# The impact of training on data from genetically-related lines on the accuracy of genomic predictions for feed efficiency traits in pigs

Amir Aliakbari, Emilie Delpuech, Yann Labrune, Juliette Riquet, Hélène Gilbert

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## To cite this version:

Amir Aliakbari, Emilie Delpuech, Yann Labrune, Juliette Riquet, Hélène Gilbert. The impact of training on data from genetically-related lines on the accuracy of genomic predictions for feed efficiency traits in pigs. Genetics Selection Evolution, 2020, 52 (1), pp.57. 10.1186/s12711-020-00576-0. hal-03138490

HAL Id: hal-03138490

https://hal.inrae.fr/hal-03138490v1

Submitted on 31 Jul 2025

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# The impact of training on data from genetically-related lines on the accuracy of genomic predictions for feed efficiency traits in pigs

Amir Aliakbari*, Emilie Delpuech, Yann Labrune, Juliette Riquet and Hélène Gilbert

## Abstract

**Background:** Most genomic predictions use a unique population that is split into a training and a validation set. However, genomic prediction using genetically heterogeneous training sets could provide more flexibility when constructing the training sets in small populations. The aim of our study was to investigate the potential of genomic prediction of feed efficiency related traits using training sets that combine animals from two different, but genetically-related lines. We compared realized prediction accuracy and prediction bias for different training set compositions for five production traits.

**Results:** Genomic breeding values (GEBV) were predicted using the single-step genomic best linear unbiased prediction method in six scenarios applied iteratively to two genetically-related lines (i.e. 12 scenarios). The objective for all scenarios was to predict GEBV of pigs in the last three generations (~400 pigs, G7 to G9) of a given line. For each line, a control scenario was set up with a training set that included only animals from that line (target line). For all traits, adding more animals from the other line to the training set did not increase prediction accuracy compared to the control scenario. A small decrease in prediction accuracies was found for average daily gain, backfat thickness, and daily feed intake as the number of animals from the target line decreased in the training set. Including more animals from the other line did not decrease prediction accuracy for feed conversion ratio and residual feed intake, which were both highly affected by selection within lines. However, prediction biases were systematic for these cases and might be reduced with bivariate analyses.

**Conclusions:** Our results show that genomic prediction using a training set that includes animals from genetically-related lines can be as accurate as genomic prediction using a training set from the target population. With combined reference sets, accuracy increased for traits that were highly affected by selection. Our results provide insights into the design of reference populations, especially to initiate genomic selection in small-sized lines, for which the number of historical samples is small and that are developed simultaneously. This applies especially to poultry and pig breeding and to other crossbreeding schemes.

## Background

Given the large economic impact of feed efficiency in the swine industry, its evaluation requires accurate estimation of breeding values (BV) and selection of animals [1]. The most commonly used criterion to measure feed efficiency in livestock species is feed conversion ratio

<footnote>*Correspondence: amir.alikbari@inrae.fr
GenPhySE, Université de Toulouse, INRAE, 31326 Castanet-Tolosan, France</footnote>
(FCR) and is defined as feed intake per unit of live weight gain [2]. However, in 1963, residual feed intake (RFI) was introduced in cattle as an alternative criterion for feed efficiency [3]. In general, FCR and RFI are highly genetically correlated [4]. Nevertheless, selection of animals based on FCR can be accompanied by undesirable correlated responses in other traits such as appetite [5, 6], whereas selection for RFI is almost independent of these traits since RFI is feed intake adjusted for production trait by linear regression. Due to the high cost of measuring daily feed intake (DFI), and thus RFI and FCR [7], fewer phenotypic records are available, which reduces the accuracy of selection. Genomic selection has the potential to improve pig feed efficiency in some populations [8, 9]. Recent advances in genomic evaluation methodologies, such as single-step genomic best linear unbiased prediction (ssGBLUP), enable more accurate evaluations in small populations. The ssGBLUP combines phenotypic, genotypic, and pedigree information in a single genomic evaluation of animals [10–13]. The number of animals in the reference population has been shown to affect the accuracy of genomic predictions [14]. Multi-breed or admixed genomic evaluations have been proposed to increase the number of animals in reference sets for small populations [15], resulting in increases in prediction accuracy in some cases [16]. A study on multi-breed genomic evaluation using real data from Holstein and Jersey bulls showed that using a combined reference population resulted in comparable accuracies of genomic estimated breeding values (GEBV) in purebred validation sets, or exceeded that achieved with a purebred reference population of the same breed [17]. Adding a smaller population, i.e. Brown Swiss, to a reference population of Holstein and Jersey bulls resulted in slight increases in accuracy of predictions when breeds were considered as a single, joint population, while slight increases in accuracy were also observed if the breeds were treated as genetically-related traits [18]. Simulation studies with mixed reference populations also showed increases in prediction accuracy. A simulation study on genomic prediction across multiple populations in cattle showed that adding relatively few individuals from another population to a training set substantially increased the accuracy of predictions in the first population, regardless of the heritability ($h^2$) or marker density [19]. Another simulation study reported that genomic predictions using a combined versus a single reference population increased the accuracy of genomic predictions by 25%, with traits with a lower heritability benefiting more from the combination of populations [20]. However, using a combined reference population can be challenging if relationships between populations are absent: allele frequencies at the marker and/or causal loci, or causal variants themselves,

can differ between populations, [15, 16]. Another limitation for across-breed genomic prediction is the inconsistency of linkage disequilibrium (LD) between markers and quantitative trait loci (QTL) between breeds, which is one of the assumptions of most genomic prediction models [17].

Given the presence of (ancestral) relationships between animals and the greater consistency of LD between genetically-related lines within a breed than between breeds that have been separated for decades, using a multi-line reference population may be more beneficial than using a multi-breed reference population [16]. However, the changes in allele frequency since separation of the lines may still represent a challenge for using a multi-line reference population [21]. To the best of our knowledge, the use of a multi-line genomic evaluation strategy in small, related lines using real data has not been studied, in spite of the existence of numerous related lines worldwide. Our hypothesis was that, in small porcine populations with few available ancestral samples, i.e. for which it is not possible to build large reference populations, including information from a genetically-related line in the training population could provide similar prediction accuracies as a within-line training population. Therefore, we explored reference populations with different structures that combined data from two lines that descended from a common origin, and compared the prediction accuracy obtained with that obtained when only information from the target line was used for training.

# Methods

## Population and data structure

The data were collected during a selection experiment that was conducted at INRAE (UE GenESI, Surgères, France, https://doi.org/10.15454/1.5572415481185847E12) on French Large White pigs. Two lines were established by nine generations of divergent selection for RFI from 2000 to 2015 [22]. The G0 generation resulted from the mating of 30 boars and 30 gilts from generation F0 using artificial insemination. Among the G0 animals, 116 boar candidates for selection from all 30 litters were tested for RFI to select six extreme founder boars for each line (LRFI: low RFI, and HRFI: high RFI). The two lines were initiated by mating the selected boars to about 35 random G0 gilts per line. Inbreeding was minimized at each generation. The development of each line continued with the selection of six boars out of 96 tested candidates in each generation from G1 to G9. In each generation, at least one additional parity was produced to evaluate correlated responses to selection for production traits on both females and castrated males (henceforth referred to as response animals). Selection candidates were evaluated
for RFI from 35 to 95 kg of body weight (BW), and response animals were evaluated from 10 weeks of age until slaughter (105 kg BW until G5 and 115 kg BW from G6 onwards). Animals were raised in four pens per batch and at least four batches per generation. Test pens were equipped with single-place electronic feeders ACEMA64 (ACEMO, France). Animals were offered ad libitum access to a pelleted diet based on cereals and soya bean meal containing 10 MJ net energy (NE)/kg and 160 g CP/ kg, with a minimum of 0.80 g digestible Lys/MJ NE. In each generation, boars were selected based on a fixed RFI selection index that was established from pre-computed phenotypic correlations between DFI (g/day) and average daily gain (ADG, g/day) between 35 and 95 kg BW, and live backfat thickness (BFT, mm) at 95 kg BW [23], as RFI = DFI - 1.06 × ADG - 37 × BFT. The average metabolic BW (AMBW) was the same for all selection candidates and therefore excluded from the selection index equation. Selection candidates had records for feed intake, body weight, and live body composition traits. In addition to these phenotypes, gilts and castrated males had records for carcass composition traits [23]. For the present study, RFI, FCR, DFI, ADG and BFT were analyzed. These traits were available for both selection candidates and response animals. The number of observations for the five traits for each line are in Table 1. RFI of selection candidates was computed between 35 and 95 kg BW as the residual of a multiple linear regression of DFI on the traits included in the selection index. For gilts and castrated males from the correlated response batches, RFI was estimated from 10 weeks of age to slaughter as the residual of a multiple linear regression of DFI on AMBW, ADG from 10 weeks of age to slaughter, carcass BFT (carcBFT), and lean meat content (LMC; computed from cut weights) at slaughter. AMBW was included to account for maintenance requirements and the other traits were included to account for production requirements. [22]. Fixed effects included in the regression model to compute RFI of response animals were sex, pen size, contemporary group and BW at the beginning of the test. Complete pedigree information was collected from F0 to G9, plus up to 10 generations of ancestors, and contained 7046 animals (Table 1).

## Combining and standardizing traits

Preliminary analyses on the five traits showed high genetic correlations between similar traits measured in selection candidate and response animals (> 0.80 ± 0.11, except 0.75 ± 0.08 between live BFT and carcass BFT). Therefore, to increase the amount of information, corresponding traits in selection candidate and response animals were combined for further analyses. Since animals differed in age and BW when measurements were taken,

for each trait, records from selection candidates were standardized to the variance of the corresponding trait in the response animals as:

$$y_{Rij} = \frac{y_{sij}}{\sigma_{si}} \sigma_{Ri}$$

where $y_{Rij}$ is the standardized trait $i$ ($i=1,..., 5$) for selection candidate $j$, $y_{sij}$ is the record of trait $i$ measured on animal $j$, $\sigma_{si}$ is the phenotypic standard deviation of trait $i$ measured on selection candidates, and $\sigma_{Ri}$ is the phenotypic standard deviation of trait $i$ measured on females and castrated males in the response batches. Descriptive statistics of these traits are in Table 2.

## Single nucleotide polymorphism (SNP) genotyping data and imputation

SNP genotyping data were available for all selected boars and their mates from G0 to G9, additional pigs from response batches of G6 to G8, and all selection candidates in G9. In total, 1647 animals had SNP genotypes, of which 286 animals were genotyped with the Porcine SNP60v2 BeadChip (Illumina) (64,232 SNPs) and 1361 animals with the GGP Porcine HD Array (Illumina) (68,516 SNPs). Genotype quality control excluded SNPs with a call rate lower than 95%, individuals with a call rate lower than 90%, SNPs that were not in Hardy-Weinberg equilibrium ($p < 10^{-10}$), SNPs with a minor allele frequency lower than 0.01, and individuals with parent-offspring incompatibility (e.g., opposite homozygotes) with at least one parent. The PLINK software was used for SNP and individual genotype quality control [24]. SNPs on the sex chromosomes were removed. After quality control of each SNP chip dataset, the SNPs present in each panel were imputed to the alternative panel using the FImpute software [25] in a single step. The two SNP chips shared 42,800 SNPs. The number of genotyped animals retained after imputation was 1643, and the final genotype dataset contained 64,233 informative SNPs. Thus, all animals had equal genotypic information. Genotypes were coded as 0, 1, or 2 for later calculation of the genomic relationship matrix. The number of animals with genotype data per generation and line is in Table 1.

## Model and analyses

Predictions obtained with BLUP are based on the assumption of no genetic differences between subpopulations [26, 27]. Therefore, to account for selection in our dataset, all genetic and genomic analyses were carried out with bivariate approaches, i.e. the five other traits were individually paired with the selection index in two-trait model analyses. By including the selection criterion, the analyses of other
<table><caption>Table 1 Numbers of animals in the pedigree and data structure</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Ancestors</th><th rowspan="2">F0</th><th rowspan="2">G0</th><th rowspan="2">HRFI</th><th colspan="10">Ancestors</th></tr><tr><th>G0</th><th>G1</th><th>G2</th><th>G3</th><th>G4</th><th>G5</th><th>G6</th><th>G7</th><th>G8</th><th>G9</th><th>Total</th></tr></thead><tbody><tr><td>Pedigree</td><td>159</td><td>67</td><td>104</td><td>48</td><td>216</td><td>297</td><td>277</td><td>260</td><td>270</td><td>795</td><td>474</td><td>292</td><td>280</td><td>3209</td></tr><tr><td>Pedigree only</td><td></td><td></td><td></td><td>1</td><td>2</td><td>89</td><td>78</td><td>62</td><td>68</td><td>352</td><td>149</td><td>5</td><td>0</td><td>806</td></tr><tr><td>Pedigree and genotype only</td><td></td><td></td><td></td><td>41</td><td>41</td><td>42</td><td>44</td><td>36</td><td>47</td><td>40</td><td>35</td><td>42</td><td>91</td><td>459</td></tr><tr><td>ADG</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Phenotype only</td><td></td><td></td><td></td><td>0</td><td>167</td><td>160</td><td>149</td><td>156</td><td>149</td><td>304</td><td>194</td><td>148</td><td>93</td><td>1520</td></tr><tr><td>Phenotype and genotype</td><td></td><td></td><td></td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>71</td><td>73</td><td>66</td><td>92</td><td>338</td></tr><tr><td>Missing</td><td></td><td></td><td></td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>28</td><td>23</td><td>31</td><td>4</td><td>86</td></tr><tr><td>BFT</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Phenotype only</td><td></td><td></td><td></td><td>0</td><td>167</td><td>160</td><td>149</td><td>156</td><td>149</td><td>237</td><td>176</td><td>62</td><td>84</td><td>1340</td></tr><tr><td>Phenotype and genotype</td><td></td><td></td><td></td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>71</td><td>73</td><td>66</td><td>92</td><td>338</td></tr><tr><td>Missing</td><td></td><td></td><td></td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>95</td><td>41</td><td>117</td><td>13</td><td>266</td></tr><tr><td>DFI</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Phenotype only</td><td></td><td></td><td></td><td>0</td><td>166</td><td>160</td><td>149</td><td>156</td><td>149</td><td>263</td><td>182</td><td>138</td><td>93</td><td>1456</td></tr><tr><td>Phenotype and genotype</td><td></td><td></td><td></td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>71</td><td>73</td><td>66</td><td>92</td><td>338</td></tr><tr><td>Missing</td><td></td><td></td><td></td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>69</td><td>35</td><td>41</td><td>4</td><td>150</td></tr><tr><td>FCR</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Phenotype only</td><td></td><td></td><td></td><td>0</td><td>166</td><td>160</td><td>148</td><td>156</td><td>149</td><td>263</td><td>182</td><td>138</td><td>93</td><td>1455</td></tr><tr><td>Phenotype and genotype</td><td></td><td></td><td></td><td>4</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>71</td><td>73</td><td>66</td><td>92</td><td>336</td></tr><tr><td>Missing</td><td></td><td></td><td></td><td>2</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>69</td><td>35</td><td>41</td><td>4</td><td>153</td></tr><tr><td>RFI</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Phenotype only</td><td></td><td></td><td></td><td>0</td><td>164</td><td>159</td><td>146</td><td>156</td><td>143</td><td>185</td><td>147</td><td>56</td><td>80</td><td>1236</td></tr><tr><td>Phenotype and genotype</td><td></td><td></td><td></td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>71</td><td>73</td><td>66</td><td>92</td><td>338</td></tr><tr><td>Missing</td><td></td><td></td><td></td><td>0</td><td>3</td><td>1</td><td>3</td><td>0</td><td>6</td><td>147</td><td>70</td><td>123</td><td>17</td><td>370</td></tr></tbody></table><table><thead><tr><th rowspan="2"></th><th rowspan="2">Ancestors</th><th rowspan="2">0</th><th rowspan="2">G0</th><th rowspan="2">LRFI</th><th colspan="10">Ancestors</th></tr><tr><th>G0</th><th>G1</th><th>G2</th><th>G3</th><th>G4</th><th>G5</th><th>G6</th><th>G7</th><th>G8</th><th>G9</th><th>Total</th></tr></thead><tbody><tr><td>Pedigree</td><td>159</td><td>67</td><td>104</td><td>46</td><td>203</td><td>303</td><td>314</td><td>327</td><td>357</td><td>826</td><td>481</td><td>344</td><td>280</td><td>3481</td></tr><tr><td>Pedigree only</td><td></td><td></td><td></td><td>0</td><td>1</td><td>98</td><td>100</td><td>107</td><td>130</td><td>337</td><td>132</td><td>8</td><td>0</td><td>913</td></tr><tr><td>Pedigree and genotype only</td><td></td><td></td><td></td><td>40</td><td>35</td><td>40</td><td>41</td><td>43</td><td>43</td><td>48</td><td>55</td><td>48</td><td>93</td><td>486</td></tr><tr><td>ADG</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Phenotype only</td><td></td><td></td><td></td><td>0</td><td>161</td><td>159</td><td>167</td><td>171</td><td>178</td><td>359</td><td>211</td><td>203</td><td>95</td><td>1704</td></tr><tr><td>Phenotype and genotype</td><td></td><td></td><td></td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>74</td><td>73</td><td>74</td><td>90</td><td>347</td></tr><tr><td>Missing</td><td></td><td></td><td></td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>8</td><td>10</td><td>11</td><td>2</td><td>31</td></tr><tr><td>BFT</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Phenotype only</td><td></td><td></td><td></td><td>0</td><td>161</td><td>159</td><td>167</td><td>171</td><td>178</td><td>284</td><td>206</td><td>105</td><td>86</td><td>1517</td></tr><tr><td>Phenotype and genotype</td><td></td><td></td><td></td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>74</td><td>73</td><td>74</td><td>90</td><td>347</td></tr><tr><td>Missing</td><td></td><td></td><td></td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>83</td><td>15</td><td>109</td><td>1</td><td>1</td><td>218</td></tr><tr><td>DFI</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Phenotype only</td><td></td><td></td><td></td><td>0</td><td>160</td><td>159</td><td>167</td><td>171</td><td>178</td><td>316</td><td>206</td><td>194</td><td>95</td><td>1646</td></tr><tr><td>Phenotype and genotype</td><td></td><td></td><td></td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>74</td><td>73</td><td>74</td><td>90</td><td>347</td></tr><tr><td>Missing</td><td></td><td></td><td></td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>51</td><td>15</td><td>20</td><td>2</td><td>89</td></tr><tr><td>FCR</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Phenotype only</td><td></td><td></td><td></td><td>0</td><td>159</td><td>159</td><td>167</td><td>171</td><td>178</td><td>316</td><td>208</td><td>195</td><td>95</td><td>1648</td></tr><tr><td>Phenotype and genotype</td><td></td><td></td><td></td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>74</td><td>73</td><td>74</td><td>90</td><td>90</td><td>347</td></tr><tr><td>Missing</td><td></td><td></td><td></td><td>0</td><td>2</td><td>0</td><td>0</td><td>0</td><td>0</td><td>51</td><td>13</td><td>19</td><td>2</td><td>87</td></tr><tr><td>RFI</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Phenotype only</td><td></td><td></td><td></td><td>0</td><td>160</td><td>158</td><td>161</td><td>171</td><td>173</td><td>230</td><td>165</td><td>101</td><td>80</td><td>1399</td></tr><tr><td>Phenotype and genotype</td><td></td><td></td><td></td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>74</td><td>73</td><td>74</td><td>90</td><td>347</td></tr><tr><td>Missing</td><td></td><td></td><td></td><td>0</td><td>1</td><td>1</td><td>6</td><td>0</td><td>5</td><td>137</td><td>56</td><td>113</td><td>17</td><td>336</td></tr></tbody></table>

HRFI high RFI line, LRFI low RFI line, Ancestors animals before the base generation, F0 base generation, G0 to G9 generations of selection 0 to 9, RFI residual feed intake, ADG average daily gain, FCR feed conversion ratio, DFI daily feed intake, BFT backfat thickness
<table><caption>Table 2 Descriptive statistics of the data for the studied traits in the HRFI and LRFI lines</caption><thead><tr><th>Line</th><th>Trait</th><th>Number of records</th><th>Minimum</th><th>Maximum</th><th>Average</th><th>Coefficient of variation</th></tr></thead><tbody><tr><td rowspan="5">HRFI</td><td>ADG</td><td>1868</td><td>0.44</td><td>1.07</td><td>0.76</td><td>11.03</td></tr><tr><td>BFT</td><td>1687</td><td>9.67</td><td>49.27</td><td>27.33</td><td>26.62</td></tr><tr><td>DFI</td><td>1802</td><td>1.37</td><td>3.20</td><td>2.18</td><td>12.54</td></tr><tr><td>FCR</td><td>1799</td><td>2.13</td><td>3.81</td><td>2.8</td><td>9.26</td></tr><tr><td>RFI</td><td>1581</td><td>-0.29</td><td>0.86</td><td>0.05</td><td>-</td></tr><tr><td rowspan="5">LRFI</td><td>ADG</td><td>2053</td><td>0.45</td><td>1.06</td><td>0.76</td><td>10.69</td></tr><tr><td>BFT</td><td>1866</td><td>10.00</td><td>44.63</td><td>26.45</td><td>24.60</td></tr><tr><td>DFI</td><td>1995</td><td>1.05</td><td>2.92</td><td>2.01</td><td>12.91</td></tr><tr><td>FCR</td><td>1997</td><td>1.72</td><td>3.70</td><td>2.60</td><td>9.11</td></tr><tr><td>RFI</td><td>1748</td><td>-0.56</td><td>0.46</td><td>-0.04</td><td>-</td></tr></tbody></table>

HRFI high RFI line, LRFI low RFI line, ADG average daily gain (kg/day), BFT backfat thickness (mm), DFI daily feed intake (kg/day), FCR feed conversion ratio (kg/kg), RFI residual feed intake (kg/day)

traits are conditioned based on all the information that was used for selection [28–30].

Preliminary analyses were carried out using a general linear model in R (glm procedure) to evaluate the significance (p<0.05) of fixed environmental sources of variation. The significant fixed factors included pen size (5 levels: 8, 9, 10, 11, 12 pigs per pen), herd of birth (2 levels), sex (3 levels), and contemporary groups (CG, 99 levels). BW at slaughter was fitted in the model as a covariate only for BFT. CG were defined as animals born in the same week and raised in the same enclosure. Litter was fitted as a random environmental source of variation and its significance at the 5% level was determined using a likelihood ratio test.

The genetic analyses were performed using the AIREMLF90 and BLUPF90 software [31] for the BLUP and ssGBLUP methods, respectively. Prior to ssGBLUP evaluations, the variance components of the traits were obtained using the restricted maximum likelihood algorithm implemented in AIREMLF90. These analyses were performed using all available data and only the full pedigree relationship matrix (A). Variance components were estimated with the bivariate animal mixed model as follows:

$$y = Xb + Z_1a + Z_2l + e$$

where y is the vector of observations for the index and one of the five studied traits, b is the vector of fixed effects (described above), a is the vector of additive genetic effects, l is the vector of litter effects, and e is the vector of random residuals. X, Z₁ and Z₂ are the incidence matrices for b, a, and l, respectively. Distributions assumed for the random terms are a ~ N(0, G₀ ⊗ A), l ~ N(0, R₁ ⊗ I), e ~ N(0, Rₑ ⊗ I), where G₀ is a 2 × 2 symmetric (co)variance matrix of direct additive genetic effects, and R₁ and Rₑ are 2 × 2 symmetric (co)variances

matrices of litter and residual effects, respectively. I denotes the identity matrix.

Genomic breeding values were estimated using ssGBLUP with the same models in the BLUPF90 software, with the previously estimated (co)variances and using the H matrix, which is a combined relationship matrix of the A matrix and marker-based relationship matrix (G) of genotyped animals [10, 12]. The G matrix was constructed and scaled by $2 \sum \{p_i(1 - p_i)\}$, where $p_i$ is the frequency of the second allele at locus i, following Van Raden [32]. Computation of the H matrices used outputs of BLUPF90 (G) and the full A matrix, which was obtained using the AGHmatrix R package [33]. In all scenarios, G had similar average diagonal elements as the pedigree relationship matrix for the genotyped animals (A₂₂).

### Scenarios

Two symmetric series of six scenarios, one for each line, were defined for genomic prediction. An overview of the scenarios is shown in Fig. 1. In all scenarios, genotyped animals of the last three generations (G7 to G9, 433 pigs for the LRFI and 399 pigs for the HRFI line) were considered for validation in a given line (target line), and their information was removed from the training dataset.

The training sets were structured based on which generations and line were used. Scenario 1 comprised only animals from the target line and was the control scenario since it represented a routine genomic prediction design where all data would be available from the same line. All other scenarios were compared to this control scenario to evaluate which combination of training populations from the two lines achieved a prediction accuracy similar to the control scenario. Scenarios 2 and 3 included the training set of scenario 1 and in addition, either the
<figure><img src="image_4.png" /></figure>

animals from G4 to G9 (scenario 2), or G7 to G9 (scenario 3) of the other line.

For scenarios 4 to 6, animals from the target line in the training set were limited to the three generations nearest to the validation set (G4 to G6). In scenarios 4 and 5, the contribution to the training set of the animals from the other line was as in scenario 2 (G4 to G9) and scenario 3 (G7 to G9), respectively. For scenario 6, the number of animals in the training set was close to that of scenario 1 and only animals from the G9 generation of the other line. Performance data of animals from the generation and line combinations that did not contribute to the training or validation sets were removed from the analysis, but their pedigree information was kept in order to trace relationships back to the founding generation. For example, phenotypes and genotypes of animals from G0 to G3 of both lines were removed for scenario 4, since they were not part of the training or validation sets. The number of genotyped animals in the training and validation sets for the 12 scenarios are in Table 3.

## Accuracy and bias of genomic predictions

Usually the correlation between the vector of estimated breeding values (EBV) to be evaluated and the vector of true breeding values (TBV), r(TBV, EBV), cannot be computed. In the literature, multiple criteria have been proposed to quantify and compare prediction accuracies of genomic predictions between training and validation set structures and between prediction methods. Cross-validation approaches are often conducted based on r(EBV, y*), where y* is either the vector of phenotypes adjusted for fixed effects or the vector of deregressed EBV of the validation set. Thus, a widely used criterion is r(EBV, y*)/√h², where h² is the heritability of the trait. However, this criterion requires all the genotyped animals to have a sufficiently accurate y* value [34]. When y* is an adjusted phenotype of the animal's own measurement, it suffers from the inability to adjust for the random residual effects. In the optimum situation, the expected value of the correlation would then be the square root of heritability [35]. Alternatively, using an
<table><caption>**Table 3** Number of genotyped animals in the training and validation sets for the six scenarios for the HRFI and LRFI validation sets</caption><thead><tr><th rowspan="2"></th><th colspan="2">HRFI</th><th colspan="2">LRFI</th></tr><tr><th>Training</th><th>Validation</th><th>Training</th><th>Validation</th></tr></thead><tbody><tr><td>Scenario 1</td><td>398</td><td>399</td><td>400</td><td>433</td></tr><tr><td>Scenario 2</td><td>1051</td><td>399</td><td>1005</td><td>433</td></tr><tr><td>Scenario 3</td><td>831</td><td>399</td><td>799</td><td>433</td></tr><tr><td>Scenario 4</td><td>859</td><td>399</td><td>825</td><td>433</td></tr><tr><td>Scenario 5</td><td>639</td><td>399</td><td>619</td><td>433</td></tr><tr><td>Scenario 6</td><td>389</td><td>399</td><td>403</td><td>433</td></tr></tbody></table>

HRFI high RFI line, LRFI low RFI line

EBV obtained from a complete dataset as the best predictor of TBV would cause autocorrelation between the reference and evaluated EBV when the training and validation sets are closely related through the pedigree, leading to higher correlations [35]. Legarra and Reverter [34] proposed to complement the cross-validation approach with a semi-parametric approach that can be used in a large number of cases, with the advantage of not requiring knowledge of the TBV or adjustment of phenotypes. The underlying assumptions of this approach are (1) the variance components are similar in the training and validation datasets, and (2) the validation set is sufficiently diverse and large (i.e. composed of various families). In brief, with their approach, the correlation between EBV using part of the dataset (partial) and EBV obtained using the whole dataset results in an estimator of the ratio of the accuracies of the EBV from these two datasets. We followed this approach to evaluate the potential for genomic prediction when including data from a related line compared to genomic prediction using all data from the target line, which will be referred to as GEBV<sub>w</sub> (GEBV obtained using the whole dataset), i.e., to obtain GEBV<sub>w</sub> for the validation set of each line, two separate ssGBLUP analyses were performed (one per line). GEBV<sub>p</sub> (GEBV obtained using partial dataset) were the GEBV obtained from the six scenarios for the validation sets in each target line. The criterion for prediction accuracy for each trait and each scenario was then the correlation between GEBV<sub>p</sub> and GEBV<sub>w</sub>, r(GEBV<sub>p</sub>, GEBV<sub>w</sub>). Bias of the genomic predictions was computed as the deviation of the regression coefficient of GEBV<sub>w</sub> on GEBV<sub>p</sub> from 1, as also proposed in [34].

Standard errors of the prediction accuracy correlations, r, were obtained as $\sqrt{[(1 - r^2)/(n - 2)]}$, where n is the number of animals used to obtain correlations in the validation sets. Differences between correlations in different scenarios were tested using the Williams t-test in the

<table><caption>**Table 4** Estimates of variance components (SE) of the studied traits</caption><thead><tr><th>Trait</th><th>Phenotypic variance</th><th>Heritability</th><th>Litter effects<sup>a</sup></th></tr></thead><tbody><tr><td>ADG</td><td>5811.70 (164.75)</td><td>0.25 (0.04)</td><td>0.10 (0.02)</td></tr><tr><td>BFT</td><td>14.37 (0.47)</td><td>0.36 (0.05)</td><td>0.12 (0.02)</td></tr><tr><td>DFI</td><td>0.04 (0.001)</td><td>0.24 (0.04)</td><td>0.09 (0.02)</td></tr><tr><td>FCR</td><td>0.04 (0.001)</td><td>0.24 (0.04)</td><td>0.07 (0.02)</td></tr><tr><td>RFI</td><td>0.01 (0.004)</td><td>0.12 (0.02)</td><td>0.08 (0.02)</td></tr></tbody></table>

ADG average daily gain (g/day), BFT backfat thickness (mm), DFI daily feed intake (kg/day), FCR feed conversion ratio (kg/kg), RFI residual feed intake (kg/day)

psych R package [36–38]. Significant differences between each scenario and the control scenario (scenario 1) are reported to identify the scenarios that provide prediction accuracies similar to the control scenario.

## Relationships between training and validation sets

For each scenario, the maximum, average, and minimum relationship coefficients between training and validation sets in the H matrix were computed. To distinguish the strength of relationships originating from the two lines, all three measurements were computed separately for pigs of the validation set with the subset of the training set that belonged to (1) the target line and (2) the other line. The average relationships were calculated as the mean of the off-diagonal elements of the corresponding relationship matrices for the genotyped individuals.

## Results

### Variance components

The five studied traits showed low to moderate heritabilities that ranged from 0.12±0.02 (RFI) to 0.36±0.05 (BFT) (Table 4). The ratio of litter effect variance to phenotypic variance (I<sup>2</sup>) was lower than the heritability for all traits, ranging from 0.07±0.02 (FCR) to 0.12±0.02 (BFT).

### Prediction accuracies

Prediction accuracies, r(GEBV<sub>p</sub>, GEBV<sub>w</sub>), for the different scenarios are shown in Fig. 2 for the two lines. Accuracies ranged from 0.07 to 0.73, depending on the validation line, trait, and scenario. The tested scenarios could be classified into two groups based on their design and how it affected the prediction accuracy of each trait. Removing the earlier generations of the target line from the training set (from scenarios 1, 2, 3 to scenarios 4, 5, 6) tended to decrease the prediction accuracy for ADG, BFT, and DFI, while FCR and RFI showed different patterns in response to changes in the structure of the training set.

<footnote><sup>a</sup> As a proportion of phenotypic variance</footnote>
The differences in prediction accuracies for ADG, BFT and DFI from scenario 1 to scenario 2 and 3 showed that the inclusion of different generations of the other line in the training set led to marginal changes in accuracy, with decreased correlations in most cases (BFT in the HRFI line and DFI). In scenarios 4, 5, and 6, the proportion of animals from the target line was low in the training set compared to scenarios 1, 2, and 3. This reduction generally led to a decrease in the prediction accuracies for ADG, BFT, and DFI compared to scenario 1. However, these differences in accuracy were only significant for ADG and BFT in the HRFI line and for DFI in the LRFI line.

Scenarios for FCR and RFI showed different patterns compared to the previous traits. Prediction accuracies for FCR followed a pattern similar to those of the other traits for all scenarios, except for scenario 3, which showed a 17 to 21% higher accuracy compared to scenario 1. Prediction accuracies for RFI decreased from scenario 1

to scenario 2, and scenario 1 to scenario 4 for the LRFI target line, which were the scenarios with the maximum number of individuals from the other line in the training set. In the other scenarios, the prediction accuracies for RFI were similar or higher than for scenario 1.

The prediction accuracies for FCR in all scenarios, except scenario 6, were higher for validation animals in the HRFI line than in the LRFI line. The average differences in accuracy by trait ranged from +0.07 for ADG to +0.40 for RFI (Fig. 2).

### Prediction biases

Overall, regression coefficients of GEBV<sub>w</sub> on GEBV<sub>p</sub> were consistently below 1 for FCR and RFI for both validation sets (Fig. 3). Regression coefficients for these two traits also showed more variation across the scenarios compared to ADG, BFT and DFI.

Bias for GEBV in the HRFI validation set followed the same trend, but at different magnitudes, for all traits,

<figure><img src="image_5.png" /></figure>
except ADG (Fig. 3a). On average, scenarios 1, 2, and 3 showed less biases than scenario 4, 5, and 6 for BFT, DFI, and FCR. The regression coefficient in scenario 1 was equal to 0.98 for RFI, slightly higher than 1 for BFT (1.08) and DFI (1.19), and lower than 1 for ADG (0.83) and FCR (0.74).

Prediction of GEBV for the LRFI validation set did not follow the same pattern of change across scenarios between the traits. Regression coefficients of all scenarios showed biases smaller than 1 for BFT, FCR, and RFI (Fig. 3b). Biases were smallest for DFI (scenario 6) and ADG (scenarios 1, 5 and 6). Overall, biases of GEBV for this line were moderate for scenario 6 compared to the other scenarios, except for BFT (0.53). Biases were larger for scenarios 2 and 4, compared to scenarios 5 and 6, for all traits except for BFT.

## Relationships between and within training and validation sets

Relationships between the validation set and the training individuals from the target line were on average higher in scenarios 4 to 6 than in scenarios 1 to 3 (Fig. 4a and c). The highest average was obtained for scenario 4 (around 0.25) and the smallest average for scenarios 1 and 3 (around 0.16 and 0.17). The maximum relationship coefficient between these two cohorts was greater than 0.66 for all scenarios, with the smallest maximum found for scenario 1 when the training set included only individuals from the target line, and the highest maximum for scenario 4 (around 0.78), when the relative number of animals from the other line in the training set was larger.

Relationship coefficients between the validation set and the training individuals of the other line were lower than those with the training individuals of the target line, but the maximum values were reached for scenario 6, i.e. equal to 0.18 and 0.20 for the HRFI and LRFI target lines,

<figure><img src="image_6.png" /></figure>
<figure><img src="image_7.png" /></figure>

respectively (Fig. 4b and d). All other scenarios had lower maximum relationships, ranging from 0.12 to 0.15.

Discussion

The aim of our study was to investigate different combinations of two lines derived from a common origin to evaluate the potential of building a training set for

the genomic prediction of feed efficiency related traits in lines that are small or do not have much data available. Multiplying by ~2.5 (scenario 2), ~2 (scenarios 3 and 4), and ~1.5 times (scenario 5) the number of genotyped individuals in the training set by recruiting animals from the other line show no or little increase of prediction accuracy. This would probably not justify the
additional genotyping costs involved. However, they can
be considered for practical implementation of combined
training sets since, in most cases, the prediction accura-
cies obtained in scenarios 5 and 6 were similar to those
of the control scenario 1. These scenarios reflect most
of the practical situations targeted in our study. Indeed,
for breeding programs in small populations, phenotypic
or genotypic information of individuals from earlier gen-
erations might not be available, and the sampling size
in recent generations might be limited to a few hun-
dred. Our results show that, a training population that
includes recent generations of one population and data
from a more distant subpopulation, could be a solution
to achieve prediction accuracies similar to what would be
achieved if data were available for individuals of the same
population. This could even improve the prediction accu-
racies for traits under selection.

Computation of prediction accuracies and biases

Variance components of the evaluated traits were esti-
mated using the A matrix on the full dataset with both
lines combined. All estimated heritabilities were in the
range of values reported in the literature for these traits
[8, 39–42]. Using these variance components, the accu-
racy of GEBV was computed for the six scenarios to pre-
dict validation animals from each line using ssGBLUP.
Prediction accuracies were computed using a cross-
validation method combined with a semi-parametric
approach [30]. Indeed, in our case, accuracies of the
adjusted phenotypes or of deregressed EBV were too
low to be used in a criterion such as r(GEBVp, y*)/√h²,
since only two-thirds of the individuals had their own
phenotype. This would result in larger standard errors
of the correlations and, thus, less power to test differ-
ences between scenarios, as shown in Additional file 1:
Figures S1 and S2. The underlying assumptions of the
semi-parametric approach are that (1) the validation set
is sufficiently diverse and large (i.e. composed of various
families), and (2) variance components are similar in the
training and validation datasets. The first assumption was
well covered in our study, since all breeding individu-
als, plus some progeny of each family, were phenotyped
and genotyped. The second assumption was potentially
less covered, which could explain some of the biases
in prediction observed. Indeed, when estimating vari-
ance components separately in the two lines, different
residual variances were estimated for some traits, result-
ing in lower heritability estimates for DFI (24%), FCR
(43%), and RFI (22%) in the LRFI line than in the HRFI
line. Legarra and Reverter [30] indicated that inflation of
predictions in one or the other dataset due to changes in
variances can cause biased GEBV. Thus, we also tested
the use of estimates of variance components from the

target line for the GEBV predictions, but this resulted in
increases in biases by 0.016 to 0.121 in all situations but
one (results not shown). In practice, scaling the observa-
tions by the residual or phenotypic standard deviations,
or accounting for the heterogeneity of residual variance
across lines, could be considered to account for such dif-
ferences, as proposed by Reverter et al. [43] for hetero-
geneous variances across herds. An alternative could be
to run bivariate analyses to consider correlated traits
in the two lines, instead of a single trait across the two
lines. Nevertheless, in our populations, estimates of the
genetic variance of RFI as the trait under selection were
consistent over the nine generations in each line. There-
fore, differences in observed accuracy and bias between
lines could not be explained by the heterogeneity of the
genetic variance over the nine generations for the trait
under selection.

Prediction accuracies for production traits

Although production traits and ssGBLUP have been
discussed in the literature, few investigations have ana-
lyzed such traits in pigs with this method. Therefore,
in the discussion that follows, we refer to published
genomic prediction studies on these traits that often
use other methods. Our objective in this part is to vali-
date the prediction accuracies obtained with scenario 1,
in which the structure of the training population is close
to those of previous studies. When comparing studies,
it is worth noting that ssGBLUP generally has a higher
accuracy than the usual GBLUP or Bayesian approaches
that use only data of genotyped animals. Thus in theory,
the comparisons should favor ssGBLUP approaches.
However, most previous studies were based on predic-
tion to a single generation of candidates, which could
favor higher prediction accuracies. In spite of these dif-
ferences, overall, our estimates were within the range of
accuracies reported in the literature, except for FCR and
RFI, for which accuracies were higher in the HRFI valida-
tion set and lower in the LRFI line than those reported
in the literature. In an investigation on 8113 Danish
Duroc pigs with 60K imputed SNP genotyping infor-
mation, an r(GEBVp, y*)/√h² of 0.41 was reported for
ADG [41]. In a study with 620 commercial boars, an
r(GEBVp, y*)/√h² of 0.61 was reported for BFT with
ridge regression BLUP (RR-BLUP) and of 0.56 with Bayes-
ian LASSO [39]. A similar value of 0.55 was reported
for Danish Duroc pigs [41]. Zhang et al. [9] reported an
r(GEBVp, y*)/√h² of 0.38 for DFI in a Duroc popula-
tion using a 80K SNP chip and the GBLUP method in a
design with 1167 training animals and 196 validation ani-
mals. They reported a higher accuracy (0.45) when using
a 650k SNP chip and the BayesB method. Prediction
accuracies of GEBV for FCR and RFI are rarely reported
in the literature. Christensen et al. [8] reported a prediction accuracy of 0.16 for FCR using a bivariate ssGBLUP model. Jiao et al. [42] obtained a low prediction accuracy of 0.09 for RFI (measured as $r(GEBV_p, y^*)/\sqrt{h^2}$) using the BayesA method with 1047 training animals and 516 validation animals for the Duroc boars. Thus, overall in pig studies, prediction accuracies are low to moderate for ADG and BFT, and low for feed efficiency traits.

## Prediction accuracies depending on the training set composition

Compared to FCR and RFI, ADG, BFT, and DFI showed different changes in prediction accuracy compared to scenario 1 when the structure of the training set was changed. For ADG, BFT, and DFI, removing the earlier generations of the target line from the training set (from scenarios 2 and 3 to scenarios 4, 5 and 6) generally decreased prediction accuracy to a lesser extent. The average and maximum relationships between the validation set and the training subsets were higher in scenarios 4, 5, and 6 than in scenario 1. The maximum relationship between the validation set and the training subsets, which was previously recommended as an indicator of potential accuracies [44], was lowest in scenario 1 and highest in scenario 4, likely due to changes in allele frequencies between the early and late generations within a line. This implies that the general decrease in accuracy in the scenarios 4, 5, and 6 could be attributed neither to these changes in relationships between sets, nor to the differences in prediction accuracies between lines. Moreover, the accuracy of GEBV resulting from ssGBLUP analyses should be less sensitive to the structure of the set of genotyped animals, and accordingly, to the strength of relationships between and within training and validation sets [45] because the **H** matrix aggregates information from both **A** and **A**<sub>22</sub>. This structure of the **H** matrix has two major effects on the GEBV of a given animal: first, it contributes the parent average EBV of the animal using the **A** matrix, and second, it adjusts for the different levels of relationships of the animal with other genotyped animals using the **A**<sub>22</sub> matrix [45, 46]. de Roos et al. [19] reported that the benefits of combining populations in a training set are greatest when the populations have diverged for only a few generations and when the heritability of the trait is low. They also showed that increasing the number of animals from a given population in the training set increased prediction accuracy in that population. Considering that de Roos et al. [19] did not include the effect of selection in their simulations, this could partly explain our results for ADG, BFT, and DFI.

## Impact of selection on accuracy and bias of predictions

The changes of accuracy across the scenarios were more diverse for RFI and FCR, with either increases or relatively similar accuracies compared to scenario 1. In some cases, the accuracy even increased as genotypes of closer generations were eliminated from the training set, which could be regarded as an effect of the different relationships between training and validation sets in these scenarios. Regarding the low prediction accuracy reported for FCR and RFI in our results and in the literature, denser SNP genotyping could probably increase the accuracy of predictions by better capturing the differences in LD between the lines. In addition, for low heritability traits, such as RFI in our study, large training populations have been reported to increase the accuracy of GEBV [47–49]. However, given that scenarios 5 and 6 resulted in accuracies that were comparable to that of the control scenario for FCR and in greater accuracies for RFI, they can be considered as optimum scenarios for an across-line genomic prediction program. Based on results from simulation, Pszczola et al. [50] declared that minimizing relationships within the reference population and maximizing them between training and validation sets maximizes the accuracy of genomic predictions. This means that including a diverse set of animals in the training set is desirable to some extent. This is consistent with our results for FCR and RFI, for which selection created two diverse sets of animals. For example, in scenario 6, including animals from G4 to G6 of the target line in the training set provided sufficient genetic links between training and validation sets, and animals from the G9 generation of the other line provided additional diversity to the training set. Overall, it seems that including animals from later generations of both lines (more diverse animals) in the training set contributed to higher accuracies of GEBV in the validation set for FCR and RFI. This might be because the SNP effects segregating in the validation set were better estimated with such a training set.

Overall, the comparison of accuracies between scenarios 4 to 6 and scenario 1 did not show an obvious effect of the removal of data of earlier generations from the training dataset. In a study using six levels of truncated data of past generations, accuracies of GEBV of young genotyped pigs were very similar for various reproductive traits [51].

## Bias of genomic predictions

Our results showed that GEBV were more biased for traits that were more affected by selection, especially when early generations of the target line were not included in the training set. The scenarios that yielded better accuracies were not those with the smaller biases, except for FCR and RFI, for which predictions were low and their regression coefficients were systematically
below 1. The average and maximum relationships between training and validation sets did not affect the prediction biases in the same way for all traits, which could be due to the effect of selection. Selection in historical generations has been shown to result in considerable biases in EBV or GEBV [34, 52]. Tonussi et al. [53] emphasized that, to have accurate and unbiased GEBV with the ssGBLUP method, the G matrix should be compatible with the $A_{22}$. Inappropriate merging of these matrices can originate from ignoring inbreeding in the structure of A and from changes in allele frequencies at QTL for the traits under selection. In our scenarios, the effect of selection in the last three generations of the validation sets was not explicitly accounted for. However, changes in marker allele frequencies in those generations were accounted for through the G matrix. Furthermore, the (co)variances used for genomic predictions were obtained from bivariate analyses including the selection criterion using the whole dataset (including validation generations). Therefore, there should be no effect of selection on the estimations of the variance components, and the prediction bias of the GEBVs should not be due to biased variance components. Computing separate accuracies and biases for sires (heavily selected) versus dams (not directly selected), could enable quantification of the effect of selection on the prediction biases. However, on the one hand, the dams had lower individual accuracies (no own phenotype), and on the other hand, only 18 sires were selected per line in these generations. Therefore, the resulting prediction accuracies and biases differed between sires and dams due to factors other than just the effect of selection and no clear conclusion could be reached. Finally, it should be mentioned that these three generations were combined into the validation set in our study to have enough individuals, but in practice, new candidates to be predicted pertain to a single unselected cohort, therefore this selection effect would be small and likely negligible.

Heritability, marker density and size of the training population have been shown to be important factors to control biases of prediction [54]. Therefore, the biases for some scenarios in this study could be explained by the low to medium heritability of the traits, the medium marker density information, and the small number of individuals in the training population. Testing similar prediction scenarios while ignoring pedigree relationships in the non-genotyped generations would lead to substantially biased predictions, especially for traits affected by selection (for instance, 1.61 for RFI predictions in the HRFI line for scenario 6). Combining full pedigree and genomic information appeared to limit bias, which is consistent with Tonussi et al. [53].

## Conclusions

The results of our study show that genomic prediction using a training set that includes animals from related lines selected in different directions could be as accurate as genomic prediction using a within-line training set. Thus, this can be a solution to create a reference set in the case of small populations, or when ancestral samples are not available at low additional costs. Combined reference sets had better prediction accuracies for traits that were highly affected by selection, which can be attributed to the inclusion of more diverse animals in the training set. Overall, among all evaluated scenarios, scenarios 5 and 6 showed optimal accuracies in most cases, which is consistent with our hypothesis that data from a related line can be used in a combined training population for genomic predictions without losing prediction accuracy. Our results also proved that absence of phenotypic records from past generations did not affect prediction accuracy but increased bias of predictions. Some of these issues could be solved by using bivariate analyses or models with heterogeneous variances to better account for changes in variances with selection in different lines. Taken together, the results of our study provide insights into the design of reference populations for small populations, particularly when lines are being developed simultaneously, which is common in poultry and pig industries, and some plant breeding plans. This strategy can be recommended to initiate a genomic selection program when historical samples are not available, or when two lines are considered and genotyping costs need to be limited.

## Supplementary information

**Supplementary information** accompanies this paper at https://doi.org/10.1186/s12711-020-00576-0.

**Additional file 1. Figure S1.** Correlation between $GEBV_p$ and $y^*$ and their SE as bars for the HRFI (a) and LRFI (b) lines. No scenario resulted in correlations that differed from those with scenario 1 based on a Williams t-test at 5%. RFI residual feed intake, ADG average daily gain, FCR feed conversion ratio, DFI daily feed intake, BFT backfat thickness. **Figure S2.** Correlation between $GEBV_p$ and $y^*$ divided by the square root of the heritability of corresponding traits for the HRFI (a) and LRFI (b) lines. RFI residual feed intake, ADG average daily gain, FCR feed conversion ratio, DFI daily feed intake, BFT backfat thickness.

## Acknowledgements

The authors thank Andres Legarra for his comments and help. This study was financially supported by the French National Research Agency via the Micro-Feed project, under grant ANR-16-CE20-0003. The authors would like to thank the experimental farm staff for data collection and breeding of the animals. The authors are also grateful to Yvette Steyn for proof-reading the manuscript.

## Authors' contributions

AA performed the statistical analyses and wrote the first draft of the paper. ED and YL performed the imputation and quality control of the genotypic data. AA, JR and HG participated in the design of the study. HG provided scientific supervision. All authors read and approved the final manuscript.
Competing interests

The authors declare that they have no competing interests.

Received: 23 September 2019 Accepted: 21 September 2020

Published online: 07 October 2020

References

1. Patience JF, Rossoni-Serão MC, Gutiérrez NA. A review of feed efficiency in swine: biology and application. J Anim Sci Biotechnol. 2015;6:33.

2. Gaines AM, Peterson BA, Mendoza OF. Herd management factors that influence whole herd feed efficiency. In: Patience JF, editor. Feed efficiency in swine. Wageningen: Wageningen Academic Publishers; 2012. p. 15-39.

3. Koch RM, Swiger LA, Chambers D, Gregory KE. Efficiency of feed use in Beef cattle. J Anim Sci. 1963;22:486-94.

4. Hoque MA, Suzuki K, Kadowaki H, Shibata T, Oikawa T. Genetic parameters for feed efficiency traits and their relationships with growth and carcass traits in Duroc pigs. J Anim Breed Genet. 2007;124:108-16.

5. Ollivier L, Gueblez R, Webb AJ, van der Steen HAM. Breeding goals for nationally and internationally operating pig breeding organisations. In: Proceedings of the 4th World Congress on Genetics applied to Livestock Production: 23-27 July 1990. Edinburgh; 1990

6. Pym RAE, Nicholls PJ. Selection for food conversion in broilers: direct and correlated responses to selection for body-weight gain, food consumption and food conversion ratio. Br Poult Sci. 1979;20:73-86.

7. Rexroad C, Vallet J, Matukumalli LI, Reecy J, Bickhart D, Blackburn H, et al. Genome to phenotype: improving animal health, production and well-being a new USDA blueprint for animal genome research 2018-2027. Front Genet. 2019;10:327.

8. Christensen OF, Madsen P, Nielsen B, Ostersen T, Su G. Single-step methods for genomic evaluation in pigs. Animal. 2012;6:1565-71.

9. Zhang C, Kemp RA, Stothard P, Wang Z, Boddicker N, Krivushin K, et al. Genomic evaluation of feed efficiency component traits in Duroc pigs using 80 K, 650 K and whole-genome sequence variants. Genet Sel Evol. 2018;50:14.

10. Legarra A, Aguilar I, Misztal I. A relationship matrix including full pedigree and genomic information. J Dairy Sci. 2009;92:4656-63.

11. Misztal I, Legarra A, Aguilar I. Computing procedures for genetic evaluation including phenotypic, full pedigree, and genomic information. J Dairy Sci. 2009;92:4648-55.

12. Aguilar I, Misztal I, Johnson D, Legarra A, Tsuruta S, Lawlor T. Hot topic: a unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score. J Dairy Sci. 2010;93:743-52.

13. Christensen OF, Lund MS. Genomic prediction when some animals are not genotyped. Genet Sel Evol. 2010;42:2.

14. VanRaden PM, O'Connell JR, Wiggans GR, Weigel KA. Genomic evaluations with many more genotypes. Genet Sel Evol. 2011;43:10.

15. Carillier C, Larroque H, Robert-Granie C. Comparison of joint versus purebred genomic evaluation in the French multi-breed dairy goat population. Genet Sel Evol. 2014;46:67.

16. Lund MS, Su G, Janss L, Guldbrandtsen B, Brøndum RF. Genomic evaluation of cattle in a multi-breed context. Livest Sci. 2014;166:101-10.

17. Hayes BJ, Bowman PJ, Chamberlain AC, Verbyla K, Goddard ME. Accuracy of genomic breeding values in multi-breed dairy cattle populations. Genet Sel Evol. 2009;41:51.

18. Olson KM, VanRaden PM, Tooker ME. Multibreed genomic evaluations using purebred Holsteins,Jerseys, and Brown Swiss. J Dairy Sci. 2012;95:5378-83.

19. de Roos AP, Hayes BJ, Goddard ME. Reliability of genomic predictions across multiple populations. Genetics. 2009;183:1545-53.

20. Zhang S-Y, Olasebe GS, Liu D-Y, Wang Q-S, Pan Y-C, Ma P-P. The genetic connectedness calculated from genomic information and its effect on the accuracy of genomic prediction. PLoS One. 2018;13:e0201400.

21. Fangmann A, Bergfelder-Drüing S, Tholen E, Simianer H, Erbe M. Can multi-subpopulation reference sets improve the genomic predictive ability for pigs? J Anim Sci. 2015;93:5618-30.

22. Gilbert H, Billon Y, Brossard L, Faure J, Gatellier P, Gondret F, et al. Review: divergent selection for residual feed intake in the growing pig. Animal. 2017;11:1427-39.

23. Gilbert H, Bidanel J-P, Gruand J, Caritez J-C, Billon Y, Guillouet P, et al. Genetic parameters for residual feed intake in growing pigs, with emphasis on genetic relationships with carcass and meat quality traits. J Anim Sci. 2007;85:3182-8.

24. Purcell S, Neale B, Todd-Brown K, Thomas L, Ferreira MA, Bender D, et al. PLINK: a tool set for whole-genome association and population-based linkage analyses. Am J Hum Genet. 2007;81:559-75.

25. Sargolzaei M, Chesnais JP, Schenkel FS. A new approach for efficient genotype imputation using information from relatives. BMC Genomics. 2014;15:478.

26. Careau V, Wolak ME, Carter PA, Garland T Jr. Limits to behavioral evolution: the quantitative genetics of a complex trait under directional selection. Evolution. 2013;67:3102-19.

27. Hadfield JD, Wilson AJ, Garant D, Sheldon BC, Kruuk LE. The misuse of BLUP in ecology and evolution. Am Nat. 2010;175:116-25.

28. Fernando R, Gianola D. Statistical inferences in populations undergoing selection or non-random mating. In: Gianola D, Hammond K, editors. Advances in statistical methods for genetic improvement of livestock. Berlin: Springer; 1990. p. 437-53.

29. Henderson C. Accounting for selection and mating biases in genetic evaluations. In: Gianola D, Hammond K, editors. Advances in statistical methods for genetic improvement of livestock. Berlin: Springer; 1990. p. 413-36.

30. Sorensen D, Fernando R, Gianola D. Inerring the trajectory of genetic variance in the course of artificial selection. Genet Res. 2001;77:83-94.

31. Misztal I, Tsuruta S, Lourenco D, Masuda Y, Aguilar I, Legarra A, et al. Manual for BLUPF90 family of programs. Athens: University of Georgia; 2018.

32. VanRaden PM. Efficient methods to compute genomic predictions. J Dairy Sci. 2008;91:4414-23.

33. Amadeu RR, Cellon C, Olmstead JW, Garcia AA, Resende MF Jr, Muñoz PR. AGHmatrix: R package to construct relationship matrices for autotetraploid and diploid species: a blueberry example. Plant Genome. 2016. https://doi.org/10.3835/plantgenome.2016.01.0009.

34. Legarra A, Reverter A. Semi-parametric estimates of population accuracy and bias of predictions of breeding values and future phenotypes using the LR method. Genet Sel Evol. 2018;50:53.

35. Gunia M, Saintilan R, Venot E, Hoze C, Fouilloux MN, Phocas F. Genomic prediction in French Charolais beef cattle using high-density single nucleotide polymorphism markers. J Anim Sci. 2014;92:3258-69.

36. Steiger JH. Tests for comparing elements of a correlation matrix. Psychol Bull. 1980;87:245-51.

37. Williams EJ. The comparison of regression variables. J R Stat Soc Series B Stat Methodol. 1959;21:396-9.

38. Revelle WR. Package Psych V1.8.12: Procedures for psychological, psychometric, and personality research. Evanston: Northwestern University; 2019.

39. de Campos CF, Lopes MS, Silva FF, Veroneze R, Knol EF, Lopes PS, et al. Genomic selection for boar taint compounds and carcass traits in a commercial pig population. Livest Sci. 2015;174:10-7.

40. Do DN, Janss LL, Strathe AB, Jensen J, Kadarmideen H, editors. Genomic prediction and genomic variance partitioning of daily and residual feed intake in pigs using Bayesian Power Lasso models. In: Proceedings of the 10th World Congress on Genetics Applied to Livestock Production: 17-22 Aug 2014; Vancouver, 2014.

41. Guo X, Christensen OF, Ostersen T, Wang Y, Lund MS, Su G. Genomic prediction using models with dominance and imprinting effects for backfat thickness and average daily gain in Danish Duroc pigs. Genet Sel Evol. 2016;48:67.

42. Jiao S, Maltecca C, Gray KA, Cassady JP. Feed intake, average daily gain, feed efficiency, and real-time ultrasound traits in Duroc pigs: I. Genetic parameter estimation and accuracy of genomic prediction. J Anim Sci. 2014;92:2377-86.

43. Reverter A, Tier B, Johnston DJ, Graser HU. Assessing the efficiency of multiplicative mixed model equations to account for heterogeneous variance across herds in carcass scan traits from beef cattle. J Anim Sci. 1997;75:1477-85.
44. Clark SA, Hickey JM, Daetwyler HD, van der Werf JH. The importance of information on relatives for the prediction of genomic breeding values and the implications for the makeup of reference data sets in livestock breeding schemes. *Genet Sel Evol.* 2012;44:4.

45. Lourenco DA, Fragomeni BO, Tsuruta S, Aguilar I, Zumbach B, Hawken RJ, et al. Accuracy of estimated breeding values with genomic information on males, females, or both: an example on broiler chicken. *Genet Sel Evol.* 2015;47:56.

46. Misztal I, Tsuruta S, Aguilar I, Legarra A, VanRaden P, Lawlor T. Methods to approximate reliabilities in single-step genomic evaluation. *J Dairy Sci.* 2013;96:647-54.

47. Goddard M. Genomic selection: prediction of accuracy and maximisation of long term response. *Genetica.* 2009;136:245-57.

48. Hayes BJ, Bowman PJ, Chamberlain A, Goddard M. Invited review: genomic selection in dairy cattle: Progress and challenges. *J Dairy Sci.* 2009;92:433-43.

49. Hoze C, Fritz S, Phocas F, Boichard D, Ducrocq V, Croiseau P. Efficiency of multi-breed genomic selection for dairy cattle breeds with different sizes of reference population. *J Dairy Sci.* 2014;97:3918-29.

50. Pszczola M, Strabel T, Mulder HA, Calus MP. Reliability of direct genomic values for animals with different relationships within and to the reference population. *J Dairy Sci.* 2012;95:389-400.

51. Lourenco DA, Misztal I, Tsuruta S, Aguilar I, Lawlor TJ, Forni S, et al. Are evaluations on young genotyped animals benefiting from the past generations? *J Dairy Sci.* 2014;97:3930-42.

52. Bijma P. Accuracies of estimated breeding values from ordinary genetic evaluations do not reflect the correlation between true and estimated breeding values in selected populations. *J Anim Breed Genet.* 2012;129:345-58.

53. Tonussi RL, de Oliveira Silva RM, Magalhães AFB, Espigolan R, Peripolli E, Olivieri BF, et al. Application of single step genomic BLUP under different uncertain paternity scenarios using simulated data. *PLoS One.* 2017;12:e0181752.

54. Karimi K, Sargolzaei M, Plastow GS, Wang Z, Miar Y. Opportunities for genomic selection in American mink: a simulation study. *PLoS One.* 2019;14:e0213873.

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