`
`Use of haplotypes to estimate Mendelian sampling effects and
`selection limits
`J.B. Cole & P.M. VanRaden
`
`Animal Improvement Programs Laboratory, ARS, USDA, Beltsville, MD, USA
`
`Keywords
`
`Summary
`
`genetic gain; haplotypes; Mendelian sampling;
`
`selection limits.
`
`Correspondence
`
`J.B. Cole, Animal Improvement Programs
`
`Laboratory, ARS, USDA, Room 306, Bldg 005,
`
`BARC-West, 10300 Baltimore Avenue,
`
`Beltsville, MD 20705-2350, USA. Tel: 301-504-
`
`8334; Fax: 301-504-8092; E-mail:
`
`john.cole@ars.usda.gov
`
`Received: 22 September 2010;
`accepted: 13 February 2011
`
`Limits to selection and Mendelian sampling (MS) terms can be calcu-
`lated using haplotypes by summing the individual additive effects on
`each chromosome. Haplotypes were imputed for 43 382 single-nucleo-
`tide polymorphisms (SNP) in 1455 Brown Swiss, 40 351 Holstein and
`4064 Jersey bulls and cows using the Fortran program findhap.f90,
`which combines population and pedigree haplotyping methods. Lower
`and upper bounds of MS variance were calculated for daughter
`pregnancy rate (a measure of fertility), milk yield, lifetime net merit (a
`measure of profitability) and protein yield assuming either no or com-
`plete linkage among SNP on the same chromosome. Calculated selection
`limits were greater than the largest direct genomic values observed in all
`breeds studied. The best chromosomal genotypes generally consisted of
`two copies of the same haplotype even after adjustment for inbreeding.
`Selection of animals rather than chromosomes may result in slower pro-
`gress, but limits may be the same because most chromosomes will
`become homozygous with either strategy. Selection on functions of MS
`could be used to change variances in later generations.
`
`Introduction
`
`Mendelian sampling (MS) variance is generated by
`the process of randomly sampling parental chromo-
`somes during meiotic division in gametogenesis and
`is commonly estimated from the difference between
`an individual’s predicted transmitting ability (PTA)
`and its parent average (PA, the average of the sire
`and dam PTA). Individual PTA does not provide any
`information about
`the MS term for
`individual
`gametes or parents, and the within-family variance
`is not affected by selection (Bulmer 1971). However,
`genotypic information can provide early estimates of
`MS effects by allowing direct inspection of markers
`at the chromosomal level (Dekkers & Dentine 1991).
`Woolliams
`(1999)
`showed that
`sustained
`et al.
`genetic gain under selection depends on MS vari-
`ance, and the increase in reliability of PTA observed
`
`in genomic selection programmes is because of more
`precise estimation of MS effects (Hayes et al. 2009).
`Better estimates of MS also permit increased rates of
`genetic gain with lower increases in inbreeding than
`in traditional breeding programmes (Daetwyler et al.
`2007).
`Substantial benefits are not realized from genomic
`selection until there is a large enough pool of geno-
`typed animals
`to provide accurate estimates of
`marker effects, which are essential for reliable pre-
`diction of MS terms. Marker-assisted selection
`(MAS) programmes have increased short-term selec-
`tion response because the markers explain a portion
`of MS variance (Meuwissen & Van Arendonk 1992;
`Meuwissen & Goddard 1996), but in the long term,
`MAS results in decreased MS because the paternal
`and maternal genotypes become more similar as
`allele frequencies for the QTL near fixation when it
`
`doi:10.1111/j.1439-0388.2011.00922.x
`
`ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 446–455
`
`Exhibit 1041
`Select Sires, et al. v. ABS Global
`
`

`

`J. B. Cole & P. M. VanRaden
`
`Mendelian sampling and selection limits
`
`is assumed that populations are closed and there is
`no mutation.
`The objective of this paper is to describe the MS
`variance present in the US Brown Swiss (BS), Hol-
`stein (HO), and Jersey (JE) populations using dense
`single-nucleotide polymorphism (SNP) genotypes, as
`well as to discuss selection limits based on haplo-
`types present
`in the genotyped population. Four
`traits representing a range of heritabilities and aver-
`age reliabilities are included in the analysis.
`
`Material and methods
`
`Genotypes
`
`Genotypes for 43 382 SNP in 1455 BS, 40 351 HO
`and 4064 JE bulls and cows were obtained using
`the
`Illumina BovineSNP50 BeadChip (Illumina
`Inc., San Diego, CA, USA). Marker solutions from
`the June 2010 US genomic evaluation were used
`to calculate MS variance and selection limits for
`daughter pregnancy rate (DPR; a measure of
`female fertility) (VanRaden et al. 2004), milk yield,
`lifetime net merit
`(NM$; a measure of
`lifetime
`profitability) (Cole et al. 2010) and protein yield.
`Haplotypes were imputed with the Fortran pro-
`gram findhap.f90 (VanRaden et al. 2011), which
`combines population and pedigree haplotyping
`methods. Calculations were performed with SAS
`9.2 (SAS Institute Inc., Cary, NC, USA), and plots
`were produced with R 2.10.1 (R Development
`Core Team, 2010) and ggplot2 0.8.7 (Wickham
`2009) on a workstation running 64-bit Red Hat
`Enterprise Linux 5 (Red Hat
`Inc., Raleigh, NC,
`USA).
`
`Mendelian sampling variances
`
`the mth
`for
`estimated allele substitution effect
`marker, c is the cth chromosome, and nc is the num-
`ber of markers present on the cth chromosome. Mar-
`ker effects were calculated using a Bayes A model as
`described in Cole et al. (2009). Calculations included
`markers from the pseudoautosomal region of the X
`chromosome, which contribute to MS, but not those
`located only on the X chromosome. For the purposes
`of comparison, expected MS was computed as half
`of the additive genetic variance (Va) and inbreeding
`was ignored. It was assumed that there were no
`dominance or epistasis effects.
`Allele substitution effects were estimated using an
`infinitesimal alleles model with a heavy-tailed prior
`(also known as a Bayes A model) in which smaller
`effects are regressed further towards 0 and markers
`with larger effects are regressed less to account for a
`non-normal prior distribution of marker effects
`(VanRaden 2007, 2008). Marker effects were ran-
`domly distributed with a heavy-tailed distribution
`generated by dividing a normal variable by h|s)2|,
`where h determines departure from normality and s
`is the size of the estimated marker effect in standard
`deviations (VanRaden 2008). Marker effects are nor-
`mally distributed with no additional weight in the
`tails when h is 1, and variance in the tails grows
`with increasing values of h; a parameter of 1.12 is
`used in this study (Cole et al. 2009). Variances of
`estimated MS and marker effects are less than true
`effects in the same way that PTA has less variance
`than true transmitting abilities.
`
`Selection limits
`
`Marker values were summed for each genotyped
`animal to obtain chromosomal estimated breeding
`values (CEBV) for lifetime net merit, and the CEBV
`were summed to obtain the direct genomic values
`(DGV). Genomic estimated breeding values (GEBV),
`which include base adjustments, polygenic effects
`and information from non-genotyped relatives, were
`taken from the June 2010 genetic evaluation run.
`Empirical selection limits were calculated by combin-
`ing the haplotypes with the best unadjusted or
`adjusted CEBV for DPR, milk, NM$ and protein
`yield. These estimated limits represent progress that
`could be achieved with the current data. In the
`future, with more data and larger reference popula-
`tions, true limits would be larger with more accurate
`SNP and haplotype estimates.
`Lower bounds of selection limits (SLC) were pre-
`dicted by selecting the 30 best haplotypes for each
`trait, and upper bounds (SLU) were calculated by
`
`Estimated MS terms were computed for each trait
`assuming that loci on the same chromosome were in
`perfect linkage (MSC), or that all loci in the genome
`were unlinked (MSU), as:
`
`
`
`X3
`
`0
`
`c¼1
`
`m¼1
`
`!
`
`2
`
`Xn
`
`c
`
`dmam
`
`m¼1
`
`smam
`
`Xn
`
`c
`
`MSC ¼
`
`and
`
`X
`
`43 382
`
`m¼1
`
`MSU ¼
`
`
`
`smam dmamð
`
`Þ2
`
`respectively, where m denotes a marker, s and d are
`the haplotypes for the mth marker inherited from
`the animal’s sire and dam, respectively, am is the
`
`ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 446–455
`
`447
`
`Exhibit 1041
`Select Sires, et al. v. ABS Global
`
`

`

`Mendelian sampling and selection limits
`
`J. B. Cole & P. M. VanRaden
`
`the population. New genotypes are continuously
`being collected, and the accuracy of the SNP effects
`will increase as the reference population used to cal-
`culate those effects increases in size. MSC and MSU
`are expected to increase asymptotically towards the
`true MS variance as the correlation between the true
`and predicted SNP effect approaches 1.
`The SNP used for genotyping were selected to
`have high average minor allele frequencies, and
`most predicted allele substitution effects were near
`0. If all loci are unlinked, then selection for a desir-
`able allele has no effect on the frequency of other
`alleles,
`the frequency of other alleles does not
`change in response to selection, and the population
`average, which depends on allele frequency, remains
`close to 0. When loci are linked, however, selection
`for markers with positive effects generates LD blocks
`in which the sum of effects is >0. Therefore, we
`expect that the sums of squared differences between
`chromosome haplotypes will be larger than the sum
`of squared differences between individual alleles,
`which was confirmed for all breeds and traits
`(Table 1). The range was largest for HO for all traits,
`reflecting the greater number of observed haplotypes
`in that breed than BS or JE. Results were generally
`similar for BS and JE, although in some cases, there
`was slightly more variation in JE than in BS. Ratios
`of MSC to MSU were generally smaller for HO and
`larger for BS and JE, ranging from 4.0 for JE milk to
`17.4 for BS DPR. These results may reflect more
`
`Table 1 Predicted upper and lower bounds and expectations of Men-
`delian sampling variance for daughter pregnancy rate (DPR), milk yield,
`lifetime net merit (NM$) and protein yield for US Brown Swiss (BS),
`Holstein (HO) and Jersey (JE) cattle
`
`Mendelian sampling variance
`
`Trait
`
`Breed
`
`Lower bound
`
`Expecteda,b Upper bound
`
`DPR (%)
`
`Milk yield (kg)
`
`NM$ (USD)
`
`BS
`HO
`JE
`BS
`HO
`JE
`BS
`HO
`JE
`Protein yield (kg) BS
`HO
`JE
`
`0.09
`0.57
`0.09
`7264
`46 879
`30 855
`2539
`16 601
`3978
`6.40
`35.95
`10.33
`
`1.45
`1.45
`0.98
`44 238
`53 736
`42 238
`19 602
`19 602
`19 602
`37.29
`37.29
`33.47
`
`1.57
`4.02
`1.27
`104 255
`219 939
`123 813
`40 458
`87 449
`44 552
`91.11
`145.25
`92.35
`
`aExpected Mendelian sampling variances were calculated as ½Va
`assuming no inbreeding.
`bThe same additive genetic variance is used for all breeds for NM$.
`
`!
`
`Xn
`
`c
`
`
`
`X3
`
`0
`
`taking the allele at each marker locus with the most
`desirable value, as:
`
`SLC ¼
`
`max
`H
`
`c¼1
`
`m¼1
`
`lmam
`
`and
`
`X
`
`43 382
`
`m¼1
`
`SLU ¼
`
`ð
`lmam
`
`Þ;
`
`max
`L
`
`indicates a chromosome, m
`respectively, where c
`denotes a marker, am is the estimated allele substitu-
`tion effect for the mth marker, H represents the set
`of all unique haplotypes in the genotyped popula-
`tion, nc is the number of markers present on the cth
`chromosome, hm represents the mth marker of an
`individual haplotype, L is the set of all marker loci
`in the genotyped population, and lm represents the
`genotype of the mth marker locus.
`The CEBV for NM$ also were adjusted for inbreed-
`ing by subtracting 6% of an additive genetic
`standard deviation ($11.88) per 1% increase in
`homozygosity above the breed average (Smith et al.
`1998). Animals with above-average heterozygosity
`were credited in the same manner. Adjusted and
`unadjusted values were compared to determine the
`impact of such adjustments on GEBV. Homozygosity
`averaged 0.70  0.01 in BS, 0.67  0.01 in HO and
`0.72  0.02 in JE and was calculated as the average
`marker homozygosity of each pair of chromosomes
`in the genotyped animals.
`
`Results
`
`Mendelian sampling
`
`Lower- and upper-bound estimates of MS are pro-
`vided by MSU and MSC, respectively. In theory, the
`true MS variance should be calculated using individ-
`ual linkage disequilibrium (LD) blocks or map dis-
`tances rather than assuming that all markers on the
`same chromosome are a single linkage group, and
`MSC may be overestimating the true variance. In a
`completely inbred population, all genotypes would
`be homozygous, and MSU and MSC both would be
`0. In a heterozygous population in which all marker
`frequencies are 0.5, MSU £ MSC, and both are pro-
`portional to the true MS variance.
`The ai used to compute MSC and MSU are esti-
`mates of marker effects rather than true marker
`effects and are therefore regressed towards the popu-
`lation mean. As a result, the calculated bounds on
`MS variance underestimate the true MS variance in
`
`448
`
`ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 446–455
`
`Exhibit 1041
`Select Sires, et al. v. ABS Global
`
`

`

`J. B. Cole & P. M. VanRaden
`
`Mendelian sampling and selection limits
`
`precise estimation of MS variances for HO than BS
`or JE.
`Expected MS variance was calculated for each
`breed and trait (assuming no inbreeding) as ½Va,
`and all estimates were bounded by MSU and MSC, as
`expected. This provides confirmation that MSU and
`MSC provide plausible estimates of MS variance. The
`expected HO variances were much closer to the
`lower bounds than those of BS and JE, which
`reflects the much larger number of HO haplotypes
`that have been sampled. As a greater number and
`more diverse groups of BS and JE animals are geno-
`typed, the expected MS variances should increase.
`While the inbreeding of parents was not accounted
`for, relationships among mates would have needed
`to be very large to result in substantial reductions in
`estimated variances, and those kinds of close matings
`generally are avoided.
`Bulmer (1971) showed that within-family vari-
`ance should decrease as homozygosity increases, and
`it
`is well known that
`inbreeding levels have
`increased in dairy cattle over time (Young & Seykora
`1996). Figures 1, 2 and 3 show the change in MSC
`of NM$ for genotyped BS, HO and JE cattle, respec-
`tively, born between 1990 and 2010 and represent-
`ing approximately four generations of
`selection.
`Slopes were slightly negative for all breeds, and a
`decrease in MS variance was expected in all breeds
`based on the increased levels of pedigree inbreeding
`over that time (Figure 4), but only the HO slope dif-
`fered from 0 (p < 0.05). The HO trend may reflect
`high statistical power because of a large sample size
`rather than a biologically meaningful decrease in
`
`variance. These results suggest that while inbreeding
`in the population has increased over time,
`inbred
`matings have not been used to produce the geneti-
`cally elite animals with genotypes in this study, or
`levels of inbreeding have not increased enough to
`result in a substantial
`loss of haplotypes. Changes
`over time may have been different for grade cows.
`Correlation among genomic (FG) and pedigree (FP)
`inbreeding, MSC and MSU were calculated for each
`trait to confirm that MS decreases with inbreeding,
`which should result in a strong, negative correlation
`(Table 2). For DPR, correlations of FG with MSU ran-
`ged from )0.73 to )0.83, and FP with MSU ranged
`from )0.38 to )0.53. Pedigree inbreeding was
`expected to have lower correlations with MS than
`FG because the incidence of pedigree errors has been
`shown to be approximately 10% in US Holsteins
`(Banos et al. 2001). However, correlations of FG and
`FP with MSC were consistently near 0 across breeds
`and traits. This is probably because MSC was calcu-
`lated assuming that markers on the same chromo-
`some were in perfect linkage, and the impact of a
`small number of loci becoming homozygous is small
`when blocks
`rather
`than individual alleles are
`selected. The observed range of genomic inbreeding
`was small, and there were no extremely inbred ani-
`mals, in which you would expect to see whole LD
`blocks fixed, which also may contribute to the low
`correlations.
`The correlations among MSU for milk with
`inbreeding were near 0 for HO and JE, which was
`unexpected, as was the correlations of MSU with FG
`and FP for HO NM$. Holstein and JE differ from BS
`
`Figure 1 Changes in Mendelian sampling variance (upper bound) for lifetime net merit (NM$) in US Brown Swiss cattle born between 1990 and
`2010.
`
`ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 446–455
`
`449
`
`Exhibit 1041
`Select Sires, et al. v. ABS Global
`
`

`

`Mendelian sampling and selection limits
`
`J. B. Cole & P. M. VanRaden
`
`Figure 2 Changes in Mendelian sampling variance (upper bound) for lifetime net merit (NM$) in US Holstein cattle born between 1990 and 2010.
`
`Figure 3 Changes in Mendelian sampling variance (upper bound) for lifetime net merit (NM$) in US Jersey cattle born between 1990 and 2010.
`
`in that the DGAT1 locus is not segregating in the lat-
`ter population. Similarly, in addition to DGAT1, there
`is a large QTL for NM$ segregating on Bos taurus
`autosome 18 in HO (Cole et al. 2009). Individual
`QTL can have a large effect on the sampling variance
`but no effect on inbreeding because fixation at single
`locus has only a small effect on homozygosity. Note
`that in JE, in which there are no QTL for NM$ seg-
`regating, the correlation of MSU with inbreeding is
`similar to that of BS. Results for MSU confirm that as
`inbreeding increases, sampling variance decreases.
`Correlations of GEBV for NM$ with MSU and MSC
`were calculated to determine whether animals with
`high GEBV also had greater MS variances. The
`GEBV were negatively correlated with MSU and MSC
`
`in all breeds, ranging from )0.04 to )0.14. This sug-
`gests that efforts to reduce the rate of the increase in
`inbreeding have been successful, although the ani-
`mals with the most desirable GEBV still are more
`inbred than average animals.
`
`Selection limits
`
`Selection limits for the current population were esti-
`mated assuming that either whole chromosome hapl-
`otypes or individual alleles can be selected and
`combined at will
`to produce whole genomes, as
`described in Cole & VanRaden (2010). Lower and
`upper bounds for each trait, as well as the largest DGV
`observed in the genotyped population, are presented
`
`450
`
`ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 446–455
`
`Exhibit 1041
`Select Sires, et al. v. ABS Global
`
`

`

`J. B. Cole & P. M. VanRaden
`
`Mendelian sampling and selection limits
`
`Figure 4 Changes in average inbreeding (%) between 1990 and 2010 for US Brown Swiss (solid line), Holstein (short-dashed line) and Jersey (long-
`dashed line) cattle.
`
`Table 2 Correlations of
`lower and upper
`bounds of Mendelian sampling variance with
`genomic and pedigree inbreeding (F)
`for
`daughter pregnancy rate (DPR), milk yield,
`lifetime net merit (NM$) and protein yield
`for US Brown Swiss (BS), Holstein (HO) and
`Jersey (JE) cattle
`
`Trait
`
`DPR (%)
`
`Milk yield (kg)
`
`NM$ (USD)
`
`Protein yield (kg)
`
`Lower bound
`
`Upper bound
`
`Breed
`
`Genomic F
`
`Pedigree F
`
`Genomic F
`
`Pedigree F
`
`BS
`HO
`JE
`BS
`HO
`JE
`BS
`HO
`JE
`BS
`HO
`JE
`
`)0.73
`)0.77
`)0.83
`)0.86
`)0.12
`)0.01a
`)0.85
`)0.21
`)0.86
`)0.86
`)0.84
`)0.82
`
`)0.38
`)0.40
`)0.53
`)0.55
`)0.05
`0.03a
`)0.49
`)0.12
`)0.53
`)0.54
`)0.47
`)0.54
`
`)0.02a
`)0.11
`)0.01a
`)0.05
`)0.10
`)0.04
`0.03a
`)0.11
`)0.11
`)0.06
`)0.15
`)0.06
`
`0.09
`)0.03
`0.06
`0.03a
`)0.03
`0.04
`0.13
`)0.03
`)0.02a
`0.00a
`)0.08
`0.01a
`
`aNot different from 0 (p > 0.05).
`
`in Table 3. The lower bounds represent selection
`limits attainable by selection among haplotypes
`already in the population, while the upper bounds
`are limits attainable under the assumption that com-
`plete haplotypes can be constructed from individual
`alleles in the population. In all cases, SLC and SLU
`were largest for HO, reflecting the larger number of
`HO genotypes represented in the analysis. Limits
`were generally similar for BS and JE across traits.
`
`Lifetime net merit
`Lower selection limits for NM$ with no adjustment for
`inbreeding were $3857 (BS), $7515 (HO) and $4678
`(JE). Adjusted values were slightly smaller and were
`$3817 (BS), $7494 (HO) and $4606 (JE). Upper
`
`bounds had values of $9140 (BS), $23 588 (HO) and
`$11517 (JE) and were not adjusted for inbreeding
`because they were calculated from individual
`loci
`rather than complete haplotypes. The largest DGV
`among all genotyped animals in each breed were
`$1102 (BS), $2528 (HO) and $1556 (JE). The top
`active bulls (AI and foreign bulls with semen distrib-
`uted in the US that are in or above the 80th percentile,
`based on NM$) in each breed following the August
`2010 genetic evaluation had GEBV for NM$ of +$1094
`(BS: 054BS00374), +$1588 (HO: 001HO08784) and
`+$1292 (JE: 236JE00146). Because DGV and GEBV
`include different
`information, and no reliability
`restriction was imposed, they are not directly compa-
`rable, but all DGV and GEBV were well below SLC.
`
`ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 446–455
`
`451
`
`Exhibit 1041
`Select Sires, et al. v. ABS Global
`
`

`

`Mendelian sampling and selection limits
`
`J. B. Cole & P. M. VanRaden
`
`Table 3 Predicted upper and lower bounds of selection limits and
`largest observed direct genomic values (DGV) for daughter pregnancy
`rate (DPR), milk yield, lifetime net merit (NM$) and protein yield for US
`Brown Swiss (BS), Holstein (HO) and Jersey (JE) cattle
`
`Trait
`
`DPR (%)
`
`Milk yield (kg)
`
`NM$ (USD)
`
`Protein yield (kg)
`
`Breed
`
`BS
`HO
`JE
`BS
`HO
`JE
`BS
`HO
`JE
`BS
`HO
`JE
`
`Lower
`bound
`
`20
`40
`19
`6461
`11 310
`7333
`3857
`7515
`4678
`180
`312
`218
`
`Upper
`bound
`
`53
`139
`53
`15 465
`35 419
`18 295
`9140
`23 588
`11 517
`470
`1138
`568
`
`Largest
`DGVa
`
`8
`8
`5
`2065
`3634
`2554
`1102
`2528
`1556
`61
`114
`79
`
`aDirect genomic values were calculated by summing the marker
`effects for each genotyped animal.
`
`If two copies of each of the 30 best haplotypes in
`the US Holstein population were combined in a sin-
`gle animal (SLC for NM$), it would have a GEBV for
`NM$ of +$7515 (Figure 5), approximately five times
`larger than that of the current best Holstein bull in
`the US, whose GEBV for NM$ are +1588. Cole &
`VanRaden (2010) presented a similar result based on
`CEBV that were averages of the actual parental hapl-
`otypes. When actual haplotypes are used rather than
`averages of haplotypes, there is an increase in SLC of
`approximately 20%.
`Correlations among the unadjusted and adjusted
`DGV ranged from 0.997 to 0.999 in BS and JE, and
`
`all were >0.999 in HO. The best genotype after
`adjusting for inbreeding consisted of two copies of
`the same haplotype for 26 chromosomes in BS and
`HO and 22 in JE, although the differences between
`the first- and second-ranked haplotypes were usually
`very small (<$10). Top unadjusted haplotype values
`ranged from $82 for BTA 18 to $192 for BTA 2 in
`BS, from $71 for BTA 24 to $309 for BTA 5 in JE
`and from $143 for BTA 26 to $375 for BTA 14 in
`HO. These values may seem large, but each of the
`top haplotypes was from a different animal
`in all
`three breeds. Differences between the best and poor-
`est unadjusted haplotypes of a chromosome ranged
`from $136 for BTA 26 to $338 for BTA 1 in BS, from
`$147 for BTA 24 to $475 for BTA 5 in JE and from
`$269 for BTA 26 to $713 for BTA 14 in HO. The dif-
`ferences are larger for HO than BS and JE because
`many more haplotypes have been measured in that
`breed, and consequently, more haplotypes from each
`tail of the distribution have been identified. Results
`were similar for adjusted haplotypes, but the values
`were slightly smaller.
`
`Daughter pregnancy rate, milk yield and protein yield
`While individual values varied across traits, results
`for DPR, milk and protein yield were similar to those
`for NM$ (Table 3). Selection limits were estimated to
`be lowest for BS, intermediate for JE and largest for
`HO, again reflecting differences in the number of
`genotyped animals in each breed. Direct genomic
`values were similar for BS and JE and larger for HO.
`The DGV and GEBV for all traits were well below
`SLC, as was the case with NM$.
`
`Figure 5 Chromosomal estimated breeding values (EBV) of lifetime net merit (NM$) for a hypothetical animal whose genotype consists of two
`copies of each of the best haplotypes in the current US Holstein population. The sum of the individual chromosome effects is $7515.
`
`452
`
`ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 446–455
`
`Exhibit 1041
`Select Sires, et al. v. ABS Global
`
`

`

`J. B. Cole & P. M. VanRaden
`
`Mendelian sampling and selection limits
`
`The top active bulls in each breed for DPR (%)
`had GEBV of +3.6 (BS: 001BS00553), +7.2 (HO:
`001HO06360) and +4.6 (JE: 200JE00990), which are
`much smaller than the predicted lower selection lim-
`its. The upper limits are probably substantial overes-
`timates of GEBV attainable in practice, particularly
`for a lowly heritable trait, but do show that DPR
`could be improved considerably if its economic value
`increases to the point that more weight in selection
`indices is warranted.
`Selection for increased milk yield over the past
`40 years was very successful (Hansen 2000), although
`milk volume has not received direct weight in the
`NM$ index since 2003. The top active bulls in each
`breed had GEBV of +1451 (BS: 054BS00456), +2306
`(HO: 014HO03831) and +1718 (JE: 001JE00604). In
`all cases, the GEBV were much smaller than the
`upper and lower bounds on the selection limit for
`each breed (Table 3). Despite the strong emphasis
`placed on milk yield in the past, it does not appear
`that the population is approaching a selection limit,
`and given the increasing emphasis on non-yield traits
`in NM$ and breed association indices, it is possible
`that progress towards the limits will slow dramati-
`cally.
`Protein yield now receives 16% of the emphasis in
`the 2010 revision of NM$ (Cole et al. 2010) and also
`is an important selection objective in other countries
`(Miglior et al. 2005). The top active bulls in each
`breed had GEBV (kg) of +44 (BS: 054BS00456), +64
`(HO: 014HO04929) and +40 (JE: 029JE03487). As
`was the case for DPR, milk yield and NM$, the GEBV
`for the top animals in each breed are not near the
`selection limits. The increased weight placed on pro-
`tein in NM$ will result in faster rates of gain, but
`many generations of more intensive selection will
`be needed before the most extreme animals in the
`population near the selection limit.
`
`Discussion
`
`The objective of this study was to use genotypes
`from US BS, HO and JE cattle to estimate MS vari-
`ances and predict selection limits for fertility, yield
`and economic merit. Lower and upper bounds for
`MS variance were calculated assuming either com-
`plete or no linkage among loci on the same chromo-
`some. It is possible that those estimates are biased
`because of the shrinkage of the allele effect estimates
`in the genomic prediction model, and Goddard et al.
`(2009) provide an excellent discussion of sources of
`bias in genomic evaluation models and the magni-
`tude of their importance. However, in all cases, the
`
`expected MS variance calculated from population
`data falls between those upper and lower bounds, so
`the magnitude of any bias in the estimators likely is
`small and should not substantially affect our results.
`Selection limits were calculated using the allele
`substitution effects and marker frequencies observed
`in the current BS, HO and JE populations in a man-
`ner that implies that those limits could be reached in
`one round of selection. That is useful to obtain initial
`estimates of
`limits to selection, but
`in reality,
`it
`would take many generations of selection for the
`same objective to reach those limits, and over such
`long periods of time epistasis (and even mutation)
`could prove to be important. The calculations also
`assume that the breeds are closed populations, but
`over very long periods of time, there almost certainly
`will be admixture with other groups. Current results
`are limited to four traits in three populations, and
`there are opportunities for future studies to provide
`limits for other traits of interest, as well as develop
`more sophisticated methodology.
`Pong-Wong & Woolliams (1998) found that opti-
`mal index weights when selecting on MS variance
`depend on allele frequencies of the QTL and noted
`that there is a conflict between optimal short- and
`long-term selection responses. Goddard et al. (2009)
`and Hayes et al. (2009) have discussed weighting
`schemes for preserving low-frequency alleles in pop-
`ulations using genome-assisted selection programmes
`as a way of balancing selection response over time.
`Supporting this idea are the recent results of Jannink
`(2010), who showed that a simple weighting scheme
`can increase long-term selection gains with no appre-
`ciable loss of short-term gains, although accuracies
`are lower than in unweighted schemes. Cole & Van-
`Raden (2010) recently suggested possible uses of
`marker data for mate selection, but noted that haplo-
`types were needed to make many schemes useful.
`Now that haplotypes routinely are available for
`genotyped animals, repeated matings among parents
`of interest can be simulated and posterior distribu-
`tions of resulting additive genetic values and MS
`variances computed. There are 229 possible combina-
`tions of autosomes when haplotypes are sampled at
`random during gametogenesis (many more when
`recombination is considered) and haplotypes segre-
`gate independently, so there is no guaranteed way
`to produce animals with a specified set of haplotypes
`short of crossing completely inbred lines (if mutation
`is ignored). Matings can then be planned using vari-
`ous strategies, such as a factorial design in which
`potential sires and dams are cross-classified and sim-
`ulated matings performed to identify the matings
`
`ª 2011 Blackwell Verlag GmbH • J. Anim. Breed. Genet. 128 (2011) 446–455
`
`453
`
`Exhibit 1041
`Select Sires, et al. v. ABS Global
`
`

`

`Mendelian sampling and selection limits
`
`J. B. Cole & P. M. VanRaden
`
`most likely to produce the desired progeny geno-
`types. Offspring of matings with high expected addi-
`tive genetic merit and low MS variance may be
`appealing to producers because differences between
`the expected and realized performance may be
`reduced.
`If embryos could be genotyped rapidly,
`cheaply and without adverse effects on viability,
`then such screening could increase the rate at which
`the MS variance is decreased.
`Conversely, artificial
`insemination organizations
`may prefer matings that produce flushes of embryos
`with high expected additive genetic merit and high
`MS variance to maximize the probability of identify-
`ing individuals with extreme (high) genetic merit in
`the future. This represents a blending of traditional
`selection schemes that emphasize means gains at the
`expense of heterozygosity with optimal contribution
`systems (Sa´ nchez et al. 2003) that constrain inbreed-
`ing by selection on MS with some loss of selection
`response. Such a scheme is easy to implement,
`should result in reduced rates of inbreeding with little
`or no loss in the rate of response to selection and will
`provide balance between short- and long-term gains.
`Daughter pregnancy rate, milk yield and protein
`yield were investigated to determine whether there
`were differences in selection limits among traits of
`varying heritabilities and which had been subjected
`to differing amounts of selection pressure. Milk yield
`receives no direct weight in NM$, but was an impor-
`tant selection criterion in the past, while fertility and
`protein yield account for 37% of the relative empha-
`sis in NM$. Most producers using artificial insemina-
`tion in their herds are using indices rather than
`single-trait selection to choose bulls, so these results
`are hypothetical rather than representative of the
`real world. Even if long-term single-trait selection
`were common, there are antagonistic relationships
`among loci affecting many traits that will prevent
`GEBV from reaching the calculated selection limits.
`(2009) compared
`For example, Sonstegard et al.
`selected and unselected lines of Holstein cattle and
`found that several genomic regions had favourable
`effects on milk yield and unfavourable effects on
`DPR, suggesting an antagonistic mechanism underly-
`ing milk yield and fertility.
`In the United States, estimated breeding values
`(EBV) are adjusted for inbreeding using a method
`very similar to that described above for adjusting for
`homozygosity. The animal model
`removes past
`inbreeding from EBV by regression and then adds
`back expected future inbreeding based on the cur-
`rent population (VanRaden 2005). In this paper, we
`took EBV that contain expected future inbreeding
`
`and made an additional adjustment for inbreeding
`even farther in the future, when the chromosomes
`are projected to become even more homozygous.
`Adjustments
`for homozygosity were
`calculated
`assuming that the effect of inbreeding on lifetime
`performance described by Smith et al. (1998) was
`linear through the values observed in this study,
`which were much higher
`than typical pedigree
`inbreeding estimates. Such an assumption would
`probably not hold in the case of extremely inbred
`animals with