animals Communication A Bayesian Multivariate Gametic Model in a Reciprocal Cross with Genomic Information: An Example with Two Iberian Varieties Houssemeddine Srihi 1 , David López-Carbonell 1 , Noelia Ibáñez-Escriche 2 , Joaquim Casellas 3 , Pilar Hernández 2 , Sara Negro 4 and Luis Varona 1, * 1 Facultad de Veterinaria, Instituto Agrolimentario de Aragón (IA2), Universidad de Zaragoza, 50013 Zaragoza, Spain; houssemsrihi@unizar.es (H.S.) 2 Institute for Animal Science and Technology, Universitat Politècnica de València, 46022 Valencia, Spain 3 Department of Animal and Food Science, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain 4 Programa de Mejora Genética “Castúa”, INGA FOOD S.A. (Nutreco), 06200 Almendralejo, Spain * Correspondence: lvarona@unizar.es Simple Summary: INGA FOOD, S.A. initiated a crossbreeding program involving two Iberian pig varieties: Retinto and Entrepelado. The primary objective of this program is to produce an F1 hybrid sow that exhibits enhanced reproductive performance. In a previous investigation, variations in the reproductive performance of sows, specifically litter size, were observed among the reciprocal crosses. These variations indicate the presence of genomic imprinting effects. To assess the influence of genetic origin, we developed a multivariate gametic model to estimate the gametic correlations between paternal and maternal effects. Gametic correlations lower than one could potentially explain the performance differences observed across the reciprocal crosses. Despite having limited data, the study’s findings suggest that the gametic correlation estimate between paternal and maternal effects on litter size is lower in the Entrepelado population compared to the Retinto population. Abstract: INGA FOOD, S.A. initiated a crossbreeding program between two Iberian pig varieties, Citation: Srihi, H.; López-Carbonell, D.; Retinto (R) and Entrepelado (E), with the goal of producing a hybrid sow (F1). Several studies have Ibáñez-Escriche, N.; Casellas, J.; been conducted to evaluate its productive performance, and these studies have revealed differences Hernández, P.; Negro, S.; Varona, L. in litter size between the two reciprocal crosses, suggesting the presence of genomic imprinting A Bayesian Multivariate Gametic effects. To further investigate these effects, this study introduces a multivariate gametic model Model in a Reciprocal Cross with designed to estimate gametic correlations between paternal and maternal effects originating from Genomic Information: An Example both genetic backgrounds involved in the reciprocal crosses. The dataset consisted of 1258 records with Two Iberian Varieties. Animals (the total number born—TNB and the number born alive—NBA) from 203 crossbred dams for the 2023, 13, 1648. https://doi.org/ Entrepelado (sire) × Retinto (dam) cross and 700 records from 125 crossbred dams for the Retinto 10.3390/ani13101648 (sire) × Entrepelado (dam) cross. All animals were genotyped using the GeneSeek® GPP Porcine 70 K Academic Editor: Michael E. Davis HDchip (Illumina Inc., San Diego, CA, USA). The results indicated that the posterior distribution of Received: 19 April 2023 the gametic correlation between paternal and maternal effects was distinctly different between the Revised: 11 May 2023 two populations. Specifically, in the Retinto population, the gametic correlation showed a positive Accepted: 13 May 2023 skew with posterior probabilities of 0.78 for the TNB and 0.80 for the NBA. On the other hand, the Published: 16 May 2023 Entrepelado population showed a posterior probability of a positive gametic correlation between paternal and maternal effects of approximately 0.50. The differences in the shape of the posterior distribution of the gametic correlations between paternal and maternal effects observed in the two varieties may account for the distinct performance outcomes observed in the reciprocal crosses. Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. Keywords: gametic model; Iberian pig; crossbreeding; Retinto; Entrepelado This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Animals 2023, 13, 1648. https://doi.org/10.3390/ani13101648 https://www.mdpi.com/journal/animals Animals 2023, 13, 1648 2 of 9 1. Introduction The Iberian breed is widely renowned for its ability to produce some of the highest- quality pork [1]. This breed is particularly well-adapted to the “Dehesa” environment in southwestern Spain, which is characterized by a savannah landscape and is composed of grass, cork, and holm oaks with seasonal production. Traditionally, Iberian pig production was dominated by purebred varieties and extensive management practices. However, in recent decades, there has been a shift toward more intensive farming practices that incor- porate crossbreeding with Duroc boars to improve growth and efficiency at commercial stages [2]. The regulatory norms for Iberian pig production allow crossbreeding, as long as the sow is of purebred Iberian stock. The reproductive performance of the Iberian sows is lower than that of white pig populations [3], which is a major limitation of its use in intensive farms. Therefore, improvement in the reproductive efficiency of Iberian sows is crucial for their economic sustainability. Several studies have identified genetic variability for prolificacy within and between varieties of Iberian pig [4,5]. To take advantage of this variability, the INGA FOOD, S.A. company has developed a crossbreeding scheme between two Iberian varieties (Retinto and Entrepelado) to generate an F1 hybrid sow, which exhibits significant heterosis for litter size [6]. However, this study also found differences in the reproductive performance between the two reciprocal crosses (Entrepelado × Retinto, ER, vs. Retinto × Entrepelado, RE), suggesting that these differences may be attributed to parental imprinting [7] (i.e., the effects from alleles may differ whether they are transmitted by paternal or maternal gametes). In fact, there is increasing evidence of the importance of imprinting in placenta development [8], and certain imprinted genes have been proposed as candidates for pig litter size [9]. In recent years, some algorithms have been proposed to develop a genomic analysis of imprinting [10] from the genomic information provided by commercial genotyping devices. However, knowledge of the parental haplotype phase of the SNP markers is required to differentiate the paternal or maternal gametic effects. Some approaches have been developed to reconstruct haplotype phases [11]. Phenotypic information from reciprocal crosses offers the opportunity to compare the paternal and maternal effects of each parental population. In the absence of imprinting, the correlation between the paternal and maternal effects from the same population should be one. Imprinting, on the other hand, results in a lower correlation. Accordingly, the goal of this study was to apply the multivariate gametic model developed in a previous study [12] that utilizes genomic information and is capable of estimating the paternal and maternal gametic contributions of Retinto and Entrepelado varieties in the ER and RE crosses, along with their correlations. 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. Table 1. The number of records (and sows between brackets), mean (±standard deviation) of the total number born and the number born alive, for Entrepelado × Retinto and Retinto × Entrepelado crosses. Entrepelado × Retinto Retinto × Entrepelado 1 N (NS) 2 1258 (203) 700 (125) TNB 3 8.78 ± 2.24 8.85 ± 2.37 NBA 4 8.55 ± 2.23 8.62 ± 2.34 1 N: number of records. 2 NS: number of sows. 3 TNB: total number born. 4 NBA: number born alive. Animals 2023, 13, 1648 3 of 9 Genotyping was performed with the GeneSeek® 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 sepa- rately, 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. Table 2. Parameters (core and tail length) in the nine scenarios of haplotype phasing. Scenario Core Length Tail Length S1 75 100 S2 75 150 S3 75 200 S4 100 100 S5 100 150 S6 100 200 S7 125 100 S8 125 150 S9 125 200 Statistical Model. Once the haplotype phases were calculated, data were analyzed with the model proposed by Shiri et al. [12]: y(ER) = X(ER) b(ER) + B(ER) s(ER) + Z(ER) p(E) + W(ER) m( R) + e(ER) y( RE) = X( RE) b( RE) + B( RE) s( RE) + Z( RE) p( R) + W( RE) m(E) + e( RE) In this equation, y(ER) and y( RE) refer to the vectors of phenotypic records (TNB or NBA) for the ER and RE crosses, respectively. The terms b(ER) and b( RE) correspond to systematic effects, and s(ER) and s( RE) represent the permanent sow environmental effects. Paternal effects for the Entrepelado (E) and Retinto (R) populations are denoted by p(E) and p( R) , respectively. Maternal effects for the Entrepelado (E) and Retinto (R) are represented by m(E) and m( R) . Additionally, e(ER) and e( RE) are the residual effects for the ER and RE crosses, respectively. The systematic effects vectors included the order of parity with five levels (first, second, third, fourth, and fifth or more) and herd–year–season with thirty- four levels. Further,XER , XRE , BER , BRE , ZER , ZRE , WER , and WRE are the corresponding incidence matrices. Following [12], the prior distribution of the permanent sow environmental effects was:     s(ER) 0 ∼N , I⊗S s( RE) 0 Animals 2023, 13, 1648 4 of 9 where: " σ2 # 0 S = s(ER) 0 σs2( RE) where σs2(ER) and σs2( RE) are the variances of the permanent sow environmental effects for ER and RE, respectively. The prior distributions of the gametic effects for the Entrepelado (E) and Retinto (R) populations are: " # " # p( E ) p( R )    0 0 ∼ N , GE ⊗VE ∼ N , GR ⊗VR m( E ) 0 m( R ) 0 where: σp2(E) " # σpm(E) VE = 2 σpm(E) σm ( E) and: σp2( R) " # σpm( R) VR = 2 σpm( R) σm ( R) where σp2(E) , σm2 ( E) , and σpm( E) refer to the variances of the paternal and maternal gametic effects and the covariance between them, respectively, for the Entrepelado population. Similarly, σp2( R) , σm 2 ( R) , and σpm( R) represent the variances of the paternal and maternal gametic effects and the covariance between them, respectively, for the Retinto population. Additionally, GE and GR are the gametic relationship matrices of the Entrepelado or Retinto gametes, respectively, regardless of whether they are transmitted as paternal or maternal gametes. These matrices describe the relationships among the gametes from Entrepelado and Retinto origins, and they are calculated using the algorithm proposed by Nishio and Satoh [10]: ME ME 0 MR MR 0 GE =   GR =   N N ∑i SNP q(E)i 1 − q(E)i ∑i SNP q( R)i 1 − q( R)i where ME and MR are the matrices of the number of genotyped individuals (n) × the number of SNP (NSNP ), whose elements ME (i, j) (or MR (i, j) take the value q( E) j (or     q( R) j ) or − 1 − q( E) j (or − 1 − q( R) j ), depending on whether the jth allele of the gametes transmitted for the ith individual is A1 or A2 and of Entrepelado (or Retinto) origin. Additionally, q( E) j and q( R) j represent the allelic frequencies of the A2 allele in the Entrepelado (E) and Retinto (R) populations, respectively. The prior distributions for the (co) variance components and the systematic effects were assumed to be flat. The analysis was performed using Bayesian inference with the Gibbs sampler [13] and implemented with Gibbsf90 software [14]. The analysis was performed using 10 million iterations after discarding the first million. At each iteration of the Gibbs sampler, the (co) variances components samples were utilized to compute the samples from the marginal posterior distribution of the correlations between the paternal and maternal gametic effects for Entrepelado (r pm(E) ) and Retinto (r pm( R) ): σpm(E) σpm( R) r pm(E) = q and r pm( R) = q σp2(E) σj2(E) σp2( R) σj2( R) 3. Results and Discussion Haplotype Phasing. The results of comparing haplotype phasing using nine combi- nations of core length and core tail parameters using Alphaphase software are presented in Figure 1. mals 2023, 12, x FOR PEER REVIEW 5 of 9 Animals 2023, 13, 1648 5 of 9 Figure 1. Degree of similitude between estimated haplotype phases in the nine scenarios of phasing. Figure 1. Degree of similitude between estimated haplotype phases in the nine scenarios of phasing. The average degree of similitude was 0.89, and it was consistently above 0.86. Specifi- cally, the The average predicted degree haplotypewas of similitude phase wasand 0.89, identical it wasacross all nine scenarios consistently for only 78.74% above 0.86. of the analyses but had concordance in more than seven scenarios for Specifically, the predicted haplotype phase was identical across all nine scenarios for only 92.5% of SNPs. These findings indicated that the output of the phasing algorithm 78.74% of the analyses but had concordance in more than seven scenarios for 92.5% of was highly dependent on the SNPs. Thesespecific findingssetindicated of parameters that used for its implementation the output when medium-density of the phasing algorithm was highly SNP chips dependent on weretheused. specific set of parameters used for its implementation when medium- density SNP chips were used.of Gametic Matrices. The diagonal values of the gametic matrices for Calculation Calculation of Gameticpopulation the Entrepelado ranged Matrices. The from 0.894 diagonal valuestoof1.100, while formatrices the gametic the Retinto for population, the Entrepelado population ranged from 0.894 to 1.100, while for the Retinto population,relationships they ranged from 0.901 to 1.179. Table 3 shows the distribution of the gametic they ranged observed from 0.901intothe off-diagonal 1.179. elements Table 3 shows of the gametic the distribution matrices. of the gametic relationships observed in the off-diagonal elements of the gametic matrices. Table 3. Distribution of gametic relationships between the Entrepelado and Retinto gametic effects. Table 3. Distribution of gametic relationships between the Entrepelado and Retinto gametic effects. Gametic Relationship Entrepelado Retinto Gametic Relationship <0.05 Entrepelado Retinto 92,276 (86.03%) 94,144 (87.77%) <0.05 0.05–0.10 92,276 (86.03 %) 8130 (7.58%)94,144 (87.77 %)8900 (8.29%) 0.05–0.10 0.10–0.20 8130 (7.58 %) 4670 (4.35%)8900 (8.29 %) 3130 (2.92%) 0.20–0.30 1076 (1.00%) 582 (0.54%) 0.10–0.20 0.30–0.40 4670 (4.35 %) 480 (0.44%) 3130 (2.92 %) 252 (0.23%) 0.20–0.30 0.40–0.50 1076 (1.00 %) 396 (0.36%) 582 (0.54 %) 188 (0.18%) 0.30–0.40 >0.50 480 (0.44 %) 228 (0.21%) 252 (0.23 %) 60 (0.05%) 0.40–0.50 396 (0.36 %) 188 (0.18 %) >0.50 228 (0.21 %) 60 (0.05 The calculated gametic matrices yielded results %) consistent with the familiar relation- ships of the individuals, as gametic relationships around 0.50 indicated that the individuals The calculated shared siregametic matrices (or dam), yieldedrelationships while gametic results consistent withsuggested around 0.25 the familiar that the sires (or relationshipsdams) of theofindividuals, as gametic the individuals relationships around 0.50 indicated that the were fullsibs. individuals shared sire (orComponents. Variance dam), while gametic relationships The posterior around mean and 0.25 suggested standard deviationthat estimate of the the sires (or variance dams) of components the individuals are were fullsibs. presented in Table 4. Variance Components. The posterior mean and standard deviation estimate of the variance components are presented in Table 4. mals 2022, 12, x. https://doi.org/10.3390/xxxxx www.mdpi.com/journal/animals Animals 2023, Animals 2023, 12, 12, xx FOR FOR PEER PEER REVIEW REVIEW 66 of of 99 Animals 2023, 13, 1648 6 of 9 Table 4. Table 4. Posterior Posterior mean mean (and (and standard standard deviation) deviation) of of the the variance variance components components for for the the total total number number Table born, Posterior 4.TNB, and mean the (and born number standard deviation) alive, NBA. of the variance components for the total number born, TNB, and the number born alive, NBA. born, TNB, and the number born alive, NBA. Variance Component Variance Component TNB TNB NBA NBA 𝟐 Component 𝝈𝝈𝟐𝒔(𝑬𝑹) Variance 𝒔(𝑬𝑹) 0.144 TNB 0.144 (0.098) (0.098) 0.142NBA 0.142 (0.097) (0.097) 𝝈 𝟐𝟐 σ 2 𝝈𝒔(𝑹𝑬) 𝒔(𝑹𝑬)s(ER) 0.357 0.144 (0.098) 0.357 (0.187) (0.187) 0.3650.142 (0.097) (0.191) 0.365 (0.191) 𝟐σ 2 𝝈𝝈𝟐𝒑(𝑬) 𝒑(𝑬) s(RE) 0.206 0.357 (0.187) 0.206 (0.103) (0.103) 0.365 (0.191) 0.199 (0.100) 0.199 (0.100) 𝝈 𝟐𝟐 σ 2 0.206 (0.103) 0.1990.199 (0.100) 𝝈𝒎(𝑬)𝒎(𝑬) p(E) 0.197 (0.114) 0.197 (0.114) 0.199 (0.115) (0.115) 2 𝟐𝟐 σm(E) 𝝈𝝈𝒑(𝑹) (0.132) (0.114) 0.197 0.224 (0.132) 0.199 (0.115) 0.222 (0.128) (0.128) 𝒑(𝑹) 0.224 0.222 𝟐 σ2 0.224 (0.132) 0.222 (0.128) 𝝈𝝈𝟐𝒎(𝑹) 𝒎(𝑹) p(R) 0.163 (0.087) 0.163 (0.087) 0.151 (0.080) 0.151 (0.080) 𝟐 σ2 0.163 (0.087) 𝝈𝝈𝒆(𝑬𝑹) 𝟐 𝒆(𝑬𝑹)m(R) 4.296 (0.187) 4.296 (0.187) 4.2510.151 4.251 (0.080) (0.185) (0.185) 2 4.296 (0.187) 4.251 (0.185) 𝝈 𝟐𝟐 σe(ER) 𝝈𝒆(𝑹𝑬) 𝒆(𝑹𝑬) 4.795 (0.288) 4.795 (0.288) 4.607 (0.278) 4.607 (0.278) σe2(RE) 4.795 (0.288) 4.607 (0.278) Furthermore, Figure Furthermore, Figure 22 shows shows thethe posterior posterior distributions distributions of of the the ratios ratios of of gametic gametic var- var- iances in the Furthermore, iances Entrepelado × Retinto Figure 2×shows in the Entrepelado Retintothe(E × R) and (Eposterior Retinto × Entrepelado × R) and distributions (R of the ratios Retinto × Entrepelado × E) crosses. (R ×ofE)gametic The crosses.vari- The posterior ances in the posterior mean estimates Entrepelado mean were estimates×were similar, Retinto ranging (E ×ranging similar, between 0.034 between×0.034 R) and Retinto for the Entrepelado Retinto maternal (R × E)maternal for the Retinto crosses. gametic The effects posterior gametic mean effects in the in the ER cross cross estimates ER and were and 0.043 for similar, 0.043 for the the Entrepelado ranging Entrepelado between 0.034paternal gametic for the gametic paternal effects in Retinto maternal effects in the RE RE cross. gametic the cross. effects in the ER cross and 0.043 for the Entrepelado paternal gametic effects in the RE cross. Figure2.2. Figure Figure 2.Posterior Posteriordistributions Posterior distributionsofof distributions ofthe theratio the ratioofof ratio ofgametic gameticeffect gametic effectinin effect inthe theEntrepelado the Entrepelado Entrepelado×××Retinto Retintoand Retinto andin and inthe in the the Retinto × Entrepelado crosses. Retinto×× Entrepelado crosses. Retinto Theseresults These These resultsindicate results indicatethat indicate thatthere that thereare there areno are norelevant no relevantdifferences relevant differencesin differences inthe in theamount the amountof amount ofgenetic of genetic genetic variance variance contributed contributed by by the the paternal paternal and and maternal maternal origins origins in in either either of of the the two two variance contributed by the paternal and maternal origins in either of the two reciprocal reciprocal reciprocal crosses, crosses,based crosses, basedon based onthe on theavailable the availableinformation. available information. information. Gametic Gametic Correlations.The GameticCorrelations. Correlations. Theposterior The posteriordistribution posterior distributionof distribution ofthe of thegametic the gameticcorrelations gametic correlationsfor correlations forthe for the the TNB TNB and NBA and NBA in the in theEntrepelado Entrepelado and andRetinto populations Retinto populationsare presented are presentedin Figures in TNB and NBA in the Entrepelado and Retinto populations are presented in Figures 3 and 3 Figuresand 3 4, and respectively. 4, respectively. 4, respectively. Figure 3. Posterior distributions of the gametic correlation between the paternal and maternal effects Figure 3. Figure 3.Posterior Posterior distributions distributions of the gametic correlation between the paternal and maternal effects in the Entrepelado population. of the gametic correlation between the paternal and maternal effects in the in the Entrepelado Entrepelado population. population. Animals 2022, Animals 2022, 12, 12, x. x. https://doi.org/10.3390/xxxxx https://doi.org/10.3390/xxxxx www.mdpi.com/journal/animals www.mdpi.com/journal/animals Animals Animals2023, 13,12, 2023, 1648 x FOR PEER REVIEW 7 of 99 7 of Figure 4. Posterior distributions of the gametic correlation between the paternal and maternal effects Figure 4. Posterior distributions of the gametic correlation between the paternal and maternal effects in the Retinto population. in the Retinto population. The posterior distribution of the correlation between gametic effects in Retinto and The posterior distribution of the correlation between gametic effects in Retinto and Entrepelado showed notable differences in shape. Specifically, the posterior distributions Entrepelado showed notable differences in shape. Specifically, the posterior distributions of the gametic correlations in the Retinto population exhibited a higher degree of positive of the gametic correlations in the Retinto population exhibited a higher degree of positive asymmetry compared to those in the Entrepelado population. In fact, the posterior proba- asymmetry bilities compared of a positive gameticto those in the Entrepelado correlation in the Retintopopulation. population In fact, were 0.80theand posterior 0.78 forprob- the abilities TNB of a positive and NBA, gametic respectively. Incorrelation contrast, the in posterior the Retinto population of probabilities were 0.80 and a positive 0.78 for gametic the TNB and correlation NBA, in the respectively. Entrepelado In contrast, population were the0.50posterior (TNB) and probabilities 0.54 (NBA).of a positive ga- meticAlthough caution is needed in interpreting the results due toand correlation in the Entrepelado population were 0.50 (TNB) 0.54 (NBA). the limited amount of Although caution is needed in interpreting phenotypic and genotypic information, the shape of the posterior distributionthe results due to the limitedofamount gameticof phenotypic and genotypic information, the shape of the correlations suggests a potential role of genomic imprinting. This is because a gametic posterior distribution of gametic correlations correlation suggests a potential substantially lower than roleone of indicates genomic that imprinting. the same This is because of combination a gametic alleles in a gamete may produce different effects on offspring depending on whether they arein correlation substantially lower than one indicates that the same combination of alleles a gamete may transmitted produceordifferent by paternal maternaleffects gametes, on offspring dependingwith which is consistent on whether the theory they are trans- of genomic mitted by paternal or maternal gametes, which imprinting. Genomic imprinting is an epigenetic phenomenon that causes genesis consistent with the theory of genomic to be expressed depending on whether they are inherited from the father or mother [7]. to be ex- imprinting. Genomic imprinting is an epigenetic phenomenon that causes genes pressed Severaldepending theories on have whether they are inherited been postulated to explain from thethe father or mother evolutionary origin [7]. of genomic Several imprinting theories [15], and one have been of the postulated most populartoisexplain the evolutionary the parental investment theory origin of genomic [16]. This imprinting theory argues[15], thatand one of the imprinting is themost popular result is the parental of a conflict between investment the evolutionary theory [16]. This success of theory argues that imprinting is the result of a conflict paternally and maternally derived genes. In mammalian reproduction, the evolutionary between the evolutionary success of paternally success and maternally of paternally inherited genes derived genes. In mammalian is associated reproduction, with the increase the evolution- in fetal growth, while ary for success ofinherited maternally paternally inherited genes, genes is associated it is associated with theofincrease with the number offspring. in fetal This growth, theory iswhile for maternally reinforced inherited by the discovery genes, it isimprinted of numerous associatedgenes with known the number of offspring. to regulate aspectsThis of theory is reinforced mammalian development by the[17],discovery including of numerous growth, imprinted behavior, genes known and placental functionto[18] regulate and, aspects of mammalian furthermore, development there is increasing evidence [17],ofincluding imprintedgrowth, genes in behavior, and placental the pig genome func- [9,19,20]. tionFrom a practical [18] and, perspective, furthermore, there aislow or null gametic increasing evidencecorrelation of imprinted between genespaternal in the pig andge- maternal gametes nome [9,19,20]. within the same population indicates that a selection program to im- prove From the performance of the crossbreeding a practical perspective, a low or individuals null gameticneeds to be specifically correlation designed, between paternal and especially maternalingametes the Entrepelado within the population. same population This is because indicates thethat selection of purebred a selection program animals to im- toprove increase the the performance performance of thein crossbreeding the Entrepelado × Retintoneeds individuals cross tomaybe not have any specifically notice- designed, able consequences especially in the performance in the Entrepelado population. in the ThisRetinto × Entrepelado is because the selectioncross. Furthermore, of purebred animals this result also may explain the differences in performance to increase the performance in the Entrepelado × Retinto cross may not have any noticea-among the reciprocal crosses observed by Noguera ble consequences et al. in the [6], who proposed performance using ×the in the Retinto Retinto variety Entrepelado cross.as a boar and the Furthermore, this Entrepelado as a sow, providing better performance than the result also may explain the differences in performance among the reciprocal crosses ob- opposite cross. served by Noguera et al. [6], who proposed using the Retinto variety as a boar and the 4. Conclusions Entrepelado as a sow, providing better performance than the opposite cross. The bivariate model proposed in this study provides estimates of the gametic effects of4.each founder population as either paternal or maternal, as well as their correlation. Conclusions In the absence of parental imprinting, a perfect correlation of one would be expected. The bivariate model proposed in this study provides estimates of the gametic effects However, our results detect a significant deviation from this ideal scenario, indicating of each founder population as either paternal or maternal, as well as their correlation. In possible differences in the performance of crossbred individuals depending on the paternal the absence of parental imprinting, a perfect correlation of one would be expected. How- or maternal origin of the gametes. These findings provide evidence of the presence of ever, our results detect a significant deviation from this ideal scenario, indicating possible Animals 2022, 12, x. https://doi.org/10.3390/xxxxx www.mdpi.com/journal/animals Animals 2023, 13, 1648 8 of 9 imprinting effects in Iberian pig populations, which could have implications for the design of future breeding programs. Author Contributions: Conceptualization, L.V.; methodology, H.S., D.L.-C. and L.V.; software, H.S. and L.V.; validation, H.S., D.L.-C. and L.V.; formal analysis, H.S. and D.L.-C.; investigation, H.S.; resources, N.I.-E. and J.C.; data curation, S.N., P.H. and N.I.-E.; writing—original draft preparation, H.S. and L.V.; writing—review and editing, N.I.-E., P.H. and J.C.; visualization, D.L.-C. and H.S.; supervision, L.V.; project administration, N.I.-E. and J.C.; funding acquisition, N.I.-E. and J.C. All authors have read and agreed to the published version of the manuscript. Funding: The research was partially funded by grants CGL2016-80155-R, PID2020-114705RB-I00 (Ministerio de Ciencia e Innovación), and IDI-20170304 (CDTI). Srihi received funding from the European Union’s H2020 research and innovation program under a Marie Sklodowska–Curie grant agreement, No. 801586. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The dataset used in this study will be available upon reasonable request to the corresponding author (lvarona@unizar.es). Acknowledgments: We thank INGA FOOD, S.A. (Almendralejo, Spain) and its technicians (E. Magallón, L. Muñoz, P. Díaz, and D. Iniesta) for their cooperation and technical support. Conflicts of Interest: The authors declare no conflict of interest. References 1. Serra, X.; Gil, F.; Pérez-Enciso, M.; Oliver, M.A.; Vázquez, J.M.; Gispert, M.; Díaz, I.; Moreno, F.; Latorre, R.; Noguera, J.L. A comparison of carcass, meat quality and histochemical characteristics of Iberian (Guadyerbas line) and Landrace pigs. Livest. Prod. Sci. 1998, 56, 215–223. [CrossRef] 2. Serrano, M.P.; Valencia, D.G.; Nieto, M.; Lázaro, R.; Mateos, G.G. Influence of sex and terminal sire line on performance and carcass and meat quality of Iberian pigs reared under intensive production systems. Meat Sci. 2008, 78, 420–428. [CrossRef] 3. Silio, L.; Rodriguez, M.C.; Rodrigañez, J.; Toro, M.A. La selección de cerdos ibéricos. In Porcino Ibérico: Aspectos Claves; Buxade, C., Daza, A., Eds.; Mundi-Press: Madrid, Spain, 2001; pp. 125–149. 4. Fernández, A.; Rodrigáñez, J.; Zuzúarregui, J.; Rodríguez, M.C.; Silió, L. Genetic parameters for litter size and weight at different parities in Iberian pigs. Span. J. Agric. Res. 2008, 6, 98–106. [CrossRef] 5. García-Casco, J.M.; Fernández, A.; Rodríguez, M.C.; Silió, L. Heterosis for litter size and growth in crosses of four strains of Iberian pig. Livest. Sci. 2012, 147, 1–8. [CrossRef] 6. Noguera, J.L.; Ibáñez-Escriche, N.; Casellas, J.; Rosas, J.P.; Varona, L. Genetic parameters and direct, maternal and heterosis effects on litter size in a diallel cross among three commercial varieties of Iberian pig. Animal 2019, 13, 2765–2772. [CrossRef] [PubMed] 7. Reik, W.; Walter, J. Genomic imprinting: Parental influence on the genome. Nat. Rev. Genet. 2001, 2, 21–32. [CrossRef] [PubMed] 8. Hanna, C.W. Placental imprinting: Emerging mechanisms and functions. PLoS Genet. 2020, 16, e1008709. [CrossRef] [PubMed] 9. Coster, A.; Madsen, O.; Heuven, H.C.M.; Dibbits, B.; Groenen, M.A.M.; van Arendonk, J.A.M.; Bovenhuis, H. The imprinted gene DIO3 is a candidate gene for litter size in pigs. PLoS ONE 2012, 7, e31825. [CrossRef] [PubMed] 10. Nishio, M.; Satoh, M. Genomic best linear unbiased prediction method including imprinting effects for genomic evaluation. Genet. Sel. Evol. 2015, 47, 32. [CrossRef] [PubMed] 11. Hickey, J.M.; Kinghorn, B.P.; Tier, B.; Wilson, J.F.; Dunstan, N.; Van Der Werf, J.H.J. A combined long-range phasing and long haplotype imputation method to impute phase for SNP genotypes. Genet. Sel. Evol. 2011, 43, 12. [CrossRef] [PubMed] 12. Srihi, H.; Ibáñez-Escriche, N.; Casellas, J.; Noguera, J.L.; Hernández, P.; Martín de Hijas, M.; Vázquez-Gómez, M.; Negro, S.; Rosas, J.P.; Varona, L. Bayesian analysis of paternal and maternal gametic effects in a reciprocal cross between two Iberian varieties. In Proceedings of the 12th World Congress on Genetics Applied to Livestock Production, Rotterdam, The Netherlands, 3–8 July 2022; pp. 3180–3183. 13. Gelfand, A.E.; Smith, A.F.M. Sampling-Based Approaches to Calculating Marginal Densities. J. Am. Stat. Assoc. 1990, 85, 398–409. [CrossRef] 14. Misztal, I.; Tsuruta, S.; Lourenco, D.; Aguilar, I.; Legarra, A.; Vitezica, Z. Manual for BLUPF90 Family of Programs; University of Georgia: Athens, GA, USA, 2018; p. 142. 15. Patten, M.M.; Ross, L.; Curley, J.P.; Queller, D.C.; Bonduriansky, R.; Wolf, J.B. The evolution of genomic imprinting: Theories, predictions and empirical tests. Heredity 2014, 113, 119–128. [CrossRef] [PubMed] 16. Moore, T.; Haig, D. Genomic imprinting in mammalian development: A parental tug-of-war. Trends Genet. 1991, 7, 45–49. [CrossRef] [PubMed] Animals 2023, 13, 1648 9 of 9 17. Thamban, T.; Agarwaal, V.; Khosla, S. Role of genomic imprinting in mammalian development. J. Biosci. 2020, 45, 20. [CrossRef] [PubMed] 18. Fowden, A.L.; Coan, P.M.; Angiolini, E.; Burton, G.J.; Constancia, M. Imprinted genes and the epigenetic regulation of placental phenotype. Prog. Biophys. Mol. Biol. 2011, 106, 281–288. [CrossRef] [PubMed] 19. Wu, Y.Q.; Zhao, H.; Li, Y.J.; Khederzadeh, S.; Wei, H.J.; Zhou, Z.Y.; Zhang, Y.P. Genome-wide identification of imprinted genes in pigs and their different imprinting status compared with other mammals. Zool. Res. 2020, 41, 721–725. [CrossRef] [PubMed] 20. Zhang, F.W.; Han, Z.B.; Deng, C.Y.; He, H.J.; Wu, Q. Conservation of genomic imprinting at the NDN, MAGEL2 and MEST loci in pigs. Genes Genet. Syst. 2012, 87, 53–58. [CrossRef] [PubMed] Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.