Genomic evaluation and genome-wide association studies for total number of teats in a combined American and Danish Yorkshire pig populations selected in China

Abstract

Joint genomic evaluation by combining data recordings and genomic information from different pig herds and populations is of interest for pig breeding companies because the efficiency of genomic selection (GS) could be further improved. In this work, an efficient strategy of joint genomic evaluation combining data from multiple pig populations is investigated. Total teat number (TTN), a trait that is equally recorded on 13,060 American Yorkshire (AY) populations (~14.68 teats) and 10,060 Danish Yorkshire (DY) pigs (~14.29 teats), was used to explore the feasibility and accuracy of GS combining datasets from different populations. We first estimated the genetic correlation $(r_{\mathrm{g}})$ of TTN between AY and DY pig populations ($r_{\mathrm{g}}$ = 0.79, se = 0.23). Then we employed the genome-wide association study to identify quantitative trait locus (QTL) regions that are significantly associated with TTN and investigate the genetic architecture of TTN in different populations. Our results suggested that the genomic regions controlling TTN are slightly different in the two Yorkshire populations, where the candidate QTL regions were on SSC 7 and SSC 8 for the AY population and on SSC 7 for the DY population. Finally, we explored an optimal way of genomic prediction for TTN via three different genomic best linear unbiased prediction models and we concluded that when TTN across populations are regarded as different, but correlated, traits in a multitrait model, predictive abilities for both Yorkshire populations improve. As a conclusion, joint genomic evaluation for target traits in multiple pig populations is feasible in practice and more accurate, provided a proper model is used.

Joint genomic evaluation for target traits in multiple populations is feasible and accurate, provided a proper model is used.

Introduction

Genomic selection (GS) has been widely applied in many species since being first proposed (Meuwissen et al., 2001). Although GS is considered as a mature technology (Misztal, 2016), it is still a new technology in the Chinese pig breeding system. Recently, many Chinese pig breeding companies started applying GS in the nucleus herds. Nevertheless, due to the limited number of animals in the nucleus herds and inadequate budgets for genotyping, many companies have small reference population sizes (typically around 500 to 2,000) at the initial stage of implementing GS. To increase the efficiency of GS, some pig companies agreed to execute a joint genomic evaluation program, which integrates the information from different pig populations to expand the reference population size. Studies have shown that the accuracy of genomic prediction would increase if the reference population is formed by combining several closely related populations (VanRaden et al., 2009; Brøndum et al., 2011; Lund et al., 2011). Therefore, joint genomic evaluation by combining data recordings and genomic information from different pig herds is of great interest for the pig breeding companies.

To verify the feasibility of GS using datasets from different populations, a trait that can be identically measured across different populations is ideal for study. Thus, total teat number (TTN) was chosen as the studied trait because it is identically scored in different pig populations, and the influence of possible errors, inconsistencies, or disagreements on recording phenotypes is therefore eliminated. Furthermore, TTN is an important reproductive trait in pig production. Due to the intensive selection on increasing the number of piglets born, more than 75% of litters in Danish Yorkshire (DY) pigs have more than 14 alive piglets (Nielsen et al., 2013), which caused a high proportion of Yorkshire sows do not have enough teats to feed piglets. To overcome the issue, cross-fostering is commonly implemented in sow farms (Calderón Díaz et al., 2018). Selection thereby has also been suggested to be focused on enhancing the TTN (Rohrer and Nonneman, 2016). So far, studies on TTN were mostly carried out on the detection of candidate quantitative trait loci (QTL) and genes (Lopes et al., 2014; Verardo et al., 2015; Martin et al., 2016; Uzzaman et al., 2018). Only a limited number of studies have focused on genomic prediction for TTN (Tan et al., 2017), and almost no studies investigated the feasibility of joint genomic evaluation for TTN combining multiple pig populations.

Thus, the objective of this study was to develop an efficient strategy for joint genomic evaluation for TTN in multiple pig populations. To achieve the objective, we first estimated variance components and genetic correlations of TTN between different pig populations. Then we employed a genome-wide association study (GWAS) to identify QTL regions that are significantly associated with TTN and investigated the proportion of total genetic variance explained by significantly associated QTL regions, which provided an insight into understanding the genetic architecture of TTN in different populations. Finally, we explored an optimal way of genomic prediction for TTN using three different models.

Materials and Methods

Data

All the datasets were provided by two national pig nucleus herds in South China, each of them with a single population. One herd included 13,060 American Yorkshire (AY) pigs born between March 2014 and January 2018, and the other one included 10,060 DY pigs born between September 2013 and April 2018. TTNs were counted and recorded at the weaning time. Pedigrees for AY and DY populations were traced back as far as possible, including in all cases more than three generations. In total, there were 17,346 pigs in AY pedigree and 15,639 in DY pedigree. Since the GS program did not start until the end of 2016 and the beginning of 2017 in AY population and DY population, respectively, only a limited number of DNA samples from these pigs were collected. According to the guidance of the national genetic improvement of livestock and poultry breeding program (https://www.moa.gov.cn/nybgb/2021/202106/202110/t20211026_6380483.htm), in principle, the companies’ genotype at least 1 boar and 2 sows for each litter. In the second half of 2018, when the African swine fever broke in China, the DNA sample collections and genotyping process were stopped. In total, 2,782 AY and 2,486 DY were genotyped using the GeneSeek Porcine 50K SNP Beadchip.

SNPs were mapped to pig chromosomes using Sscrofa genome build 11.1. Quality controls were applied on the combined AY and DY populations as follows: animals with call-rate less than 90% were first removed; SNPs with call-rate less than 90% were removed as well; SNPs with a minor allele frequency lower than 0.05 across two Yorkshire populations were removed; SNPs that deviated strongly from Hardy–Weinberg equilibrium within the breed (P < 10⁻⁷) were also excluded. Then, all the sparsely missing genotypes were imputed by using the software Beagle 4.1 (Browning and Browning, 2007). Finally, 33,326 SNPs were available for both AY and DY populations.

Principle components analysis of relationship matrix

Principal components analysis (PCA) of the matrix of genomic relationships was investigated for the combined DY and AY populations, because PCA can be used to investigate the ethnic background of individuals (McVean, 2009). The genomic relationship matrix (GRM) G was constructed as Makgahlela et al. (2014) and Wientjes et al. (2017):

$${\displaystyle \begin{array}{l}{\displaystyle \mathbf{G}=\left[\begin{array}{cc}\frac{Z_{\mathrm{A}\mathrm{Y}}{Z}_{\mathrm{A}\mathrm{Y}}^{\prime }}{{\displaystyle \sum ^{}}2p_{\mathrm{A}{\mathrm{Y}}_i}(1-p_{\mathrm{A}{\mathrm{Y}}_i})}& {\displaystyle \frac{Z_{\mathrm{A}\mathrm{Y}}{Z}_{\mathrm{D}\mathrm{Y}}^{\prime }}{\sqrt{{\displaystyle \sum ^{}}2p_{\mathrm{A}{\mathrm{Y}}_i}(1-p_{\mathrm{A}{\mathrm{Y}}_i})}\sqrt{{\displaystyle \sum ^{}}2p_{\mathrm{D}{\mathrm{Y}}_i}(1-p_{\mathrm{D}{\mathrm{Y}}_i})}}}\\ \frac{Z_{\mathrm{D}\mathrm{Y}}{Z}_{\mathrm{A}\mathrm{Y}}^{\prime }}{\sqrt{{\displaystyle \sum ^{}}2p_{\mathrm{A}{\mathrm{Y}}_i}(1-p_{\mathrm{A}{\mathrm{Y}}_i})}\sqrt{{\displaystyle \sum ^{}}2p_{\mathrm{D}{\mathrm{Y}}_i}(1-p_{\mathrm{D}{\mathrm{Y}}_i})}}& {\displaystyle \frac{Z_{\mathrm{D}\mathrm{Y}}{Z}_{\mathrm{D}\mathrm{Y}}^{\prime }}{{\displaystyle \sum ^{}}2p_{\mathrm{D}{\mathrm{Y}}_i}(1-p_{\mathrm{D}{\mathrm{Y}}_i})}}\end{array}\right],}\end{array}}$$

where $Z_{\mathrm{A}\mathrm{Y}}$ and $Z_{\mathrm{D}\mathrm{Y}}$ are the centralized genotypes in AY and DY populations, respectively; $p$ is the allelic frequencies for each SNP marker with subscripts indicating for either AY or DY population. This GRM is similar to VanRaden method 1 (2008), but considers the different allelic frequencies in multiple populations. The first two main principal components on the GRM of each individual across AY and DY pigs were plotted, via the prcomp() function in software R.

Statistical analysis

A single-step genomic best linear unbiased prediction (ssGBLUP) method was used to estimate variance components and genomic estimated breeding values (GEBVs) within each population (Legarra et al., 2009; Christensen and Lund, 2010). The model was as follows:

$${\displaystyle \begin{array}{l}{\displaystyle y=X\beta +Za+e,}\end{array}}$$

where $y$ is a vector of the original phenotypes of TTN in either AY or DY population; $\beta$ is a vector of fixed effects, including effects of herd-year-season (HYS), sex and birth parities; $a$ represents a vector of additive genetic effects, assumed to follow a normal distribution as $a\sim N(0,H{\sigma }_a^2)$, where $H$ is a combined pedigree-based and marker-based additive genetic relationship matrix, constructed as Legarra et al. (2009) and Christensen and Lund (2010); $e$ is a vector of residual effects, which was assumed following a normal distribution as $e\sim N(0,I{\sigma }_e^2)$, where $I$ is an identity matrix; $X$ and $Z$ are the corresponding incidence matrices. Software DMU (Madsen and Jensen, 2013) was used to estimate the variance components and solve the ssGBLUP equations. The adjusted phenotypes $y_c$ were calculated as the sum of estimated additive genetic effects plus the estimated residual effects ($y_c=\mathrm{G}\widehat{\mathrm{E}\mathrm{B}}\mathrm{V}+\widehat{e}$) on animals who have phenotypic recordings in both AY and DY populations. These adjusted phenotypes $y_c$, on either 2,782 genotyped AY pigs or 2,486 genotyped DY pigs, were used as inputs for all subsequent analyses.

Genetic parameters estimation

In order to investigate the feasibility and efficiency of GS using datasets from combing two populations, we implemented the genomic evaluation via using genomic BLUP (GBLUP) method in either a single population or the combined two populations.

Pedigree-based univariate BLUP model was first used for investigating the heritability of TTN in either AY or DY population. The models used as follows:

Model 1:

$${\displaystyle \begin{array}{l}{\displaystyle y_c=1\mathrm{\mu }+Za+e,}\end{array}}$$

where $y_c$ is a vector of adjusted phenotypes of TTN on either 2,782 genotyped AY pigs or 2,486 genotyped DY pigs; $\mu$ is the overall mean for the adjusted phenotypes and 1 is a vector of ones; $Z,a,e$ are as above. It was assumed that the additive genetic effects follow normal distribution as $a_{\mathrm{A}\mathrm{Y}}\sim N(0,A_{\mathrm{A}\mathrm{Y}}{\sigma }_{a_{\mathrm{A}\mathrm{Y}}}^2)$ and $a_{\mathrm{D}\mathrm{Y}}\sim N(0,A_{\mathrm{D}\mathrm{Y}}{\sigma }_{a_{\mathrm{D}\mathrm{Y}}}^2)$, where the subscripts AY and DY represent American Yorkshire and Danish Yorkshire pig populations, respectively; A is pedigree-based relationship matrix, constructed as Henderson (1976); ${\sigma }_{a_{\mathrm{A}\mathrm{Y}}}^2$ and ${\sigma }_{a_{\mathrm{D}\mathrm{Y}}}^2$ are the additive genetic variances within AY and DY population, respectively.

We also employed the following bivariate genomic model to estimate the variance components in both AY and DY populations:

Model 2:

$${\displaystyle \begin{array}{l}{\displaystyle \left[\begin{array}{l}{y}_{c_{\mathrm{A}\mathrm{Y}}}\\ y_{c_{\mathrm{D}\mathrm{Y}}}\end{array}\right]=1\left[\begin{array}{l}{\mu }_{\mathrm{A}\mathrm{Y}}\\ {\mu }_{\mathrm{D}\mathrm{Y}}\end{array}\right]+\left[\begin{array}{cc}{Z}_{\mathrm{A}\mathrm{Y}}& {\displaystyle 0}\\ 0& {\displaystyle Z_{\mathrm{D}\mathrm{Y}}}\end{array}\right]\left[\begin{array}{l}{a}_{\mathrm{A}\mathrm{Y}}\\ a_{\mathrm{D}\mathrm{Y}}\end{array}\right]+\left[\begin{array}{l}{e}_{\mathrm{A}\mathrm{Y}}\\ e_{\mathrm{D}\mathrm{Y}}\end{array}\right],}\end{array}}$$

where the subscripts AY and DY represent American Yorkshire and Danish Yorkshire pig populations, respectively; $y_c$ represents a vector of adjusted phenotypes for TTN. All the other symbols are the same as those in model 1. It was assumed that the random effects $\left(\begin{array}{l}{a}_{\mathrm{A}\mathrm{Y}}\\ a_{\mathrm{D}\mathrm{Y}}\end{array}\right)$ follow a multivariate normal distribution, as:

$${\displaystyle \begin{array}{l}{\displaystyle \left(\begin{array}{l}{a}_{\mathrm{A}\mathrm{Y}}\\ a_{\mathrm{D}\mathrm{Y}}\end{array}\right)\sim N(0,G\otimes \left(\begin{array}{ll}{\sigma }_{a_{\mathrm{A}\mathrm{Y}}}^2& {\displaystyle {\sigma }_{a_{\mathrm{A}\mathrm{Y},\mathrm{D}\mathrm{Y}}}}\\ {\sigma }_{a_{\mathrm{D}\mathrm{Y},\mathrm{A}\mathrm{Y}}}& {\displaystyle {\sigma }_{a_{\mathrm{D}\mathrm{Y}}}^2}\end{array}\right)),}\end{array}}$$

where ${\sigma }_{a_{\mathrm{A}\mathrm{Y}}}^2$ and ${\sigma }_{a_{\mathrm{D}\mathrm{Y}}}^2$ are the additive genetic variances within AY and DY population, respectively; ${\sigma }_{a_{\mathrm{A}\mathrm{Y},\mathrm{D}\mathrm{Y}}}$ and ${\sigma }_{a_{\mathrm{D}\mathrm{Y},\mathrm{A}\mathrm{Y}}}$ are the additive genetic covariance between AY and DY populations. G is the GRM, constructed as Wientjes et al. (2017). It was assumed that the residual effects follow a normal distribution as:

$${\displaystyle \begin{array}{l}{\displaystyle \left(\begin{array}{l}{e}_{\mathrm{A}\mathrm{Y}}\\ e_{\mathrm{D}\mathrm{Y}}\end{array}\right)\sim N(0,I\otimes \left(\begin{array}{ll}{\sigma }_{e_{\mathrm{A}\mathrm{Y}}}^2& {\displaystyle 0}\\ 0& {\displaystyle {\sigma }_{e_{\mathrm{D}\mathrm{Y}}}^2}\end{array}\right)),}\end{array}}$$

where ${\sigma }_{e_{\mathrm{A}\mathrm{Y}}}^2$ and ${\sigma }_{e_{\mathrm{D}\mathrm{Y}}}^2$ are the residual variances in AY and DY populations, respectively, and I is an identity matrix. The heritabilities for TTN were calculated as: $h^2={\sigma }_a^2/({\sigma }_a^2+{\sigma }_e^2)$ and the genetic correlation of TTN between the two populations as:

$${\displaystyle \begin{array}{l}{\displaystyle r_{\mathrm{g}}=\frac{{\sigma }_{a_{\mathrm{A}\mathrm{Y},\mathrm{D}\mathrm{Y}}}}{\sqrt{{\sigma }_{a_{\mathrm{A}\mathrm{Y}}}^2{\sigma }_{a_{\mathrm{D}\mathrm{Y}}}^2}}.}\end{array}}$$

Scenarios and predictive abilities

In this study, in order to investigate the feasibility and reliability of implementing GS for TTN in multiple pig populations, we studied three different scenarios. Note that for each scenario, the corresponding estimated (co)variance components were used to solve the mixed model equations.

Scenario 1, Model 1 with GBLUP method separately applied to AY and DY populations:

$${\displaystyle \begin{array}{l}{\displaystyle y_c=1\mu +Za+e.}\end{array}}$$

It was assumed that $a\sim N(0,G{\sigma }_a^2),$ where ${\sigma }_a^2$ is the additive genetic variance and G is the GRM, constructed as VanRaden method 1 (2008) within each population.

Scenario 2, the GBLUP Model 1 was changed to the following model:

$${\displaystyle \begin{array}{l}{\displaystyle y_c=1\mu +Xp+Za+e,}\end{array}}$$

where $y_c$ is a vector of adjusted phenotypes of TTN on all 5,268 genotyped animals (2,782 genotyped AY pigs and 2,486 genotyped DY pigs), pretending that it is a single population at all effects; $p$ is a vector of fixed population effect, with two levels (either Danish population or American population); $X$ is the corresponding incidence matrix; the other symbols are the same as those in the Model 1. Similarly, it was assumed that $a\sim N(0,G{\sigma }_a^2),$ where ${\sigma }_a^2$ is the additive genetic variance and $G$ is the GRM, constructed as VanRaden method 1 (2008) using raw allele frequencies from the 5,268 animals.

Scenario 3, the bivariate Model 2 was applied for genomic prediction for TTN in the combined DY and AY populations. All the assumptions were exactly the same as those in Model 2.

Among the above-mentioned scenarios, scenario 2 regarded TTN as a same biological trait in the AY and DY populations, but in scenario 3, it regarded TTN as two independent, but correlated, biological traits in different Yorkshire populations. In theory, it is the genetic correlation of TTN between AY and DY populations that decide how to distinguish the trait of TTN in the joint genomic evaluation for the combined populations. If the genetic correlation is close to 1, TTN should be regarded as one same biological trait in different populations and the accuracies of genomic prediction in scenarios 1 and 2 should not be worse than that in scenario 3.

To investigate the accuracies of genomic prediction in different scenarios, data recordings on genotyped pigs (2,782 AY and 2,486 DY pigs) were divided into training populations and validation populations by using two cut-off dates in AY (1 July 2017) and DY (1 December 2017) populations. Thus, AY validation population consisted of young pigs born between 1 July 2017 and 31 January 2018 and DY validation population consisted of young pigs born between 1 December 2017 and 30 April 2018. Consequently, 604 AY pigs and 548 DY pigs were included in the validation population and 2,178 AY pigs and 1,938 DY pigs were included in the training population. The predictive abilities were determined as the correlation between adjusted phenotypes ($y_c$) and genomic estimated breeding values ($\mathrm{G}\widehat{\mathrm{E}\mathrm{B}}\mathrm{V}$) in validation populations ($\mathrm{c}\mathrm{o}\mathrm{r}(y_c,\mathrm{G}\widehat{\mathrm{E}\mathrm{B}}\mathrm{V})$) (Christensen et al., 2012). A Hotelling–Williams t-test at a 5% confidence level was performed to evaluate the statistically significant differences in predictive abilities among different scenarios. Regression coefficients of adjusted phenotypes ($y_c$) on the genomic estimated breeding values ($\mathrm{G}\widehat{\mathrm{E}\mathrm{B}}\mathrm{V}$) were calculated in different scenarios, which were used as indicators of dispersion bias of the genomic predictions. In addition, to check the possible impact of different models on the ranking of GEBVs, Spearman’s rank correlations (Spearman, 1904) between GEBVs for pigs in the validated AY and DY populations were calculated in different scenarios.

Genome-wide association analyses

Linear mixed model

After obtaining 2,782 $y_c$ in the AY population and 2,486 $y_c$ in the DY population, genome-wide association analysis of adjusted phenotypes was performed by using the LMM algorithm in software GCTA (Yang et al., 2011). The LMM was as follows:

$${\displaystyle \begin{array}{l}{\displaystyle y_c=1\mu +Xg+Za+e,}\end{array}}$$

where $y_c$ is a vector of either 2,782 AY adjusted phenotypes or 2,486 DY adjusted phenotypes; 1 is a vector of ones; $\mu$ is the general mean; X is a matrix of the SNP genotypes with entries 0, 1, and 2 indicating genotypes AA, AB, and BB, respectively; $g$ is the fixed additive genetic effect of the SNP used; $a$ is a vector of additive genetic effects, with an assumption that $u\sim \mathrm{N}(0,A{\sigma }_a^2)$, where A is the pedigree-based additive genetic relationship matrix and ${\sigma }_a^2$ is the additive genetic variance, which is in agreement with many Sahana et al. (2014). Some papers also assumed that $a\sim \mathrm{N}(0,G{\sigma }_a^2)$. In theory, we can use leave-one-chromosome-out (LOCO) approach to construct different G matrix to capture the additive effects. However, we have experienced that LOCO gives large inflation of P-values and thus, we chose pedigree-based A matrix. Z is an incidence matrix relating adjusted phenotypes to corresponding random polygenic effect; e is a vector of random residual effect, with an assumption that $e\sim \mathrm{N}(0,I{\mathrm{\Sigma }}_{\mathrm{e}}^2)$. Bonferroni corrections were set as the genome-wide significant threshold (−log10(0.05/number of SNPs) = 5.823).

Bayes Cπ model

In addition, to investigate the proportion of genetic variances explained by individual SNP, a Bayes Cπ model is used to estimate the SNP effects in AY and DY populations, respectively

$${\displaystyle \begin{array}{l}{\displaystyle y_c=1\mu +{\displaystyle \underset{j=1}{{\displaystyle \sum ^n}}}{Z}_j{g}_j{\delta }_j+\mathbf{e},}\end{array}}$$

where $y_c$ is a vector of either 2,782 AY adjusted phenotypes or 2,486 DY adjusted phenotypes; 1 is a vector of ones; $\mu$ is the overall mean; $n$ is the number of SNPs; $Z_j$ represents genotype covariates at the jth $\mathrm{s}\mathrm{n}\mathrm{p}$, coded as 0, 1, and 2 for genotypes AA, AB, and BB, respectively; ${\delta }_j$ is an indicator variable indicating whether $\mathrm{s}\mathrm{n}{\mathrm{p}}_j$ is present (${\delta }_j=1$ with probability of π) or absent (${\delta }_j=0$ with probability of (1−π)) in the model. $g_j$ is the additive effect of $\mathrm{s}\mathrm{n}{\mathrm{p}}_j$ and it was assumed that the additive effects $g_j$ are normally distributed as $g_j\sim N(0,{\sigma }_g^2)$ with probability π and 0 otherwise. The π was assigned a prior beta distribution with alpha=1 and beta=10, as suggested by Legarra et al. (2011) and sampled with the Markov chain Monte Carlo (MCMC) algorithm. The additive genetic variances ${\sigma }_g^2$ and residual variances ${\sigma }_e^2$ were assumed following inverted chi-square distribution with $\mathrm{\nu }=4$ degrees of freedom and scale parameter

$${\displaystyle \begin{array}{l}{\displaystyle s_a^2=\frac{{{\displaystyle \widehat{\sigma }}}_g^2(\nu -2)}{\nu }\mathrm{a}\mathrm{n}\mathrm{d}{s}_e^2=\frac{{{\displaystyle \widehat{\sigma }}}_e^2(\nu -2)}{\nu },}\end{array}}$$

respectively. Bayes Cπ analyses were performed using software GS3 (Legarra et al., 2011). The number of iterations was 100,000 with a burn-in of 20,000 and a thinning interval of 25. The genetic variance explained by one SNP is calculated as $\mathrm{v}\mathrm{a}\mathrm{r}\left(a_i\right)=2p_i{q}_i{\widehat{g}}_i^2$, where the $p_i$ is the allelic frequency at marker i and $q_i=1-p_i$. ${\widehat{g}}_i$ is the estimated additive SNP effect for marker i. Proportion of genetic variance explained by each sliding window of 5 consecutive SNP markers across the genome were surveyed.

Haplotype block analysis

To identify the candidate QTL regions that were significantly associated with TTN, software Haploview (Barrett et al., 2005) was used to perform haplotype block analysis. Haplotype block detection was performed on the whole chromosome containing the most significant SNPs. Haplotype blocks were defined as the upper and lower confidence intervals of the estimates of pairwise Dʹ falling within certain threshold values, as reported by Gabriel et al. (2002). A haplotype block containing the most significant SNP was considered as a candidate QTL region.

Identification of candidate genes

Ensemble database (www.ensembl.org) was used to identify genes located within the candidate haplotype block regions. The genes located within the haplotype block regions were considered the possible candidate genes.

Results

PCA of relationship matrix

The two main principal components on the matrix of genomic relationships of each individual across AY and DY populations are shown in Figure 1. The first two components explained 16.61% and 1.44% of variability across individuals, respectively. The first principal component (x-axis) clearly separates the two populations, whereas the second component (y-axis) could not distinguish the two Yorkshire populations clearly. Within each population, there is no existing of apparent population stratification.

Figure 1.

Principal components analysis on the matrix of genomic relationships across two Yorkshire populations. The first two main principal components are presented on the x-axis and y-axis, respectively. The proportions of variability across individuals explained by PC1 and PC2 were 16.61% and 1.44%, respectively.

Estimates of variance components, heritabilities, and genetic correlations

The descriptive statistics of TTN for the two Yorkshire populations are shown in Table 1. The mean of TTN in the two populations were 14.5 and the standard deviations were 0.44 and 0.83 for DY and AY pigs, respectively. The distribution of TTN in two populations is shown in Supplementary Figure S1. Estimates of variance components and heritabilities for TTN in AY and DY pigs with bivariate models are shown in Table 2. In both BLUP and GBLUP methods, heritabilities of TTN in AY were always higher than that in DY. For AY, heritabilities were similar in BLUP and GBLUP, whereas, in the DY population, the estimate of heritability in GBLUP ($h^2=0.10,se=0.03$) was lower than in BLUP ($h^2=0.17,se=0.02$). The genetic correlation of TTN between AY and DY was high (0.789), with a standard error of 0.228.

Table 1.

Descriptive statistics of total teat number in two Yorkshire populations

Population1	No.	Mean	Standard deviation	Max	Min
AY	13,060	14.68	0.83	19	10
DY	10,060	14.29	0.44	18	10

AY, American Yorkshire; DY, Danish Yorkshire.

Table 2.

Estimation of total teat number variance components and heritability with their standard errors in American Yorkshire and Danish Yorkshire

Estimate	BLUP		GBLUP
	AY1	DY2	AY1	DY2
Additive genetic variance (${\sigma }_a^2$)	0.37 (0.03)	0.06 (0.01)	0.44 (0.06)	0.03 (0.01)
Residual variance (${\sigma }_e^2$)	0.51 (0.01)	0.27 (0.01)	0.65 (0.03)	0.25 (0.01)
Heritability ($h^2$)	0.42 (0.02)	0.17 (0.02)	0.40 (0.04)	0.10 (0.03)

AY, American Yorkshire.

DY, Danish Yorkshire.

Predictive abilities

Table 3 shows the predictive abilities of TTN in AY and DY populations in three different scenarios. In AY, the correlation between the estimated GEBVs ($\widehat{a}$) and the adjusted phenotypes ($y_c$) ranged from 0.369 in Scenario1 to 0.372 in Scenario3. For DY, $\mathrm{c}\mathrm{o}\mathrm{r}(y_c,\mathrm{G}\widehat{\mathrm{E}\mathrm{B}}\mathrm{V})$ increased from 0.120 in Scenario2 to 0.155 in Scenario3. In both two populations, the highest accuracies were obtained in Scenario3, which uses a multiple trait model. However, based on the Hotelling–Williams t-test, there was no significant difference in predictive abilities among different scenarios in the AY population, whereas in the DY population, Scenario3 significantly outperformed the others.

Table 3.

Predictive abilities for TTN in three scenarios

Scenarios1	$\mathrm{c}\mathrm{o}\mathrm{r}(\widehat{c},{\mathbf{y}}_{\mathbf{c}})$ 2		Regression coefficients3
	AY	DY	AY	DY
Scenario 1	0.370a	0.144a	0.979	1.056
Scenario 2	0.371a	0.120b	1.062	0.956
Scenario 3	0.372a	0.155c	0.979	1.079

Scenario 1, GBLUP method separately applied to AY and DY populations; Scenario 2, GBLUP method was applied in a univariate model to the combined AY and DY populations; Scenario 3, GBLUP method was applied in a bivariate Model in the combined DY and AY populations.

$\mathrm{c}\mathrm{o}\mathrm{r}(\widehat{c},{\mathbf{y}}_{\mathbf{c}})$ is Pearson correlation coefficients between GEBVs and adjusted phenotypes.s

Regression coefficients is the regression coefficients of adjusted phenotypes on GEBVs.

Regression coefficients of adjusted phenotypes on the GEBVs are also shown in Table 3. Overall, all the regression coefficients were close to 1. Regardless of the population, there were no clear trends in which scenario outperformed the others.

Spearman’s rank correlations between GEBVs across different scenarios for AY and DY pigs are shown in Table 4. For AY pigs (below the diagonal), Spearman’s rank correlations were higher than 0.99. For DY pigs (above the diagonal), Spearman’s rank correlations ranged from 0.89 to 0.94.

Table 4.

Spearman’s rank correlations between GEBVs of TTN for DY (above the diagonal) and AY (below the diagonal) pigs in the pairwise scenarios¹

Model	Scenario 1	Scenario 2	Scenario 3
Scenario 1		0.885	0.936
Scenario 2	0.990		0.924
Scenario 3	0.994	0.996

Scenario 1, GBLUP method separately applied to AY and DY populations; Scenario 2, GBLUP method was applied in a univariate model to the combined AY and DY populations; Scenario 3, GBLUP method was applied in a bivariate Model in the combined DY and AY populations.

GWAS results for DY and AY

As shown in Figure 2, a total of 23 and 1 SNPs were found to be significantly associated with TTN in AY and DY populations, respectively. The most significant SNP associated with TTN are shown in Table 5, and all the significant SNPs are shown in Supplementary Table S1. As shown in Figure 2, for AY, the most significantly associated SNP (H3GA0022648) was located on chromosome 7 at position 97279129 bp; for DY, the most significantly associated SNP (MARC0038565) was located on chromosome 7 at position 97652632 bp. For the most significantly associated SNPs in AY and DY populations, the mean values and the standard deviations of TTN in each genotype are shown in Supplementary Table S3.

Figure 2.

Manhattan plots of LMM genome-wide association analysis for TTN. Manhattan plot for AY population (A). Manhattan plot for DY population (B). Y-axis represents −log₁₀ of P-values and x-axis represents chromosome.

Table 5.

The most significantly associated SNPs and candidate genes for TTN in GWAS

Population	SNP name	Chromosome	Position	P-value	Candidate genes
AY	H3GA0022648	7	97279129 bp	4.42E-12	ZNF410,FASCENARIO161B, COQ6,ENTPD5, BBOF1,ALDH6A1, LIN52, VSX2, ABCD4,VRTN.
DY	MARC0038565	7	97652632 bp	1.35E-06	LIN52, VSX2, ABCD4,VRTN.

Three candidate QTL regions that contained the most significantly associated SNPs on SSC 7 and SSC 8 were identified through haplotype block analysis (Figure 3). For AY, we detected two haplotype blocks, one ranged from 97195350 bp to 97617907 bp on SSC 7 (Figure 3A) and the other ranged from 47858191 bp to 48328522 bp on SSC 8 (Figure 3B). For DY, one haplotype block ranging from 97394296 bp to 97652632 bp on SSC 7 was detected (Figure 3C). The genes located within these blocks were regarded as candidate genes (Table 5). Thus, for AY, the identified TTN-related candidate genes were on zinc finger protein 410 (ZNF410), FASCENARIO161 centrosomal protein B (FASCENARIO161B), coenzyme Q6, monooxygenase (COQ6), ectonucleoside triphosphate diphosphohydrolase 5 (ENTPD5), basal body orientation factor 1 (BBOF1), aldehyde dehydrogenase 6 family member A1 (ALDH6A1), lin-52 DREAM MuvB core complex component (LIN52), visual system homeobox 2 (VSX2), ATP binding cassette subfamily D member 4 (ABCD4), and vertebrae development associated (VRTN), relaxin family peptide receptor 1 (RXFP1), chromosome 8 C4orf46 homolog (C4orf46), electron transfer flavoprotein dehydrogenase (ETFDH), peptidylprolyl isomerase D (PPID), folliculin interacting protein 2 (FNIP2), chromosome 4 open reading frame 45 (C4orf45), U6 spliceosomal RNA (U6), and Rap guanine nucleotide exchange factor 2 (RAPGEF2). For DY, the identified TTN-related candidate genes were LIN52, VSX2, ABCD4, and VRTN.

Figure 3.

Haplotype block analysis for genomic regions that are significantly associated with TTN in both AY and DY populations. Markers in the blocks are in bold. Linkage disequilibrium block region (block 2) ranges from 97195350 bp to 97617907 bp on SSC7 in AY population (A); linkage disequilibrium block region (block 2) ranges from 47858191 bp to 48328143 bp on SSC8 in AY population (B); linkage disequilibrium block region (block 2) ranges from 97394296 bp to 97652632 bp on SSC7 in DY population (C).

In addition, the proportions of genetic variance explained by each sliding window of five consecutive SNP are shown in Figure 4. We considered regions that accounted for more than 1% of total genetic variance as potential QTL regions for TTN. Based on Figure 4, for the AY population, 7 potential QTL regions were identified on SSC3, SSC4, SSC5, SSC7, SSC8, SSC10, and SSC15. For the DY population, potential QTL regions on SSC1, SSC7, and SSC16 were identified. The detailed information on the relevant genome regions and the genes that are involved in these genome regions were listed in Supplementary Table S2. Among these identified potential QTL regions, those on SSC7 (SSC7: 97082645-97779063 bp in AY population; SSC7: 97147161-97954258 bp in DY population) totally covered the GWAS detected potential QTL regions (SSC7: 97195350-97617907 bp in AY population; SSC7: 97394296-97652632 bp in DY population). These identified potential QTL regions on SSC7 were overlapped, but not the same, in AY and DY populations.

Figure 4.

Proportion of genetic variance explained by each sliding window of five consecutive SNP markers across the genome. American Yorkshire population (A); Danish Yorkshire population (B). Y-axis is the percent of genetic variance explained by each sliding window.

Discussion

In this study, we implemented genomic evaluation for TTN in AY and DY pig populations using three different genomic models (separate predictions, pooling both populations, or multiple traits). Compared with a univariate model with dataset from one single population, the bivariate model with combined AY and DY populations increased predictive abilities, which indicated that the TTN should be regarded as two independent, but correlated, traits in the joint genomic evaluation and also implied the genetic correlation of TTN between AY and DY is lower than 1. The study of the genetic correlation of TTN between AY and DY populations supported our inference, which showed the $r_{\mathrm{g}}$ was high (0.78), but deviated from 1. This result indicates that the genes or QTLs controlling TTN are similar, but not completely the same, in AY and DY populations. To understand the genetic architecture for TTN, we employed GWAS to investigate the possible candidate genes and QTLs in both populations. Results showed that significant QTL regions and genes in AY and DY were different, in line with the fact that estimates of genetic correlations of TTN between AY and DY populations could be lower than 1.

In this study, we first employed ssGBLUP method to calculate the adjusted phenotypes within each population. ssGBLUP method used a combined pedigree-based and genomic-based relationship matrix (H matrix) to solve mixed model equations and the accuracies of adjusted phenotypes are assuring. Due to the fact that the numbers of genotyped individuals are limited in each population, we did not use GBLUP to estimate fixed effects and calculate the adjusted phenotypes. Nevertheless, to investigate the predictive abilities across different scenarios and study the efficiency of joint genomic evaluation, we used adjusted phenotypes as the dependency variables and employed GBLUP method to implement genomic predictions. We did not use ssGBLUP further because the pedigrees of AY and DY populations cannot be combined directly to build neither the pedigree-based relationship matrix nor the regular H matrix in ssGBLUP method. Note that some articles also used ssGBLUP method with either unknown parent groups (Cesarani et al., 2022) or metafounders (Fu et al., 2021) to study the performances of genomic evaluation in multiple populations. These methods commonly constructed relationship matrix with estimated ancestral genealogy, but they have not been used in pig productive system due to the high complexity. In this article, since our objective is to provide an applicable strategy of using genomic evaluation for multiple pig populations in practice, we, therefore, did not apply the above-mentioned complex unusual ssGBLUP methods to the datasets. This deserves to be analyzed in the future.

The genetic parameters were estimated by using either pedigree-based BLUP model or genomic-based GBLUP model. Regardless a univariate model or a bivariate model was used, the estimated heritabilities were similar within each population. In AY population, the heritabilities of TTN ranged from 0.40 to 0.42, in agreement with previous estimates of about 0.44 (Pumfrey et al., 1980). There were no significant differences of estimates of $h_{\mathrm{A}\mathrm{Y}}^2$ between BLUP and GBLUP models when taking the standard errors into account. Nevertheless, the estimated heritabilities of TTN in DY population ($h_{\mathrm{D}\mathrm{Y}}^2$, 0.10 to 0.17) were much lower than that in AY population. These heritabilities were also in agreement with some previous studies. Actually, a number of studies have shown that the heritabilities of TTN ranged from 0.1 to 0.6 (Allen et al., 1959; Vukovic et al., 2007) in different populations, and TTN was considered as a medium heritable trait (Lee and Wang, 2001; Andonov, 2010). In this study, the additive genetic variance for TTN in AY population $\left({\sigma }_{a_{\mathrm{A}\mathrm{Y}}}^2\right)$ were about 6 (BLUP) to 16 (GBLUP) times larger than that in DY population $\left({\sigma }_{a_{\mathrm{D}\mathrm{Y}}}^2\right),$ but the residuals in AY population were only about 2 times larger than that in DY populations, which caused that heritabilies in AY population were much higher than that in DY population. The differences of additive genetic variances between the two populations were in line with the corresponding phenotypic variations, where the standard deviations of TTN in AY (0.83) were almost twice as large as that in DY (0.44) population. The possible reasons were that direct or indirect selection, such as nurse capacity (Nielsen et al., 2016), on TTN has been intensively implemented in DY pigs for several generations and thus, the variances of TTN in DY populations were relatively small. Another possible reason was related to the numbers of genealogy. The fact that the numbers of genealogy in DY population (7) were smaller than that in AY (11) population may also led to a lower additive genetic variance of TTN in DY population than that in AY population. It was found that the estimates of heritabilities of TTN in DY population via BLUP method were dramatically different from that via GBLUP method. There are two possible reasons causing this phenomenon: first, the average depth of pedigree in DY population was only 3.1, and little pedigree depth may affect the accuracy of estimating variance components; second, the scope of pedigree-based parameters is not the same as for genomic-based parameters (de Los Campos et al., 2015). Similar phenomena have also been reported in previous studies (Christensen et al., 2012).

To our knowledge, this is the first study reporting the genetic correlation of TTN between different pig populations. The genetic correlation of TTN between AY and DY populations was 0.79, but the standard errors were very large (0.23), because the datasets are small. In other words, it is deserved to study whether the genes or QTL regions that control TTN are exactly the same or not, which may support the estimates of $r_{\mathrm{g}}$. Thus, we implemented GWAS via a linear mixed model, and the GWAS results provided an insight into the genetic architecture for TTN in different Yorkshire populations. In both models, SNPs that were significantly associated with TTN were detected on SSC 7 in AY and DY populations. These findings were in agreement with other studies (Wada et al., 2000; Zhang et al., 2007; Bidanel et al., 2008; Andonov, 2010), but the identified significantly associated QTL regions were not exactly the same as results in other studies. For example, 102.1 to 105.2 Mb on SSC7 were identified by Duijvesteijn et al. (2014), 103.03 to 104.35 Mb on SSC7 were identified by Lopes et al. (2014), 102.9 to 105.2 Mb on SSC7 were identified by Verardo et al. (2016), and 102.9 to 106.0 Mb on SSC7 were identified by Tan et al. (2017). In Lopes et al. (2014), they considered VRTN gene as the most promising candidate gene associated with TTN, which was in agreement with our analyses.

However, although we found the identified QTL regions were slightly different between AY and DY populations, in this study, only ~35k SNPs were used for GWAS in both two populations, and there are only 373 kb apart for the most significantly associated SNPs in these two populations, which is not reassuring. Thus, we further employed Bayes Cπ model to study the proportion of genetic variances explained by the same genomic regions in AY and DY populations. The identified QTL regions using the Bayes Cπ model were similar to that in the mixed linear model, and meanwhile, we found the same genomic regions explained different proportions of genetic variances in AY and DY populations, which further suggested the genetic correlations of TTN between AY and DY populations could be lower than 1.

Based on the above-mentioned results of genetic correlations and GWAS, there were reasons to believe that when implementing a GS of TTN in both AY and DY populations, TTN needs to be considered as two correlated traits rather than a single biological trait in a univariate model. Therefore, we compared the predictive abilities of TTN in AY and DY populations by using three different genomic models. When comparing the predictive abilities in Scenario 2 with that in Scenario 1, no improvements of predictive abilities were obtained, especially for DY population, where a worse predictive ability was observed in Scenario 2 than that in Scenario 1. Since the linkage disequilibrium (LD) patterns and allele frequencies are different in different pig lines (Pryce et al., 2011; Veroneze, 2015), SNP substitution effects are population specific. Thus, putting weak-related pig populations into a single reference population was not useful to improve genomic prediction using single nucleotide polymorphism (SNP) chip data compared with within-population genomic. Similar results showing that admixed pig reference population did not increase the performance of genomic predictions have been reported (Hidalgo et al., 2015). However, some other studies showed that the accuracies of GEBVs can be increased by enlarging the reference population (Hayes et al., 2009; VanRaden et al., 2009; Ye et al., 2020). In Ye et al. (2020), researchers reported that by using imputed whole-genome sequence data, combining different swine populations, even if these populations are not strongly related, can lead to increased accuracy of GS because high-density markers increased the linkage disequilibrium (LD) between QTL and SNP markers and broke the restriction of different LD patterns across populations.

Furthermore, our analysis indicates that regarding TTN in different populations as the same trait in a univariate model was not appropriate for genomic evaluation. Our result further supports that the genetic correlation of TTN between AY and DY populations could be lower than 1. On the basis of predictive abilities, it can be found that if the size of a single pig population was not large enough for genomic evaluation, it may be useful to combine multiple related pig populations and implement genomic evaluation using a multi-trait genomic model. In the multivariate model, when the genetic correlations between the traits were high, the predictive ability could be increased much for the trait with lower heritability, but little for the trait with higher heritability (Juliana et al., 2019). Thus, the reason why only predictive ability in DY was improved could be that the heritability of TTN in AY was much higher than that in DY population. Note that this does not mean that combining multiple populations are always working. Previous studies have shown that the weaker the genetic correlation between the populations, the smaller gain in reliabilities when combining different populations (Su et al., 2009).

Results of Spearman’s rank correlation were in line with the results of predictive abilities. For AY populations, different scenarios did not affect the predictive abilities and thus did not influence the ranking of GEBVs. For DY population, different models had significant effects on predictive abilities and also the ranking of GEBVs.

In addition, models with three main principal components were also considered in model 1 to calculate the adjusted phenotypes, aiming at accounting for the possible existing population stratifications (Yano et al., 2019). Since the performances of GWAS and genomic evaluations in models with or without principal components were very close (results were not shown), we did not use the models with principal components. This result is in agreement with PCA (Figure 1), where the population stratifications within AY or DY population were not detected.

Conclusions

Our study shows that total number of teats on pig were controlled by different QTL regions and genes in AY and DY populations. It is suggested that the genetic correlation of TTN between AY and DY populations could be lower than 1. Joint genomic evaluation for TTN in multiple pig populations was applicable. To obtain the highest predictive abilities, TTN should be regarded as different biological traits in different populations and a multitrait model together with the combined datasets was recommended for genomic evaluation.

Glossary

Abbreviations

AY

American Yorkshire pigs

BLUP

best linear unbiased prediction

DY

Danish Yorkshire pigs

GBLUP

genomic best linear unbiased prediction

GEBV

genomic estimated breeding value

GS

genomic selection

GWAS

genome-wide association study

LD

linkage disequilibrium

LMM

linear mixed model

QTL

quantitative trait locus

ssGBLUP

single-step genomic best linear unbiased prediction

TTN

total teats number

Conflict of interest statement

The authors declare that they have no conflicts of interest.