Improving production efficiency in the presence of genotype by environment interactions in pig genomic selection breeding programmes

Historical population

A historical population was simulated with an effective population size of 200 by randomly selecting and mating breeding parents for 2000 generations to create a population in a mutation drift balance (Fisher 1930; Wright 1931). Simultaneously, a diploid genome simulated with a length of 18M consisting of 18 chromosomes each with a length of 100 cm. Polymorphism and recombination were simulated as in Sonesson & Meuwissen (2009). In the last generation of the historical population, 100 single nucleoid polymorphisms (SNP) with a minor allele frequency above 0.05 were randomly selected from each chromosome and were designated as quantitative trait loci (QTL). Among the remaining SNP on each chromosome, the 500 SNP with the greatest minor allele frequency were regarded as SNP markers to be used for estimating genomic breeding values. This resulted in a total number of 1800 QTL and 9000 SNP markers. The QTL effects were sampled from a multivariate normal distribution, assuming the QTL effects were normally distributed with a mean 0 and variance

In which, is the genetic variance of nucleus efficiency, is the genetic variance for production efficiency and is the genetic covariance between nucleus and production efficiencies. The true breeding value for feed efficiency traits in the nucleus and production was the sum of QTL allele effects for each trait for each individual. The phenotypic records for both traits were simulated as the sum of the true breeding value and environmental normally distributed errors N(0, R), where

In which, is the residual variance for nucleus efficiency trait and is the residual variance for production efficiency trait. Nucleus efficiency is a term used to describe for feed efficiency trait in the nucleus environment, and production efficiency is a term used to describe for feed efficiency trait in the production environment.

After simulating the historical population, we randomly sampled 200 females and 200 males to create a base generation. These animals were the foundation of all the selection schemes and served as parents for the first two rounds of selection before the breeding schemes had produced their own selection candidates. Each breeding schemes is replicated 100 times. For each replicate, a new historical population was simulated and SNP markers, QTL and QTL effects were resampled.

Breeding schemes: recording and reference population design

A pig breeding scheme was simulated with 25 breeding sires and 50 dams per generation for six distinct generations. The breeding schemes contained two distinct environments, a nucleus and a production. Breeding parents were selected based on genotype and phenotype information of either nucleus animals, production animals or a combination of nucleus and production animals. Animals in the production environment were cross-breeds, descendants of the nucleus. The breeding schemes were simulated under two different scenarios, where production animals are either offspring or grand offspring of nucleus animals (See Figure 1). In a three-way cross, the maternal line was cross-bred and the paternal line was purebred line.

Nucleus efficiency (h² = 0.3) and production efficiency (h² = 0.25) were considered as two separate traits that are partly under the influence of different sets of genes related on a lower (r_g = 0.2), medium (r_g = 0.5) or higher (r_g = 0.8) genetic correlation (Falconer 1952).

The breeding goal was to improve production efficiency by designing the reference population using different information sources for genetic evaluation of the selection candidates in the nucleus environment. Therefore, we simulated three different breeding schemes based on the reference population design: (i) nucleus (N), (ii) mixture of nucleus and production (N+P) and (iii) production (P) breeding schemes. In the N breeding scheme, the reference population contained only nucleus animals and all animals in the nucleus were genotyped and recorded for feed efficiency. In this case, the reference population was designed using the selection candidates own and relatives’ records from only the nucleus population. All animals in the production environment were genotyped and had no phenotype records. In the P breeding scheme, the reference population contained only production animals. In this case, the reference population was designed including only relatives information from the production environment. In the N+P breeding schemes, the reference population was a mixture of a fixed number of nucleus and various proportion of production animals. Both nucleus and production animals were genotyped and recorded for feed efficiency. The reference population was a mixture of own and relative's records from the nucleus and production environment. For a general overview of the breeding schemes, see Table 1.

Breeding parents were always selected from the nucleus environment by truncation selection on a genomewide estimated breeding values (GEBV). In all breeding schemes, the breeding goal was to improve production efficiency and selection was always based on GEBV of production efficiency. A hierarchal mating structure was assumed in all breeding schemes, and generations were discrete.

Marker effects and breeding value estimation

For each of the breeding schemes, the breeding value of selection candidates were estimated using n phenotypes and 9000 SNP loci using the genomic selection Meuwissen et al. 2001 based on the approach of best linear unbiased prediction (Henderson 1984) with a multitrait statistical model.

where is the vector of response variables for nucleus and production efficiency traits, I₁ and I₂ are identity matrices relating to the vector of intercepts for nucleus and production efficiency. is the vector of random errors assumed to be drawn from a normal distribution with a mean 0 and variance R. is vector of estimated SNP effects for nucleus and production efficiency. is matrix of standardized number of reference allele (allele ‘1’) for animal i and SNP j as assed by SNP i for nucleus and production efficiency, respectively, and was calculated as:

where p_j the frequency of allele ‘1’ at SNP j and is the number of alleles ‘1’ genotyped for animal i at SNP_j. The SNP effects were estimated as:

In the above mixed model equation, is the vector of estimated SNP effects at the marker loci for nucleus and production efficiency and is inverse matrix of variance and covariance for nucleus and production traits. The variance of each marker effect was assumed to be , where m is the number of SNP markers. Finally, the genomic EBV ()of selection candidate i for both traits was estimated as:

The accuracy of selection was obtained as the correlation between the predicted breeding values of the selection candidates with their true breeding values.

Effect of environment-specific reference population on genetic gain

The genetic gain and accuracy of selection generated in the production environment for alternative reference population design breeding schemes when the production animals were offspring of the selection candidates are presented in Table 2.

A higher genetic gain was generated in the production environment when the reference population was designed using only production animals to predict the breeding value of selection candidates in the nucleus environment as compared to using only nucleus animals for both offspring (Table 2) and grand offspring (results not shown) scenarios. It should be noted that in the offspring scenario, the production animals were offspring of the selection candidates and in the grand offspring scenario, the production animals were grand offspring of the selection candidates. At generation 6, P breeding schemes, where production animals’ record were used for prediction of breeding value, generated 45% more production efficiency than the N breeding scheme when the genetic correlation (r_g) between production and nucleus animals was 0.2. This figure decreased as the r_g between the nucleus and production population increased, 31% when r_g is 0.5 and 15% when r_g is 0.8.

Effects of combined reference population on genetic gain

A higher genetic gain was generated in the production environment for breeding schemes with a combined environment reference population as compared to breeding schemes with a single-environment reference population. The increase in genetic gain was higher when large proportion of production animals were included into the reference population maintaining equal number of nucleus animal records. However, it should be noted that this was also accompanied by an increase of the genotyping and phenotyping costs (more reference animals). At generation 6, production efficiency increased by 46% (r_g = 0.2), 34% (r_g = 0.5) and 24% (r_g = 0.8) in the N+P breeding schemes compared with the N breeding schemes and by 2% (r_g = 0.2), 4% (r_g = 0.5) and 10% (r_g = 0.8) compared with P breeding schemes containing 2400 nucleus and 1200 production animals’ record in the reference population (Table 3). There was a substantial increase in production efficiency when more numbers of animals from the production environment were added to the reference population maintaining equal nucleus reference population size. Specifically, the increase in production efficiency was large when there were large numbers of production animals in the reference population. Similar patterns were observed with regard to selection accuracy (Table 4).

Effect of genetic distance between production and nucleus animals on genetic gain

Figures 2 and 3 show production efficiency and selection accuracy generated for breeding schemes when the production animals were offspring or grand offspring of the selection candidates. Results are only presented for r_g = 0.2 because there was similar patterns when r_g was medium (r_g = 0.5) or higher (r_g = 0.8).

In the production environment, genetic gain and accuracy of selection increased when the production and nucleus animals were on average more related to each other than they were less related. At generation 6, genetic gain (Figure 2) and selection accuracy (Figure 3) were higher when the production animals were offspring of the selection candidates as compared to when they were grand offspring.

Environment-specific reference population

Using only production animals in the reference population to estimate SNP marker effects provided a substantial genetic gain in the production environment than using nucleus animals when the breeding goal was to improve genetic gain in the production environment. Specifically, a larger selection response was observed when the genetic correlation (r_g) between performances of production and nucleus environments was lower. When r_g between nucleus and production environment was 0.2, genetic gain increased from 0.724 to 1.31 (81%) for offspring and from 0.561 to 1.01 (80%) for grand offspring scenarios. With r_g = 0.8, production efficiency increased from 1.08 to 1.27 (18%) for offspring scenario and from 0.889 to 0.989 (11%) for grand offspring scenario. Similar findings were observed in a simulation study where a cross-breed reference population provided a higher selection response for cross-breed animals compared with using a pure breed reference population when the breeding goal was to improve selection response for cross-breed populations (Dekkers 2007; Esfandyari et al. 2015; Van Grevenhof & van der Werf 2015). Although a larger selection response was observed when the reference population was designed using production animals, technical challenges exist with regard to the large-scale genotyping and phenotyping of production animals. On the other hand, in a breeding scheme if the aim was often to achieve genetic change in the nucleus herds, afterwards disseminate to the production or commercial population, where the return of investment in a breeding scheme is achieved. Hence, we might not accurately estimate the breeding value of selection candidates in the nucleus with a reference population designed using only production animals. This is because the nucleus and production herds are at different genetic level. Therefore, the true genetic superiority might be impaired by environmental effects if we use production records to estimate breeding value of nucleus herds. The best option would be to find a balance between accounting environmental sensitivity and impairing genetic effects by environmental effects. The balance would be to design the reference population based on a mixture of nucleus and production records.

On the other hand, attempting to achieve similar selection response in the production population when nucleus animals were included in the reference population to estimate SNP marker effects provided a smaller genetic progress in the production population. This is a typical breeding scheme used in practice and such reference population designs would be ideal for populations where there is little interaction between genotypes and the environments. In a study using similar breeding structure, where there was more than 90% genetic correlation between nucleus and production environments, the accuracy of selection was higher for production traits when the reference population was designed using only nucleus animals (Hidalgo et al. 2016). In such cases, we expect less benefit by including animals from production environment into the reference population (Mulder et al. 2006). It would be even preferable to use more nucleus records for an accurate estimation of the genetic effects.

Mixed-environment reference population

Compared to the environment-specific reference population, selection response further increased in the production environment when the reference population was designed including a mixture of nucleus and production animals which fed on different quality diets. A highest selection response was observed in the production environment when various proportion of production animals were included into the reference population. At a lower genetic correlation between nucleus and production environments, a highest selection response occurred when large proportion of production animals were included in the reference population. When r_g = 0.2, production efficiency increased in the production environment from 1.31 to 1.48 for offspring scenario and from 1.01 to 1.08 for grand offspring scenario when the number of production animals in the reference population increased from 2400 to 4800. In addition, there was a slight increase in production efficiency after the number of animals in the reference population was doubled. The increase in production efficiency was small in the production environment when r_g was large. In a similar study, a higher selection response was observed for cross-breed population when the reference population to estimate marker effects contained a mixture of parental lines and cross-breed animals compared to using parental lines or cross-breeds (Dekkers 2007; Van Grevenhof & van der Werf 2015). Even though including production animals into the reference population increased genetic gain and selection accuracy, recording a large proportion of production animals may be a challenge for two reasons. First, feed efficiency is expensive to measure and it is not economical to record large number of production animals. Second, in most practical breeding schemes, performance test is based on a recording routine of nucleus animals and there is no individual feeding record in the production environment. Therefore, the mixture reference population would require the availability of individual feeding record in the nucleus and production environments.

The goal of any breeding scheme was to achieve a substantial selection response in the production environment. Breeding parents are normally selected from the nucleus environment, and genetic change is often realized in the production environment after disseminating from the nucleus to the production or commercial populations. Compared to the nucleus environment, a smaller genetic response is often observed in the production environment. This is because the realized genetic gain in the production environment depends on management practices, genetic distance, non-additive gene action and the interaction of genetic and management practices. To optimize the breeding goal in the production environment, various studies suggested different performance test designs for traditional breeding schemes (Hartmann 1992; Lo et al. 1993; Bijma & van Arendonk 1998) when the performances of nucleus and production animals are different.

For GS breeding schemes, Silva et al. (2014) reported a higher accuracy of selection when genotype by environment interaction was considered as compared to the traditional selection methods. In addition, recent studies have shown alternative reference population designs which optimizes the accuracy of selection and selection response for cross-breed animals when breeding parental lines (Dekkers & Chakraborty 2004; Dekkers 2007; Ibanz-Escriche et al. 2009; Esfandyari et al. 2015; Van Grevenhof & van der Werf 2015). On the other hand, designing the reference population using parental lines provided a higher selection response for cross-breed animals when the linkage disequilibrium (LD) between the SNP markers is higher (Esfandyari et al. 2015). One may argue that the consistency of the linkage phase in both populations is more important than the LD level, that is if the alleles of marker and QTL are in the same arrangement (coupling or repulsion). However, this was under the assumption of GS model, where performance differences between parental lines and cross-breed were due to direct genetic effect and non-additive gene action. The outcome might have been different if estimation was made in the presence of genotype by environment interaction effects. Although there are some reported results in the literature often based on simulation study, there is no unifying method to design the reference population which optimizes a breeding goal in an environment where selection is not taking place.

Our results are in agreement with Van Grevenhof & van der Werf (2015) who observed an increase in selection response for cross-breed population when the reference population included a combination of nucleus and various proportions of production animals. We found a higher selection response in the production environment for a mixture reference population as compared to only using nucleus or production animals. This is because the reference population design accounted the environmental sensitivity occurred due to feeding differences in the nucleus and production environments. The mixture reference population used an existing conventional performance testing structure and records obtained from both environments to improve the genetic gain in the production environment. In a reference population with only nucleus animals, which is the typical breeding scheme often implemented in practice, performance testing of selection candidates was basically using records obtained from animals which were fed high-quality feed sources in the nucleus. In this case, all the genetic improvements achieved in the nucleus environment were not realized in the production environment due to gene by environment interactions.

In our simulation, comparisons were not made at equal reference population size. The focus was to observe selection response in the production environment with increasing or decreasing number of production animals in the reference population at a fixed number of nucleus animals. In a mixture reference population, a larger number of animals were in the reference population compared to the environment-specific reference population breeding schemes. Therefore, selection response observed in breeding scheme with a mixture reference population might have been a contribution from a reference population design and the large number of records used in the reference population. This is because the number of records in the reference population is one factor which determines the accuracy of selection in GS breeding schemes (Goddard 2009).

In traditional selection, it has been shown that the precision to estimate genetic correlation of environments (r_g) is determined by the number of families (N) in both environments, the family size (n), heritability of the trait (h²) and the intraclass correlation (t) (Robertson 1959).

where t = ah² and a is the additive genetic relationship between two individuals.

This was extended by Bijma & Bastiaansen 2014 to precisely estimate genetic correlation of cross-breed and pure breed lines performance and have shown to require more than 100 half-sib families. Genomic selection breeding programmes may require less number of families. This could relate to the increase in selection response observed in the production environment when large proportion of production animals were included into the reference population to estimate the breeding value of selection candidates. It should be noted that a larger selection response observed for a parent offspring relationship of nucleus and environment animals as compared to a grand offspring relationship. However, in practical pig breeding programmes, the nucleus and production animals are in different generations. Thus, we might not achieve similar genetic gain with the breeding schemes where the production animals are offspring of the nucleus animals.

With the mixed reference population design, a significant number of animals are required for accurate estimation of breeding value. Hence, this would increase the cost of genotyping as both the selection candidates and all animals included in reference population must be genotyped. To minimize the cost of genotyping, it is not recommended to genotype all animals in the nucleus environment. Genotyping could be performed in some animals from the nucleus environment and some animals from the production environment providing a mixture environment animal in the reference population.

Assumptions and implications

In both simulations and data analysis, we did not assume genetic lag between the nucleus and production populations. The main focus was to observe improvements in feed efficiency by designing a reference population including nucleus and production animals that had access to different quality diets. A further difference in genetic lag between the nucleus and production environment was assumed to complicate the simulated breeding schemes. Therefore, it was decided to focus on diet differences between the nucleus and production environments. It should be noted that the larger selection response observed in the simulated breeding schemes are only applicable in the absence of genetic lag. It should be noted that in practical pig breeding programmes, there exists a significant genetic lag between the nucleus and commercial animals. Thus, our results would not be replicated in breeding schemes where the nucleus and production animals are assumed to be at different genetic level. However, the outcome of this study might be considered as a maximum threshold that can be achieved for pig breeding programmes. The aim of this study was only intended to show a general overview how one can improve feed efficiency in pig genomic selection breeding programmes by designing the reference population. Therefore, implications of this study are only limited in the absence of genetic lag and a strong genetic relationship between a nucleus and production environments. A further research could be considered to verify the results including genetic lag between the nucleus and production environments.