## 2 Materials and Methods  
**Phenotypic and Genomic Data. ** The phenotypic data used in this study consisted of the total number born, TNB, and the number of piglets born alive, NBA, in 203 ER and 125 RE sows. The ER sows were the offspring of 38 purebred Entrepelado boars and 139 Retinto dams, whereas the RE sows were generated from 38 Retinto boars and 92 Entrepelado dams. A summary of the data is presented in Table 1. \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Entrepelado \(\times\) Retinto** & **Retinto \(\times\) Entrepelado** \\ \hline N1  (NS)2  & 1258 (203) & 700 (125) \\ TNB3  & 8.78 \(\pm\) 2.24 & 8.85 \(\pm\) 2.37 \\ NBA4  & 8.55 \(\pm\) 2.23 & 8.62 \(\pm\) 2.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The number of records (and sows between brackets), mean (\(\pm\)standard deviation) of the total number born and the number born alive, for Entrepelado \(\times\) Retinto and Retinto \(\times\) Entrepelado crosses. Genotyping was performed with the GeneSeek(r) GPP Porcine 70 K HDchip (Illumina Inc., San Diego, CA, USA) on all ER and RE crossbred sows, as well as on 341 Retinto and 350 Entrepelado purebred individuals. Due to shared purebred ancestors, there was some degree of relationship between a subset of the ER and RE crossbred sows and the purebred individuals, although not all of them were genotyped. The original genotype data consisted of 60,224 autosomal SNPs, which were filtered by excluding SNP markers with a call rate below 0.90 and a minor allele frequency lower than 0.05 in each population. Among these, 4212 were discarded due to a call rate lower than 0.90, 11,234 were found to be monomorphic, and 9876 and 11,516 had a minor allele frequency lower than 0.05 in the Entrepelado and Retinto populations, respectively. Finally, a total of 23,386 SNPs were retained. **Haplotype Phasing. ** AlphaPhase software [11] was used for each chromosome separately, utilizing genotypes of both crossbred and purebred individuals, as well as a pedigree of 1601 individuals. AlphaPhase was executed with a tolerance of 1% of genotype errors and 1% disagreement between genotypes and haplotypes. The number of surrogates and percentage of surrogate disagreement was set to 10. Nine different scenarios were applied with core lengths of 75, 100, and 125 SNPs and tail lengths of 100, 150, and 200 SNPs (see Table 2). The scenarios were evaluated for concordance, and haplotype assignments that coincided in seven or more scenarios were retained for subsequent analysis. **Statistical Model. ** Once the haplotype phases were calculated, data were analyzed with the model proposed by [PERSON] et al. [12]:  
\[ \begin{array}{l}\boldsymbol{y}_{(ER)}=\boldsymbol{X}_{(ER)}\boldsymbol{b}_{( ER)}+\boldsymbol{B}_{(ER)}\boldsymbol{s}_{(ER)}+\boldsymbol{Z}_{(ER)}\boldsymbol{p}_{( E)}+\boldsymbol{W}_{(ER)}\boldsymbol{m}_{(R)}+\boldsymbol{e}_{(ER)}\\ \boldsymbol{y}_{(RE)}=\boldsymbol{X}_{(RE)}\boldsymbol{b}_{(RE)}+\boldsymbol{ B}_{(RE)}\boldsymbol{s}_{(RE)}+\boldsymbol{Z}_{(RE)}\boldsymbol{p}_{(R)}+ \boldsymbol{W}_{(RE)}\boldsymbol{m}_{(E)}+\boldsymbol{e}_{(RE)}\end{array} \]  
In this equation, \(\boldsymbol{y}_{(ER)}\) and \(\boldsymbol{y}_{(RE)}\) refer to the vectors of phenotypic records (TNB or NBA) for the ER and RE crosses, respectively. The terms \(\boldsymbol{b}_{(ER)}\) and \(\boldsymbol{b}_{(RE)}\) correspond to systematic effects, and \(\boldsymbol{s}_{(ER)}\) and \(\boldsymbol{s}_{(RE)}\) represent the permanent sow environmental effects. Pateral effects for the Entrepelado (E) and Retinto (R) populations are denoted by \(\boldsymbol{p}_{(E)}\) and \(\boldsymbol{p}_{(R)}\), respectively. Maternal effects for the Entrepelado (E) and Retinto (R) are represented by \(\boldsymbol{m}_{(E)}\) and \(\boldsymbol{m}_{(R)}\). Additionally, \(\boldsymbol{e}_{(ER)}\) and \(\boldsymbol{e}_{(RE)}\) are the residual effects for the ER and RE crosses, respectively.