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Effects of genotype x environment interaction on genetic gain in breeding programs¹

Animal Breeding and Genetics Group, Wageningen University, 6700 AH Wageningen, The Netherlands

	Abstract

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Genotype x environment interaction (G x E) is increasingly important, because breeding programs tend to be more internationally oriented. The aim of this theoretical study was to investigate the effects of G x E on genetic gain in sib-testing and progeny-testing schemes. Loss of genetic gain due to G x E was predicted for different values of heritability, number of progeny per dam, number of progeny per sire, proportion of selected sires, and population size in the selection environment. Two environments were considered: a selection environment (SLE) and a production environment (PDE). The breeding goal was only for performance in PDE. A pseudo-BLUP selection index was used to predict genetic gain. Recording of half-sibs or progeny in PDE limited the loss in genetic gain in PDE due to G x E between SLE and PDE. Progeny-testing schemes had less loss in genetic gain than sib-testing schemes. Higher heritability increased the loss in genetic gain, whereas increasing the number of progeny per sire in PDE decreased the loss in genetic gain. The number of progeny per sire required to minimize loss in genetic gain due to G x E was greater for sib-testing schemes than for progeny-testing schemes. More progeny per dam slightly increased the loss in genetic gain. Genetic gains for sex-limited and carcass traits were less affected by G x E than traits measured on both sexes. Loss in genetic gain was due to decreased accuracy of selection in most situations, but it was due to decreased selection intensity in situations with small population size and a low proportion of selected sires. It was concluded that recording performance of relatives in PDE minimizes loss in genetic gain due to G x E, and that progeny-testing schemes rather than sib-testing schemes are preferable in situations with low to moderate heritability (h² 0.3), relatively short generation interval of progeny-tested sires (L_prog/L_sib 1.7), and moderate to severe G x E interaction (r_g 0.8).

Key Words: Breeding Program • Genetic Gain • Genotype x Environment Interaction • Progeny Testing • Sib Testing

	Introduction

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Livestock breeding programs are becoming more international, which means that the goals of such programs are to breed animals that can perform well in a variety of environments. As a consequence, knowledge of the effects of genotype x environment interaction (G x E) on genetic gain in breeding programs is increasingly important. Due to G x E, genetic rank of animals might change, so that the best animal in one environment might not be the best animal in another environment (Falconer and Mackay, 1996). The concept of a genetic correlation between performances in different environments can be used as a measure of ranking differences due to G x E (Falconer, 1952). In many situations, estimates of such genetic correlations are less than unity (Merks, 1988; Wei and Van der Werf, 1995; Weigel et al., 2001), indicating that selection of parents in one environment may not optimize progeny performance in another environment.

Research has been carried out to optimize specific breeding programs of different species in the presence of G x E (e.g., Meuwissen and Woolliams, 1993, Bijma and Van Arendonk, 1998; Jiang and Groen, 1999). Based on these studies, however, it is difficult to identify the effects of G x E on genetic gain in combination with other parameters, such as heritability and number of progeny per sire. Furthermore, none of those studies compared sib-testing and progeny-testing schemes.

The objective of this study was to investigate the effects of G x E on genetic gain in sib-testing and progeny-testing schemes. Loss of genetic gain due to G x E was predicted for different values of heritability, number of progeny per dam, number of progeny per sire, proportions of selected sires, and population sizes of the selection environment. Furthermore, differences in breeding goal and differences between traits measured on both sexes, sex-limited traits, and carcass traits were investigated.

	Materials and Methods

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Breeding Schemes
In this study, two environments were considered: a selection environment (SLE), with all candidates for selection, and a production environment (PDE), with commercial animals, which were not eligible for selection. The breeding goal was performance in PDE. Different degrees of G x E between SLE and PDE were created by varying the genetic correlation (Falconer, 1952). Breeding schemes were based on either sib testing or progeny testing. Selection under sib testing was based on BLUP-EBV using the animals’ own performance, average performance of full-sibs and half-sibs, and pedigree information, whereas selection under progeny testing replaced sib performance with average performance of progeny. Own performance, average performance of full-sibs and half-sibs in SLE were always available, whereas average performance of half-sibs or progeny in PDE was optional. Progeny testing in SLE was not considered, because of the limited size of SLE.

Ultimately, three breeding schemes were designed: 1) selection environment sib testing (SEsib), 2) combined selection environment and production environment sib testing (CSPsib), and 3) combined selection environment and production environment progeny testing (CSPprog). With SEsib and CSPsib, sires and dams were sib-tested, whereas in CSPprog, sires were progeny-tested and dams were sib-tested. Sires and dams were selected by truncation on animal model BLUP EBV. In SEsib, EBV were based only on records of relatives in SLE, whereas in CSPsib and CSPprog, EBV were based on records of relatives in SLE and PDE. In addition to records from SLE, in CSPsib, sires and dams had records of half-sibs from PDE, whereas in CSPprog, sires had records of progeny from PDE and dams had records of half-sibs (same animals as progeny of sires) also from PDE (Table 1). A hierarchical mating structure was assumed and generations were discrete. Each generation ns sires and nd dams were selected in SLE. Each sire was mated to nds (= nd/ns) dams. Each dam produced noff offspring in SLE. The number of full-sibs (nfs) in SLE was equal to noff –1 (excluding individual). The number of half-sibs (nhs) in SLE was equal to (nds –1) x noff (excluding full-sibs and individual). Half-sibs (nhs) or progeny (np) in PDE were produced by ndp dams born in PDE.

Carcass traits were not measured on the selection candidates themselves. In SLE, the slaughter of animals decreased the number of candidates for selection and decreased selection intensity. In SLE 20% of the animals were assumed to be slaughtered. The number of selected dams and sires was held constant compared with measuring traits on both sexes. All animals in PDE were slaughtered. Other values of parameters were as shown in Table 2.

Case 2: Including SLE Performance in Breeding Goal.
In practice, increased performance in SLE might be of economical interest. The economic value of performance in SLE was varied between 0 and 1. The economic value of performance in PDE was equal to 1 minus the economic value of performance in SLE. Other values of parameters were as shown in Table 2.

Genetic Gain, Relative Genetic Gain and Break-Even Genetic Correlation
Genetic Gain per Unit of Time.
Genetic gain was calculated deterministically by approximating BLUP-selection under an animal model using a pseudo-BLUP selection index (Wray and Hill, 1989; Villanueva et al., 1993). Genetic gain in the breeding goal (performance in PDE) was predicted for sires and dams for each generation. To account for the longer generation interval for CSPprog sires, the formula of Dickerson and Hazel (1944) and Rendel and Robertson (1950) was modified to two selection paths (sires and dams) to calculate genetic gain per unit of time, which was equal to the generation interval of sib-testing schemes:

[1]

where G = genetic gain per unit of time in the breeding goal; R_s, R_d = selection differentials for sires and dams; L_s, L_d = generation interval for sires and dams relative to sib testing (L_sib = 1); i_s, i_d = selection intensity for sires and dams; b = vector with selection index weights; P = variance-covariance matrix of information sources used in the index; ²_H = v'Cv = genetic variance of the breeding goal; v = vector with economic values, and C = genetic variance-covariance matrix.

Results were based on genetic gain at equilibrium for the breeding goal per unit of time, accounting for build up of pedigree information (Dekkers, 1992) and reduction of genetic variance due to selection (Bulmer, 1971). Equilibrium was reached after 5 to 10 generations of selection. The matrices and vectors used to calculate accuracies of selection and the genetic variance of the breeding goal will be further described in the next section. In Case 2, the selection differential per generation for environment j resulting from selection path k (sires or dams) was:

[2]

where g_j,k is a vector of covariances between information sources of selection path k and the true breeding value for environment j, and _I,k is the square root of the variance of the selection index for selection path k. The results of Eq. [2] were substituted for R_s and R_d in Eq. [1] to obtain genetic gain per unit of time for each environment.

Selection intensities (i_s or i_d) were corrected for finite population size and correlated index values (Meuwissen, 1991a). The approximation of Burrows (1972) was used to correct selection intensity for finite population size. Correlations among index values of relatives in a finite population reduce the selection intensity because of a higher than random probability of selecting related selection candidates (Meuwissen, 1991a). As the correlation between index values of relatives increased, selection moves from within-family toward between-family selection. The method of Meuwissen (1991a), which is a three-dimensional application of the correction of Rawlings (1976), was used to correct selection intensities for correlated index values of candidates for selection. Correlations between index values of full-sibs and half-sibs were calculated as by De Boer and Van Arendonk (1991) and Bijma and Van Arendonk (1998). The corrected selection intensities (i_s or i_d) were equal to i_r(t_fs, t_ks) in the notation of Meuwissen (1991a).

Relative Genetic Gain.
To measure loss in genetic gain due to G x E relative to no G x E (r_g = 1), relative genetic gain (G_rel) was calculated as:

[3]

Because the generation interval of sires and dams was constant within a scheme, the sum of generation intervals of sires and dams dropped out in Eq. [3].

Break-Even Genetic Correlation.
The rank order of breeding schemes based on genetic gain changes with decreasing genetic correlation. Rank changes of breeding schemes will occur at the "break-even" genetic correlation (i.e., when genetic gains of breeding schemes are equal). In this study, break-even genetic correlations were calculated to compare CSPprog with CSPsib and SEsib.

Pseudo-BLUP Selection Index
A pseudo-BLUP selection index approximates BLUP selection by including pedigree information using the EBV of sires and dams as sources of information in the selection index (Wray and Hill, 1989; Villanueva et al., 1993). These EBV of sires and dams include all information, which was available in the previous generation at selection. The advantages of using a pseudo-BLUP selection index were that genetic gain was predicted deterministically saving computation time and it provided insight on the effects of different parameters on the underlying components of genetic gain.

Construction of a selection index started with the breeding goal. The breeding goal contained two traits: performance in SLE and performance in PDE. Because the breeding goal was performance in PDE, a zero economic value was given to SLE performance. The breeding goal was H = v'a, where a is the vector of true breeding values for SLE and PDE performance. Each animal performed in one environment and was recorded one time. Phenotypic observations (P) are the sums of additive genetic effects (A) and environmental effects (E): P = A + E. The selection index I in generation t was:

where b_(t) = P^–1_(t)G_(t)v, where P_(t) = variance-covariance matrix of information sources in x_(t) in generation t, and G_(t) = covariance matrix between information sources in x_(t) in generation t and true breeding values in a, and x_(t) = vector of records in generation t.

The potential records in x_(t) were as follows: 1) own performance; 2) mean of full-sibs (excluding the individual); 3) mean of half-sibs in SLE or PDE (excluding full-sibs and the individual); 4) EBV dam; 5) EBV sire; 6) mean EBV of dams of half-sibs in SLE; and 7) mean of progeny in PDE. The mean EBV of dams of half-sibs or progeny in PDE was not taken into account because EBV were calculated only for animals in SLE. For pigs and poultry, EBV are usually not available for commercial animals because of incomplete dam pedigree. Information sources used with the three different breeding schemes are summarized in Table 1.

The EBV of sires and dams were used to include pedigree information. The EBV contained all information that was available in the previous generation. The mean EBV of dams of half-sibs in SLE was used to account for the genetic level of these dams. The EBV of sires and dams in generation t were:

where EBV_j(t) = estimated breeding value for trait j in generation t, and b_j(t) = P^–1_(t)g_j(t), where g_j(t) is the column of G_(t) corresponding to trait j in generation t.

Variance-Covariance Matrix of Information Sources (P-Matrix).
The P_(t)-matrix was partitioned into submatrices (P_ij(t)) corresponding to two traits (SLE = 1 and PDE = 2):

with

in which the order of rows and columns corresponded to the order of the information sources in x_(t), where OP_ij(t) = C_ij(t) + E_ij, where C_ij(t) is the ijth element of the genetic variance-covariance matrix in generation t, and E_ij is the ijth element of the environmental variance-covariance matrix; PC1_ij(t) = Cs_ij(t) + Cd_ij(t), where Cs_ij(t) is the ijth element of the sire genetic variance-covariance matrix in generation t, and Cd_ij(t) is the ijth element of the dam genetic variance-covariance matrix in generation t; _ij(t) = Cs_ij(t) + Cd_ij(t) + (Cms_ij(t=0) + E_ij)/nfs, where Cms_ij(t=0) is the ijth element of the genetic variance-covariance matrix of Mendelian sampling terms; PC2_ij(t) = PC3_ij(t) = Cs_ij(t); _ij(t) = Cs_ij(t) + (Cd_ij(t))/(nds – 1) + (Cms_ij(t=0) + E_ij)/nhs; PC4_ij(t) = C_ij(t); PC5_ij(t) = Cs_ij(t) + Cd_ij(t); PC6_ij(t) = Cs_ij(t); _ij(t) = C_ij(t) + (C_ij(t))/ndp + (Cms_ij(t=0) + E_ij)/np; and D_ij(t), S_ij(t) = see below.

The elements corresponding to half-sibs or progeny in PDE were not always used dependent on breeding scheme (see Table 1).

Covariances Between Selection Index and Breeding Goal (G-Matrix).
The G_(t)-matrix was partitioned in vectors g_ij(t) or g_j(t), where i is the trait of information in the selection index and j is the trait in the breeding goal:

Genetic Variance-Covariance Matrix (C-Matrix).
The C_(t)-matrix was a 2 x 2 matrix. The genetic (co)variance in generation t was partitioned into:

where C_ij(t) = genetic covariance between traits i and j in generation t; Cs_ij(t) = genetic sire covariance between traits i and j in generation t; Cd_ij(t) = genetic dam covariance between traits i and j in generation t; and Cms_ij(t=0) = C_ij(t=0) = genetic Mendelian sampling covariance between traits i and j, which is half of the initial genetic covariance in generation 0.

Genetic parameters change due to linkage disequilibrium caused by selection (Bulmer, 1971). The Cs_(t)-matrix and Cd_(t)-matrix, therefore, were updated each generation according to Cochran (1951). For instance, for an element Cs_ij(t) in generation t:

where Cov(A_i, I)_t–1 = b'_(t–1)g_i(t–1); ²_I(t–1) = b'_(t–1)P_(t–1)b_(t–1) = variance of the selection index, I, in generation t – 1, and k_s = i_s(i_s – x_s), where i_s is the selection intensity for sires and x_s is the standardized truncation point for sires.

The variance-covariance matrix Cd_(t) was calculated similarly, but k_d was used instead of k_s. After 5 to 10 generations of selection the genetic variance-covariance matrix reached Bulmer equilibrium (Bulmer, 1971).

Variance-Covariance Matrix of EBV (S-Matrix and D-Matrix).
The S_(t)-matrix contains the variances and covariances between EBV of sires; the D_(t)-matrix contains the variances and covariances between EBV of dams. In multivariate analysis the elements of S_(t) and D_(t) are equal to the covariances between the true additive genetic effects and the EBV (Villanueva et al., 1993). Elements of S_(t)-matrix and D_(t)-matrix change due to selection so these were updated each generation (e.g., for an element S_ij(t) in generation t:

where Cov(A_i, EBV_j)_t–1 = b'_j(t–1)g_i(t–1); Cov(A_i, I)_t–1 = b'_(t–1)g_i(t–1); and Cov(EBV_j, I)_t–1 = b'_j(t–1)G_(t–1)v.

	Results

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General
Figure 1 shows genetic gain per unit of time as a function of genetic correlation for SEsib, CSPsib, and CSPprog. Genetic gain increased as genetic correlation approached unity or minus unity, for which genetic gain was similar for the three breeding schemes. For a genetic correlation of unity, genetic gains with CSPsib and SEsib were similar because the extra information from half-sibs in PDE included in CSPsib added little to the accuracy of selection. The genetic gain with CSPprog was similar to the genetic gains with SEsib and CSPsib because of the choice of the relative generation interval of sires. For other choices of generation interval, genetic gain per unit of time would have been different.

View larger version (20K): [in this window] [in a new window]   Figure 1. Genetic gain per unit of time as a function of genetic correlation for selection environment sib testing (SEsib), combined selection environment and production environment sib testing (CSPsib), and combined selection environment and production environment progeny testing (CSPprog). Heritability = 0.3; phenotypic variance = 1.0; proportion of selected sires = 0.05; number of progeny per dam = 8; number of animals in selection environment = 2,000; number of progeny-tested sires (CSPprog) = 400; number of progeny per sire in production environment = 100; and relative generation interval CSPprog sires = 1.4.

View larger version (21K): [in this window] [in a new window]   Figure 2. Relative genetic gain (G[rg = x]/G[rg = 1]); rg = genetic correlation) as a function of heritability for combined selection environment and production environment sib testing (CSPsib) and combined selection environment and production environment progeny testing (CSPprog), with rg = 0.5 and 0. Phenotypic variance = 1.0; proportion of selected sires = 0.05; number of progeny per dam = 8; number of animals in selection environment = 2,000; number of progeny-tested sires (CSPprog) = 400; number of progeny per sire in production environment = 100; and relative generation interval for CSPprog sires = 1.4.

View larger version (26K): [in this window] [in a new window]   Figure 3. Relative genetic gain (G[rg = x]/G[rg = 1]); rg = genetic correlation) as a function of number of progeny per dam in the selection environment for combined selection environment and production environment sib testing (CSPsib) and combined selection environment and production environment progeny testing (CSPprog), with a genetic correlation of zero and heritabilities (h2) of 0.1, 0.3, and 0.5. Phenotypic variance = 1.0; proportion of selected sires = 0.05; number of animals in selection environment = 2,000; number of progeny-tested sires (CSPprog) = 400; number of progeny per sire in production environment = 100; and relative generation interval for CSPprog sires = 1.4.

View larger version (27K): [in this window] [in a new window]   Figure 4. Relative selection intensity of sires for combined selection environment and production environment sib-testing schemes (CSPsib) (i[rg = 0]/i[rg = 1]); i = selection intensity, rg = genetic correlation) as a function of population size of the selection environment (SLE) for different proportions of selected sires (p = 0.01, 0.02, 0.05, 0.10, and 0.20). Heritability = 0.3; phenotypic variance = 1.0; number of progeny per dam = 8; and number of progeny per sire in production environment = 100.

View larger version (25K): [in this window] [in a new window]   Figure 5. Relative genetic gain (G[rg = x]/G[rg = 1]); rg = genetic correlation) as a function of number of half-sibs per sire in production environment (PDE) for combined selection environment and production environment sib testing (CSPsib) and relative genetic gain as a function of number of PDE progeny per sire for combined selection environment and production environment progeny testing (CSPprog), with a genetic correlation of zero and heritabilities (h2) of 0.1, 0.3, and 0.5. Phenotypic variance = 1.0; proportion of selected sires = 0.05; number of progeny per dam = 8; number of animals in selection environment = 2,000; number of progeny-tested sires (CSPprog) = 400; and relative generation interval for CSPprog sires = 1.4.

Heritability
Figure 2 shows relative genetic gain (Eq. [3]) as a function of heritability for CSPsib and CSPprog at genetic correlations of 0.5 and 0. Relative genetic gain was higher for CSPprog than for CSPsib, indicating less sensitivity for CSPprog to G x E. Relative genetic gain decreased as heritability increased. At high heritabilities and a genetic correlation of unity, own performance in SLE is an important information source, but it is of no importance with a genetic correlation of zero. At high heritabilities, the denominator of the relative genetic gain equation (Eq. [3]) increases more than the numerator, which explains the lower relative genetic gain in Figure 2. The decrease in relative genetic gain was smaller for CSPprog than for CSPsib for both values of the genetic correlation because only the dam selection path contributed to losses in genetic gain (Table 3).

Number of Progeny per Dam in SLE
Figure 3 shows relative genetic gain as a function of the number of progeny per dam in SLE for CSPsib and CSPprog at different heritabilities and with a genetic correlation of zero. The relative genetic gain was less for higher heritability, as was also shown in Figure 2. Relative genetic gain with CSPprog decreased exponentially as number of progeny per dam increased. The contribution of the dam selection path to the total genetic gain increased with more progeny per dam (higher selection intensity), and the dam selection path was the only source of losses in genetic gain due to G x E with CSPprog (Table 3). The effect of the dam selection path on relative genetic gain was marginal with a small number of progeny per dam but substantial with a large number of progeny. Relative genetic gain with CSPsib decreased marginally as the number of progeny per dam increased because of only small changes in selection intensity, accuracy, and variance in the breeding goal, which partly counteracted each other.

Proportion of Selected Sires and SLE Population Size
Changing the SLE population size, or the proportion of selected sires, had little effect on relative genetic gain with CSPsib and CSPprog when the proportion of selected sires was at least 0.05 and the SLE population size was at least 2,000 animals (not shown). Relative genetic gain with CSPsib, however, was less if the proportions of selected males and SLE population sizes were smaller due to corrections to the selection intensity for correlated index values and finite population size. Figure 4 shows that the relative selection intensity was substantially decreased with a genetic correlation of zero for small population sizes (0 to 2,000 animals) and small proportions of selected sires (p = 0.01 to 0.05). The correlation between index values increased from 0.69 to 1.00 for full-sibs and from 0.43 to 0.94 for half-sibs, as the genetic correlation decreased from 1.00 to 0.00. With a genetic correlation of zero, selection was mainly between sire families. With CSPprog relative genetic gain and relative selection intensity were fairly stable, as the proportion of selected sires and the number of progeny-tested sires were varied (not shown). With progeny testing the correlation between index values of related sires changed very little (full-sibs = 0.41 to 0.43; half-sibs = 0.20 to 0.21), when the genetic correlation decreased from 1.00 to 0.00.

Number of PDE Progeny per Sire
Figure 5 shows relative genetic gain with a genetic correlation of zero as a function of number of half-sibs per sire in PDE with CSPsib and as a function of number of progeny per sire in PDE with CSPprog. Relative genetic gain was higher with CSPprog than with CSPsib. Relative genetic gain increased asymptotically as number of progeny/half-sibs per sire increased. The required number of half-sibs/progeny per sire to reach the asymptote was higher with CSPsib than with CSPprog. With CSPsib, the genetic gain at a genetic correlation of zero increased considerably as the number of half-sibs per sire increased, whereas genetic gain at a genetic correlation of unity increased marginally, resulting in an increasing relative genetic gain. With CSPprog, however, genetic gain increased similarly at both values of the genetic correlation, resulting in a fairly stable relative genetic gain, as the number of progeny per sire was larger than 50. More half-sibs/progeny per sire were necessary to reach the asymptote for a low heritability of 0.1 for CSPsib and CSPprog.

Generation Interval
When generation interval of sires in CSPprog was varied, absolute genetic gain changed in the opposite direction, but relative genetic gain was unaffected because it is independent of the sum of the generation intervals (see Eq. [3]). However, when the absolute genetic gain of CSPprog was compared with genetic gain of CSPsib or SEsib, the generation interval of sires in CSPprog played an important role.

Figure 6 shows the break-even genetic correlation as a function of the generation interval of sires of CSPprog comparing CSPprog with SEsib or CSPsib. When the genetic correlation (0 to 1) was less than the break-even genetic correlation, the genetic gain of CSPprog was higher than the genetic gain of SEsib or CSPsib, and vice versa. When the relative generation interval of CSPprog sires was short (e.g., 1.2), the break-even genetic correlation was 1.00, indicating that genetic gain of CSPprog was higher than genetic gain of CSPsib or SEsib. When the relative generation interval of CSPprog sires was more than 1.8, however, genetic gain of CSPprog was less than the genetic gain of CSPsib. When the relative generation interval of CSPprog sires was between 1.2 and 1.8 or 2.0, the break-even genetic correlation decreased as the generation interval of sires of CSPprog increased relative to CSPsib and SEsib. The effect was larger for CSPprog relative to CSPsib than relative to SEsib. The break-even genetic correlation decreased as heritability increased. Sib-testing schemes, therefore, are relatively better than progeny-testing schemes at high heritabilities (h² 0.3) and small G x E interactions (r_g 0.8), whereas progeny-testing schemes are better than sib-testing schemes at low heritabilities (h² 0.3) and moderate to severe G x E interactions (r_g 0.8).

View larger version (26K): [in this window] [in a new window]   Figure 6. Break-even genetic correlation as a function of generation interval of sires with combined selection environment and production environment progeny testing (CSPprog) relative to the generation interval of selection environment sib testing (SEsib) or combined selection environment and production environment sib testing (CSPsib) comparing genetic gain of CSPprog with genetic gains of CSPsib or SEsib for heritabilities (h2) of 0.1, 0.3, and 0.5. Phenotypic variance = 1.0; proportion of selected sires = 0.05; number of progeny per dam = 8; number of animals in selection environment = 2,000; number of progeny-tested sires (CSPprog) = 400; and number of progeny per sire in production environment = 100.

View larger version (23K): [in this window] [in a new window]   Figure 7. Genetic gain in each environment (SLE = selection environment; PDE = production environment) as a function of the economic value of performance in the selection environment in the breeding goal (economic valuePDE = 1 – economic valueSLE), with a genetic correla tion of 0.5 for selection environment sib testing (SEsib), combined selection environment and production environment sib testing (CSPsib), and combined selection environment and production environment progeny testing (CSPprog; Case 2). Heritability = 0.3; phenotypic variance = 1.0; proportion of selected sires = 0.05; number of progeny per dam = 8; number of animals in selection environment = 2,000; number of progeny-tested sires (CSPprog) = 400; number of progeny per sire in production environment = 100; and relative generation interval for CSPprog sires = 1.4.

	Discussion

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Without G x E, sib-testing schemes resulted in a slightly higher genetic gain than progeny-testing schemes, which agrees with studies on MOET in dairy cattle (Nicholas and Smith, 1983; Bovenhuis et al., 1989; Meuwissen, 1991b). Nicholas and Smith (1983) found an increase of 30% in genetic gain comparing sib-testing with progeny-testing schemes, which is much larger than that reported here. Nicholas and Smith (1983) did not account for decreased genetic variance due to selection (Bulmer, 1971) and decreased selection intensity due to finite population size and correlated index values (Meuwissen, 1991a), leading to an overestimation of the advantage of sib testing over progeny testing.

With G x E no study was found comparing sib-testing and progeny-testing schemes. As in Wei and Van der Werf (1994), Bijma and Van Arendonk (1998), and Jiang and Groen (1999), including information of half-sib performance in the production environment in the selection index resulted in a higher genetic gain, especially when the genetic correlation between performance in selection and production environment was low. Progeny-testing schemes were rather robust for G x E between selection and production environment, which is in agreement with Meuwissen and Woolliams (1993), who simulated an open nucleus in dairy cattle. The above studies are all species specific. The uniqueness of this study is that effects of G x E on genetic gain were investigated in sib-testing and progeny-testing schemes using parameter values that represented pig, poultry and dairy cattle breeding schemes.

Effects of G x E on Genetic Gain
The G x E affected accuracy of selection, selection intensity, and the genetic variance of the breeding goal. Loss in genetic gain was determined mainly by loss in accuracy of selection.

Accuracy of Selection.
Accuracy of selection is affected by the genetic correlation as a measure of G x E, heritability, type of information (own, sib, or progeny performance) and the number of records of certain information sources (number of sibs; number of progeny). As the genetic correlation decreased, the importance of SLE information in the index decreased and the importance of PDE information increased because performance in PDE was the breeding goal. An increase in the number of half-sibs or progeny in PDE replaced SLE information by PDE information, which limited the loss in genetic gain due to G x E. In the absence of G x E (r_g = 1), importance of own performance in SLE increased with heritability, as expected, whereas with maximum G x E (r_g = 0) own performance in SLE did not contribute to accuracy of selection for PDE at all. Consequently, relative loss of genetic gain due to G x E increased with heritability. Progeny performance in PDE was an important information source regardless of the breeding goal and the genetic correlation. Therefore, progeny-testing schemes guarantee high genetic gain in PDE, but they are less flexible for increasing performance in SLE, unless progeny testing is possible in SLE.

Selection Intensity.
Selection intensity is a function of the proportion selected and is reduced with small population size (Burrows, 1972) or correlated index values of relatives (Meuwissen, 1991a). Within a breeding scheme, G x E would not be expected to change the selection intensity very much, because the proportion of animals selected and the population size remain the same. With a small proportion of selected sires (<0.05) or a small population size (<2,000), however, selection intensity was decreased with CSPsib due to a higher correlation between index values of relatives. With a genetic correlation of zero, selection was mainly between sire families, and the number of sire families was small (e.g., five families for 1% selected from 500 males). The selection intensity of sires with CSPprog was hardly affected by G x E.

Genetic Variance of the Breeding Goal.
The genetic variance of the breeding goal in this study was equal to the genetic variance for performance in PDE. Due to selection linkage disequilibrium, genetic variance decreased. The magnitude of the decrease was determined by the accuracy of selection and selection intensity (Bulmer, 1971). Due to G x E, the accuracy of selection decreased, which resulted in an increase in genetic variance of the breeding goal. The increase in genetic variance was largest with SEsib and smallest with CSPprog. The increase in genetic variance compensated partly for the decreases in accuracy and selection intensity.

Dealing with G x E in Livestock Breeding Programs
When G x E interaction plays a role in breeding schemes, different strategies can be used to deal with this interaction. Strategies can be classified into aspects related to environment, trait definition, statistical models used in breeding value estimation and aspects related to breeding schemes. Environmental strategies attempt to decrease G x E by choosing a selection environment as similar as possible to commercial environments with respect to feeding regimen, housing system, and health status (Webb and Curran, 1986). Measurements of traits should be standardized between environments to avoid G x E as a consequence of differences in trait definition. When breeding value estimation is done separately in different countries, G x E might arise from use of different statistical models. The goal of organizations such as Interbull (Uppsala, Sweden) is to harmonize statistical models and trait definitions in different countries (Van der Linde and De Jong, 2002).

In many situations, however, G x E cannot be avoided because it is beyond the control of breeders and statisticians. In these situations, breeding schemes need to be optimized to limit the loss in genetic gain in the presence of G x E. Robertson (1959) suggested as a guideline that a genetic correlation of 0.8 or higher could be interpreted as G x E with little biological importance. Assuming a genetic correlation of 0.8 between SLE and PDE, however, would mean that 20% of the genetic gain might be sacrificed if no records were available on relatives performing in PDE. Recording of half-sibs can limit the loss in genetic gain to 10% and recording of progeny can limit the loss to 4%. Brascamp et al. (1985), Webb and Curran (1986), and Hartmann (1990) considered testing of half-sibs under commercial situations as a good option to maintain genetic gain in the presence of G x E. Merks and De Vries (2002) proposed efficient use of large amounts of commercial information on pigs stored by farmers and slaughterhouses. In poultry breeding, however, commercial information is difficult to use because recording of pedigrees is difficult under commercial circumstances. Recurrent testing of cross-bred offspring of purebred selection candidates is used in layer breeding programs to maintain genetic gain under commercial conditions (Albers et al., 2002). Cold and normal conditions are used in broiler breeding programs to increase ascites resistance (Albers et al., 2002). In dairy cattle, sires are selected based on progeny records performing in different commercial dairy farms, whereas dams are selected partly in a nucleus herd. Meuwissen and Woolliams (1993) concluded that open MOET nucleus breeding schemes with progeny testing are robust even with significant G x E. In environments where no progeny are tested, loss in genetic gain might be larger because genetic gain in that environment is a correlated response.

Breeding schemes differ in loss in genetic gain due to G x E. Based on results in this study, progeny-testing schemes have less loss in genetic gain than sib-testing schemes and tend to have greater genetic gain when the genetic correlation is low to moderate (r_g 0.8). Progeny-testing schemes are preferable in situations with low to moderate heritability (h² 0.3), relatively short generation interval for progeny-tested sires (L_prog/L_sib 1.7), and moderate to severe G x E interaction (r_g 0.8). The concept of break-even genetic correlation (the value of the genetic correlation when genetic gain with different breeding schemes is equal) can be used to determine whether sib testing or progeny testing is preferable. Costs of the breeding program and rate of inbreeding are other criteria to consider in deciding whether sib testing or progeny testing is preferable. Progeny-testing schemes are more expensive than sib-testing schemes because more progeny need to be produced and recorded and because housing costs for sires are more due to the longer generation interval. Rates of inbreeding will favor progeny testing, even in situations without G x E (Bovenhuis et al., 1989). With increasing G x E, however, the advantage of progeny testing could increase even more because the correlation between index values of relatives is fairly stable with progeny testing, whereas the correlation increases with sib testing. The higher correlation between index values of relatives with sib testing causes a higher rate of inbreeding (Burrows, 1984; Bijma et al., 2001). Economic aspects of the breeding program and rate of inbreeding must be considered when optimizing a specific breeding program.

	Implications

Top Abstract Introduction Materials and Methods Results Discussion Implications Literature Cited

 
This study showed that the genotype x environment interaction between selection environment and production environment decreased genetic gain under commercial conditions. Recording of half-sibs or progeny under commercial conditions limited the loss in genetic gain. Progeny-testing schemes had less loss in genetic gain than sib-testing schemes. Higher heritability resulted in substantially more loss in genetic gain, but increasing the number of progeny per sire in the production environment limited the loss. Progeny-testing schemes were preferable in situations with low heritability, relatively short generation interval of progeny-tested sires, and moderate to severe genotype x environment interaction. The break-even genetic correlation (the value of genetic correlation when the genetic gain of different breeding schemes is equal) is useful for determining whether sib testing or progeny testing is preferable.

	Footnotes

 
¹ The authors thank J. A. M. van Arendonk, R. Veerkamp, and B. Ducro for helpful suggestions and comments on the manuscript and for fruitful discussions about this study. The authors are thankful to M. Grossman giving technical comments and suggestions on the manuscript.

² Correspondence: P.O. Box 338 (phone: +31-(0)317-485798; fax: +31-(0)317-483929; e-mail: herman.mulder{at}wur.nl).

Received for publication July 12, 2004. Accepted for publication October 12, 2004.

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