Large-Sample Genome-Wide Association Study of Resistance to Retained Placenta in U.S. Holstein Cows

Abstract

A genome-wide association study of resistance to retained placenta (RETP) using 632,212 Holstein cows and 74,747 SNPs identified 200 additive effects with p-values < 10⁻⁸ on thirteen chromosomes but no dominance effect was statistically significant. The regions of 87.61–88.74 Mb of Chr09 about 1.13 Mb in size had the most significant effect in LOC112448080 and other highly significant effects in CCDC170 and ESR1, and in or near RMND1 and AKAP12. Four non-ESR1 genes in this region were reported to be involved in ESR1 fusions in humans. Chr23 had the largest number of significant effects that peaked in SLC17A1, which was involved in urate metabolism and transport that could contribute to kidney disease. The PKHD1 gene contained seven significant effects and was downstream of another six significant effects. The ACOT13 gene also had a highly significant effect. Both PKHD1 and ACOT13 were associated with kidney disease. Another highly significant effect was upstream of BOLA-DQA2. The KITLG gene of Chr05 that acts in utero in germ cell and neural cell development, and hematopoiesis was upstream of a highly significant effect, contained a significant effect, and was between another two significant effects. The results of this study provided a new understanding of genetic factors underlying RETP in U.S. Holstein cows.

1. Introduction

Retained placenta in dairy cattle refers to the failure of timely separation of the placenta from the dam after calving. This disease creates a number of problems in health and fertility including inflammation, fever, decreased milk yield, longer calving intervals, higher incidence of metritis and lower conception rate [1]. In U.S. Holstein cows, retained placenta has an incidence rate of 3.6%, and is a low-heritability trait with 1% heritability [2]. In humans, retained placenta was found to have inherited risk where the mother’s having retained placenta increased the risk of this disease in the next generation [3]. Only limited research was available on the association between retained placenta and genetic variants. A genome-wide association study (GWAS) using U.S. Holstein bulls and single nucleotide polymorphism (SNP) markers included retained placenta but found no significant effects [4]. Another study on retained placenta using Canadian Holstein bulls identified several chromosome regions with higher heritability estimates than in other chromosome regions [5]. Starting in 2018, national genetic and genomic evaluations for resistance to retained placenta (RETP) started for U.S. Holstein cattle [6] and have since accumulated a large sample of Holstein cows with RETP phenotypic observations and genotypes of genome-wide SNPs, providing a unique opportunity with unprecedented statistical power for identifying genetic variants associated with RETP. Using this large sample, this study aimed to identify genetic variants and chromosome regions affecting RETP in U.S. Holstein cows using a GWAS approach.

2. Results and Discussion

2.1. Overview of GWAS Results

The GWAS of RETP using 614,035 first-lactation Holstein cows and 74,747 SNPs identified 200 additive effects and no dominance effects with log₁₀(1/p) > 8 (Figure 1a, Table S1). The 200 significant additive effects were distributed on twelve chromosomes (Figure 1a): 5, 6, 7, 9, 10, 15, 17, 19, 24, 25, 29 and 31, where Chr31 is the X-Y nonrecombining region of the X chromosome. Allelic effects of the 200 SNPs (Figure 1b) showed that negative allelic effects had larger effect sizes than the positive effect sizes for most chromosomes. The average of the negative allelic effects was −0.089 and the average of the positive allelic effects was 0.077. Chr05 had the most positive allelic effect in C5H12orf75, and the X-Y nonrecombining region of the X chromosome (Chr31) had the most negative allelic effect between MAGED1 and MAGED4B. The detailed descriptions of candidate genes of the significant effects will use gene symbols for most genes and the full gene names are provided in Table S2.

2.2. Additive Effects of Chr09

Chr09 had twenty-three significant effects including the #1 effect in LOC112448080, #2 upstream of AKAP12, #3 in CCDC170, and #5 in RMND1 (

Table 1. Significant additive effects of Chr09 for RETP.

SNP	Position	Candidate Gene	Effect	Log10(1/p)	al+	ae+	f_al+	al−	ae−	f_al−
rs42026926	87610236	PLEKHG1 (u)	0.183	13.74	1	0.080	0.564	2	−0.103	0.436
rs42026914	87634273	PLEKHG1 (u)	0.158	10.75	1	0.075	0.526	2	−0.0833	0.474
rs43615609	88220932	MTHFD1L (d)	0.175	11.80	1	0.062	0.644	2	−0.112	0.356
rs43615544	88254314	AKAP12 (u)	−0.210	15.96	2	0.062	0.706	1	−0.148	0.294
rs43612983	88482928	RMND1	0.197	15.10	1	0.070	0.643	2	−0.127	0.357
rs43611719	88519048	LOC112448080	−0.246	21.16	2	0.071	0.71	1	−0.175	0.29
rs43611710	88529494	CCDC170	−0.199	15.76	2	0.070	0.646	1	−0.128	0.354
rs43611701	88540232	CCDC170	−0.182	14.33	2	0.081	0.556	1	−0.102	0.444
rs43610539	88598336	CCDC170	−0.189	13.13	2	0.057	0.699	1	−0.132	0.301
rs43608567	88684552	ESR1	−0.177	12.70	2	0.063	0.642	1	−0.114	0.358
rs3423297865	88722921	ESR1	0.188	13.46	1	0.068	0.641	2	−0.12	0.359
rs43767108	88739977	ESR1	0.188	13.48	1	0.068	0.641	2	−0.121	0.359

‘u’ indicates the SNP is upstream of the gene. ‘d’ indicates the SNP is downstream of the gene. ‘effect’ is the additive effect of the SNP as the difference between allelic effects of ‘allele 1’ and ‘allele 2’ (Equation (6)). ‘al+’ is the positive allele, ‘al–’ is the negative allele, ‘ae+’ is the allelic effect of the positive allele, and ‘ae−’ is the allelic effect of the negative allele (Equation (7)). ‘f_al+’ is the frequency of the positive allele. ‘f_al−’ is the frequency of the negative allele.

and Table S1, Figure 2a). These effects were in the 87.61–88.73 Mb region about 1.12 Mb in size. An interesting aspect of this region was the estrogen receptor 1 (ESR1) gene fusions observed in humans. This region had PLEKHG1, MTHFD1L, AKAP12, RMND1, and CCDC170 genes upstream of ESR1 (Table 1), and four of these five upstream genes were involved in ESR1 fusions associated with human breast cancer, ESR1-CCDC170, ESR1-AKAP12, ESR1-MTHFD1, and ESR1-PLEKHG1 fusions [7,8,9,10]. In addition, ESR1 had gene fusions with multiple other genes [7]. These human ESR1 fusions indicated the potential involvement of ESR1 fusions in RETP of Holstein cows. The protein encoded by ESR1 regulates the transcription of many estrogen-inducible genes that play a role in growth, metabolism, sexual development, gestation, and other reproductive functions; and is expressed in many non-reproductive tissues [11]. An SNP in ESR1 had a significant dominance effect on daughter pregnancy rate in Holstein cows [12]. The well-documented ESR1 functions including ESR1 fusions pointed to the possible involvement of ESR1 in the significant effects of RETP in the 87.61–88.73 Mb region of Chr09.

2.3. Additive Effects of Chr23

Chr23 had fifty-two significant effects, the largest number of significant effects among all chromosomes. These effects except one were distributed in the 21.29–35.47 Mb region, about 14 Mb in size (Table S1), but the most interesting region was the 23.70–33.08 Mb region about 9.4 Mb in size due to the genes potentially contributing to or known to be associated with kidney disease (

Table 2. Top-20 significant additive effects of Chr23 for RETP.

SNP	Position	Candidate Gene	Effect	Log10(1/p)	al+	ae+	f_al+	al−	ae−	f_al−
rs110556135	23704336	PKHD1 (u)	0.224	13.33	1	0.042	0.813	2	−0.182	0.187
rs43561755	23750046	PKHD1 (u)	−0.216	11.75	2	0.039	0.819	1	−0.177	0.181
BTA-81662-no-rs	23890370	PKHD1 (u)	−0.166	11.30	2	0.062	0.629	1	−0.104	0.371
rs41670209	24060064	PKHD1 (u)	−0.183	11.88	2	0.052	0.718	1	−0.131	0.282
rs136181786	24252119	PKHD1	−0.180	11.94	2	0.058	0.68	1	−0.123	0.32
rs137762108	25024407	LOC112443711-LOC112443751	−0.199	12.65	2	0.051	0.746	1	−0.148	0.254
rs135832378	25119540	GSTA1 (u)	0.186	13.95	1	0.073	0.609	2	−0.113	0.391
rs110144575	25142236	GSTA5	0.218	11.54	1	0.039	0.821	2	−0.179	0.179
rs110043199	25175265	LOC112443730	0.219	12.14	1	0.039	0.82	2	−0.180	0.18
rs135146076	25491332	ELOVL5, BOLA-DQA2	−0.190	14.48	2	0.067	0.645	1	−0.123	0.355
rs133177329	27122907	ENSBTAG00000048304	0.172	12.15	1	0.105	0.388	2	−0.067	0.612
rs110358203	27231641	PPT2	−0.192	14.51	2	0.124	0.353	1	−0.068	0.647
rs110277462	28345983	DHX16	0.186	13.72	1	0.121	0.351	2	−0.065	0.649
rs3423504515	28367574	MRPS18B	0.193	14.78	1	0.126	0.35	2	−0.068	0.65
rs3423514031	28777609	LOC785873	0.183	13.50	1	0.115	0.373	2	−0.068	0.627
rs3423494105	28783122	TRIM26	0.193	12.48	1	0.051	0.737	2	−0.142	0.263
rs3423498878	31063056	TRNAF-GAA_18, TRNAI-UAU_6	−0.165	11.75	2	0.085	0.486	1	−0.080	0.514
rs109821904	32057953	SLC17A1	−0.196	15.50	2	0.125	0.363	1	−0.071	0.637
rs134698463	32498379	CARMIL1	−0.178	13.46	2	0.086	0.514	1	−0.091	0.486
rs3423509404	33077628	ACOT13	−0.177	13.65	2	0.085	0.517	1	−0.091	0.483

‘u’ indicates the SNP is upstream of the gene. ‘effect’ is the additive effect of the SNP as the difference between allelic effects of ‘allele 1’ and ‘allele 2’ (Equation (6)). ‘al+’ is the positive allele, ‘al–‘ is the negative allele, ‘ae+’ is the allelic effect of the positive allele, and ‘ae−’ is the allelic effect of the negative allele (Equation (7)). ‘f_al+’ is the frequency of the positive allele. ‘f_al−’ is the frequency of the negative allele.

, Figure 2b). The most significant effect of this chromosome (#4 overall) was in SLC17A1, followed by SNPs in or near MRPS18B, PPT2, and the region of ELOVL5 to BOLA-DQA2 (Table 2). SLC17A1 with the most significant effect was involved in urate metabolic process and urate transport [13] and elevated serum urate concentrations could contribute to kidney disease [14]. The PKHD1 gene had six significant effects and was downstream of another five significant effects (Table S1). This gene was associated with a severe form of polycystic kidney disease named autosomal recessive polycystic kidney disease (ARPKD) that presents primarily in infancy and childhood [15,16]. The ACOT13 gene had a significant effect (#16 overall) and was also reported as a candidate gene for ARPKD kidney disease [17]. It was interesting that the two genes known to be associated with kidney disease, PKHD1 and ACOT13, were near the two ends of the Chr23 region with significant RETP effects (Table 2, Figure 2b). BOLA-DQA2 is a bovine MHC class II gene [18] and MHC class II molecules are critical for the initiation of the antigen-specific immune response [19]. The last significant effect at the very downstream end of the Chr23 region with significant RETP effects was between PRL and HDGFL1, where PRL is the prolactin gene and is essential for lactation [20].

2.4. Additive Effects of Chr05 and Chr17

Chr05 had thirty-five significant additive effects (Table S1). The most significant effect of Chr05 (#17 overall) was at 27,005,657 bp between the KRT18 and KRT8 genes, 3394 bp downstream of KRT18 and 34,610 bp upstream of KRT8, noting that neither KRT18 nor KRT8 had any SNP inside the gene. Gene Ontology (GO) analysis showed that KRT8 was involved in embryonic placenta development (Table S3), and this biological function could be directly relevant to retained placenta. A SNP upstream of KRT18 (in EIF4B-KRT18) at 26,984,066 bp was also significant (#97 overall). It should be noted that another SNP in EIF4B-KRT18 at 26,964,045 bp had a sharply negative recessive genotype for age at first calving (AFC) [21]. The effects in or near KITLG were also interesting due to KITLG’s known biological functions. KITLG was upstream of the second-most significant effect of Chr05 (#25 overall), contained a significant effect and was between another two significant effects (

Table 3. Significant additive effects of Chr05 and Chr17 for RETP.

SNP	Chr	Position	Candidate Gene	Effect	Log10(1/p)	al+	ae+	f_al+	al−	ae−	f_al−
rs110165899	5	27005657	KRT18-KRT8	0.184	13.51	1	0.118	0.358	2	−0.066	0.642
rs41587994	5	18367350	KITLG (d)	0.198	13.22	1	0.147	0.258	2	−0.051	0.742
rs41603721	5	19295836	POC1B	−0.187	13.06	2	0.129	0.307	1	−0.057	0.693
rs29012239	5	18679362	LOC104972350- LOC104972370	0.185	12.51	1	0.131	0.292	2	−0.054	0.708
rs135127542	5	26178969	CALCOCO1 (u)	−0.178	11.99	2	0.122	0.313	1	−0.056	0.687
rs136124246	5	17909902	CEP290	0.176	11.91	1	0.117	0.332	2	−0.058	0.668
rs110506590	5	17780338	C5H12orf50 (u)	0.175	11.84	1	0.117	0.332	2	−0.058	0.668
rs137107793	5	28970729	HIGD1C	0.162	11.19	1	0.070	0.564	2	−0.091	0.436
rs137455368	5	18799786	LOC104972350- LOC104972370	0.161	10.75	1	0.101	0.373	2	−0.060	0.627
rs109747382	5	19468540	ATP2B1 (u)	−0.159	10.58	2	0.099	0.376	1	−0.060	0.624
rs110739449	17	15056547	LOC112442091	−0.187	14.94	2	0.079	0.575	1	−0.107	0.425
rs135912416	17	12902838	LOC112441992- LOC112442089	−0.180	13.70	2	0.092	0.487	1	−0.088	0.513
rs137219013	17	13350634	ANAPC10-HHIP	0.176	13.31	1	0.078	0.559	2	−0.098	0.441
rs109572161	17	16399921	IL15-ZNF330	−0.174	13.18	2	0.079	0.546	1	−0.095	0.454
rs109486788	17	17090817	TBC1D9	0.169	11.88	1	0.077	0.543	2	−0.092	0.457
rs108973145	17	16489833	IL15-ZNF330	−0.164	11.64	2	0.072	0.561	1	−0.092	0.439
rs137504512	17	13801294	TRNAC-GCA_189, TRNAG-UCC_41	−0.163	11.34	2	0.081	0.503	1	−0.082	0.497
rs41838712	17	12116917	REELD1	0.168	11.32	1	0.102	0.394	2	−0.066	0.606
rs41599601	17	12866447	LOC112441992	0.160	11.28	1	0.075	0.531	2	−0.085	0.469

‘u’ indicates the SNP is upstream of the gene. ‘d’ indicates the SNP is downstream of the gene. ‘effect’ is the additive effect of the SNP as the difference between allelic effects of ‘allele 1’ and ‘allele 2’ (Equation (6)). ‘al+’ is the positive allele, ‘al–’ is the negative allele, ‘ae+’ is the allelic effect of the positive allele, and ‘ae−’ is the allelic effect of the negative allele (Equation (7)). ‘f_al+’ is the frequency of the positive allele. ‘f_al−’ is the frequency of the negative allele.

, Figure 3a). The KITLG gene encodes the ligand of the tyrosine-kinase receptor encoded by the KIT locus, and this ligand is a pleiotropic factor that acts in utero in germ cell and neural cell development, and hematopoiesis [22]. The ‘in utero’ biological functions of KITLG could be directly relevant to RETP. The POC1B gene had the third most significant effect of Chr05 (#28 overall). This gene has an important role in basal body and cilia formation [23].

Chr17 had fifty-one significant effects (Table S1). The most significant effect of Chr17 (#6 overall) was in LOC112442091, and the second-most significant effect of Chr17 (#16 overall) was between LOC112441992 and LOC112442089. All the above three genes had unknown biological functions. The third-most significant effect of Chr17 was between ANAPC10 and HHIP. A 388,434 bp region between IL15 and ZNF330, 31,334 bp downstream of IL15 and 1245 bp upstream of ZNF330, had the fourth-most significant effect of Chr17 (#26 overall) and seven other significant effects (Table 3, Figure 3b). IL15 is a cytokine that regulates T and natural killer cell activation and proliferation [24], and ZNF330 is predicted to enable zinc ion binding activity [25].

2.5. Additive Effects of Other Chromosomes

For the remaining nine chromosomes with significant additive effects, only Chr15 and Chr24 had substantial numbers of significant effects, fifteen effects for Chr15 and eleven effects for Chr24, whereas chromosomes 6, 7, 10, 19, 25, 29 and 31 each had 1–3 effects. Examples of these effects are summarized in

Table 4. Significant additive effects of seven selected chromosomes for RETP.

SNP	Chr	Position	Candidate Gene	Effect	Log10(1/p)	al+	ae+	f_al+	al−	ae−	f_al−
rs109034709	6	87316810	NPFFR2	−0.152	9.53	2	0.057	0.628	1	−0.096	0.372
rs110434046	6	87184768	GC-NPFFR2	−0.152	9.47	2	0.056	0.628	1	−0.095	0.372
rs137664040	6	86795926	SLC4A4	−0.143	8.45	2	0.057	0.603	1	−0.086	0.397
rs3423224824	7	8274451	OR7A5 (d)	−0.174	10.18	2	0.128	0.264	1	−0.046	0.736
rs109718130	10	34176744	RASGRP1	−0.150	8.41	2	0.047	0.689	1	−0.104	0.311
rs43626966	10	51788612	LIPC	0.166	8.23	1	0.036	0.785	2	−0.130	0.215
rs133296429	15	65887087	SLC1A2	0.163	11.46	1	0.072	0.56	2	−0.091	0.440
rs110222319	15	28670668	IL10RA	0.200	9.88	1	0.035	0.827	2	−0.165	0.173
rs133481154	15	38458720	SPON1	0.198	9.83	1	0.035	0.823	2	−0.163	0.177
rs110235930	19	61387218	ABCA10	−0.153	9.62	2	0.057	0.625	1	−0.096	0.375
rs41932313	19	61518347	ABCA9	−0.179	9.24	2	0.038	0.788	1	−0.141	0.212
rs43772736	24	30783746	SS18 (d)	0.178	13.68	1	0.078	0.559	2	−0.099	0.441
rs136103342	24	30564828	TAF4B	−0.179	13.51	2	0.076	0.579	1	−0.104	0.421
rs207730478	24	30578431	TAF4B	−0.170	12.47	2	0.072	0.579	1	−0.099	0.421
rs110190049	24	30486009	KCTD1-TAF4B	−0.167	11.95	2	0.070	0.579	1	−0.097	0.421
rs133376988	31	89494444	MAGED1-MAGED4B	0.299	10.41	1	0.022	0.927	2	−0.277	0.073
rs136268223	31	89068436	NUDT11 (d)	−0.184	10.36	2	0.042	0.772	1	−0.142	0.228
rs137683400	31	89839370	LOC100297099	−0.226	9.32	2	0.027	0.883	1	−0.200	0.117

‘d’ indicates the SNP is downstream of the gene. ‘effect’ is the additive effect of the SNP as the difference between allelic effects of ‘allele 1’ and ‘allele 2’ (Equation (6)). ‘al+’ is the positive allele, ‘al–’ is the negative allele, ‘ae+’ is the allelic effect of the positive allele, and ‘ae−’ is the allelic effect of the negative allele (Equation (7)). ‘f_al+’ is the frequency of the positive allele. ‘f_al−’ is the frequency of the negative allele.

, whereas effects not discussed in the main text can be found in Table S1.

The fifteen effects of Chr15 were distributed over the 26–67 Mb region and the four most significant effects of Chr15 were in SLC1A2 (#48), IL10RA (#89), SPON1 (#90), and downstream of DCDC1 ($95) covering a large distance of the 26–67 Mb region (Figure 4a). SLC1A2 encodes a membrane-bound protein as the principal transporter that clears the excitatory neurotransmitter glutamate and glutamate clearance is necessary for proper synaptic activation and to prevent neuronal damage from excessive activation of glutamate receptors [26]. IL10RA encodes a protein that is a receptor for interleukin 10, and is structurally related to interferon receptors [27]. SPON1 is predicted to be an extracellular matrix structural constituent and to be involved in cell adhesion [28]. The four most significant effects of Chr24 were in a narrow 30.38–31.01 Mb region about 0.63 Mb in size (Figure 4b), downstream of SS18, in TAF4B (2 effects) and upstream of TAF4B with overall rankings of #15, #18, #33 and #37, respectively, where SS18 is involved in positive regulation of transcription by RNA polymerase II [29], and TAF4B is involved in initiation of transcription of genes by RNA polymerase II [30]. Chr31, the X-Y nonrecombining region of the X-chromosome, had three significant effects (Figure 4c). The top two effects of this chromosome were in MAGED1-MAGED4B (#73) and downstream of NUDT11 (#75). The SNP in MAGED1-MAGED4B had the most negative allelic effect among all SNPs with a low allele frequency of 0.07. Chr06 had three significant effects (#104, #108 and #175 overall) in the SLC4A4-GC-NPFFR2 region (Figure 4d), which had been reported to have highly significant effects on milk yield, fertility and somatic cell score [12,31]. Chr10 had two significant effects slightly above the log₁₀(1/p) = 8 cutoff value for declaring significance, one in RASGRP1, which activates the Erk/MAP kinase cascade and regulates T-cells and B-cells development, homeostasis and differentiation [32], and one in LIPC which Enables phospholipase A1 activity and triglyceride lipase activity [33]. Chr07 had one significant effect (#78 overall) downstream of OR7A5. Olfactory receptors interact with odorant molecules in the nose, to initiate a neuronal response that triggers the perception of a smell. Chr19 had two significant effects, one in ABCA10 (#96 overall) and one in ABCA9 (#125 overall).

2.6. Gene Ontology Analysis

Gene Ontology (GO) analysis was conducted to understand the potential biological functions of candidate coding genes of the 200 significant additive effects, and the results are summarized in Table S3 and Figure S1. The GO results provided many more details about the biological functions of the candidate genes than described thus far in this article, e.g., ESR1 and KITLG each had over one hundred biological functions (Table S3). The GO results also identified a few genes involved in embryonic placenta development, including KRT8 of Chr05 downstream of the #17 effect (Table 2), EDNRA of Chr17 upstream of the #61 effect, GCM1 of Chr23 upstream of the #157 and #168 effects, and MAP3K4 of Chr09 with the #155 effect (Table S1). However, the GO results did not include some of the information we collected from journal articles and the National Center for Biotechnology Information (NCBI), e.g., the ESR1 fusions, the in utero biological functions of KITLG, and the association of PKHD1 and ACOT13 with kidney disease. Although the GO analysis identified over 2000 biological functions of the candidate genes (Table S3), none of those biological functions was identified to have a direct effect on retained placenta. In contrast, the GWAS results of this study provided Holstein-specific and high-confidence evidence for the potential associations between the candidate genes and RETP. The combination of the GWAS results of this study with the GO results as well as the biological information of the candidate genes collected elsewhere should provide useful functional annotations of the candidate genes and indications of the potential genetic mechanisms of the significant SNP effects affecting RETL in Holstein cows.

3. Materials and Methods

3.1. Holstein Population and SNP Data

The Holstein population in this study had 632,212 cows with RETP phenotypic observations and 78,964 original and imputed SNPs. With the requirement of 0.05 minor allele frequency, 74,747 SNPs were used in the GWAS analysis. The SNP positions were those from the ARS-UCD1.3 cattle genome assembly. Genes containing or in proximity to highly significant SNP effects were identified as candidate genes affecting RETP. The RETP phenotypic values used in the GWAS analysis were the phenotypic residuals after removing fixed nongenetic effects available from the December 2023 U.S. Holstein genomic evaluation data.

3.2. GWAS Analysis

The GWAS analysis used an approximate generalized least squares (AGLS) method. The AGLS method combines the least squares (LS) tests implemented by EPISNP1mpi [34,35] with the estimated breeding values from a routine genetic evaluation using the entire U.S. Holstein population. The statistical model was:

$$y=\mathsf{\mu }I+X_{\mathrm{g}}g+Za+e=Xb+Za+e$$

(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; µ = common mean; I = identity matrix; g = column vector of genotypic values; $X_{\mathrm{g}}$ = model matrix of g; $b={(\mathsf{\mu }, g^{\prime })}^{\prime }$, $X=(I, X_{\mathrm{g}})$; a = column vector of additive polygenic values; Z = model matrix of a; and e = column vector of random residuals. The first and second moments of Equation (1) are: $\mathrm{E}(y)=Xb$ and $\mathrm{var}(y)=V={ZGZ}^{\prime }+R={\mathsf{\sigma }}_{\mathrm{a}}^2{ZAZ}^{\prime }+{\mathsf{\sigma }}_{\mathrm{e}}^{2}I$, where ${\mathsf{\sigma }}_{\mathrm{a}}^2$ = additive variance, A = additive relationship matrix, and ${\mathsf{\sigma }}_{\mathrm{e}}^2$ = residual variance. The problem of estimating the b vector that includes SNP genotypic values in Equation (1) is the requirement of inverting the V if the generalized least squares (GLS) method is used, or solving the mixed model equations (MME) [36]. Either the GLS or MME method for each of the genome-wide SNPs is computationally demanding for our sample size. To avoid these computing difficulties, the GWAS used the method of approximate GLS (AGLS) that replaces the polygenic additive values (a) with the best linear unbiased prediction based on pedigree relationships [12,21,31,37]. The significance tests for additive and dominance SNP effects used the t-tests of the additive and dominance contrasts of the estimated SNP genotypic values [34,38]. The t-statistic of the AGLS was calculated as:

$${\mathrm{t}}_{\mathrm{j}}=\frac{{|\mathrm{L}}_{\mathrm{j}}|}{\sqrt{{\mathrm{var}(\mathrm{L}}_{\mathrm{j}})}}=\frac{\left|s_{\mathrm{j}}\widehat{g}\right|}{\mathrm{v}\sqrt{s_{\mathrm{j}}{(X^{\prime }X)}_{\mathrm{gg}}^{-}{s}_{\mathrm{j}}^{\prime }}}, \mathrm{j}=\mathrm{a},\mathrm{d}$$

(2)

where ${\mathrm{L}}_{\mathrm{j}}$ = additive or dominance contrast; $\sqrt{{\mathrm{var}(\mathrm{L}}_{\mathrm{j}})}$ = standard deviation of the additive or dominance contrast; $s_{\mathrm{a}}$ = row vector of additive contrast coefficients = $\left[\begin{array}{ccc}{\mathrm{P}}_{11}{/\mathrm{p}}_1& 0{.5\mathrm{P}}_{12}{(\mathrm{p}}_2-{\mathrm{p}}_1)/({\mathrm{p}}_1{\mathrm{p}}_2)& -{\mathrm{P}}_{22}{/\mathrm{p}}_2\end{array}\right]$; $s_{\mathrm{d}}$ = row vector of dominance contrast coefficients = $\left[\begin{array}{ccc}-0.5& 1& 0.5\end{array}\right]$; ${\mathrm{v}}^2=(y-X\widehat{b}{)}^{\prime }(y-X\widehat{b})/(\mathrm{n}-\mathrm{k})$ = estimated residual variance; $\widehat{g}$ = column vector of the AGLS estimates of the three SNP genotypic effects of ${\mathrm{g}}_{11}$, ${\mathrm{g}}_{12}$, and ${\mathrm{g}}_{22}$ from Equation (4); ${(X^{\prime }X)}_{\mathrm{gg}}^{-}$ = submatrix of ${(X^{\prime }X)}^{-}$ corresponding to $\widehat{g}$; and where ${\mathrm{p}}_1$ = frequency of $A_1$ allele, ${\mathrm{p}}_2$ = frequency of $A_2$ allele of the SNP, ${\mathrm{P}}_{11}$ = frequency of $A_1{A}_1$ genotype, ${\mathrm{P}}_{12}$ = frequency of $A_1{A}_2$ genotype, ${\mathrm{P}}_{22}$ = frequency of $A_2{A}_2$ genotype, n = number of observations and k = rank of X.

Additive effects of each SNP were estimated using three measures, the average effect of gene substitution, allelic mean, and allelic effect of each allele based on quantitative genetics definitions [38,39]. The allelic mean (${\mathsf{\mu }}_{\mathrm{i}}$), the population mean of all genotypic values of the SNP (μ), the allelic effect (${\mathrm{a}}_{\mathrm{i}}$), and the average effect of gene substitution of the SNP (α) are:

$${\mathsf{\mu }}_1={\mathrm{P}}_{11.1}{\mathrm{g}}_{11}+ 0{.5\mathrm{P}}_{12.1}{\mathrm{g}}_{12}$$

(3)

$${\mathsf{\mu }}_2=0{.5\mathrm{P}}_{12.2}{\mathrm{g}}_{12}+ {\mathrm{P}}_{22.2}{\mathrm{g}}_{22}$$

(4)

$$\mathsf{\mu }={\displaystyle {\sum }_{\mathrm{i}=1}^2{\mathrm{p}}_{\mathrm{i}}{\mathsf{\mu }}_{\mathrm{i}}}$$

(5)

$${\mathrm{a}}_{\mathrm{i}} = {\mathsf{\mu }}_{\mathrm{i}}-\mathsf{\mu },\mathrm{i}=1,2$$

(6)

$$\mathsf{\alpha } = {\mathrm{L}}_{\mathrm{a}}=s_{\mathrm{a}}\widehat{g} = {\mathrm{a}}_1-{\mathrm{a}}_2= {\mathsf{\mu }}_1-{\mathsf{\mu }}_2$$

(7)

where ${\mathrm{P}}_{11.1}={\mathrm{P}}_{11}{/\mathrm{p}}_1$, ${\mathrm{P}}_{12.1}={\mathrm{P}}_{12}{/\mathrm{p}}_1$, ${\mathrm{P}}_{12.2}={\mathrm{P}}_{12}{/\mathrm{p}}_2$, and ${\mathrm{P}}_{22.2}={\mathrm{P}}_{22}{/\mathrm{p}}_2$. The additive effect measured by the average effect of gene substitution of Equation (7) is the distance between the two allelic means or effects of the same SNP, and is the fundamental measure for detecting SNP additive effects as shown by the t-statistic of Equation (2). However, the allelic effect of Equation (7) is not comparable across SNPs because the allelic effect is affected by the genotypic mean of the SNP defined by Equation (6). To compare allelic effects across SNPs, we replaced the SNP genotypic mean (μ) in Equation (6) with the average of all SNP genotypic means (${\mathsf{\mu }}_{\mathrm{all}}$):

$${\mathrm{a}}_{\mathrm{i}} = {\mathsf{\mu }}_{\mathrm{i}}-{\mathsf{\mu }}_{\mathrm{all}},\mathrm{i}=1,2$$

(8)

Equation (8) was used only for the purpose of graphical display of allelic effects.

3.3. Gene Ontology (GO) Analysis

To understand the potential functions of selected candidate genes, the Gene Ontology (GO) analysis was performed using the OmicShare platform (www.omicshare.com/tools, accessed on 15 May 2024).

4. Conclusions

The GWAS results in this study indicated that RETP in U.S. Holstein cows was affected by multiple genetic variants with additive effects. Although the exact genetic mechanism underlying RETP remained unknown, these significant effects involved genes with a variety of biological functions reported elsewhere including ESR1 gene fusions, immunity, genetic effects on fertility, health and milk production, kidney disease, lactation, KIT ligand in utero, and basal body and cilia formation. The SNP effects detected in this study along with known biological functions of genes with or near the SNP effects provided a new understanding of genetic factors underlying RETP in U.S. Holstein cows and provided comparative information about the genetic mechanism of retained placenta in other species.