# Integrating Casein Complex SNPs Additive, Dominance and Epistatic Effects on Genetic Parameters and Breeding Values Estimation for Murciano-Granadina Goat Milk Yield and Components

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Milk Yield Standardization and Composition Analysis

_{j}) was computed through the equation described in Pizarro Inostroza et al. [7]. Official control policies are stated by the Royal Decree-Law 368/2005, on 8

^{th}April 2005, regulating official milk yield controls for the genetic evaluation in the bovine, ovine, and caprine species of the Spanish Ministry of Agriculture (2005). Milking policies varied across farms depending on whether milking was performed every 4 or 6 weeks, during the morning or afternoon (AT4, AT4T, AT4M, A6, AT6M, and AT6T). First control (d

_{1}) and the last (d

_{2}) were assessed individually for every goat computing the days between the day the animal was born (BD) and the date of the first control (FC), and the days between the penultimate control (PC) and the last control (LC), respectively using the formulas in Pizarro Inostroza et al. [7]. To save interindividual differences that could be ascribed to differences in milking period among other factors, birthdate information, and the date on which several controls were performed until 210 lactation days were included to normalize milk yield for each goat. An average of approximately five controls was performed per goat. Standardized yield to 210 days per goat was calculated using the formula and model described in Pizarro Inostroza, et al. [7]. Milk sampling was carried out monthly and officially analyzed at the Milk Quality Laboratory, in Cordoba (Spain) to quantify protein, fat, solids, lactose content, and somatic cells count with a MilkoScan™ analyzer FT1.

#### 2.2. Animals

_{1}is the weight for milk yield, W

_{2}for fat, W

_{3}for protein, and W

_{4}for lactose in kg and standardized to 210 days; and $\mu $ the mean for each of the traits included in the ICO computed in Kg and at 210 days. After ICO was computed for each of the animals included in the matrix, we sorted a total of 200 animals from the whole routine milk recording of Murciano-Granadina goat breed in a ranking considering their ICO value obtained at the previous genetic evaluation. Animals with extreme PBVs may be less efficient and less balanced than we could expect at first. Furthermore, not all traits are affected to the same degree by selection for these extremes. For these reasons, initially, 200 animals were randomly selected and ranked as follows: 67 females presenting the lowest ICO values in the rank, 66 females with values around percentile 50, and 67 females presenting the highest ICO values in the rank, respectively. This sample selection process was performed to ensure that we worked on an adjusted representative sampling of the genotype distribution in the population. Out of these 200 animals initially considered, we discarded those whose phenotype registries were missing or incomplete. As a result, the final sample set for genotyping consisted of 2594 direct records of 159 studbook registered goats from which blood samples were taken for genotyping. Direct records were collected from 28 Southern Spanish farms in random periods, from 2005 to 2018. The age of the animals in the sample ranged from 1 to 9.15 years (1.57±1.11 years, mean ± sd).

#### 2.3. Genotyping

#### 2.4. Single-Nucleotide Polymorphisms (SNPs) Additive and Dominance Genetic Effects Identification and Codification and Dimensionality Reduction Using Linkage Disequilibrium (LD) and Categorical Principal Component Analysis (CATPCA)

^{2}(linkage disequilibrium coefficient of determination). The total length of casein loci and distances between adjacent loci were determined following the premises presented by Dagnachew et al. [20]. Using a unique test to evaluate genotype-phenotype association, we lost the ability to control for confounding factors such as those derived from the structure of the population, genomic stratification, genetic environment, and gene interaction (epistatic relationships). Contextually, CATPCA can determine the variability explained by a certain set of factors that can derive from genome-wide analyses (single-nucleotide polymorphisms (SNP). This way, potential redundancies can be reduced through a rather, hence, more effective comparison space between SNPs [20,21]. This way, CATPCA, and particularly Bonferroni correction corrects for the bias derived from the inclusion of a large number of factors (increased likelihood of false positives), maximizing the variability explanatory power of factors combinations identifying and ruling out potential misinterpretations of SNP/phenotype associations [20,22]. Horne and Camp [23] proposed that principal component analysis (PCA) can evaluate SNP correlations determining clusters in LD (LD-clusters), setting an optimal set of group-tagging SNPs (gtSNPs) determining intra-genic diversity more efficiently and minimizing the necessary requirements for the evaluation of informative association. Unlike haplotype block (HB) and haplotype-tagging SNP (htSNP) methods based on Linkage Disequilibrium Analysis (LD), PCA technique (also applicable to CATPCA) does not require SNPs to be in Hardy-Weinberg’s equilibrium [24]. Furthermore LD-groups of SNPs do not need to be located in close DNA fragments. This way, there is a fraction of diversity variance, that of fragments located at different fragment being related, which would be lost and which can be computed through CATPCA [24,25]. Kaiser Varimax Rotation was used as well, as it corrects the bias derived from high correlations among factors and a small number of variables and zero correlations in the rest.

#### 2.5. Study of OVERALs/Nonlinear Canonical Correlations (NLCC) to Identify and Encode Epistatic Effects

#### 2.6. Preliminary Statistical Assumption Testing

#### 2.7. Non-Genetic and Genetic Fixed Effect Statistical Analysis

^{2}) was computed as it expresses inter category differences and their associated error variance as a percentage. Afterwards, univariate tests must be carried to isolate the pairs of categories of each factor between which a significant difference in the mean value for the independent variable exist. Past research suggests ηp

^{2}may be more appropriate than eta square (η

^{2}) after performing a multifactorial design, as ηp

^{2}provides a score for the association strength between independent factors and dependent variables, excluding the variance produced by the rest of factors considered in the model as suggested by Brown [36].

^{2}be equal to η

^{2}. Contextually, this may be of remarkable importance when we consider non-possibly overlapping empirical variables as suggested in Pizarro et al. [32]. A complete description of the statistical analyses carried out on the nongenetic and genetic fixed effects included in the genetic model can be found in Pizarro et al. [32].

#### 2.8. Genetic Model Comparison, Phenotypic and Genetic Parameter Estimation

_{yfpdmlsc}is the separate score of milk yield (y) and components (fat (f), protein (p), solids (dm), lactose (l) in kg and somatic cells (sc) count cs/mL) for a given animal; μ is the overall mean; Far

_{a}is the fixed effect of the ath farm/owner (a = 28 farms); Pye

_{b}is the fixed effect of the bth year of parturition (b = 2005–2018); Pmon

_{c}is the fixed effect of the cth month of parturition (c = January to December); Pse

_{d}is the fixed effect of the dth season of evaluation (d = Autumn, Winter, Summer, and Spring); Bnum

_{e}is the fixed effect of the eth birth number (e = 1-9 Birth); Cye

_{f}is the fixed effect of the fth control year (f = 2005–2018); Cmon

_{g}is the fixed effect of the gth control month (g = January to December); Cse

_{h}is the fixed effect of the hth control season (h=Autumn, Winter, Summer, and Spring); Nci is the fixed effect of the ith number of control (i=1-31 controls); Mrout

_{j}is the fixed effect of the jth milking routine (j = A4, AT4T, AT4M, A6, AT6M, AT6T); Bty

_{k}is the fixed effect of the kth birth type (k = Simple, Double, Triple, abortion in lactation); Dye

_{l}is the fixed effect of the lth drying year (l = 2005–2018); Dmon

_{m}is the fixed effect of the mth drying month (m = January to December); Dse

_{n}is the fixed effect of the nth drying season (n = Autumn, Winter, Summer, and Spring); DIM

_{o}is the fixed effect of the oth number of days in milk (o = 1-183 days); DFPC is the fixed effect of the pth number of days to first control (p = 1-226 days); DLD

_{q}is the fixed effect of the qth number of days from last control to drying (q = 1-61 days); Aln

_{r}is the fixed effect of the rth number of kids born alive (r = 0-5 kids); Den

_{s}is the fixed effect of the sth number of kids born death ( s= 0-3 kids); PC1

_{t}is the fixed effect of the tth additive and dominance effect of SNPs in PC1 (t = 1-17); PC2

_{u}is the fixed effect of the uth additive and dominance effect of SNPs in PC2 (u = 1-6); PC3

_{v}is the fixed effect of the vth additive and dominance effect of SNPs in PC3 (v = 1-17); PC4

_{w}is the fixed effect of the wth additive and dominance effect of SNPs in PC4 (w = 1-20); PC5

_{x}is the fixed effect of the xth additive and dominance effect of SNPs in PC5(x = 1-15); PC6

_{y}is the fixed effect of the yth additive and dominance effect of SNPs in PC6 (y = 1-14); PC7

_{z}is the fixed effect of the zth additive and dominance effect in PC7 (z = 1-12); NLCC

_{aa}is the fixed effect of the aath epistatic nonlinear canonical correlation between SNPs (NLCC) (aa = 1-10); age in months was considered a linear and quadratic covariate, hence ${b}_{1}$ and ${b}_{2}^{2}$ are the linear and quadratic regression coefficients on the age of evaluation (A

_{ab}), Animal

_{ac}is the random additive genetic effect of the acth goat, PE

_{ad}is its permanent environmental effect of each goat, and ε

_{yfpdmlsc}is the random residual effect.

^{−12}. Link functions and their mathematical development is shown in Boldman et al. [37]

#### 2.9. Non-Genetic Best Linear Unbiased Estimators (BLUE) for Fixed Effects and Covariates and Best Linear Unbiased Predictors/Breeding Value Prediction (BLUP, PBVs)

#### 2.10. Predicted Breeding Values (PBV), Standard Error of Prediction (SEP), Accuracies (RTi), and Reliability (Rap) Comparison

#### 2.11. Ethics Approval and Consent to Participate

## 3. Results

#### 3.1. SNPs Dimensionality Reduction Using Linkage Disequilibrium and CATPCA

#### 3.2. Study of OVERALs/Nonlinear Canonical Linear Correlations (NLCC) to Identify and Encode Epistatic Effects

#### 3.3. Non-Genetic and Genetic Fixed Effect Analysis

^{2}), and Pearson Product-Moment Correlation Coefficient (ρ) providing information regarding the existence of differences in the distribution across levels within the same factor and the variance explanatory power of these independent variables factors.

#### 3.4. Genetic Model Comparison, Phenotypic and Genetic Parameters Estimation

_{G}) and phenotypic (r

_{P}) correlations [39] are shown in Table 2.

#### 3.5. Predicted Breeding Values (PBV), Standard Error of Prediction (SEP), Accuracies (RTi), and Reliability (Rap) Comparison

## 4. Discussion

^{2}), thus, variance explanatory power, when compared to those models, comprises higher numbers of SNPs used in genomic selection. This is supported by Pizarro et al. [32], who reported determination coefficients or percentages of variance explained that ranged from only around 15% to 40% for the models comprising the 40 SNPs in our study.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Categorical principal component analysis (CATPCA). Rotated component loadings for each dimension included in the rotated model using the Varimax method with Kaiser normalization (Red rectangle marks all single-nucleotide polymorphisms (SNPs) significantly loading (≥|0.5|) across the seven PC dimensions, hence, contributing to the explained variance). Accessed from Pizarro Inostroza et al. [7].

**Table 1.**Estimated components of variance, heritability (h

^{2}), and standard error (SE) for milk yield (kg), protein (kg), fat (kg), solids (kg), lactose (kg), and cells somatic (cs/mL) obtained from multivariate analyses through REML methods in goat milk including and excluding αS1-Casein, αS2-Casein, β-casein, and κ-casein additive, dominance, epistatic factors as a fixed effect.

Model/Genetic Effects as a Fixed Effect | Trait (Kg) | ${\mathit{\sigma}}_{\mathit{a}}^{2}$ | ${\mathit{\sigma}}_{\mathit{p}}^{2}$ | ${\mathit{\sigma}}_{\mathit{p}\mathit{e}}^{2}$ | ${\mathit{\sigma}}_{\mathit{e}}^{2}$ | h^{2}±SE |
---|---|---|---|---|---|---|

Including genetic effects as a fixed effect. | Milk yield | 0.75450 | 1.63632 | 0.140011 | 0.74180 | 0.46±0.05 |

Fat | 0.37663 | 1.72151 | 0.204217 | 1.14066 | 0.22±0.01 | |

Protein | 0.06216 | 0.24909 | 0.0276599 | 0.15927 | 0.25±0.01 | |

Solids | 0.53164 | 2.58194 | 0.285996 | 1.76430 | 0.21±0.05 | |

Lactose | 0.03361 | 0.11198 | 0.0213750 | 0.05699 | 0.30±0.01 | |

Somatic cells | 1,450,503.8674 | 3,373,095.25 | 36,251.9 | 1,886,339.4833 | 0.43±0.07 | |

Excluding genetic effects as a fixed effect. | Milk yield | 0.34930 | 1.65896 | 0.172186 | 1.13747 | 0.21±0.01 |

Fat | 0.42176 | 1.72965 | 0.177331 | 1.13056 | 0.24±0.01 | |

Protein | 0.06541 | 0.26935 | 0.0286661 | 0.17527 | 0.24±0.02 | |

Solids | 0.67591 | 2.80513 | 0.291377 | 1.83785 | 0.24±0.01 | |

Lactose | 0.02505 | 0.11168 | 0.0114023 | 0.07523 | 0.22±0.01 | |

Somatic cells | 483,509.3208 | 2,368,170.87 | 244,535. | 1,640,126.5503 | 0.20±0.05 |

**Table 2.**Estimated heritabilities (h

^{2}) (diagonal), phenotypic (r

_{P}) (above diagonal), and genetic (r

_{G}) (below diagonal) correlations for milk yield (kg), protein (kg), fat (kg), solids (kg), lactose (kg), and somatic cells (cs/mL) obtained in bivariate analyses through REML methods in goat milk including and excluding αS1-Casein, αS2-Casein, β-casein, and κ-casein additive, dominance, epistatic factors as a fixed effect.

Model/Genotype as a Fixed Effect | Trait | Milk Yield | Fat | Protein | Solids | Lactose | Somatic Cells Count |
---|---|---|---|---|---|---|---|

Including genotype as a fixed effect | Milk yield | 0.46 | −0.41 | −0.48 | −0.46 | 0.12 | −0.24 |

Fat | −0.42 | 0.22 | 0.56 | 0.96 | −0.10 | 0.16 | |

Protein | 0.09 | 0.43 | 0.25 | 0.71 | −0.29 | 0.29 | |

Dry mater | 0.08 | 0.85 | 0.60 | 0.21 | −0.03 | 0.15 | |

Lactose | −0.07 | 0.05 | −0.20 | 0.03 | 0.30 | −0.38 | |

Cells somatic | −0.27 | 0.18 | 0.18 | 0.16 | −0.22 | 0.43 | |

Excluding genotype as a fixed effect | Milk yield | 0.21 | −0.33 | −0.41 | −0.38 | 0.09 | −0.25 |

Fat | −0.29 | 0.24 | 0.46 | 0.95 | −0.10 | 0.16 | |

Protein | −0.33 | 0.39 | 0.24 | 0.66 | −0.28 | 0.28 | |

Dry mater | −0.34 | 0.73 | 0.51 | 0.24 | 0.03 | 0.14 | |

Lactose | 0.08 | −0.08 | −0.16 | 0.02 | 0.22 | −0.36 | |

Cells somatic | −0.18 | 0.13 | 0.24 | 0.12 | −0.32 | 0.20 |

^{a}h

^{2}± SE;

^{b}r

_{P}± SE

_{;}

^{c}r

_{G}± SE.

**Table 3.**Summary of the descriptive statistics for standard error of prediction (SEP) and accuracies (RTi) between models when genetic effects (additive, dominance, or epistatic effects) were included or excluded.

Model | Including Additive, Dominance and Epistatic Genetic Effects | Excluding Additive, Dominance and Epistatic Genetic Effects | |||||||
---|---|---|---|---|---|---|---|---|---|

Descriptive | Min | Max | Mean | SD | Min | Max | Mean | SD | |

Parameters | |||||||||

Milk yield (Kg) | SEP | 0.59 | 0.69 | 0.59 | 0.01 | 0.87 | 1.02 | 0.87 | 0.01 |

Rti | 0.00 | 0.66 | 0.01 | 0.03 | 0.00 | 0.02 | 0.00 | 0.00 | |

Fat (Kg) | SEP | 0.00 | 0.76 | 0.65 | 0.01 | 0.61 | 0.72 | 0.61 | 0.01 |

Rti | 0.00 | 0.96 | 0.01 | 0.05 | 0.00 | 0.02 | 0.00 | 0.00 | |

Protein (Kg) | SEP | 0.17 | 0.30 | 0.26 | 0.00 | 0.25 | 0.29 | 0.25 | 0.00 |

Rti | 0.00 | 0.76 | 0.01 | 0.04 | 0.00 | 0.02 | 0.00 | 0.00 | |

Solids (Kg) | SEP | 0.00 | 0.96 | 0.82 | 0.02 | 0.73 | 0.85 | 0.73 | 0.01 |

Rti | 0.00 | 0.96 | 0.02 | 0.06 | 0.00 | 0.02 | 0.00 | 0.00 | |

Lactose (Kg) | SEP | 0.13 | 0.19 | 0.16 | 0.00 | 0.18 | 0.21 | 0.18 | 0.00 |

Rti | 0.00 | 0.61 | 0.01 | 0.03 | 0.00 | 0.02 | 0.00 | 0.00 | |

Somatic cells count (cs/mL) | SEP | 554.46 | 815.37 | 696.41 | 8.81 | 1204.37 | 1412.25 | 1206.80 | 14.82 |

Rti | 0.00 | 0.60 | 0.01 | 0.03 | 0.00 | 0.02 | 0.00 | 0.00 |

**Table 4.**Pearson Product Moment (ρ) correlation comparison of Predicted breeding values’ (PBVs), Standard error of prediction (SEP) and accuracies (RTi) between models when genetic effects (additive, dominant, or epistatic effects) were included or excluded.

PBV Parameters | Pearson Product Moment Correlation |
---|---|

SEP Milk yield (Kg) | 0.994 ** |

RTi Milk yield (Kg) | 0.103 ** |

SEP Fat (Kg) | 0.674 ** |

RTi Fat (Kg) | 0.097 ** |

SEP Protein (Kg) | 0.671 ** |

RTi Protein (Kg) | 0.099 ** |

SEP Solids (Kg) | 0.022 ** |

RTi Solids (Kg) | −0.009 |

SEP Lactose (Kg) | 0.045 ** |

RTi Lactose (Kg) | 0.012 * |

SEP Somatic cells (cs/mL) | 0.036 ** |

RTi Somatic cells count (cs/mL) | −0.010 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pizarro Inostroza, M.G.; Landi, V.; Navas González, F.J.; León Jurado, J.M.; Delgado Bermejo, J.V.; Fernández Álvarez, J.; Martínez Martínez, M.d.A.
Integrating Casein Complex SNPs Additive, Dominance and Epistatic Effects on Genetic Parameters and Breeding Values Estimation for Murciano-Granadina Goat Milk Yield and Components. *Genes* **2020**, *11*, 309.
https://doi.org/10.3390/genes11030309

**AMA Style**

Pizarro Inostroza MG, Landi V, Navas González FJ, León Jurado JM, Delgado Bermejo JV, Fernández Álvarez J, Martínez Martínez MdA.
Integrating Casein Complex SNPs Additive, Dominance and Epistatic Effects on Genetic Parameters and Breeding Values Estimation for Murciano-Granadina Goat Milk Yield and Components. *Genes*. 2020; 11(3):309.
https://doi.org/10.3390/genes11030309

**Chicago/Turabian Style**

Pizarro Inostroza, María Gabriela, Vincenzo Landi, Francisco Javier Navas González, Jose Manuel León Jurado, Juan Vicente Delgado Bermejo, Javier Fernández Álvarez, and María del Amparo Martínez Martínez.
2020. "Integrating Casein Complex SNPs Additive, Dominance and Epistatic Effects on Genetic Parameters and Breeding Values Estimation for Murciano-Granadina Goat Milk Yield and Components" *Genes* 11, no. 3: 309.
https://doi.org/10.3390/genes11030309