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Detecting effective starting point of genomic selection by divergent trends from best linear unbiased prediction and single-step genomic best linear unbiased prediction in pigs, beef cattle, and broilers

Abstract Genomic selection has been adopted nationally and internationally in different livestock and plant species. However, understanding whether genomic selection has been effective or not is an essential question for both industry and academia. Once genomic evaluation started being used, estimation of breeding values with pedigree best linear unbiased prediction (BLUP) became biased because this method does not consider selection using genomic information. Hence, the effective starting point of genomic selection can be detected in two possible ways including the divergence of genetic trends and Realized Mendelian sampling (RMS) trends obtained with BLUP and single-step genomic BLUP (ssGBLUP). This study aimed to find the start date of genomic selection for a set of economically important traits in three livestock species by comparing trends obtained using BLUP and ssGBLUP. Three datasets were used for this purpose: 1) a pig dataset with 117k genotypes and 1.3M animals in pedigree, 2) an Angus cattle dataset consisted of ~842k genotypes and 11.5M animals in pedigree, and 3) a purebred broiler chicken dataset included ~154k genotypes and 1.3M birds in pedigree were used. The genetic trends for pigs diverged for the genotyped animals born in 2014 for average daily gain (ADG) and backfat (BF). In beef cattle, the trends started diverging in 2009 for weaning weight (WW) and in 2016 for postweaning gain (PWG), with little divergence for birth weight (BTW). In broiler chickens, the genetic trends estimated by ssGBLUP and BLUP diverged at breeding cycle 6 for two out of the three production traits. The RMS trends for the genotyped pigs diverged for animals born in 2014, more for ADG than for BF. In beef cattle, the RMS trends started diverging in 2009 for WW and in 2016 for PWG, with a trivial trend for BTW. In broiler chickens, the RMS trends from ssGBLUP and BLUP diverged strongly for two production traits at breeding cycle 6, with a slight divergence for another trait. Divergence of the genetic trends from ssGBLUP and BLUP indicates the onset of the genomic selection. The presence of trends for RMS indicates selective genotyping, with or without the genomic selection. The onset of genomic selection and genotyping strategies agrees with industry practices across the three species. In summary, the effective start of genomic selection can be detected by the divergence between genetic and RMS trends from BLUP and ssGBLUP.


Introduction
Genomic selection has been widely recognized as a successful tool for genetic improvement, as evident by the extensive genotyping in various livestock and plant species VanRaden, 2020). The genomic selection allows to preselect young animals and also parents with higher accuracy than with best linear unbiased prediction (BLUP; Patry and Ducrocq, 2011a;Tyrisevä et al., 2018b). However, the actual gains with genomic selection depend on a number of factors, aside from the variance components. These include the choice of animals for genotyping, prediction accuracy of genomic methods, and fraction of genotyped animals used for breed improvement. Genotyping is not effective if only parents with a large progeny number are genotyped because their BLUP evaluations are already accurate. A genomic selection scheme using simple single-trait models, possibly with few phenotypes, may be less accurate than BLUP selection with more complete data and models (Muir, 2007). Finally, if genotyping is used only for marketing, e.g., young bull sales to commercial farms, such genotyping has no effect on the genetic improvement of the breeding population.
With a large investment in genomic selection, it is of interest to find out the onset of the genomic selection and whether it is successful over the long run. There are several possible ways to find out the starting date of genomic selection. One way is by analyzing differences in genetic trends by BLUP and singlestep genomic BLUP (ssGBLUP). Under genomic selection, BLUP cannot account for the fact that animals are being selected based on genomic information before having their phenotypes recorded (i.e., genomic preselection) and is, therefore, biased (Patry and Ducrocq, 2009;Patry and Ducrocq, 2011b). On the contrary, ssGBLUP accounts for all sources of information jointly and is expected to be less affected by preselection bias (Legarra et al., 2009(Legarra et al., , 2014VanRaden and Wright, 2013). Superior genetic trends by ssGBLUP compared with BLUP have been reported in several cases. Masuda et al. (2018) presented trends for milk yield in Holsteins by BLUP and ssGBLUP. While the trend by ssGBLUP increased at the expected beginning of the genomic selection, the trend by BLUP leveled off. Koivula et al. (2018) reported that including the genotypes of culled bull calves in the ssGBLUP analysis leads to higher genetic trends for milk production traits of Nordic Red Dairy Cattle compared with the situation where genomic information of the culled bull calves is ignored.
Another way to investigate the onset of genomic selection is by analyzing genetic and phenotypic trends, expecting accelerating trends under genomic selection . However, both trends are affected by changes in selection practices and incur some lag time. Lag time depends on the generation interval, feeding, and management program. Additionally, changes in genetic parameters over time may cause fluctuations in the genetic trends (Hidalgo et al., 2020). The third way is by analyzing realized Mendelian sampling (RMS) trends derived by genomic and traditional evaluations (Tyrisevä et al., 2018a(Tyrisevä et al., , 2018b. Genetic selection works by selecting animals with superior Mendelian sampling. The selection is based on phenotypes and progeny records in BLUP, and additionally on genomic information with genomic methods . When some animals are selected for superior Mendelian sampling, the average Mendelian sampling for all the animals is still zero, but for the selected animals it is different than zero. Therefore, RMS for genotyped animals is likely to be different than zero with selective genotyping based on performance for both BLUP and ssGBLUP. Additionally, RMS is likely to be zero for both methods when genotyping involves all young animals or is random. However, the magnitude of RMS by ssGBLUP will be greater because of the higher accuracy of genomic estimated breeding value (GEBV). Not only the accuracy is greater, but also the average GEBV is usually higher than the average EBV, which translates into superior genetic trends. This study aimed to find the onset of genomic selection by comparing the genetic and Mendelian sampling trends derived by ssGBLUP vs. BLUP in pigs, Angus cattle, and broiler chickens.

Pig data
The pig data consisted of 934,148 records for average daily gain (ADG) and 856,546 for backfat (BF) collected until 2019, and 1,310,240 animals in pedigree, of which 116,943 were genotyped for 43,910 single-nucleotide polymorphism (SNP) markers after quality control. The quality control of genotypes was performed as in Lourenco et al. (2016). This dataset was provided by Genus PIC (Hendersonville, TN). The descriptive statistics of studied traits are presented in Table 1.

American Angus data
Phenotypes for three traits including birth weight (BTW; N = 9,003,125), weaning weight (WW; N = 9,506,570), and postweaning gain (PWG; N = 4,671,702) of Angus beef cattle were provided by the American Angus Association (St. Joseph, MO). The pedigree consisted of 11,573,108 animals, of which 842,199 were genotyped and a common set of 39,766 SNP markers were available after imputation. The quality control of genotypes was conducted as in Lourenco et al. (2015b). The descriptive statistics of studied traits in American Angus are presented in Table 2.

Broiler chicken data
The broiler chicken data were provided by Cobb-Vantress Inc.
(Siloam Springs, AR). The dataset included phenotypic records from a purebred broiler chicken line across 32 breeding cycles for three production traits referred to as T1, T2, and T3. Each eight breeding cycles comprise one generation. The number of records for T1, T2, and T3 was 1,072,854, 228,992, and 265,891, respectively. The genotype file after quality control consisted of 154,318 birds genotyped for 54,713 SNP markers, and the pedigree consisted of 1,252,619 birds. The SNP data underwent the same quality control process as described in Lourenco et al. (2015a).

Statistical models
The statistical model for pig traits was as in Steyn et al. (2020), for beef traits was as in Garcia et al. (2020), and for broiler chicken traits was as in Lourenco et al. (2015a). The (co) variance components used in all analyses were provided by PIC, Angus Genetics Inc., and Cobb-Vantress. These (co)variance components were the most recent estimates derived using pedigree BLUP. The pedigree relationship matrix (A) was used in BLUP and the realized relationship matrix (H) was used in ssGBLUP. The structure of H -1 is explained in Aguilar et al. (2010). Both BLUP and ssGBLUP were run in a multiple-trait animal model framework.

Genomic analysis and software
Because of the large number of genotyped animals, the algorithm for proven and young (APY) was used to create the inverse of G (G −1 APY ) as proposed by Misztal et al. (2014a) andFragomeni et al. (2015). In APY, the matrix of genomic relationships among genotyped animals is partitioned based on core and noncore animals. The number of core individuals was selected based on the number of eigenvalues explaining 98% of the variance of G (Pocrnic et al., 2016) using PREGSF90 (Misztal et al., 2014b). The number of core individuals for pigs, beef cattle, and broiler chickens was estimated as 11,094, 13,000, and 5,030, respectively. Core animals were randomly sampled from the genotyped population.
Solutions for BLUP and ssGBLUP were obtained by using the preconditioned conjugate gradient algorithm with iteration on data as implemented in the BLUP90IOD2 (Tsuruta et al., 2001). The convergence criterion was set to 10 −12 for all evaluations.

Genetic trends
The point of divergence in genetic trends obtained by ssGBLUP and BLUP was used as a way to identify the onset of genomic selection. To explain how the difference between predictions from ssGBLUP and BLUP can indicate the start of genomic selection, consider the decomposition of the (G)EBV of individual i as in Aguilar et al. (2010), VanRaden and Wright (2013), and Lourenco et al. (2015a): and Then, the difference between GEBV and EBV is: where PA is the parent average, YD is yield deviation (phenotypes adjusted for the fixed effects), PC is the progeny contribution, and GI is the genomic information which is equal to GP − PP, in which GP is the genomic prediction derived using G and PP is the pedigree prediction derived using A 22; the superscripts c and g denote components related to conventional BLUP and ssGBLUP, respectively, and w 1 to w 4 are weights that sum to 1.
When inbreeding is ignored in A and both parents are known, then, with superscripts omitted, w 1 = 2/den, w 2 = (n rec/ α)/den, w 3 = 0.5n prog /den, and w 4 = (g ii − a ii 22 )/den, in which α is the variance ratio (residual variance over additive genetic variance), n prog is the progeny size, n rec is the number of records, g ii and a ii are the diagonal element of G −1 and A −1 22 for animal i, respectively, and den is the sum of the numerators of w 1 to w 4 .
The components of (G)EBV equations for individual i are as follows: Where (G) EBV s(i) and (G) EBV d(i) are (genomic) breeding values of sire and dam of individual i, y i is the ith record of animal i, b is the solutions for the level of fixed effects related to record i, x ij is the element of a design matrix relating b to y i , and k refers to progeny and m indicates mate of animal i.
The components GP and PP are ignored under BLUP, which results in biased EBV if animals are selected based on genomic information. The bias arises not only from the lack of GP and PP, but also from a combination of elements including the fact that PA, PC, and YD are not adjusted based on genomic information. For instance, if parents are non-genotyped, the difference between the predictions from BLUP and ssGBLUP originates from the contributions due to PC and GI of genotyped animals. For young animals without own and progeny records, the difference between EBV and GEBV comes from GI and PA enhanced by genomic information of parents, the latter to a smaller extent. However, as own and progeny records are added to the data, the amount of weight given especially to PC increases, and the weight of GI decreases. When EBV or GEBV are used for the selection of parents, GEBVs have higher accuracy (r g a,â ). This will generate a difference in the amount of genetic gain (∆G) in the next generation. Therefore, it can be shown as ∆G g = ir g a,â σ a and ∆G c = ir c a,â σ a, and finally ∆G g ≥ ∆G c , in which i > 0 is the selection intensity and σ a is the additive genetic SD. Hence, under genomic selection, mean GEBV is higher than mean EBV because greater accuracy of GEBV allows the selection of superior animals based on GP. Subsequently, a divergence in (G)EBV trends indicates the beginning of the genomic selection.
To obtain the genetic trend under traditional BLUP and ssGBLUP, the (G)EBVs were averaged by birth year for genotyped bulls in the beef cattle population, for genotyped parents in the pig population, and for genotyped birds in the chicken populations. Only animals with phenotypes were used for deriving the genetic trends. Genetic trends were obtained using a simple linear regression of (G)EBV for each trait on year of birth. For both BLUP and ssGBLUP, the genetic base was set to where more than one thousand genotyped individuals were available per year/generation. This corresponded to breeding cycle 1 in broiler chickens, and birth year 2012 in pigs, and year 2007 in beef cattle. The mean GEBV from ssGBLUP was set to the same base as EBV from BLUP.

Realized Mendelian sampling
The RMS for the genotyped individual i was estimated as: Under some idealized evolutionary processes (e.g., random mating, absence of selection, and large population size), the components of (G)EBV are expected to be zero within each generation: and consequently, E[RMS] = 0. When all or a random subset of young animals are used as parents of the next generation, the average RMS is close to 0. Although in a population under selection the equalities may not hold, the RMS is still expected to be zero.
For simplicity, assume that parents and earlier generations are not genotyped. Let index s denotes ungenotyped animals selected for genotyping based on phenotype or BLUP (the first stage of selection), then E[YD s ] = δ, where δ = i s r a,âs σ a, in which i s is the selection intensity at the first stage of selection, r a,âs is the accuracy of evaluation based on phenotype or BLUP, and σ a is the additive genetic SD. Assuming young animals with neither progeny nor genotype: Therefore, if animals are preselected based on phenotype or BLUP, RMS from either BLUP or ssGBLUP is nonzero. Its value depends not only on the selection differential but also on the coefficient w 2, which is a function of variance ratio and the number of own records. Now assume that in the second stage of selection, the animals preselected based on phenotypes or BLUP are genotyped and reevaluated (index sg). On average, an animal with superior phenotype may also have a superior genomic prediction, E[GP sg ] = τ, where τ = i sg » r 2 a,âsg − r 2 a,âs σ a, with i sg selection intensity in the second stage of selection and r 2 a,âsg is the reliability of selection based on the genomic reevaluation. Then: With many genotyped animals, the coefficient w 4 can be close to 1, with accuracy of GEBV sg greater than the one of EBV s . Accordingly, RMS will be greater under genomic selection. The selective genotyping based on superior phenotypes (YD) can be replaced by superior progeny difference (PC) indicating that both have a similar effect on EBV, GEBV, and RMS.
The above derivations suggest that the RMS is close to zero when all animals are genotyped or when genotyping is at random. With selective genotyping, RMS is nonzero and is greater with ssGBLUP than with BLUP. Because selective genotyping is the practice in livestock populations, the divergence in RMS trends obtained based on EBV and GEBV can also indicate the starting point of the genomic selection. The same animals used for obtaining the genetic trends were also engaged in attaining the RMS trends. Figure 1 shows the genetic trends for ADG and BF in genotyped pigs. The annual changes in average breeding values, in genetic SD units, from 2012 to 2019 for ADG and BF were 0.27 and 0.04 for ssGBLUP and 0.18 and 0.02 for BLUP, respectively. The trends from ssGBLUP and BLUP diverged after 2013. In the last year of data (2019), the differences between average breeding values from ssGBLUP and BLUP were 0.67 SD for ADG and 0.17 SD for BF.

Pig production traits
The genetic trend for ADG increased over time with a slight increase in BF observed in recent years. The change in the genetic trend for BF was possibly due to the correlated response with body weight traits, as well as changes in breeding practices and in the selection objective in recent years.
The RMS (Figure 2) for ADG increased from around 0.04 in 2012, reached a peak of 0.10 in 2016, then declined. For ADG, the positive RMS and considerable difference from zero from 2013 to 2016 could be due to the use of genotypes from elite culled or active boars before 2016 that were retrieved from stored tissue samples. BF is measured after the animals are genotyped; hence, the smaller RMS for BF could be due to a correlated response to ADG.

Beef production traits
The genetic trends achieved by BLUP and ssGBLUP for BTW, WW, and PWG in genotyped Angus bulls are shown in Figure 3. The annual changes in (G)EBV for genotyped animals, in genetic SD units, from 2006 to 2018 for BTW, WW, and PWG were −0.01, 0.11, and 0.08 for ssGBLUP and −0.01, 0.09, and 0.09 for BLUP, respectively. In the last year of data (2018), the differences between average breeding values from ssGBLUP and BLUP were 0.01, 0.23, and 0.06 SD for the three traits, respectively.
For BTW, the difference between the genetic trends for ssGBLUP and BLUP was negligible, but for WW and PWG, the genetic trends diverged considerably from 2016 afterward. For WW and PWG, the annual genetic gain after 2016 from ssGBLUP was 0.06 and 0.02 SD greater than BLUP, respectively. As it can be seen in Figure 3, there is a genetic improvement for all traits. However, the genetic trend of BTW is downward relative to WW and PWG. Low BTW is desirable to avoid calving problems. On the other hand, BTW is positively correlated with WW and PWG; therefore, a stronger pressure is needed to keep BTW low while increasing WW and PWG. Based on the divergence, genomic selection is less important for BTW because this trait has already been recorded at the time of genotyping. Therefore, selection for BTW is based on PA and phenotype deviation. Differently, there was a clear impact of genomic selection for WW from 2009-with an accelerated trend in 2017, and the genomic selection on PWG is slightly visible from 2017.
The RMS (Figure 4) looks very different for the three traits. For BTW, the trend is small and negative, at around −0.02, with small changes at the end. It suggests that the heaviest calves were not genotyped; calves are selected for lower BTW to reduce calving difficulty. For WW, RMS is large and increasing over time from 0.12 to 0.29. Such a trend suggests that the primary genotyping is after weaning and based on WW. For PWG, RMS is smaller, although rising to 0.17. As the differences between EBV and GEBV were small for PWG, the values of RMS for PWG could be just a correlated response to WW as the genetic correlation between WW and PWG is high (r g = 0.48).

Broiler chicken traits
Genetic trends were favorable for all traits with faster improvement in recent years. Figure 5 shows the difference between genetic trends obtained using ssGBLUP and BLUP in genetic SD units for T1, T2, and T3 in genotyped birds. Divergence for the genetic trends by ssGBLUP and BLUP occurred in breeding cycle 6 for T2 and T3. For T1, some divergence was visible from breeding cycle 2 to 16 in favor of BLUP and then from breeding cycle 20 afterward in favor of ssGBLUP, although the divergence was reduced later. It seems that for T1, slight divergence in favor of BLUP up to breeding cycle 19 was spurious, and this divergence could represent the higher PA of animals selected for genotyping.
The RMS trends ( Figure 6) show relatively large values for T1 (up to 0.14) and small values for the other traits (0.04 or less). Animals were selected for T1 by BLUP, and then superior animals were genotyped. Therefore, RMS for T1 is high. Small RMS for the other two traits measured later suggests only a correlated response from T1 because all animals measured for these traits were already genotyped.

History of adoption of genomic selection
In this study, we used data provided by PIC, American Angus Association, and Cobb-Vantress. Although each of them took different approaches regarding genotyping and implementing genomic selection, all changed to ssGBLUP after some time which corresponds to breeding cycle 6 in broiler chickens, year 2014 in pigs, and year 2017 in beef cattle.
PIC started using ssGBLUP for genomic evaluations in this population in late 2013, so the first results of genomic selection were visible in 2014. Before that, selection was based on BLUP (William Herring, PIC, Hendersonville, TN, personal communication).
Angus Genetics Inc. incorporated genomic information on 15 markers in 2009 using a correlated trait approach (Kachman, 2008). The panel was updated to 384 markers in 2010 and moved to the 50k SNP chip after that. Angus Genetics Inc.

Genetic trends
We assessed the genetic trends of several traits in pigs, beef cattle, and broiler chickens to investigate the effectiveness of genomic selection. Assuming those differences in genetic basis between BLUP and ssGBLUP are correctly accounted for by the method described in Vitezica et al. (2011), the effectiveness of genomic selection can be evaluated indirectly by measuring the differences between genetic trends from BLUP and ssGBLUP. If the genetic trend by ssGBLUP is accelerating in a favorable direction and the genetic trend by BLUP is decelerating, genomic selection is likely practiced for the particular trait. If the genetic trends by both methods converge to the same point, the selection based on genotypes is not stronger than the selection based on PA and phenotypes. The genetic trends can also be influenced by the genetic correlations among traits, especially with sequential selection, where a trend for an earlier measured trait influences a trait measured later. Based on the divergence point of genetic trends from BLUP and ssGBLUP in our study, the starting point of genomic selection in pigs is 2014, in Angus cattle is 2013, and in broiler chickens is breeding cycle 6. These starting points agree with the history of implementation of genomic selection in those populations. If the genetic evaluations are based on ssGBLUP or GBLUP (H or G matrix), the estimates of genetic trends using BLUP (A matrix) are biased provided that a large portion of selected candidates are genotyped. As the correlation between the elements of G and A 22 increases, the genetic trends by the two methods will converge. However, some factors such as preselection of selection candidates (Jibrila et al., 2020), incomplete pedigree information, and also the existence of young animals without own and progeny records but with genotypic information (Shabalina et al., 2017) make this difference larger.
The main purpose in investigating genetic trends is to verify whether selection is effective and whether there is an agreement with phenotypic trends. A disagreement suggests changes in the environment, ineffective selection, or biased genetic trends. When there is a disagreement between BLUP and phenotypic trends, but an agreement between the latter and ssGBLUP trends, there is strong evidence for biased BLUP trends. Masuda et al. (2018) showed genetic trends for milk yield traits based on BLUP were biased downwards for U.S. Holstein bulls and cows. Especially for bulls, the bias in EBV was because of failure in accounting for genomic preselection and underestimated PC because daughters were also genotyped and, therefore, preselected before having their phenotypes recorded. In the same study, the authors showed a good agreement between phenotypic and ssGBLUP trends, meaning the latter can account for preselection and is not biased under genomic selection.
When the BLUP trends become biased due to genomic preselection, any measure derived from it such as deregressed proofs should not be used anymore. It should be noted that genomic preselection, selection on correlated traits (Sorensen and Kennedy, 1984), poorly defined unknown-parent groups (Misztal et al., 2013), preferential treatment of selection candidates (Dehnavi et al., 2018), and nonrandom mating (Tsuruta et al., 2021) can generate bias in BLUP.

Realized Mendelian sampling
The value and trends for RMS illustrate selective genotyping, where the decision to genotype is based on phenotypes or BLUP evaluations. RMS was large for ADG in pigs, for WW in Angus, and for T1 in broiler chickens, where genotyping followed phenotyping. For pigs, the RMS trend indicates that an increasing number of piglets are being genotyped, reducing selective genotyping. As genotyping becomes less expensive while the cost of phenotyping keeps constant, genotyping more young animals becomes economically justified. For WW in beef cattle, the majority of calves are genotyped after weaning, and selection at this stage is mostly based on phenotype. However, genetic trends can diverge before the time of genotyping if superior animals are genotyped retroactively. For broiler chickens, RMS for later traits such as T2 and T3 was close to zero, indicating no new preselected genotyping based on these traits.
Although we investigated RMS and genetic trends to identify the starting point of genomic selection, those two approaches are closely related. As genomic selection works by selecting animals with superior Mendelian sampling, there is a sharp increase in breeding values estimated under genomic methods. This increase in breeding values is evident for selected animals and also their progeny (Tyrisevä et al., 2018a), where animals with a large number of genotyped progeny are more likely to have greater Mendelian sampling (Masuda et al., 2018). Consequently, because of larger Mendelian sampling, there is an impact in genetic trends when animals are selected based on genomic information, especially if the selection happens before phenotypes are recorded.
Usually, the difference between genetic and RMS trends from ssGBLUP and BLUP is more obvious in species under more intense selection with shorter generation interval, as in broilers and pigs compared with beef cattle. Moreover, the effect of genomic selection will be more pronounced in species with higher use of reproduction technologies such as artificial insemination and embryo transfer, such as dairy cattle. On the other hand, fitness-related, hard to measure, or late traits will benefit more from the implementation of genomic selection, so we expect that the difference between genetic and RMS trends from BLUP and ssGBLUP will be more evident in these cases. Figure 5. The difference between genetic trends obtained using single-step genomic best linear unbiased prediction (ssGBLUP) and pedigree BLUP in genetic SD units for three production traits referred to T1, T2, and T3 in a purebred broiler chicken line across 32 breeding cycles.

Conclusions
To detect the effective starting point of genomic selection, two possible ways including the divergence point of genetic trends and RMS trends obtained by ssGBLUP and BLUP using official datasets from pigs, beef cattle, and broiler chickens were used. The effective starting point of genomic selection in pigs, Angus cattle, and broiler chickens was determined as year 2014, 2013, and breeding cycle 6, respectively. The difference between genetic and RMS trends from ssGBLUP and BLUP is more evident in populations under more intense selection, as in pigs and broilers compared with beef cattle. In general, the effective starting point of genomic selection can be detected by the divergence between genetic and RMS trends from BLUP and ssGBLUP, although RMS trends are present for traits recorded before genotyping and later used for genotyping decisions. The results and procedures presented here can help to evaluate the efficiency of the implementation of genomic selection in breeding programs.