A Large-Scale Genome-Wide Association Study of Epistasis Effects of Production Traits and Daughter Pregnancy Rate in U.S

G C A T T A C G G C A T genes

Article A Large-Scale Genome-Wide Association Study of Epistasis Effects of Production Traits and Daughter Pregnancy Rate in U.S. Holstein Cattle

Dzianis Prakapenka 1, Zuoxiang Liang 1, Jicai Jiang 2, Li Ma 3 and Yang Da 1,*

1 Department of Animal Science, University of Minnesota, Saint Paul, MN 55108, USA; [email protected] (D.P.); [email protected] (Z.L.) 2 Department of Animal Science, North Carolina State University, Raleigh, NC 27695, USA; [email protected] 3 Department of Animal and Avian Sciences, University of Maryland, College Park, MD 20742, USA; [email protected] * Correspondence: [email protected]

Abstract: Epistasis is widely considered important, but epistasis studies lag those of SNP effects. Genome-wide association study (GWAS) using 76,109 SNPs and 294,079 first-lactation Holstein cows was conducted for testing pairwise epistasis effects of five production traits and three fertility traits: milk yield (MY), fat yield (FY), protein yield (PY), fat percentage (FPC), protein percentage (PPC), and daughter pregnancy rate (DPR). Among the top 50,000 pairwise epistasis effects of each trait, the five production traits had large chromosome regions with intra-chromosome epistasis. The percentage of inter-chromosome epistasis effects was 1.9% for FPC, 1.6% for PPC, 10.6% for MY, 29.9% for FY, 39.3% for PY, and 84.2% for DPR. Of the 50,000 epistasis effects, the number of significant effects with log10(1/p) ≥ 12 was 50,000 for FPC and PPC, and 10,508, 4763, 4637 and 1 for MY, FY, PY and DPR, Citation: Prakapenka, D.; Liang, Z.; respectively, and A × A effects were the most frequent epistasis effects for all traits. Majority of the Jiang, J.; Ma, L.; Da, Y. A Large-Scale Genome-Wide Association Study of inter-chromosome epistasis effects of FPC across all chromosomes involved a Chr14 region containing Epistasis Effects of Production Traits DGAT1, indicating a potential regulatory role of this Chr14 region affecting all chromosomes for and Daughter Pregnancy Rate in U.S. FPC. The epistasis results provided new understanding about the genetic mechanism underlying Holstein Cattle. Genes 2021, 12, 1089. quantitative traits in Holstein cattle. https://doi.org/10.3390/ genes12071089 Keywords: epistasis; GWAS; milk production; fertility

Academic Editor: Ottmar Distl

Received: 11 June 2021 1. Introduction Accepted: 14 July 2021 Epistasis effects are widely considered important [1–4], but the number of reported Published: 18 July 2021 epistasis effects is far behind the number of single-point effects [2,4,5]. Genome-wide association study (GWAS) in several dairy cattle breeds have reported many single-SNP Publisher’s Note: MDPI stays neutral effects on dairy traits [6–20]. However, epistasis studies in dairy cattle were limited to with regard to jurisdictional claims in published maps and institutional affil- candidate gene tests [21–23] or had a small sample size [24]. The U.S. Holstein cattle have iations. uniquely large sample sizes [25,26] and provide an opportunity to identify epistasis effects associated with dairy traits using GWAS. The purpose of this study was to identify pairwise epistasis effects associated with five dairy production traits and one fertility trait using the same Holstein cattle population that we previously used for a large-scale GWAS to detect SNP additive and dominance effects [19]. For each SNP pair, we tested four types of Copyright: © 2021 by the authors. epistasis effects, additive × additive, additive × dominance, dominance × additive, and Licensee MDPI, Basel, Switzerland. dominance × dominance, and investigated the intra- and inter-chromosome epistasis effects. This article is an open access article distributed under the terms and 2. Materials and Methods conditions of the Creative Commons 2.1. Holstein Populations and Genotyping Data Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ The sample for GWAS analysis contained 294,079 first lactation Holstein cows with 4.0/). phenotypic observations for five milk production traits (milk, fat and protein yields, and

Genes 2021, 12, 1089. https://doi.org/10.3390/genes12071089 https://www.mdpi.com/journal/genes Genes 2021, 12, 1089 2 of 20

fat and protein percentages), and one fertility trait (daughter pregnancy rate). Daughter pregnancy rate is the percentage of cows that become pregnant during each 21-d period [26]. The number of phenotypic observations ranged from 294,079 for milk yield to 245,214 for daughter pregnancy rate. The 294,079 cows had two sets of SNP genotypes, the 80 K with original and imputed 76,109 SNPs with minor allele frequency of 0.05 and the 60 K with original and imputed 60,671 SNPs. Both the 80 K and 60 K SNPs were based on the same set of SNP chips previously described [19]. The 80 K is used in the current U.S. Holstein genomic evaluation, whereas the 60 K was used for the U.S. Holstein genomic evaluation when we reported SNP additive and dominance effects [19]. Results in this article were based on the 80 K except three inter-chromosome epistasis ﬁgures for fat percentage that used the 60 K results because the 60 K had more inter-chromosome epistasis effects for fat percentage than the 80 K. SNP positions were based on the ARS-UCD1.2 bovine genome assembly.

2.2. GWAS Analysis The GWAS analysis used the method of an approximate generalized least squares (AGLS) analysis [19,27]. The AGLS method combines the least squares (LS) tests im- plemented by EPISNP1mpi [28,29] with the estimated breeding values from routine genetic evaluation using the entire U.S. Holstein population as a covariable. The statistical model was: ~ y − Za = µI + Xgg + Za + e = Xb + Za + e (1) where y = column vector of phenotypic deviation after removing fixed nongenetic effects such as heard-year-season (termed as ‘yield deviation’ for any trait) using a standard ~ procedure for the CDCB/USDA genetic and genomic evaluation; a = column vector of 2(PTA), PTA = predicted transmission ability from routine genetic evaluation, µ = common mean; I = identity matrix; g = column vector of pairwise genotypic values; Xg = 0 0 model matrix of g; b = (µ, g ) , X = (I, Xg); a = column vector of additive polygenic values; Z = model matrix of a = identity matrix if each individual has one observation; e = random residuals. The first and second moments of Equation (1) are E(y) = Xb, and 0 2 0 2 2 var(y) = V = ZGZ + R = σaZAZ + σeI, where σa = additive variance, A = additive rela- 2 tionship matrix, and σe = residual variance. Equation (1) achieves the benefit of sample stratification correction from mixed models without the computing difficulty of inverting V or A. Four types of epistasis effects were tested: additive × additive (A × A), additive × dominance (A × D), dominance × additive (D × A), and dominance × dominance (D × D). The significance tests used the t-tests of the epistasis contrasts of the estimated SNP genotypic values [10,30], and the t-statistic was calculated as:

|Lj| |sjgˆ| tj = q = q , j = A × A, A × D, D × A, D × D (2) ( ) 0 − 0 var Lj v sj(X X)ggsj q where Lj = epistasis contrast, var(Lj) = standard deviation of the additive or dominance contrast, v2 = (y − Xbˆ )0(y − Xbˆ )/(n − k) = estimated residual variance; gˆ = column vec- 0 − tor of the AGLS estimates of the pairwise SNP genotypic effects (X X)gg = submatrix of − (X0X) corresponding to gˆ. A limitation in EPISNP1mpi causes a p value less than 10−308 to be printed as ‘0’. For such p values, empirical p values as a power function of the observed t-values were calculated using the empirical formula of p = 0.2416(t1.9713) [19]. For 76,109 SNPs and eight traits, the total number of pairwise tests was 2,896,251,886 × 4 × 8 = 92,680,060,352. The threshold p value with the Bonferroni correction for 0.05 genome-wide false positives was p = 5.39(10−13), and a pairwise epistasis effect was declared signiﬁcant if log10(1/p) > 12.26 ≈ 12. The Manhattan plots of observed log10(1/p) values for each trait were made using SNPEVG2 version 3.2 [31] for a global view of statistical signiﬁ- cance, and the circular plots for global views of intra- and inter-chromosome epistasis Genes 2021, 12, 1089 3 of 20

effects were created using CIRCOS version 0.69-9 [32,33]. The 29 autosomes and the X chromosome had 1225–4121 SNPs per chromosome. These SNPs had 104,203,650 intra- chromosome SNP pairs and 2,791,287,201 inter-chromosome SNP pairs, or, 3.6% of all SNP pairs were intra-chromosome and 96.4% were inter-chromosome. The ratio of (A × A):(A × D + D × A):(D × D) tests was 1:2:1. These percentages and ratios were used for comparison with the observed percentages and ratios.

3. Results 3.1. Overview of Epistasis Effects The pairwise epistasis analysis focused on the top 50,000 pairs of epistasis effects for each trait. All 50,000 SNP pairs of fat and protein percentages had significant epistasis effects; milk yield had 10,485 (21.5%), fat yield had 4746, (10.4%), protein yield had 4629 (15.4%) significant epistasis effects, and daughter pregnancy rate only had one significant epistasis effect (Table1). The six traits had sharp contrasts in percentages of intra- and inter- chromosome epistasis effects and in the distribution of A × A, A × D, D × A and D × D effects among the top 50,000 SNP pairs. Fat percentage (98.1%) and protein percentages (98.4%) had the highest frequencies of intra-chromosome epistasis effects, followed by milk yield (89.4%), fat yield (70.1%), protein yield (61.7%), and daughter pregnancy rate (15.8%) (Table1). The A × A effects were the most frequent effects (Table2). A major difference between daughter pregnancy rate and the five production traits was that inter-chromosome A × A effects were the most frequent A × A effects, 52.9% of the 50,000 effects for this trait. In contrast, protein yield that had the highest frequency of inter-chromosome epistasis effects among the five production traits had 34.9% of inter-chromosome A × A effects (Table2). A global view of statistical significance of the top 50,000 epistasis effects for each trait is shown in Figure1 for intra-chromosome epistasis effects and in Figure2 for inter- chromosome epistasis effects. Significant epistasis effects for the five production traits are shown in Figure S1 for intra-chromosome epistasis, and in Figure S2 for inter-chromosome epistasis. Selected tests results including locations and log10(1/p) values of significant epistasis effects are given in Table S1 for intra-chromosome epistasis effects, and Table S2 for inter-chromosome epistasis effects.

Table 1. Frequencies and statistical signiﬁcance of intra- and inter-chromosome pairwise epistasis effects among the top 50,000 epistasis effects.

Intra-Chromosome Epistasis Inter-Chromosome Epistasis (% of Intra-Chromosome SNP Pairs: 3.6) (% of Inter-Chromosome SNP Pairs: 96.4) Freq (%) Log10(1/p) Pairs with log10(1/p) ≥ 12 Freq (%) Log10(1/p) Pairs with log10(1/p) ≥ 12 FPC 98.1 13–537 49,046 (98.1%) 1.9 13–23 954 (1.9%) PPC 98.4 17–211 49,206 (98.4%) 1.6 17–82 794 (1.6%) MY 89.4 9–97 10,440 (20.9%) 10.6 13–19 68 (0.6%) FY 70.1 7–40 4715 (9.4%) 29.9 7–14 48 (1.0%) PY 61.7 7–51 4325 (8.7%) 39.3 7–21 312 (6.7%) DPR 15.8 6–13 1 (0.002%) 84.2 6–11 0 Freq = frequency. FPC = fat percentage. PPC = protein percentage. MY = milk yield. FY = fat yield. PY = protein yield. Genes 2021, 12, 1089 4 of 20

Table 2. Frequencies of A × A, A × D/D × A and D × D epistasis effects within intra- and inter-chromosome pairwise epistasis effects among the top 50,000 epistasis effects.

Intra-Chromosome Epistasis Inter-Chromosome Epistasis A × AA × D and D × AD × DA × AA × D and D × AD × D FPC Count 47,752 1023 271 952 0 1 % 95.5 2.1 0.5 1.9 0.0 0.0 PPC Count 45,379 2936 1116 10 3 780 % 90.8 5.9 2.2 0.0 0.0 1.6 MY Count 36,387 5978 2355 5197 35 48 % 72.8 12.0 4.7 10.4 0.1 0.1 FY Count 30,225 3767 1401 14,317 188 92 % 60.5 7.5 2.8 28.6 0.4 0.2 PY Count 20,582 7461 2840 17,468 200 1448 % 41.2 14.9 5.7 34.9 0.4 2.9 DPR Count 7122 602 196 26,430 10,531 5118 Genes 2021, 12, x FOR% PEER REVIEW 14.2 1.2 0.4 52.9 21.1 10.25 of 22

FPC = fat percentage. PPC = protein percentage. MY = milk yield. FY = fat yield. PY = protein yield.

Figure 1.1. ManhattanManhattan plots of statisticalstatistical signiﬁcancesignificance of intra-chromosomeintra-chromosome epistasis effects for ﬁvefive milkmilk productionproduction traitstraits Fat percentage. ( and daughterdaughter pregnancypregnancy rate.rate. ((aa):): Fat percentage. (b):): Protein percentage. (c): Milk yield. ( d): Protein yield. ( e): Fat yield. (f): Daughter pregnancy rate. (f): Daughter pregnancy rate.

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Figure 2. Manhattan plots of statistical significance of inter-chromosome epistasis effects for milk production traits. (a): Figure 2. Manhattan plots of statistical significance of inter-chromosome epistasis effects for milk production traits. (a): Fat Fat percentage. (b): Inter-chromosome epistasis effects of the 0.3-10.5 Mb region of Chr14 for fat percentage. (c): Protein percentage. (b): Inter-chromosome epistasis effects of the 0.3-10.5 Mb region of Chr14 for fat percentage. (c): Protein percentage. (d): Milk yield. (e): Fat yield. (f): Protein yield. percentage. (d): Milk yield. (e): Fat yield. (f): Protein yield. 3.2. Intra-Chromosome Epistasis Effects of Fat Percentage 3.2. Intra-Chromosome Epistasis Effects of Fat Percentage Five chromosomes had the most significant intra-chromosome epistasis effects for fat Five chromosomes had the most significant intra-chromosome epistasis effects for fat percentage, chromosomes 14, 5, 6, 23 and 20, and 13 chromosomes did not have significant percentage, chromosomes 14, 5, 6, 23 and 20, and 13 chromosomes did not have significant intra-chromosome epistasis effects for fat percentage, chromosomes 1, 4, 7, 12, 17, 21, 22, intra-chromosome epistasis effects for fat percentage, chromosomes 1, 4, 7, 12, 17, 21, 22, 24, 24, 25, 26, 28, 29 and X (Figure 1a). The five chromosomes with the highly significant epi- 25, 26, 28, 29 and X (Figure1a). The five chromosomes with the highly significant epistasis stasis effects also had highly significant SNP effects [19]. This trait had the highest fre- effects also had highly significant SNP effects [19]. This trait had the highest frequency of quency of A × A effects, 97.4% of the top 50,000 SNP pairs had A × A effects, and the A × A effects, 97.4% of the top 50,000 SNP pairs had A × A effects, and the second highest second highest frequency of intra-chromosome effects, 98.1% of the top 50,000 pairs had frequency of intra-chromosome effects, 98.1% of the top 50,000 pairs had intra-chromosome intra-chromosome epistasis effects (Table 2). epistasis effects (Table2). Chr14 had intra-chromosome epistasis effects in two regions: the 0.25–40 Mb region Chr14 had intra-chromosome epistasis effects in two regions: the 0.25–40 Mb region and the 52–74 Mb region (Figure 3a), but the latter was not among the most significant and the 52–74 Mb region (Figure3a), but the latter was not among the most significant regions (Figures 1a and 3b). These two regions had the largest number of intra-chromo- regions (Figures1a and3b). These two regions had the largest number of intra-chromosome someepistasis epistasis effects, effects, 27,806 27,806 of the of 49,046 the 49 pairs,,046 orpairs, 56.7% or 56.7% of all intra-chromosome of all intra-chromosome epistasis epistasis effects, effects,but the but 0.3–40 the Mb0.3– region40 Mb region had the had most the significant most significant and the and largest the largest number number of effects. of effects. Of the Oftop the 82 mosttop 82 significant most significant intra-chromosome intra-chromosome epistasis epistasis effects, 76 effe pairscts, each76 pairs was each between was twobe- tweenSNPs flanking two SNPsDGAT1 flanking. The DGAT1 genes with. The such genes SNPs with upstream such SNPs of DGAT1 upstreamincluded of DGAT1ZNF250 in-, cludedZNF16 ,ZNF250C14H8orf33, ZNF16, ZNF34, C14H8orf33, CYHR1,, VPS28ZNF34;, theCYHR1 genes, VPS28 downstream; the genes of DGAT1 downstreamincluded of DGAT1GPAA1, MAF1included, MROH1 GPAA1and, MAF1PARP10, MROH1. The 2.86–3.77 and PARP10 Mb region. The with 2.86PTK2–3.77, MbAGO2 region, CHRAC1 with, PTK2TRAPPC9, AGO2and, CHRAC1KCNK9 ,had TRAPPC9 the highest and KCNK9 concentration had the of highest intra-chromosome concentration epistasis of intra effects,-chro- mosome10,963 pairs epistasis out of effects, the 27,806 10,963 Chr14 pairs SNP out pairs,of the or27,806 39.4% Chr14 of the SNP Chr14 pairs, intra-chromosome or 39.4% of the Chr14epistasis intra effects.-chromosome The most epistasis significant effects. intra-chromosome The most significant epistasis intra-chrom effecto wassome between epistasis effect was between rs110508680 (ZNF250-ZNF16) and rs110929299 in GPAA1. The

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DGAT1rs110508680 gene( ZNF250-ZNF16was not heavily) andinvolvedrs110929299 in intrain-chromosomeGPAA1. The epistasisDGAT1 gene effect was for not any heavily of the fiveinvolved milk production in intra-chromosome traits, with epistasis#2245 ranking effect and for any120 epistasis of the five effects milk for production fat percentage, traits, withalthough #2245 DGAT1 ranking had and the 120 most epistasis significant effects SNP for effects fat percentage, for all five although milk productionDGAT1 hadtraits the in themost same significant dataset SNP [19]. effects As to forbe alldescribed, five milk DGAT1 production also traitswas not in the heavil samey datasetinvolved [19 in]. inter As to- chromosomebe described, epistasisDGAT1 also effects. was not heavily involved in inter-chromosome epistasis effects.

Figure 3. Chromosomes with most significant intra-chromosome epistasis effects for fat percentage. The top row shows the circular plots with red color indicating intra-4 Mb epistasis effect and blue color indicating inter-4 Mb epistasis effects; Figure 3. Chromosomes with most significant intra-chromosome epistasis effects for fat percentage. The top row shows the bottom row shows the Manhattan plots of log10(1/p) values. The black arrow indicates the location of the peak the circular plots with red color indicating intra-4 Mb epistasis effect and blue color indicating inter-4 Mb epistasis effects; epistasis effect of the chromosome. Gene name indicates the gene with a peak SNP epistasis effect, and ‘-’ indicates the the bottom row shows the Manhattan plots of log10(1/p) values, where p = the 5% genome-wide type-I error with the SNPBonferroni was between multiple the testing two genes. correction. FPC = The fat percentage.black arrow ( aindicates): Intra-chromosome the location epistasisof the peak effects epistasis of Chr14 effect for of fat the percentage. chromo- (some.b): Statistical Gene name significance indicates the of intra-chromosomegene with a peak SNP epistasis epistasis effects effect, of and Chr14 ‘-’ indicates for fat percentage.the SNP was (betweenc): Intra-chromosome the two genes. epistasisFPC = fat effects percentage. of Chr05 (a): forIntra fat-chromosome percentage. (epistasisd): Statistical effects significance of Chr14 for of fat intra-chromosome percentage. (b): epistasisStatistical effects significance of Chr05 of forintra fat-chromosome percentage. (epistasise): Intra-chromosome effects of Chr14 epistasis for fat effects percentage. of Chr06 (c): for Intra fat- percentage.chromosome (f ):epistasis Statistical effects significance of Chr05 of for intra- fat chromosomepercentage. (d epistasis): Statistical effects significance of Chr06 forof intra fat percentage.-chromosome (g): epistasis Intra-chromosome effects of Chr epistasis05 for effectsfat percentage. of Chr23 ( fore): fatIntra percentage.-chromo- (someh): Statistical epistasis effects significance of Chr06 of for intra-chromosome fat percentage. (f epistasis): Statistical effects significance of Chr23 of forintra fat-chromosome percentage. epistasis (i): Intra-chromosome effects of Chr06 epistasisfor fat percentage. effects of Chr20(g): Intra for-chromosome fat percentage. epistasis (j): Statistical effects of significance Chr23 for offat intra-chromosomepercentage. (h): Statistical epistasis significance effects of Chr20 of intra for- chromosome epistasis effects of Chr23 for fat percentage. (i): Intra-chromosome epistasis effects of Chr20 for fat percentage. fat percentage. (j): Statistical significance of intra-chromosome epistasis effects of Chr20 for fat percentage. Chr05 had intra-chromosome epistasis effects in the 64–116 Mb region (Figure3c), aboutChr05 half ofhad the intra chromosome,-chromosome with epistasis the second effects largest in the number64–116 Mb of intra-chromosomeregion (Figure 3c), aboutepistasis half effects, of the 17,057chromosome, epistasis with effects, the orsecond 34.8% largest of all intra-chromosomenumber of intra-chromosome epistasis effects. epi- stasisThe most effects, significant 17,057 epistasis intra-chromosome effects, or epistasis34.8% of effectall intra of this-chromosome chromosome epistasis was between effects. Thers41602750 most significant(LMO3-MGST1 intra-)chromosome and rs136373712 epistasisin PTPRO effect(Figure of this3 d).chromosome We reported was this between region rs41602750to have the ( mostLMO3 significant-MGST1) SNPand rs136373712 effects of fat in percentage PTPRO (Figure among 3d). all chromosomesWe reported this except re- gionChr14 to [ 19have]. the most significant SNP effects of fat percentage among all chromosomes exceptChr06 Chr14 had [19]. intra-chromosome epistasis effects mostly in the 32–44 Mb region (Figure3e ) withChr06 peak effect had intra between-chromosomers109552132 epistasisin HERC3 effectsand mostlyrs109263339 in the 3(2IBSP-LAP3–44 Mb region) (Figure (Figure3f). 3e)The with 32–44 peak Mb effect region between had significant rs109552132 SNP in effects HERC3 for alland five rs109263339 production (IBSP traits-LAP3 [19].) The(Figure top 1003f). The pairs 32 were–44 Mb located region in had the 30.15–36.70significant SNP region effects with forHERC3 all five, IBSP production, LAP3, traitsLCORL [19]., SPP1 The, topMEPE 100, PKD2 pairs, wereCCSER1 located, and inABCG2 the 30.1. 5–36.70 region with HERC3, IBSP, LAP3, LCORL, SPP1Chr23, MEPE had, PKD2 intra-chromosome, CCSER1, and ABCG2 epistasis. effects in the 8–24 Mb region with peak with peakChr23 effects had in the intra 16–17-chromosome Mb region epistasis (Figure3g), effects and thein the most 8– significant24 Mb region effect with on peak this chro-with peakmosome effects was in between the 16–17rs109288796 Mb regionin (FigureBICRAL 3g),and andrs109567499 the most insignificanMRPS18At effect(Figure on 3thish ). chromosomeThe Chr23 epistasis was between effects rs109288796 were mostly in D BICRAL× D, A and× D rs109567499 and D × A in effects, MRPS18A and most(Figure of 3h).the DThe× Chr23D effects epistasis involved effects genotype were mostly combinations D × D, A with× D and small D × frequencies A effects, and of < most 0.0001 of

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(Table S1). These effects were in the same region where significant SNP dominance effects were detected [19]. Genes 2021, 12, x FOR PEER REVIEW 8 of 22 Chr20 had intra-chromosome epistasis effects in the 25–43 Mb region (Figure3i) with peak effect between rs134342292 about 10 Kb downstream of FGF10 and rs41580285 in NNT (Figure3j). The 25–43 Mb region contained the GHR-C6-PRLR region that had highly significantthe D × D effects SNP effects involved for allgenotype five production combinations traits with [19]. small frequencies of < 0.0001 (Ta- ble S1). These effects were in the same region where significant SNP dominance effects 3.3.were Intra-Chromosome detected [19]. Epistasis Effects of Protein Percentage FiveChr20 chromosomes had intra-chromosome had the most epistasis significant effects intra-chromosomein the 25–43 Mb region epistasis (Figure effects 3i) with for proteinpeak effect percentage, between chromosomes rs134342292 about 14, 6, 23,10 20Kb anddownstream 3; six chromosomes of FGF10 didand notrs41580285 have such in effectsNNT (Figure for protein 3j). The percentage, 25–43 Mb region chromosomes contained 2, 4,the 21, GHR 24,-C6 25- andPRLR 26 region (Figure that1b). had The highly five chromosomessignificant SNP with effects the for highly all five significant production epistasis traits effects [19]. also had highly significant SNP effects [19]. This trait had the second highest frequency of A × A effects, 97.4% of the top 50,0003.3. Intra SNP-Chromosome pairs had AEpistasis× A effects, Effects and of Protein the second Percentage highest frequency of intra-chromosome effects,Five 98.4% chromosomes of the top 50,000had the pairs most had significant intra-chromosome intra-chromosome epistasis effectsepistasis (Table effects2). for proteinChr06 percentage, had intra-chromosome chromosomes 14, epistasis 6, 23, 20 effects and 3; in six two chromosomes regions: the did 16–60 not Mbhave region such (approximatelyeffects for protein the percentage, same region chromosomes with epistasis 2, effects 4, 21, for 24, fat 25 percentage) and 26 (Figure and the1b). 70–96 The five Mb regionchromosomes (Figure 4witha). Thethe highly most significant significant effects epistasis of alleffects chromosomes also had highly were significant located in SNP the 30.64–38.33effects [19]. MbThis region trait had of Chr06 the second with PKD2highest, SPP1 frequency, MEPE of, IBSP A × ,AHERC3 effects,, ABCG2 97.4% ;of whereas the top the50,000 most SNP significant pairs had effects A × A within effects, the and 70–96 the second Mb region highest were frequency located in of 84.83–86.07 intra-chromosome Mb with CSN1S2effects, 98.4%, ODAM of ,theCSN1S1 top 50,000, CSN2 pairs, LOC526979 had intra(Figure-chromosome4b). epistasis effects (Table 2).

FigureFigure 4.4. ChromosomesChromosomes with with most most significant significant intra-chromosome intra-chromosome epistasis epistasis effects effects for protein for protein percentage. percentage. The top The row top shows row theshows circular the circular plots with plots red with color red indicating color indicating intra-4 Mbintra epistasis-4 Mb epistasis effect and effect blue and color blue indicating color indicating inter-4 Mbinter epistasis-4 Mb epistasis effects; theeffects; bottom the rowbottom shows row the shows Manhattan the Manhattan plots of log10(1/p) plots of log10( values.1/p) The values, black where arrow p indicates = the 5% the genome location-wide of the type peak-I error epistasis with effectthe Bonferroni of the chromosome. multiple testing Gene correction. name indicates The black the gene arrow with indicates a peak the SNP location epistasis of effect,the peak and epistasis ‘-’ indicates effect the of SNPthe chro- was mosome. Gene name indicates the gene with a peak SNP epistasis effect, and ‘-’ indicates the SNP was between the two between the two genes. PPC = protein percentage. (a): Intra-chromosome epistasis effects of Chr06 for protein percentage. genes. PPC = protein percentage. (a): Intra-chromosome epistasis effects of Chr06 for protein percentage. (b): Statistical (b): Statistical significance of intra-chromosome epistasis effects of Chr06 for protein percentage. (c): Intra-chromosome significance of intra-chromosome epistasis effects of Chr06 for protein percentage. (c): Intra-chromosome epistasis effects epistasisof Chr23 effectsfor protein of Chr23 percentage. for protein (d): percentage.Statistical significance (d): Statistical of intra significance-chromosome of intra-chromosome epistasis effects epistasisof Chr20 effectsfor protein of Chr20 per- forcentage. protein (e): percentage. Intra-chromosome (e): Intra-chromosome epistasis effects epistasis of Chr20 effects for protein of Chr20 percentage. for protein (f percentage.): Statistical (significancef): Statistical o significancef intra-chro- ofmosome intra-chromosome epistasis effects epistasis of Chr14 effects for protein of Chr14 percentage. for protein (g percentage.): Intra-chromosome (g): Intra-chromosome epistasis effects epistasis of Chr14 effects for protein of Chr14 per- forcentage. protein (h): percentage. Statistical significance (h): Statistical of significanceintra-chromosome of intra-chromosome epistasis effects epistasis of Chr14 effects for protein of Chr14 percentage. for protein (i): percentage. Intra-chro- (mosomei): Intra-chromosome epistasis effects epistasis of Chr03 effects for protein of Chr03 percentage. for protein (j): percentage. Statistical significance (j): Statistical of intra significance-chromosome of intra-chromosome epistasis effects epistasisof Chr03 effectsfor protein of Chr03 percentage. for protein percentage.

Chr06 had intra-chromosome epistasis effects in two regions: the 16–60 Mb region (approximately the same region with epistasis effects for fat percentage) and the 70–96 Mb region (Figure 4a). The most significant effects of all chromosomes were located in the 30.64–38.33 Mb region of Chr06 with PKD2, SPP1, MEPE, IBSP, HERC3, ABCG2; whereas the most significant effects within the 70–96 Mb region were located in 84.83–86.07 Mb with CSN1S2, ODAM, CSN1S1, CSN2, LOC526979 (Figure 4b).

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Chr23 had intra-chromosomeintra-chromosome epistasis effects in 12–2412–24 Mb regionsregions (Figure(Figure4 4cc),), with with peak effects in 13.85–18.6113.85–18.61 Mb in or near PPP2R5D, MRPS18A, BICRAL, FOXP4, SUPT3H, MOCS1,, CCND3,, approximatelyapproximately thethe samesame regionregion withwith signiﬁcantsignificant epistasisepistasis andand SNPSNP domi-dom- nanceinance effects effects for for fat fat percentage percentage (Figure (Figure4d). 4d) The. The Chr23 Chr23 epistasis epistasis effects effects were were mostly mostly D × DD, × AD,× AD × D and and D D× ×A A effects, effects, and and most most of of the the D D× × DD effectseffects involvedinvolved genotypegenotype combinations with small frequenciesfrequencies << 0.0001. Chr20 had intra-chromosomeintra-chromosome epistasisepistasis effectseffects inin thethe 34–5234–52 MbMb region (Figure(Figure4 4ee)) with with peak effects in the 30.64–31.1730.64–31.17 MbMb ofof Chr20Chr20 involving a SNP 42 KbKb downstreamdownstream ofof FGF10FGF10 and a SNP in NNT (Figure4 4f)f).. Chr14 had intra intra-chromosome-chromosome epistasis epistasis effects effects in in two two regions, regions, the the 0.2 0.25–205–20 Mb Mb and and the the36–82 36–82.4.4 Mb Mbregions regions (Figure (Figure 4g).4 Peakg). Peak intra intra-chromosome-chromosome epistasis epistasis effects effects were were in the in 0.2 the5– 0.25–0.810.81 Mb regionMb region involving involving SNPs SNPs in inor or near near ZNF250ZNF250, ZNF16, ZNF16, ,GPAA1GPAA1, , MAF1,, CYHR1, MROH1, VPS28;; in in the 64.36–67.1064.36–67.10 Mb region inin oror nearnear RGS22RGS22,, MGC148714,MGC148714, VPS13BVPS13B, OSR2,, andand CPQCPQ (Figure(Figure4 4h).h). Chr03 had regions regions had had intra intra-chromosome-chromosome epistasis epistasis effects effects mostly mostly in inthe the 4–30 4–30 Mb Mb re- regiongion (Figure (Figure 44i),i), with with peak peak effects effects in in the the 15. 15.9–16.09–16.0 Mb Mb region region in or near TDRD10TDRD10,, KCNN3, ADAR; betweenbetween rs135012389 at 98.6 MbMb andand rs136744726rs136744726 atat 116.1116.1 MbMb inin LOC101904767LOC101904767 (Figure(Figure4 4j).j).

3.4. Intra-ChromosomeIntra-Chromosome Epistasis Effects of Milk Yield Chromosomes 14,14, 5, 6, 23 and 20 had the mo mostst significant signiﬁcant intra intra-chromosome-chromosome epistasis effects (Figures(Figures1 1ccand and5 ),5), and and all all the the chromosome chromosome regions regions with with peak peak epistasis epistasis effects effects also also had peak SNP effects [[19].19].

FigureFigure 5.5. ChromosomesChromosomes withwith mostmost significantsignificant intra-chromosomeintra-chromosome epistasis effects for milkmilk yield.yield. TheThe toptop rowrow showsshows thethe circularcircular plotsplots withwith redred colorcolor indicatingindicating intra-4intra-4 MbMb epistasisepistasis effecteffect andand blueblue colorcolor indicatingindicating inter-4inter-4 MbMb epistasisepistasis effects;effects; thethe bottombottom row shows the Manhattan plots of log10( log10(1/p)1/p) values, values. where The black p = the arrow 5% genome indicates-wide the location type-I err ofor the with peak the epistasis Bonfer- roni multiple testing correction. The black arrow indicates the location of the peak epistasis effect of the chromosome. effect of the chromosome. Gene name indicates the gene with a peak SNP epistasis effect, and ‘-’ indicates the SNP was Gene name indicates the gene with a peak SNP epistasis effect, and ‘-’ indicates the SNP was between the two genes. MY between the two genes. MY = milk yield. (a): Intra-chromosome epistasis effects of Chr14 for milk yield. (b): Statistical = milk yield. (a): Intra-chromosome epistasis effects of Chr14 for milk yield. (b): Statistical significance of intra-chromo- significance of intra-chromosome epistasis effects of Chr14 for milk yield. (c): Intra-chromosome epistasis effects of Chr23 for some epistasis effects of Chr14 for milk yield. (c): Intra-chromosome epistasis effects of Chr23 for milk yield. (d): Statistical milksignificance yield. (d of): intra Statistical-chromosome significance epistasis of intra-chromosome effects of Chr23 epistasisfor milk yield effects. (e of): Chr23Intra-chromosome for milk yield. epistasis (e): Intra-chromosome effects of Chr05 epistasisfor milk yield. effects (f of): Chr05Statistical for milksignificance yield. ( fof): Statisticalintra-chromosome significance epistasis of intra-chromosome effects of Chr05 epistasisfor milk effectsyield. ( ofg): Chr05 Intra-chromo- for milk yield.some epistasis (g): Intra-chromosome effects of Chr06epistasis for milk yield. effects (h of): Chr06Statistical for significance milk yield. of (h ):intra Statistical-chromosome significance epistasis of intra-chromosomeeffects of Chr06 for epistasismilk yield effects. (i): Intra of Chr06-chromosome for milk epistasis yield. ( ieffects): Intra-chromosome of Chr20 for milk epistasis yield. ( effectsj): Statistical of Chr20 significance for milk of yield. intra (-jchromosome): Statistical significanceepistasis effects of intra-chromosome of Chr20 for milk epistasisyield. effects of Chr20 for milk yield.

Genes 2021, 12, 1089 9 of 20

Chr14 had 2976 or 28.51% of the 10,440 intra-chromosome epistasis effects for milk yield mostly in the 0.25–12 Mb region (Figure5a), with peak effect between rs109752439 and VPS28 (Figure5b) that was also the peak effect for protein yield (Figure1e). However, DGAT1 that had the most significant SNP effects for all five production traits [19] only had five intra-chromosome epistasis effects with the best ranking of #6140 for milk yield and had no significant intra-chromosome epistasis effects for protein and fat yields. Chr23 had intra-chromosome epistasis effects mostly in the 10–30 Mb region (Figure5c ), with peak D × D effects between two SNPs in BICRAL and MRPS18A in the 16.4–17.2 Mb region (Figure5d). The 13.85–19.79 Mb region had a large number of D × D, D × A or A × D effects of milk and protein yields (Table S1) and was approximately the same region where significant SNP dominance effects were detected [19]. Chr05 had intra-chromosome epistasis effects mostly in the 24–50 and 84–112 Mb regions for milk yield (Figure5e) with peak D × A effect between the dominance effect of a SNP in AAAS and the additive effect of a SNP between SLC38A2 and SLC38A1 (Figure5f ). In the 24–50 Mb region, majority of the epistasis effects were D × A, A × D and D × D. The chromosome region around the peak epistasis effect had highly significant dominance effects in or near ATF7, AAAS, EIF4B and PLXNC1 [19]. Chr06 had two regions with intra-chromosome epistasis effects for the milk yield: the 30–46 Mb and the 62–102 Mb (Figure5g), with peak effects between rs109263339 ( IBSP- LAP3) and rs110012183 downstream of LCORL in the first region, and between a SNP (rs109452259) flanked by GC and NPFFR2 and multiple SNPs in SLC4A4 in the second region (Figure5h). The SLC4A4- GC-NPFFR2 region had the most significant SNP effects on milk and protein yields outside Chr14 [19]. Chr20 had intra-chromosome epistasis effects in the 30–52 Mb region for milk yield (Figure5i) with peak effect between a SNP in C6 and a SNP in PTGER4 (Figure5j). The 25–43 Mb region contained the GHR-C6-PRLR region that had highly significant SNP effects for milk and protein yields [19].

3.5. Intra-Chromosome Epistasis Effects of Protein Yield Chromosomes 14, 5, 6, 23 and 20 had the most significant intra-chromosome epistasis effects (Figures1d and6), and all the chromosome regions with peak epistasis effects also had peak SNP effects [19]. Chromosome 28 was the only chromosome without intra- chromosome epistasis effects with log10(1/p) ≥ 12 (Figure1d). Chr14 had intra-chromosome epistasis effects for protein yield mostly in the 0.25–7 Mb region (Figure6a), with peak effect between rs109752439 and VPS28 (Figure6b) that was also the peak effect for milk yield (Figure5b). Chr05 had intra-chromosome epistasis effects mostly in the 24–40 Mb for protein yield (Figure6c) with peak D × A effect between the dominance effect of a SNP in AAAS and the additive effect of a SNP between SLC38A2 and SLC38A1 (Figure6d). The same SNP pair also had peak D × A for milk yield. As for milk yield, majority of the epistasis effects in the 24–40 Mb region were D × A, A × D and D × D. Genes with highly significant intra-chromosome epistasis effects near the peak effects included ATF7, AAAS, SLC38A1, SCAF11 and ANO6. Chr06 had two regions with intra-chromosome epistasis effects for protein yield at 35.1–38.3 and 76–96 Mb (Figure6e), with peak effects between rs1095336909 (SNCA- GPRIN3) and rs110718778 downstream of LCORL in the first region, and between rs109452259 in LOC112447096 and rs135020479 flanked by ANKRD17 and ALB (Figure6f). A SNP (rs109452259) between GC and NPFFR2 and five SNPs in SLC4A4 had the #2–7 peak effects of the chromosome, noting that this region also had highly significant SNP effects for protein yield [19]. Chr23 had intra-chromosome epistasis effects mostly in the 14–20 Mb region (Figure6g ), with peak D × D effects between two SNPs in BICRAL and MRPS18A in the 16.4–17.2 Mb region (Figure6h), the same SNP pair with peak D × D for milk yield (Figure5d). The 13.85–19.79 Mb region had a large number of D × D, D × A or A × D effects of milk and Genes 2021, 12, 1089 10 of 20

protein yields (Table S1) and was approximately the same region where signiﬁcant SNP dominance effects were detected [19]. Genes 2021, 12, x FOR PEER REVIEW Chr19 only had two pairs of highly signiﬁcant intra-chromosome epistasis effect11 of be-22

tween rs110881085 in C19H17orf67 and two SNPs in BRIP1 and INTS2 (Figures1d and6i,j ).

Figure 6. ChromosomesChromosomes with with most most significant significant intra intra-chromosome-chromosome epistasis epistasis effects effects for for protein protein yield. yield. The The top toprow row shows shows the thecircular circular plots plots with with red redcolor color indicating indicating intra intra-4-4 Mb Mbepistasis epistasis effect effect and andblue blue color color indicating indicating inter inter-4-4 Mb Mbepistasis epistasis effects; effects; the thebottom bottom row rowshows shows the Manhattan the Manhattan plots of plots log10( of log10(1/p)1/p) values, values.where pThe = the black 5% genome arrow- indicateswide type the-I error location with ofthe the Bonfer- peak roni multiple testing correction. The black arrow indicates the location of the peak epistasis effect of the chromosome. epistasis effect of the chromosome. Gene name indicates the gene with a peak SNP epistasis effect, and ‘-’ indicates the Gene name indicates the gene with a peak SNP epistasis effect, and ‘-’ indicates the SNP was between the two genes. PY a SNP= protein was betweenyield. (a): the Intra two-chromosome genes. PY = epistasis protein yield. effects ( ):of Intra-chromosomeChr14 for protein yield. epistasis ((b): effects Statistical of Chr14 significance for protein of intra yield.- (chromosomeb): Statistical epistasis significance effects of intra-chromosome of Chr14 for protein epistasis yield. ( effectsc): Intra of-chromosome Chr14 for protein epistasis yield. effects (c): Intra-chromosome of Chr05 for protein epistasis yield. effects(d): Statistical of Chr05 significance for protein of yield.intra-chromosome (d): Statistical epistasis significance effects of of intra-chromosome Chr05 for protein yield. epistasis (e): effectsIntra-chromosome of Chr05 for epistasis protein yield.effects (eof): Chr06 Intra-chromosome for protein yield. epistasis (f): effectsStatistical of Chr06significance for protein of intra yield.-chromosome (f): Statistical epistasis significance effects ofof intra-chromosomeChr06 for protein epistasisyield. (g): effects Intra- ofchromosome Chr06 for protein epistasis yield. effects (g): of Intra-chromosome Chr23 for protein epistasis yield. (h effects): Statistical of Chr23 significance for protein of yield. intra (-hchromosome): Statistical significanceepistasis effects of intra-chromosome of Chr23 for protein epistasis yield. effects (i): Intra of- Chr23chromosome for protein epistasis yield. effects (i): Intra-chromosome of Chr19 for protein epistasis yield. effects (j): Statistical of Chr19 forsignificance protein yield. of intra (j):-chromosome Statistical significance epistasis effects of intra-chromosome of Chr19 for protein epistasis yield. effects of Chr19 for protein yield.

3.6. Intra-ChromosomeChr14 had intra-chromosome Epistasis Effects epistasis of Fat Yield effects for protein yield mostly in the 0.25–7 Mb regionChromosomes (Figure 6a), 14, 5,with 15, peak 6 and effect 26 had between the most rs109752439 significant intra-chromosomeand VPS28 (Figure epistasis6b) that waseffects also (Figures the peak1e effect and7). for Nine milk chromosomes yield (Figure did5b). not have intra-chromosome epistasis effectsChr05 with had log10(1/p) intra-chromosome≥ 12, chromosomes epistasis 12, effects 13, 16, mostly 17, 21, in 22, the 24, 2 25,4–40 and Mb 28. for protein yieldChr14 (Figure had 6c 259) with intra-chromosome peak D × A effect epistasis between effects the for dominance fat yield mostly effect inof thea SNP0.24–8.11 in AAAS Mb andregion the (Figure additive7a), effect with of the a SNP most between significant SLC38A2 effects and between SLC38A1rs109752439 (Figure 6d(C14H8orf33-). The same SNPZNF34 pair) and alsoMAF1 had (Figurepeak D7 ×b) A among for milk all chromosomes.yield. As for milk This yield, 0.24–8.11 majori Mbty region of the had epistasis 36 of effectsthe top in 66 the intra-chromosome 24–40 Mb region epistasis were D × effects A, A × and D and each D of × theD. Genes 36 effects with involved highly significant two SNPs intraon both-chromosome sides of DGAT1 epistasis, which effects did near not the have peak any effects significant included intra-chromosome ATF7, AAAS, SLC38A1 epistasis, SCAF11effect for and fat yield.ANO6. Chr06Chr05 hadhad 4111 two orregions 86.31% with of the intra 4763-chromosom intra-chromosomee epistasis epistasis effects effects for inprotein the 22–112 yield Mb at 35.region1–38 that.3 and covered 76–96 93% Mb of (Figure the chromosome 6e), with peak (Figure effects7c). The between most significantrs1095336909 effect (SNCA was- GPRIN3between) rs136373712 and rs110718778in PTPRO downstreamand rs41602750 of LCORL(LMO3-MGST1 in the first ) region, (Figure 7 andd), and between the rs10945225989.3–94.38 Mb in regionLOC112447096 with PTPRO and rs135020479, LMO3, MGST1 flanked, PDE3A by ANKRD17, SLC15A5 and, DERA ALB (Figure, PIK3C2G 6f)., ARERGL SNP (andrs109452259PLEKHA5) betweenhad the GC most and significant NPFFR2 Aand× Afive effects SNPs on in this SLC4A4 chromosome. had the #2 The–7 peakepistasis effects effects of the in thechromosome, 26.5–44.9 regionnoting mostlythat this involved region also dominance, had highly A × significantD, D × A SNP and effectsD × D ,for with protein the most yield significant [19]. such effect being D × A between the dominance effect of rs109675908Chr23 hadin ATF7 intra-andchromosome the additive epistasis effect ofeffectsrs42851612 mostly( inSLC38A1-SCAF11 the 14–20 Mb region) (Figure (Figure7d). 6g), with peak D × D effects between two SNPs in BICRAL and MRPS18A in the 16.4–17.2 Mb region (Figure 6h), the same SNP pair with peak D × D for milk yield (Figure 5d). The 13.85–19.79 Mb region had a large number of D × D, D × A or A × D effects of milk and protein yields (Table S1) and was approximately the same region where significant SNP dominance effects were detected [19].

Genes 2021, 12, 1089 11 of 20 Genes 2021, 12, x FOR PEER REVIEW 12 of 22

Chr15 had intra-chromosome epistasis effects mostly in the 52–66 Mb region (Figure7e ) withChr19 peak effect only betweenhad two pairsrs132656140 of highlyin significantLOC107133183 intra-andchromosomers29022897 epistasisin ABTB2 effectin thebe- 63.51–64.79tween rs110881085 Mb region in C19H17orf67 (Figure7f). and two SNPs in BRIP1 and INTS2 (Figures 1d, 6i and 6j). Chr06 had intra-chromosome epistasis effects mostly in the 80–92 Mb region (Figure7g ), with peak effects between rs136961414 in LOC100138004 and rs134391498 in SLC4A4 mboxfigfig:genes-1277371-f007h).3.6. Intra-Chromosome Epistasis Effects Similar of Fat to Yield milk and protein yields, rs109452259 between GC andChromosomesNPFFR2 and 14, five 5, SNPs15, 6 and in SLC4A4 26 had thehad most the #3 significant and #8–11 intra effects-chromosome of the chromosome. epistasis effectsChr26 (Figure hads scattered 1e and 7). intra-chromosome Nine chromosomes epistasis did effects not have in the intra 12–32-chromosome Mb region (Figure epistasis7i ) witheffects peak with effect log10(1/ betweenp) ≥ 12,rs42092371 chromosomesin NEURL1 12, 13,and 16, 17,rs41604819 21, 22, 24,in 25,SORCS1 and 28.(Figure 7j).

FigureFigure 7.7. ChromosomesChromosomes withwith mostmost significantsignificant intra-chromosomeintra-chromosome epistasisepistasis effectseffects forfor fatfat yield.yield. TheThe toptop rowrow showsshows thethe circularcircular plotsplots withwith redred colorcolor indicatingindicating intra-4intra-4 MbMb epistasisepistasis effecteffect andand blueblue colorcolor indicatingindicating inter-4inter-4 MbMb epistasisepistasis effects;effects; thethe bottom row shows the Manhattan plots of log10(1/p) values, where p = the 5% genome-wide type-I error with the Bonfer- bottom row shows the Manhattan plots of log10(1/p) values. The black arrow indicates the location of the peak epistasis roni multiple testing correction. The black arrow indicates the location of the peak epistasis effect of the chromosome. effect of the chromosome. Gene name indicates the gene with a peak SNP epistasis effect, and ‘-’ indicates the SNP was Gene name indicates the gene with a peak SNP epistasis effect, and ‘-’ indicates the SNP was between the two genes. FY = a b betweenfat yield. the(a): twoIntra genes.-chromosome FY = fat epistasis yield. (effects): Intra-chromosome of Chr14 for fat epistasisyield. (b) effects: Statistical of Chr14 significance for fat yield.of intra ( -chromosome): Statistical significanceepistasis effects of intra-chromosome of Chr14 for fat yield epistasis. (c): effectsIntra-chromosome of Chr14 for fatepistasis yield. effects (c): Intra-chromosome of Chr05 for fat epistasisyield. (d): effects Statistical of Chr05 signifi- for fatcance yield. of intra (d):- Statisticalchromosome significance epistasis ofeffects intra-chromosome of Chr05 for fat epistasis yield. (e effects): Intra of-chromosome Chr05 for fat epistasis yield. ( eeffects): Intra-chromosome of Chr15 for fat epistasisyield. (f): effects Statistical of Chr15 significance for fat yield. of intra (f):-chromosome Statistical significance epistasis effects of intra-chromosome of Chr15 for fat epistasis yield. (g effects): Intra of-chromosome Chr15 for fat epista- yield. (sisg): effects Intra-chromosome of Chr06 for fat epistasis yield. ( effectsh): Statistical of Chr06 significance for fat yield. of intra (h):-chromosome Statistical significance epistasis effects of intra-chromosome of Chr06 for fat epistasisyield. (i): effectsIntra-chromosome of Chr06 for epistasis fat yield. effects (i): Intra-chromosome of Chr26 for fat yield. epistasis (j): Statistical effects of significance Chr26 for fat of yield. intra- (chromosomej): Statistical epistasis significance effects of intra-chromosomeof Chr26 for fat yield epistasis. effects of Chr26 for fat yield.

3.7. Inter-ChromosomeChr14 had 259 intra Epistasis-chromosome Effects of epistasis Fat Percentages effects for fat yield mostly in the 0.24–8.11 Mb region (Figure 7a), with the most significant effects between rs109752439 (C14H8orf33- The most surprising inter-chromosome epistasis effects were those for fat percentage: allZNF34 29 chromosomes) and MAF1 (Figure interacted 7b) among with a all Chr14 chromosomes. region with ThisDGAT1 0.24–,8.11 which Mb hadregion the had most 36 significantof the top 66 SNP intra effect-chromosome for fat percentage epistasis [19 effects]. Figure and2 aeach shows of the 27 of36 the effects 30 chromosomes involved two hadSNPs significant on both sides inter-chromosome of DGAT1, which epistasis did not effects have forany fat significant percentage intra (log10(1/p)-chromosome≥ 12.82) epi- amongstasis effect the topfor fat 50,000 yield. pairs. However, 26 of the 27 chromosomes each only interacted withChr05 the same had 0.3–10.54111 or Mb86.31% region of the of Chr144763 intra (Figure-chromosome8a) with Aepistasis× A effects. effects Onlyin the one22– inter-chromosome112 Mb region that covered effect did 93% not of involvethe chromosome the Chr14 (Figure region: 7c). the The D most× D significant effect between effect Chr22was between and Chr23 rs136373712 (Figure in S2, PTPRO Table S2).and Thesers41602 results750 (LMO3 were-MGST1 from the) (Figure 80 K SNP 7d), setand that the had89.3– more94.38 intra-chromosome Mb region with PTPRO epistasis, LMO3 effects, MGST1 (98.1%,, Table PDE3A1) and, SLC15A5 fewer inter-chromosome, DERA, PIK3C2G, epistasisRERGL and effects PLEKHA5 (1.9%, Tablehad 1the) than most those significant from the A 60× A K SNPeffects set on that this had chromosome. 94% intra- and The 6%epistasis inter-chromosome effects in the epistasis26.5–44.9 effects. region Frommostly the involved 60 K, all do 29minance, chromosomes A × D, interacted D × A and with D × theD, with same the Chr14 most region significant (Figure such S2, effect Table being S2). Figure D × A8 b–h between shows the some dominance 80 K examples effect of showingrs109675908 each in chromosomeATF7 and the specificallyadditive effect interacted of rs42851612 with the (SLC38A1 0.3–10.5-SCAF11 Mb region) (Figure of chr14. 7d).

Genes 2021, 12, 1089 12 of 20

Such a high degree of speciﬁcity of the 0.3–10.5 Mb region of chr14 for interactions with other chromosomes provided evidence implicating a potential global regulatory role of this Genes 2021, 12, x FOR PEER REVIEW 14 of 22 region for fat percentage and indicated that fat percentage likely had genetic contributions from the entire genome.

Figure 8. Examples of inter-chromosomeinter-chromosome epistasis effects between the same Chr14 region and different chromosomes for fatfat percentage ( (log10(1/p)log10(1/p) ≥ ≥12.8212.82).). Each Each number number on the on outer the outer circle circle is the is chromosome the chromosome number, number, red color red colorrepresents represents intra- intra-chromosomechromosome epistasis epistasis effects, effects, and blue and color blue represents color represents inter-chromosome inter-chromosome epistasis epistasiseffects. Number effects. in Number () is the effect in () isrank- the ing. The arrow indicates the Chr14 region that interacted with every chromosome for fat percentage. FPC = fat percentage. effect ranking. The arrow indicates the Chr14 region that interacted with every chromosome for fat percentage. FPC = fat (a): Inter-chromosome epistasis effects between 26 chromosomes and the 0.3-10.5 Mb region of Chr14 for fat percentage. percentage. (a): Inter-chromosome epistasis effects between 26 chromosomes and the 0.3-10.5 Mb region of Chr14 for fat (b): Inter-chromosome epistasis effects between Chr05 and the 0.3-10.5 Mb region of Chr14 for fat percentage. (c): Inter- percentage. (b): Inter-chromosome epistasis effects between Chr05 and the 0.3-10.5 Mb region of Chr14 for fat percentage. chromosome epistasis effects between Chr08 and the 0.3-10.5 Mb region of Chr14 for fat percentage. (d): Inter-chromosome (epistasisc): Inter-chromosome effects between epistasis Chr21 effectsand the between 0.3-10.5 Chr08Mb region and theof Chr14 0.3-10.5 for Mb fat region percentage of Chr14. (e): for Inter fat-chromosome percentage. ( depistasis): Inter- chromosomeeffects between epistasis Chr20 effectsand the between 0.3-10.5 Chr21 Mb region and the of 0.3-10.5Chr14 for Mb fat region percentage of Chr14. (f for): Inter fat percentage.-chromosome (e): epistasis Inter-chromosome effects be- epistasistween Chr04 effects and between the 0.3-10.5 Chr20 Mb and region the of 0.3-10.5 Chr14 Mbfor fat region percentage of Chr14. (g): for Inter fat- percentage.chromosome ( fepistasis): Inter-chromosome effects between epistasis Chr02 effectsand the between 0.3-10.5 Mb Chr04 region and of the Chr14 0.3-10.5 for fat Mb percentage region of. Chr14(h): Inter for-chromosome fat percentage. epistasis (g): Inter-chromosome effects between Chr11 epistasis and the effects 0.3- between10.5 Mb region Chr02 of and Chr14 the 0.3-10.5for fat percentage Mb region. of Chr14 for fat percentage. (h): Inter-chromosome epistasis effects between Chr11 and the 0.3-10.5 Mb region of Chr14 for fat percentage. The analysis of the 0.3–10.5 Mb region of Chr14 showed that two regions flanking DGAT1The had analysis the most of the significant 0.3–10.5 Mb and region frequent of Chr14 inter- showedchromosome that two epistasis regions effects, flanking the DGAT1PPP1R16Ahad-CYHR1 the most region significant at 0.46–0 and.50 Mb frequent about 120 inter-chromosome Kb upstream of DGAT epistasis1 and effects, the 2.3 the3– PPP1R16A-CYHR13.34 Mb intergenic regionregion about at 0.46–0.50 1.71 Mb Mbdownstre aboutam 120 of Kb DGAT1 upstream including of DGAT1 rs134537992and the at 242.11192.33–3.34 Kb Mb withintergenic the most region significant about 1.71 inter Mb-chromosome downstream epistasis of DGAT1 effectsincluding (Figurers134537992 2b). Alt- houghat 242.1119 DGAT1 Kb withwas only the most0.12 Mb significant from the inter-chromosome PPP1R16A-CYHR1 epistasis region effectsthat had (Figure over2 200b). Althoughinter-chromosomeDGAT1 wasepistasis only effects, 0.12 Mb DGAT1 from was the PPP1R16A-CYHR1not involved in 98.75%region of the that 954 had pairs over of inter200 inter-chromosome-chromosome epistasis epistasis effects, effects, withDGAT1 a totalwas of 12 not (1.25%) involved effects in 98.75% and the of highest the 954 effect pairs rankingof inter-chromosome of #332 for inter epistasis-chromosome effects, with epistasis a total effects. of 12 (1.25%) In contrast, effects TRAPPC9 and the highesthad 73 (7.65%)effect ranking of the 954 of #332 inter for-chrom inter-chromosomeosome epistasis epistasis effects effects.and the In#2 contrast,effect. TheTRAPPC9 approximatelyhad 73 (7.65%)100 Kb intergenic of the 954 inter-chromosomeregion of 2.33–2.42 epistasisMb had six effects SNPs and and the five #2 effect.of these The six approximately SNPs had 159 100significant Kb intergenic inter-chromosome region of 2.33–2.42 epistasis Mb effects had six with SNPs 19 andchromosomes five of these (chromosomes six SNPs had 1, 159 2, 7–9, 11, 12, 15, 17–24, 26, 28, X), including the most significant effect of rs134537992. The 0.3–10.5 Mb region had a gap of inter-chromosome epistasis effects at 87.65 Kb–2.33 Mb (Figure 2b), a 2.24 Mb gap without inter-chromosome epistasis effects but with many intra-chromosome epistasis effects (Figure 3a, Table S1), many SNP effects [19], and at least 44 coding genes.

Genes 2021, 12, x FOR PEER REVIEW 15 of 22

Chr05 had 63 SNPs in the 0.13–119.07 Mb region interacting with the 0.46–5.68 Mb region of Chr14, showing that virtually the entire Chr05 of 120.09 Mb interacted with the same Chr14 region only, noting that nearly the entire Chr05 also had intra-chromosome epistasis effects for milk, fat and protein yields. Chr11 had the second largest number of SNPs interacting with the Chr14 regions, with 259 SNPs in the 0.65–62.52 Mb region interacting with the 0.46–6.25 Mb region of Chr14. Chr08 had the second largest number of SNPs interacting with the Chr14 regions, with 137 SNPs in the 32.72–81.71 Mb region interacting with the 0.46–6.76 Mb region of Chr14. It is interesting to note that both SNPs in DGAT1 had significant inter-chromosome epistasis effects with rs109477201 of Chr05, although DGAT1 only had 1.25% of all inter-chromosome epistasis effects.

Genes 2021, 12, 1089 3.8. Inter-Chromosome Epistasis Effects of Protein Percentage and Yield Traits 13 of 20 The inter-chromosome epistasis effects of protein percentage and the three yield traits involved many chromosome pairs (Figure 9) but did not have the specificity ob- servedsignificant for inter inter-chromosome-chromosome epistasis epistasis effects effects of with Chr14 19 for chromosomes fat percentage (chromosomes (Figure 8). 1, 2, 7–9, 11,Protein 12, 15, percentage 17–24, 26, had 28, X),794 including inter-chromosome the most significantepistasis effects, effect offewerrs134537992 than the. The954 inter0.3–10.5-chromosome Mb region epistasis had a gap effects of inter-chromosome for fat percentage epistasis (Table effects1), and at every 87.65 chromosome Kb–2.33 Mb interacted(Figure2b), with a 2.24 most Mb ofgap the other without chromosomes inter-chromosome (Figures epistasis9a and S2), effects unlike but fat with percentage many whereintra-chromosome every chromosome epistasis virtually effects (Figure interacted3a, Table with S1), the many same SNP Chr14 effects region [ 19 only], and (Figure at leasts 8a44 codingand S2). genes. Figure 10a–e show examples where every chromosome that interacted with mostChr05 of the hadother 63 chromosomes SNPs in the 0.13–119.07for protein percentage Mb region. interacting with the 0.46–5.68 Mb regionProtein of Chr14, yield showing (Figure that9b) had virtually 312 significant the entire inter Chr05-chromosome of 120.09 Mb epistasis interacted effects with with the similarsame Chr14 patterns region as protein only, noting percentage, that nearly i.e., every the entirechromosome Chr05 also had hadinter intra-chromosome-chromosome epistasisepistasis effects effects with for some milk, other fat chromosomes. and protein yields. Figure Chr11 10f–j show had the examples second of largest inter-chromo- number someof SNPs epistasis interacting effects with of protein the Chr14 yield. regions, with 259 SNPs in the 0.65–62.52 Mb region interactingMilk yield with had the 68 0.46–6.25 (0.6%) Mbinter region-chromosome of Chr14. epistasis Chr08 hadeffects the involving second largest chromosome number pairsof SNPs between interacting 20 chromosomes with the Chr14 (Figure regions, 9c). Half with of 137 these SNPs 68 in effects the 32.72–81.71 were between Mb regionChr08 andinteracting Chr13, with 29 the effects 0.46–6.76 between Mb region 5 SNPs of in Chr14. LOC101904827 It is interesting on Chr08 to note and that 14 SNPs both in SNPs the 20.63in DGAT1–46.24had Mb significantregion of Chr13. inter-chromosome Figure 10k–o epistasis show examples effects with of interrs109477201-chromosomeof Chr05, epi- stasisalthough effectsDGAT1 of milkonly yield. had 1.25% of all inter-chromosome epistasis effects. Fat yield had 48 (1.0%) inter-chromosome epistasis effects involving chromosome pairs3.8. Inter-Chromosome between 22 chromosomes Epistasis Effects (Figure of Protein9d). A surp Percentagerise was and that Yield Chr05 Traits with intra-chromo- someThe epistasis inter-chromosome effects virtually epistasis covering effects the of entire protein chromosome percentage (Figure and the 7c three) did yield not traitshave significantinvolved many inter- chromosomechromosome pairs epistasis (Figure effects.9) but Figure did not 10p have–t show the specificityexamples of observed inter-chro- for mosomeinter-chromosome epistasis effects epistasis of fat effects yield. of Chr14 for fat percentage (Figure8).

FigureFigure 9. InterInter-chromosome-chromosome epistasis epistasis effects effects with with log10(1/ log10(1/p)p) ≥ 12≥ for12 protein for protein percentage percentage and three and yield three traits. yield Each traits. number Each numberon the outer on the circle outer is circlethe chromosome is the chromosome number, number, red color red represents color represents intra-chromosome intra-chromosome epistasis epistasis effects, effects, and blue and color blue colorrepresents represents interinter-chromosomechromosome epistasis epistasis effects. effects. PPC PPC = protein = protein percentage. percentage. PY PY = =protein protein yield. yield. MY MY = = milk milk yield. yield. FY FY = fat yield. (a): Intra- and inter-chromosome epistasis effects of protein percentage. (b): Intra- and inter-chromosome epistasis yield. (a): Intra- and inter-chromosome epistasis effects of protein percentage. (b): Intra- and inter-chromosome epistasis effects of protein yield. (c): Intra- and inter-chromosome epistasis effects of milk yield. (d): Intra- and inter-chromosome effects of protein yield. (c): Intra- and inter-chromosome epistasis effects of milk yield. (d): Intra- and inter-chromosome epistasis effects of fat yield. epistasis effects of fat yield.

Protein percentage had 794 inter-chromosome epistasis effects, fewer than the 954 inter- chromosome epistasis effects for fat percentage (Table1), and every chromosome interacted with most of the other chromosomes (Figure9a and Figure S2), unlike fat percentage where every chromosome virtually interacted with the same Chr14 region only (Figure8a and Figure S2). Figure 10a–e show examples where every chromosome that interacted with most of the other chromosomes for protein percentage. Protein yield (Figure9b) had 312 signiﬁcant inter-chromosome epistasis effects with similar patterns as protein percentage, i.e., every chromosome had inter-chromosome epistasis effects with some other chromosomes. Figure 10f–j show examples of inter- chromosome epistasis effects of protein yield. Milk yield had 68 (0.6%) inter-chromosome epistasis effects involving chromosome pairs between 20 chromosomes (Figure9c). Half of these 68 effects were between Chr08 and Chr13, with 29 effects between 5 SNPs in LOC101904827 on Chr08 and 14 SNPs in Genes 2021, 12, 1089 14 of 20

the 20.63–46.24 Mb region of Chr13. Figure 10k–o show examples of inter-chromosome epistasis effects of milk yield. Fat yield had 48 (1.0%) inter-chromosome epistasis effects involving chromosome pairs between 22 chromosomes (Figure9d). A surprise was that Chr05 with intra-chromosome epistasis effects virtually covering the entire chromosome (Figure7c) did not have signiﬁ- Genes 2021, 12, x FOR PEER REVIEWcant inter-chromosome epistasis effects. Figure 10p–t show examples of inter-chromosome16 of 22 epistasis effects of fat yield.

FigureFigure 10. Examples 10. Examples of inter of- inter-chromosomechromosome epistasis epistasis effects effects with withlog10(1/ log10(1/p)p) ≥ 12 for≥ 12protein for protein percentage percentage and the and three the yield three traits. yield Each numbertraits. on Eachthe outer number circle on is the the outer chromosome circle is the number, chromosome red color number, represents red color intra represents-chromosome intra-chromosome epistasis effects, epistasis and blue effects, color rep- resentsand inter blue-chromosome color represents epistasis inter-chromosome effects. PPC = epistasisprotein percentage. effects. PPC PY = protein= protein percentage. yield. MY PY = milk = protein yield. yield. FY = MYfat yield. = milk (a)-(e): Examplesyield. of FY inter = fat-chromosome yield. (a–e): epistasis Examples effects of inter-chromosome for protein percentage. epistasis (f)- effects(j): Examples for protein of inter percentage.-chromosome (f–j): epistasis Examples effects of for protein yield. (k)-(o): Examples of inter-chromosome epistasis effects for milk yield. (p)-(t): Examples of inter-chromosome epistasis inter-chromosome epistasis effects for protein yield. (k–o): Examples of inter-chromosome epistasis effects for milk yield. effects for fat yield. (p–t): Examples of inter-chromosome epistasis effects for fat yield. 3.9. Epistasis Effects of Daughter Pregnancy Rate 3.9. EpistasisDaughter Effects pregnancy of Daughter rate only Pregnancy had one Rate significant epistasis effect with log10(1/p) ≥ 12 (FigureDaughter 1f), and pregnancy this epistasis rate only effect had wasone signiﬁcant an intra-chromosome epistasis effect A with × Alog10(1/p) effect between≥ 12 (Figurers1332228201f), and in TMPRSS11E this epistasis and effect rs43470988 was an (RUFY3 intra-chromosome-GRSF1) of Chr06. A × AlthoughA effect betweenother effects did not reach the Bonferroni significance, several epistasis effects involved genes with reported fertility effects. These included EIF5B (inter-chromosome epistasis effect between rs43652424 in EIF5B of Chr11 and rs136798451 flanked by RAP2C and MBNL3 of ChrX) associated with female sterility [34], RAP2C (inter-chromosome epistasis effect) associated with gestational duration and/or spontaneous preterm birth [35], PKP2 (intra- chromosome epistasis effect of Chr05) associated with cow conception rate [36], HSD17B6 (intra-chromosome epistasis effect of Chr05) associated with polycystic ovary syndrome [37], and SOX5 (intra-chromosome epistasis effect of Chr05) associated with nonobstructive azoospermia susceptibility [38]. Figure 11a shows the top 1000 epistasis effects for

Genes 2021, 12, 1089 15 of 20

rs133222820 in TMPRSS11E and rs43470988 (RUFY3-GRSF1) of Chr06. Although other effects did not reach the Bonferroni signiﬁcance, several epistasis effects involved genes with reported fertility effects. These included EIF5B (inter-chromosome epistasis effect between rs43652424 in EIF5B of Chr11 and rs136798451 ﬂanked by RAP2C and MBNL3 of ChrX) associated with female sterility [34], RAP2C (inter-chromosome epistasis effect) associated with gestational duration and/or spontaneous preterm birth [35], PKP2 (intra-chromosome epistasis effect of Chr05) associated with cow conception rate [36], HSD17B6 (intra-chromosome Genes 2021, 12, x FOR PEER REVIEWepistasis effect of Chr05) associated with polycystic ovary syndrome [37], and SOX517(intra- of 22

chromosome epistasis effect of Chr05) associated with nonobstructive azoospermia susceptibility [38]. Figure 11a shows the top 1000 epistasis effects for daughter pregnancy rate, withdaughter 55.2% pregnancy intra-chromosome rate, with and55.2% 48.8 intra inter-chromosome-chromosome and epistasis 48.8 inter effects.-chromosome Figure 11 epi-b–e stasisshow exampleseffects. Figure of intra-chromosome 11b–e show examples and Figure of intra 11f–j-chromosome shows examples and of Figure inter-chromosome 11f–j shows examplesepistasis effects. of inter-chromosome epistasis effects.

FigureFigure 11. Intra 11.-Intra- and inter and- inter-chromosomechromosome epistasis epistasis effects effects of daughter of daughter pregnancy pregnancy rate rate(top (top1000 1000 pairs) pairs).. For intra For intra-chromosome-chromosome epistasis effects,epistasis each number effects, on each the number outer circle on the is outerthe chromosome circle is the chromosomenumber, red number,color indicates red color intra indicates-chromosome intra-chromosome epistasis effects, epistasis and blue color indicates inter-chromosome epistasis effects. For inter-chromosome epistasis effects, each number on the outer circle is the effects, and blue color indicates inter-chromosome epistasis effects. For inter-chromosome epistasis effects, each number chromosome distance, red color indicating intra-4 Mb epistasis effects and blue color indicating inter-4 Mb epistasis effects. DPR = on the outer circle is the chromosome distance, red color indicating intra-4 Mb epistasis effects and blue color indicating daughter pregnancy rate. (a): Intra- and inter-chromosome epistasis effects of all chromosomes for daughter pregnancy rate. (b): inter-4 Mb epistasis effects. DPR = daughter pregnancy rate. (a): Intra- and inter-chromosome epistasis effects of all Intra-chromosome epistasis effects of Chr06 for daughter pregnancy rate. (c): Intra-chromosome epistasis effects of Chr05 for daughter pregnancychromosomes rate. for(d): daughterIntra-chromosome pregnancy epistasis rate. (b effects): Intra-chromosome of Chr18 for daughter epistasis pregnancy effects of rate. Chr06 (e for): Intra daughter-chromosome pregnancy epistasis effectsrate. of ChrX (c): for Intra-chromosome daughter pregnancy epistasis rate. effects(f): Inter of-chromosome Chr05 for daughter epistasis pregnancy effects of Chr11 rate. for (d): daughter Intra-chromosome pregnancy rate. epistasis (g): Inter- chromosomeeffects of epistasis Chr18 for effects daughter of Chr04 pregnancy for daughter rate. (pregnancye): Intra-chromosome rate. (h): Inter epistasis-chromosome effects ofepistasis ChrX foreffects daughter of Chr08 pregnancy for daughter pregnancyrate. ( frate.): Inter-chromosome (i): Inter-chromosome epistasis epistasis effects effects of Chr11 of Chr0 for daughter2 for daughter pregnancy pregnancy rate. ( grate.): Inter-chromosome (j): Inter-chromosome epistasis epistasis effects effects of ChrofX Chr04for daughter for daughter pregnancy pregnancy rate. rate. (h): Inter-chromosome epistasis effects of Chr08 for daughter pregnancy rate. (i): Inter-chromosome epistasis effects of Chr02 for daughter pregnancy rate. (j): Inter-chromosome epistasis effects of ChrX for daughter pregnancy rate.4. Discussion 4.1. Complex Epistasis Effects Existed in U.S. Holstein Cattle 4. DiscussionThe epistasis results of the five milk production traits showed that complex epistasis effects4.1. Complex existed Epistasis in U.S. EffectsHolstein Existed cattle. in U.S.Every Holstein production Cattle trait had intra-chromosome epistasis effects covering large chromosome distances, and inter-chromosome epistasis ef- The epistasis results of the ﬁve milk production traits showed that complex epista- fects existed. The Chr05 example for fat yield was the largest chromosome segment sis effects existed in U.S. Holstein cattle. Every production trait had intra-chromosome (nearly the entire chromosome) covered by intra-chromosome epistasis effects. In addi- epistasis effects covering large chromosome distances, and inter-chromosome epistasis tion, inter-chromosome epistasis effects also existed involving most chromosomes for every trait. For fat percentage, a Chr14 region had inter-chromosome epistasis effects with all other chromosomes. The complexity of the epistasis effects in this study was unprecedented.

4.2. Genetic Selection Based on Genome-Wide SNP Additive Effects Likely Accounted for Most Intra-Chromosome A × A Effects The chromosome regions with highly significant intra-chromosome A × A epistasis effects of the five production traits overlapped the chromosome regions with highly significant SNP additive effects we previously reported from the same data set. Given that

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effects existed. The Chr05 example for fat yield was the largest chromosome segment (nearly the entire chromosome) covered by intra-chromosome epistasis effects. In addition, inter-chromosome epistasis effects also existed involving most chromosomes for every trait. For fat percentage, a Chr14 region had inter-chromosome epistasis effects with all other chromosomes. The complexity of the epistasis effects in this study was unprecedented.

4.2. Genetic Selection Based on Genome-Wide SNP Additive Effects Likely Accounted for Most Intra-Chromosome A × A Effects The chromosome regions with highly significant intra-chromosome A × A epistasis effects of the five production traits overlapped the chromosome regions with highly significant SNP additive effects we previously reported from the same data set. Given that genomic prediction using single-SNP additive models for the production traits was successful, we hypothesize that genome-wide SNP additive effects likely accounted for most intra-chromosome A × A effects. The linkage between SNPs with intra-chromosome A × A effects should have contributed to the success of genomic prediction using SNP additive models for the production traits. As the percentage of inter-chromosome epistasis effects increases, the effectiveness of SNP prediction models is expected to decrease, as discussed next. Based on this assumption, SNP prediction models should be most effective for fat and protein percentages that had the highest frequencies of intra-chromosome A × A effects, followed by milk yield, fat yield and protein yield. Statistical significance is another factor affecting the contribution of intra- or inter-chromosome epistasis effects to the trait. For the five production traits, intra-chromosome epistasis effects were more significant than inter-chromosome effects, e.g., log10(1/p) was in the range of 13–537 for intra- and 13–23 for inter-chromosome epistasis effects of fat percentage (Table1), and the other four production traits had a similar trend. Daughter pregnancy rate was different with similar statistical significance for both intra- and inter-chromosome epistasis effects, log10(1/p) was in the range of 6–13 for intra- and 6–11 for inter-chromosome epistasis effects. Combining the frequency and statistical significance of intra-chromosome epistasis effects, genomic selection using SNP additive models is expected to be highly effective for the five production traits.

4.3. Inter-Chromosome Epistasis Effects Could Be a Genetic Mechanism for Lack of Selection Response and Low Heritability Daughter pregnancy rate had the highest frequency of inter-chromosome epistasis effects (84.2%, Table1), and more than half (52.9%) of the top 50,000 epistasis effects were A × A effects. Although only one epistasis effect reached the Bonferroni significance, the epistasis results provided the first indications that inter-chromosome A × A effects may be the primary genetic effects of daughter pregnancy rate. Assuming this was true, inter-chromosome A × A effects would be consistent with the fact that genetic selection for daughter pregnancy rate was less responsive than the yield traits because genetic selection for many independent variants would be more difficult than selection for many lined variants. As discussed later, we hypothesize that marginal effect of many epistasis effects of linked loci is a contributing factor to highly significant SNP effect. However, such marginal effect is unavailable for inter-chromosome epistasis effects of independent SNPs on different chromosomes.

4.4. Chr14-Specific Inter-Chromosome A × A Epistasis Effects Increase the Statistical Confidence of the Epistasis Results Although the statistical significance for declaring significant epistasis effects was the stringent significant level of 5% genome-wide false positives with the Bonferroni multiple testing correction, large numbers of epistasis effects for the five production traits reached this Bonferroni significance, log10(1/p) ≥ 12, e.g., all the top 50,000 epistasis effects of fat or protein percentage were significant. This raised the question whether false positive effects were substantially more than the expected 5% genome-wide false positives. While a definitive answer to this question was unavailable, the inter-chromosome A × A epistasis Genes 2021, 12, 1089 17 of 20

effects between the 0.3–10.5 Mb Chr14 region and all chromosomes for fat percentage should increase the statistical conﬁdence of the epistasis results, because the high degree of speciﬁcity of all 29 chromosomes interacting with the same chromosome region could not happen by chance.

4.5. An Intergenic Variant May Have an Important Role for Inter-Chromosome Epistasis Effects of Fat Percentage The 0.9 Mb intergenic region at 2.33–2.42 Mb of Chr14 had six SNPs and five of these SNPs had significant inter-chromosome epistasis effects including the most significant effect of rs134537992 at 242.1119 Kb for fat percentage. This 0.9 Mb intergenic region was 113.637 Kb from LOC101901918 or 311.437 Kb from TSNARE1 upstream, and 88.851 Kb from SLC45A4 downstream. These three flanking genes had eight SNPs, one in LOC101901918, five in TSNARE1 and two in SLC45A4, but none of these eight SNPs had a significant inter-chromosome effect. These results would be consistent with the hypothesis that the 0.9 Mb intergenic region at 2.33–2.42 Mb had its own biological functions affecting many chromosomes for fat percentage rather than linked effects due to linkage disequilibrium with adjacent coding genes. The 2.24 Mb gap in inter-chromosome epistasis effects at 87.65 Kb–2.30 Mb should further support this hypothesis. This gap region had many intra-chromosome epistasis effects (Figure3a, Table S1), many SNP effects [ 19], and at least 44 coding genes, but did not have significant inter-chromosome epistasis effects. Given that this 2.24 Mb gap region at 87.65 Kb–2.30 Mb was so close to the PPP1R16A-CYHR1 region at 0.46–0.50 Mb and the 2.33–3.34 Mb intergenic region with significant inter-chromosome epistasis effects, the coding genes in this 2.24 Mb gap region did not have biological functions for significant inter-chromosome epistasis effects. These results indicated that the 0.9 Mb segment of noncoding DNA at 2.33–3.34 Mb harboring rs134537992 had potential regulatory functions affecting many chromosomes for fat percentage.

4.6. Causal or Linked Epistasis Effects The results in this study did not provide evidence about potential causal variants with epistasis effects, but had indications about potential involvement of linkage disequilibrium in clusters of epistasis effects of the production traits, and an approximate chromosome region with causal effects for inter-chromosome epistasis effects. Fat percentage about is an ideal trait to discuss the issue of causal and linked effects due to the unique statistical significance and patterns of the epistasis effects. The chromosome regions with large clusters of intra-chromosome epistasis effects mostly contained the chromosome regions with large clusters of SNP effects including the Chr14 region with intra-chromosome epistasis effects. We previously reported that the region containing DGAT1 about 6.79 Mb in size had strong linkage disequilibrium, and the removal of the DGAT1 effect from the phenotypic values eliminated 63% of the top 1% effects in the region, showing that the top 1% SNP effects in that 6.79 Mb region involved both causal and linked effects. Since A × A epistasis effect of a SNP pair in this study was the contrast of the four haplotype average values and each haplotype frequency was affected by linkage disequilibrium between the two SNPs [30], A × A intra-chromosome epistasis effects due to linkage should have existed and contributed to the large clusters of intra-chromosome epistasis effects for the five production traits. Inter-chromosome epistasis effects are expected to be unaffected by linkage disequilibrium between the two SNPs of each SNP pair but some effects still could have contributions from linkage disequilibrium between a SNP adjacent to another SNP that had a significant inter-chromosome epistasis effect. An example of this possibility is the 0.9 Mb intergenic region at 2.33–2.42 Mb of Chr14 where five of the six SNPs had significant inter-chromosome epistasis effects including the most significant effect of rs134537992 at 242.1119 Kb for fat percentage. Some of these five significant epistasis effects could be due to linkage to a causal effect nearby. However, inter-chromosome epistasis effects clearly were less affected by linkage, e.g., the 2.24 Mb gap region at 87.65 Kb–2.30 Mb without significant inter-chromosome epistasis effects was very close to the PPP1R16A- Genes 2021, 12, 1089 18 of 20

CYHR1 region at 0.46–0.50 Mb and the 2.33–3.34 Mb intergenic region with signiﬁcant inter-chromosome epistasis effects.

5. Conclusions The epistasis results showed that complex intra- and inter-chromosome epistasis effects existed in U.S. Holstein cattle. Intra-chromosome A × A effects were the main epistasis effects for the five production traits, whereas inter-chromosome A × A effects were the main epistasis effects for daughter pregnancy rate. Chromosome regions with highly significant intra-chromosome epitasis effects mostly overlapped the chromosome regions with highly significant SNP effects we previously reported using the same data. A chr14 region widely reported to have highly significant SNP effects for fat percentage interacted with all other chromosomes, and this result provided evidence for a potential global regulatory role of this Chr14 region.

Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/genes12071089/s1, Figure S1: Intra-chromosome epistasis effects with log(1/p) ≥ 12, Figure S2: Inter-chromosome epistasis effects with log(1/p) ≥ 12, Table S1: Significant intra-chromosome epistasis effects, Table S2: Significant inter-chromosome epistasis effects. Author Contributions: Conceptualization, Y.D.; methodology, Y.D., D.P., Z.L., L.M. and J.J.; software, D.P., Z.L., L.M.; validation, D.P. and Z.L.; formal analysis, D.P., Z.L. and Y.D.; resources, D.P., Z.L., J.J. and L.M.; data curation, D.P.; writing—original draft preparation, Y.D.; writing—review and editing, D.P., Z.L., J.J. and L.M.; visualization, Z.L., D.P. and Y.D.; supervision, Y.D.; project administration, Y.D.; funding acquisition, Y.D. and L.M. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by grants 2018-67015-28128, 2020-67015-31133 and 2020-67015- 31398 from the USDA National Institute of Food and Agriculture, and by project MIN-16-124 of the Agricultural Experiment Station at the University of Minnesota. Institutional Review Board Statement: Ethical review and approval were waived because this study used existing data only and did not involve the use of live animals. Informed Consent Statement: Not applicable. Data Availability Statement: The original genotype data are owned by third parties and maintained by the Council on Dairy Cattle Breeding (CDCB). A request to CDCB is necessary for getting data access on research, which may be sent to: João Dürr, CDCB Chief Executive Officer ([email protected]). All other relevant data are available in the manuscript, Supplementary Materials. Acknowledgments: Members of the Council on Dairy Cattle Breeding (CDCB) and the Cooperative Dairy DNA Repository (CDDR) are acknowledged for providing the data for the GWAS analysis. The Ceres high performance computing system of USDA-ARS provided computing time and storage for the data analysis. Data access and the use of USDA-ARS computing facilities by this research were supported by USDA-ARS project 8042-31000-002-00-D, “Improving Dairy Animals by Increasing Accuracy of Genomic Prediction, Evaluating New Traits, and Redefining Selection Goals”, and USDA-ARS project 8042-31000-001-00-D, “Enhancing Genetic Merit of Ruminants Through Improved Genome Assembly, Annotation, and Selection”. The USDA is an equal opportunity provider and employer. Mention of trade names or commercial products in this manuscript is solely for the purpose of providing specific information and does not imply recommendation or endorsement by USDA. The authors thank Paul VanRaden for help with data preparation, and John Cole, Steven Schroeder and Ransom Baldwin for help with using the USDA-ARS computing facilities. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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