Introduction
In Chile, seventy per cent of dairy milk production is produced in the country's southern regions. These regions are Araucania (IX), Los Lagos (X) and Los Rios (XIV). In these three regions, milk production, similar to New Zealand, is mainly based on grazing pastures, where the goal is to obtain high production of milk solids per unit of land rather than milk yield per cow (Uribe et al., Reference Uribe, Gonzalez and Gatica2017).
The selection index as a tool to select animals for breeding replacement has had a major role in breeding programmes for dairy cattle in countries such as New Zealand (Breeding Worth); Ireland (Economic Breeding Index) and the Netherlands (Total Merit Index). In Chile, however, genetic changes in dairy cattle have been achieved mainly by importing frozen semen from proven bulls in other countries to be used in local cows (Verdugo et al., Reference Verdugo, Jara, Everett and Barría Pérez2004). Technically, this approach corresponds to migration rather than selection (Falconer and Mackay, Reference Falconer and Mackay1996). This strategy might be advised in the absence of genotype by environmental interaction (G × E) and differences in economic and production circumstances (López-Villalobos et al., Reference Lopez-Villalobos, Garrick and Holmes2001) but otherwise could produce sub-optimal genetic progress.
In Chile, a frozen semen importing company recently developed a selection index called Valor Económico Lechero (VEL) (Lama and Vargas, Reference Lama and Vargas2020). It will be applied in ranking cows and imported bulls used in dairy cattle breeding in Chile's southern region. The VEL index is calculated by weighing the estimated breeding values (EBVs) for lactation yields of milk (MY), fat (FY) and protein (PY) (production traits), somatic cell score (SCS), age at first calving (AFC), calving interval (CI), and longevity (functional traits), by their respective economic value (Lama and Vargas, Reference Lama and Vargas2020).
The selection index (Hazel, Reference Hazel1943) is a method for estimating the total aggregate genetic value of an animal by combining EBVs for traits of economic importance with their corresponding economic values. It is the basis on which the animals are ranked for selection. The optimal selection index maximises the correlation between the selection index (traits recorded as predictor) and the selection objective (traits of interest to improve) (Mrode, Reference Mrode2014). Therefore, selection indices are used as predictors of the selection objective, which is focused on traits that influence the breeding goal. In the VEL index, for example, the traits included in the selection objective are the same as those included in the index. Using the selection index theory, the estimation of genetic changes for the traits in the selection objective can be estimated from selection schemes based on the four pathways of selection (Rendel and Robertson, Reference Rendel and Robertson1950). These pathways are cows to breed cows (CC), cows to breed bulls (CB), bulls to breed cows (BC), and bulls to breed bulls (BB).
Although the VEL index is the first tool developed in Chile to genetically improve the dairy cattle population under pasture, a selection scheme for the Chilean dairy population has not been implemented. Therefore, it is of interest to design a specific selection scheme, because it dictates the potential genetic progress that can be achieved for the traits economically important to improve, and it has considerable influence on the cost-effectiveness of the selection programme (López-Villalobos and Garrick, Reference López-Villalobos and Garrick2005).
In a dairy selection scheme, the main method of evaluating bulls is progeny testing (PT). However, genomic selection (GS; Meuwissen et al., Reference Meuwissen, Hayes and Goddard2001) makes it possible to modify the conventional PT selection scheme. In this scheme, the rate of genetic gain can be as much as double compared to PT (Schaeffer, Reference Schaeffer2006). Accordingly, this study aimed to evaluate a selection scheme by estimating genetic progress in the traits included in VEL based on PT or through GS.
Material and methods
Population structure
The dairy cattle population under grazing conditions in Chile (La Araucanía, Los Ríos, and Los Lagos Regions) is around 500 000 cows (ODEPA, 2019). Considering a replacement rate of 30% (Olivares et al., Reference Olivares, Moreira and Muñoz2012), the theoretical age structure for a typical herd in Southern Chile can be estimated as follows: 30.0% 2-year-olds, 22% 3-year-olds, 16% 4-year-olds, 11% 5-year-olds, 8% 6-year-olds, 6% 7-year-olds, 4% 8-year-olds, 3% 9-year-olds, and 2% 10-year-olds. This results in a 4.0 year-old average age structure.
Derivation of cow and bull paths
Selected cows as bull mothers (CB) correspond to those cows in their second, third and fourth lactations. It was considered that 70% of these cows could be selected. The number of cows required to produce one bull for PT was assumed to be 6.6 times the number of bulls required to be progeny tested (López-Villalobos et al., Reference López-Villalobos, Garrick, Blair and Holmes2000). The proportion of cows selected (CC) was assumed 99% since generally there are limited opportunities for selection among female replacements. It was assumed that there were two yield records for cows in the CB and CC pathways (Spelman and Garrick, Reference Spelman and Garrick1997).
The selected proportions in the BB and BC pathways were 10% and 20%, respectively. Each bull was assumed to be evaluated based on the performance of 85 daughters (Spelman and Garrick, Reference Spelman and Garrick1997). The proportions of selected bulls are greater than those selected in New Zealand (Sneddon et al., Reference Sneddon, López-Villalobos, Davis, Hickson, Shalloo, Garrick and Geary2016), since for small populations (as deemed for the Chilean dairy cattle industry), it would be required to increase the proportion of bulls selected to avoid inbreeding (Lembeye et al., Reference Lembeye, López-Villalobos, Burke and Daves2021).
Generation intervals calculated for the dairy population were based on the age structure of the population for the CC pathway described above. It was assumed that heifers are naturally mated, and their offspring are not kept for milking, similar to New Zealand (Holmes et al., Reference Holmes, Brookes, Garrick, Mackenzie, Parkinson and Wilson2002). For the CB path, it was based on calves being born when 80% of cows were 4-years old and 20% were 5-years old. For the BB and BC paths, the generation intervals correspond to those reported by Sneddon et al. (Reference Sneddon, López-Villalobos, Davis, Hickson, Shalloo, Garrick and Geary2016) (Table 1).
Population size, population selected, proportion selected, and selection intensities for a progeny testing selection scheme and for a genomic selection scheme for the dairy cattle population
BB, bull to breed bull; BC, bull to breed cow; CB, cow to breed bull; CC, cow to breed cow; R 2, reliability
Genomic selection approach
This approach simulated the implementation of a theoretical GS-scheme (Turbo scheme: bulls selected based on parent average genomic enhanced breeding values (GEBVs) and used for breeding purposes as soon as they are sexually mature at 15 months) as proposed by Thomasen et al. (Reference Thomasen, Egger-Danner, William, Guldbrandtsen, Lund and Sørensen2014a). In this scenario, 2000 cows are selected as bull mothers according to their EBVs for the overall selection objective (VEL). Five hundred progeny bull calves from the selected cows are assumed to be genotyped, only 15 of them were assumed to be selected for BB and BC paths. Hence, this approach considers a proportion of bulls of 3% in the BB and BC paths and 1.19% in the CB path, respectively. This approach assumed reliabilities (R 2) of 40%, 50%, and 60%, and a two-year interval in the BB and BC paths. The assumption of this scenario are presented in Table 1.
Initially, the elite cows selected (based on their EBVs) as bull mothers are also screened (Pryce and Deatwyler, Reference Pryce and Daetwyler2012) but with the goal of estimating the SNPs effects, since these cows are part of the reference population (individuals with phenotypes records and genotypes). This reference population is used to derive prediction equations to calculate GEBVs for the selection of young bulls (Hayes et al., Reference Hayes, Bowman, Chamberlain and Goddard2009).
Selection index
In the design of the selection scheme for the Chilean dairy cattle population, selection index theory (Hazel, Reference Hazel1943) was used to investigate the selection objective indicated by VEL.
Selection index theory
The selection index (I) is a method for predicting the selection objective (H) in which several valuable traits are selected simultaneously, such as I = H. These expressions are represented in the online Supplementary File according to Cameron (Reference Cameron1997). For the selection objective investigated in this study, traits in I were the same as those included in H. Estimated genetic and phenotype parameters (heritability, repeatability, correlation, and variance) used in the selection index were from Montaldo et al. (Reference Montaldo, Trejo and Lizana2017) for MY, FY, PY, AFC, and LIC; Lembeye et al. (Reference Lembeye, López-Villalobos, Burke and Davis2016) for SCS and Pritchard et al. (Reference Pritchard, Coffey, Mrode and Wall2012) for longevity. These parameters are presented in Table 2. All (co)variances were formulated separately for the four pathways because of the differences in their sources of information. The formulas used to calculate elements of the matrices 
${\boldsymbol P}$ and 
${\boldsymbol G}$ were derived using the methodology presented by Cameron (Reference Cameron1997). The structure of the final matrices 
${\boldsymbol P}$ and 
${\boldsymbol G}$ was symmetric and positive definitive.
Genetic standard deviation (σ g), heritability (h 2), repeatability (Rep) and genetic (below the diagonal) and phenotypic (above the diagonal) correlations among traits considered in the Valor Económico Lechero selection index
MY, milk yield; FY, fat yield; PY, protein yield; AFC, age first calving; CI, calving interval; SCS, somatic cell score.
a Repeatability of age at first calving and longevity was assumed identical to heritability.
In the selection index theory, true breeding values of traits included in H are weighed according to their economic values. However, in VEL only their relative emphases (RE) are known (Lama and Vargas, Reference Lama and Vargas2020); consequently, economic values were derivated based on their RE using the reverse method described by Berry (Reference Berry2015), so that the economic value of a trait in product with its σg represents the desired relative economic emphasis assigned by VEL (Table 3).
Economic values (EV) ($) and relative emphasis (RE) for traits included in the Valor Económico Lechero selection index.
a Chilean pesos.
Calculation of genetic gain
The expected correlated response in each trait was calculated using the following equation (Cameron, Reference Cameron1997):
$$\Delta {\rm R}_{\rm j} = i\displaystyle{{{\boldsymbol b}^{\prime}{\boldsymbol G}_{\boldsymbol i}} \over {\sqrt {{\boldsymbol b}^{\prime}{\boldsymbol Pb}} }}$$where ΔRj is the correlated response for the jth trait in the selection objective, 
${\boldsymbol G}_{\boldsymbol i}$ is the ith column of the genetic (co)variances matrix 
${\boldsymbol G}$, and i is the intensity of selection. Matrix 
${\boldsymbol P}$ and row vector 
${\boldsymbol b}$ as previously defined.
In the GS-scheme proposed, it was considered the aggregate breeding value (merit for all traits included in the selection objective as a single-trait). The correlated response was calculated as defined by Rendel and Robertson (Reference Rendel and Robertson1950):
$$\Delta {\rm G} = \displaystyle{{\mathop \sum \nolimits_{{\rm i} = 1}^4 ( {\rm i}_{\rm i}{\rm r}_{\rm i}) {\rm \sigma }_{\rm g}} \over {\mathop \sum \nolimits_{{\rm i} = 1}^4 {\rm L}_{\rm i}}}$$where σg, ri, ii and Liare the genetic standard deviation of the aggregate breeding value (selection objective), the accuracy of selection (
$\sqrt {{\rm R}^2} $), selection intensity and generation interval, respectively in the ith selection pathway.
Results
Predicted responses per year in the Chilean dairy cattle population based on the proposed PT-scheme are presented in Table 4. Estimates of genetic progress were: 41.50 kg/year, 3.44 kg/year, 2.33 kg/year, −0.280 d/year, −0.017 d/year, −0.019 units/year, and 0.032 d/year for MY, FY, PY, AFC, CI, SCS, and longevity, respectively.
Correlated response (ΔG) per year from selection on the Valor Económico Lechero selection index in the Chilean dairy population from progeny testing selection scheme
Table 5 shows predicted genetic gains in overall selection objectives (which is the overall genetic merit) based on the simulated PT and GS schemes. The overall genetic gain for the simulation that considered the PT-scheme was 0.194 σg/year, meantime those that considered GS were 0.323, 0.348 and 0.371 σg/year for a 40%, 50% and 60% R 2, respectively.
Asymptotic annual response (ΔG) in genetic standard deviation (σg) per year in the Chilean dairy population based on the traditional progeny testing and an approach to genomic selection.
Discussion
The results presented in Table 4 indicate that genetic gain for MY is 25% smaller as compared with a simulation carried out in New Zealand by Sneddon et al. (Reference Sneddon, López-Villalobos, Davis, Hickson, Shalloo, Garrick and Geary2016), however, milk solids composition is 30–55% greater. Compared with another study under pastoral systems (Lembeye et al., Reference Lembeye, López-Villalobos, Burke and Daves2021), predicted genetic response for FY and PY agree with simulations for the once-daily milking population in New Zealand only when bulls were tested in twice-daily milking systems. In the simulation for the PT-scheme, the genetic response for milk solids is smaller in Lembeye et al. (Reference Lembeye, López-Villalobos, Burke and Daves2021) as compared with results shown in Table 4, and only similar for MY when udder-related type traits are included in the selection objectives. These differences result from different genetic parameters (h 2 and genetic variances) evaluated for the selected population (Chilean dairy cattle, Overo Colorado breed).
A reduction for reproduction traits in both AFC and CI is expected (−0.280 and −0.018, respectively). It is important to note that this study arbitrarily assigned an equal 8% RE for both traits because the VEL index indicated a 16% RE for reproduction traits (Lama and Vargas, Reference Lama and Vargas2020). In consequence, there might be differences in the RE for AFC and CI in the VEL index.
From this simulation study, we can expect a small reduction in SCS and a small increment in longevity. For longevity, the direction of the selection response agrees with Sneddon et al. (Reference Sneddon, López-Villalobos, Davis, Hickson, Shalloo, Garrick and Geary2016) and Lembeye et al. (Reference Lembeye, López-Villalobos, Burke and Daves2021), however, this finding cannot be directly compared with those studies since the genetic variance used in this simulation was measured in a score scale, while in Sneddon et al. (Reference Sneddon, López-Villalobos, Davis, Hickson, Shalloo, Garrick and Geary2016) and Lembeye et al. (Reference Lembeye, López-Villalobos, Burke and Daves2021) it was measured in days. There are no reported genetic parameters for longevity in Chilean dairy cattle, and this trait is not considered in VEL.
The results presented in this study are important because no other studies have predicted the potential genetic improvement for a proper selection objective in southern Chile. Nevertheless, theoretically, there is at least an eight-year period before genetic gains from the proposed PT-scheme (Lembeye Illanes, Reference Lembeye Illanes2016) may be realised. The time between the scheme implementation and the realised genetic gain may be a disincentive for implementing a PT-scheme in Chile, suggesting that the current alternative is preferred since proven bulls are already selected and available with a VEL score. This is supported by Mulder et al. (Reference Mulder, Veerkamp, Ducro, van Arendonk and Bijma2006) who advised that a specific selection programme is not justified when only a small amount of semen is available (as might be the case of the Chilean dairy population). Further, assuming no significant G × E between the traits of the selection objective evaluated in Chile and foreign countries, the practice of semen importation, from a large environment-specific selection programme (i.e. as from New Zealand or the United States), resulted in a greater (33%) rate of economic response compared to the implementation of a local PT selection scheme (Vargas and van Arendonk, Reference Vargas and van Arendonk2004), even though the response was smaller than that achieved in the exporter country. For instance, Verdugo et al. (Reference Verdugo, Jara, Everett and Barría Pérez2004) reported that in Chile, selection response for yield traits was not much more than half of the response found in the United States. These reductions are likely consequences of selection schemes designed according to the semen exporting country circumstances which vary compared with importing countries (Chile, in our case). Therefore, the practice of importing frozen semen from bulls of foreign populations must be strategically used according to production and economic circumstances if farm profitability is to be maximised (López-Villalobos et al., Reference Lopez-Villalobos, Garrick and Holmes2001). Furthermore, interactions between genotype and physical environment and between genotype and economic (milk payment and feed costs) environment must be carefully considered.
In the current calculation of the VEL index for the ranking of bulls in Chile, the imported bulls (frozen semen) are evaluated with progeny in their country of origin, and their VEL index scores are calculated through conversion (linear regression) equations (Weigel and Powell, Reference Weigel and Powell2000). However, this procedure is unclear since Chile does not routinely participate in INTERBULL (International Bull Evaluation Services) analyses. This advises evaluating foreign bulls with Chilean progeny to obtain their national (Chilean) EBVs, and then assess their economic value, taking as a starting point the VEL selection index. The challenge for the Chilean dairy industry is, therefore, to run annually an independent genetic evaluation across all bulls from the breeding companies currently in the market. An example of this model is NZAEL (New Zealand Animal Evaluation Limited) that produces the national evaluation of New Zealand dairy cattle independently of the breeding companies (López-Villalobos and Garrick, Reference López-Villalobos and Garrick2005).
Instead of a PT- scheme, it may be advisable to implement in Chile a GS- scheme given the greater genetic gain under GS compared to the conventional PT (Table 5), mainly because of a reduced generation interval, as reported by Schaeffer (Reference Schaeffer2006), Pryce et al. (Reference Pryce, Goddard, Raadsma and Hayes2010) and Thomasen et al. (Reference Thomasen, Egger-Danner, William, Guldbrandtsen, Lund and Sørensen2014a). The constraint, however, is lower accuracy compared with PT because selected young bulls are not in the reference population or they are not the progeny of proven bulls (Harris and Johnson, Reference Harris and Johnson2010; Thomasen et al., Reference Thomasen, Sørensen, Lund and Guldbrandtsen2014b). Reference populations are mostly produced with PT bulls and they have low R 2 if they belong to a small dairy cattle population (Thomasen et al., Reference Thomasen, Sørensen, Lund and Guldbrandtsen2014b).
The results of this study suggest that cow genotyping is advised to expand a reference population (Pryce and Daetwyler, Reference Pryce and Daetwyler2012). For instance, Thomasen et al. (Reference Thomasen, Sørensen, Lund and Guldbrandtsen2014b) reported that a 57–122% increase in R 2 resulted when 2000 simualted first-lactation cows were added to the reference population as compared to bulls only added to the reference population, indicating that the greatest profit is expected when animals are selected based on GEBVs and used when they are sexually mature. In agreement with that study, a 166–191% greater genetic response is expected under the GS-scheme compared with the PT-scheme (Table 5). This scenario necessarily requires an independent breeding organisation to produce the phenotypes for traits included in VEL and derive prediction equations to calculated GEBVs.
In conclusion, a GS scheme might be a preferred option in the implementation of a dairy selection programme in Chile. The results of this study leads one to consider this selection scheme to be more feasible for the southern Chilean dairy population, above a conventional PT scheme. However, to produce GEBVs for economically important traits, an organisation independent from breeding companies should be created to produce the phenotypes for these traits.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/S0022029922000504
