# Genomic Prediction in Local Breeds: The Rendena Cattle as a Case Study

^{1}

^{2}

^{*}

## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Availability

#### 2.1.1. Phenotypic and Pedigree Data

#### 2.1.2. Genotype Data

#### 2.2. Prediction Model

#### 2.2.1. Pedigree Best Linear Unbiased Prediction (PBLUP)

**y**is the vector of phenotypes,

**X**represents the incident matrix for systematic fixed effects, and

**b**is the vector of fixed effects. Two cross-classified effects were used as in [4]: the contemporary group (142 levels) and the parity order of the cow (four classes: first parity, second parity, third to seventh parity, and above the eighth parity included).

**Z**is the incident matrix of random genetic additive effects, while $a$ represents the vector of the additive genetic effects (EBVs) and $e$ is the vector of residuals sampled from a distribution $N\left(0,I{\sigma}_{e}^{2}\right)$

**,**where ${\sigma}_{e}^{2}$ is the residual variance. The additive genetic effect was sampled from a normal distribution with mean zero and variance ${\sigma}_{a}^{2}$ and a covariance structure depending on the model used. In the PBLUP, the model covariance of the random genetic effect was sampled from a distribution$N\left(0,A{\sigma}_{a}^{2}\right)$, with

**A**, which represents the identical by descendent (IBD) matrix constructed from pedigree information. All genetic and genomic prediction models were carried out with the blupf90 suite of programs [27].

**G**⊗

**A**and

**R**⊗

**I**with

**G**and

**R,**are 3 × 3 matrices, respectively, including the additive genetic and the residual (co)variances matrices, ⊗ is the Kronecker product, and

**A**and

**I**are the additive relationships matrix and an identity matrix, respectively. Prior distributions for

**G**and

**R**matrices were independent inverse Wishart. Genetic and residual correlations (r

_{a}) were calculated between trait pairs as the ratio of the covariance on the square root of the product of the respective variances.

#### 2.2.2. Single-Step Genomic Best Linear Unbiased Prediction (ssGBLUP)

#### 2.2.3. Weighted Single-Step Genomic Best Linear Unbiased Prediction (WssGBLUP)

**G**matrix was built using the following method [17]:

_{w}- Initial parameters are set to $t=1,{D}_{\left(t\right)}=I,{G}_{\left(t\right)}=\frac{M{D}_{\left(t\right)}{M}^{\prime}}{2{\displaystyle \sum}{p}_{i}\left(1-{p}_{i}\right)}$.
- GEBV ($\widehat{a}$) is obtained using ssGBLUP algorithm.
- Each ${d}_{i\left(t+1\right)}$ element of ${D}_{\left(t+1\right)}$, such as $C{T}^{\frac{\left|{\widehat{u}}_{i}\right|}{sd\left(\widehat{u}\right)}-2}$, is then calculated as in [18], where CT is a shrinkage factor determining how much the distribution of SNP effects departs from normality.
- SNP weights are normalized by keeping genetic variance constant among iteration:$${D}_{\left(t+1\right)}=\frac{tr\left({D}_{\left(1\right)}\right)}{tr\left({D}_{\left(t+1\right)}\right)}tr\left({D}_{\left(t+1\right)}\right).$$
- G is then re-built with the new obtained weights as ${G}_{\left(t+1\right)}=\frac{M{D}_{\left(t+1\right)}{M}^{\prime}}{2{\displaystyle \sum}{p}_{i}\left(1-{p}_{i}\right)}$.
- Further iterations are carried out up to convergence using WssGBLUP.

#### 2.2.4. Weighted Strategies

**A**and

**G**matrix, as reported in Supplementary Material S1.

#### 2.3. LR Cross-Validations

## 3. Results

#### 3.1. Variance Components

^{2}) and genetic and residual correlations estimated using PBLUP are reported in Table 2. All traits presented a medium to high heritability. EUROP was the trait with lowest heritability, 0.304, while ADG and DP showed an h

^{2}of 0.335 and 0.392, respectively. In addition, all traits’ pairs, as expected, presented medium to high genetic and residual correlations. ADG presented a medium-positive genetic correlation with the other two traits (0.38 on average), while DP and EUROP were strongly correlated (0.981) to be considered a unique trait.

^{2}and correlations had similar results to those estimated with the PBLUP. For what concerns h

^{2}, ADG decreased by about 0.02, while EUROP increased by about 0.04 in ssGBLUP as compared to PBLUP. On the other hand, DP remained basically unchanged comparing the two approaches. Correlations presented almost the same values in both analyses, with the only exceptions of the genetic and residual correlations between ADG and EUROP that resulted in an increase in ssGBLUP of about 0.02 and 0.08, respectively.

#### 3.2. Weighting Strategies

#### 3.3. Model Comparison

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

**A**and

^{−1}**G**

**Supplementary Material S2: Value of accuracy, dispersion, and bias divided by the genetic standard deviations (bias_std) for EUROP (1) Models presented are pedigree BLUP (PBLUP), single-step genomic BLUP (ssGBLUP), and different weighting single-step described as follow: non_linear refers to the nonlinear weighting strategies presented in the manuscript with the respective CT value, and limit_5 refers to when variance was set up to a maximum of 5. Quadratic refers to the quadratic weight applied to the SNP solutions, and sliding stands for the quadratic weight applied to a window of sliding SNPs. iter stands for the number of iterations, and NA values mean that it was not possible to obtain the solution due to blending problem between between**

^{−1}.**A**and

^{−1}**G**. Supplementary Material S3: Value of accuracy, dispersion, and bias divided by the genetic standard deviations (bias_std) for Dressing Percentage (DP). Models presented are pedigree BLUP (PBLUP), single-step genomic BLUP (ssGBLUP), and different weighting single-step described as follow: non_linear refers to the nonlinear weighting strategies presented in the manuscript with the respective CT value, and limit_5 refers to when variance was set up to a maximum of 5. Quadratic refers to the quadratic weight applied to the SNP solutions, and sliding stands for the quadratic weight applied to a window of sliding SNPs. iter stands for the number of iterations, and NA values mean that it was not possible to obtain the solution due to blending problem between

^{−1}**A**and

^{−1}**G**

^{−1}**.**

## Author Contributions

## Funding

## Institutional Review Board Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Number of animals with the phenotype (

**above**) and number of animals with the genotype (

**bottom**) for all animals used in genetic or genomic prediction. X-axes represent the birth years and y-axis the number of animals per year.

**Figure 2.**Accuracy (

**A**), dispersion (

**B**), and bias corrected by genetic standard deviations (

**C**) of breeding value estimated using different weighting strategies along the 10 iterations process of the algorithm used in WssGBLUP. The dotted line in Graphs B and C represents the expected value.

**Figure 3.**Manhattan plots for average daily gain (ADG) using different WssGBLUP strategies in iterations equal to 10; y-axes represent the percentage explained by each SNP. Variance explained was calculated with a sliding window approach.

**Figure 4.**Manhattan plots for fleshiness score (EUROP) using different WssGBLUP strategies in iteration equal to 10; y-axes represent the percentage explained by each SNP. Variance explained was calculated with the sliding window approach.

**Figure 5.**Manhattan plots for dressing percentage (DP) using different WssGBLUP strategies in iterations equal to 10; y-axes represent the percentage explained by each SNP. Variance explained was calculated with the sliding window approach.

**Figure 6.**Standardize genetic progress per year: x-axis indicates birth year of animals and y-axis the standardized EBV, from 1985 (when performance test started) to 2020 (current data).

**Table 1.**Descriptive statistics of the target phenotypic data obtained from Rendena young bulls under performance test.

Taits ^{1} | Number ^{2} | Mean | CV % | Min | Max |
---|---|---|---|---|---|

ADG (kg/d) | 1691 (690) | 1024.00 | 12.06 | 474.00 | 1562 |

EUROP (points) | 1691 (690) | 99.05 | 3.84 | 80.00 | 111.10 |

DP (points) | 1691 (690) | 54.18 | 1.74 | 50.00 | 57.70 |

^{1}ADG = Average daily gain; EUROP = in vivo fleshiness score, DP = in vivo estimate of dressing percentage.

^{2}Number of animals with records and (genotype).

**Table 2.**Mean of genetic (upper diagonal) and residual (lower diagonal) correlations and heritability (diagonal) between traits in the Rendena population, estimated with PBLUP. Numbers in parenthesis are the lower and the upper 95% highest posterior density.

ADG | EUROP | DP | |
---|---|---|---|

ADG | 0.335 (0.204 ± 0.335) | 0.364 (0.100 ± 0.597) | 0.398 (0.148 ± 0.6315) |

EUROP | 0.572 (0.660 ± 0.742) | 0.304 (0.174 ± 0.446) | 0.981 (0.962 ± 0.997) |

DP | 0.613 (0.517 ± 0.702) | 0.792 (0.753 ± 0.836) | 0.392 (0.248 ± 0.541) |

**Table 3.**Mean of genetic (upper diagonal) and residual (lower diagonal) correlation and heritability (diagonal) between traits in Rendena population, estimated with ssGBLUP. Numbers in parenthesis are the lower and the upper 95% highest posterior density.

ADG | EUROP | DP | |
---|---|---|---|

ADG | 0.313 (0.223 ± 0.489) | 0.385 (0.153 ± 0.597) | 0.392 (0.160 ± 0.622) |

EUROP | 0.651 (0.651 ± 0.718) | 0.345 (0.216 ± 0.487) | 0.985 (0.961 ± 0.999) |

CY | 0.616 (0.530 ± 0.671) | 0.790 (0.753 ± 0.826) | 0.396 (0.250 ± 0.530) |

**Table 4.**Accuracy, bias, dispersion (Disp.), and reliability (Rel.) and adjusted increased of accuracy (Incr_adj) of estimated breeding values under different models: pedigree BLUP (PBLUP), single-step genomic BLUP (ssGBLUP), and weight single-step with bias value closet to optimal value (WssGBLUP_1) and weight single-step with highest accuracy; for average daily gain (ADG), EUROP, and dressing percentage (DP).

Trait | Model | Accuracy | Bias | Disp. | Rel. | Incr_adj |
---|---|---|---|---|---|---|

ADG | PBLUP | 0.366 | −0.040 | 1.140 | 0.060 | - |

ssGBLUP | 0.472 | 0.010 | 1.045 | 0.117 | 45.10% | |

WssGBLUP_1 | 0.551 | 0.003 | 1.182 | 0.127 | 45.10% | |

WssGBLUP_2 | 0.693 | 0.020 | 1.562 | 0.206 | 49.21% | |

EUROP | PBLUP | 0.509 | −0.009 | 0.902 | 0.081 | - |

ssGBLUP | 0.596 | 0.009 | 1.100 | 0.124 | 39.98% | |

WssGBLUP_1 | 0.653 | 0.004 | 0.958 | 0.135 | 39.98% | |

WssGBLUP_2 | 0.749 | 0.014 | 1.165 | 0.192 | 45.17% | |

DP | PBLUP | 0.464 | −0.021 | 1.114 | 0.114 | - |

ssGBLUP | 0.528 | 0.021 | 1.056 | 0.158 | 26.70% | |

WssGBLUP_1 | 0.600 | 0.017 | 1.156 | 0.184 | 27.40% | |

WssGBLUP_2 | 0.727 | 0.025 | 1.468 | 0.277 | 33.90% |

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**MDPI and ACS Style**

Mancin, E.; Tuliozi, B.; Sartori, C.; Guzzo, N.; Mantovani, R.
Genomic Prediction in Local Breeds: The Rendena Cattle as a Case Study. *Animals* **2021**, *11*, 1815.
https://doi.org/10.3390/ani11061815

**AMA Style**

Mancin E, Tuliozi B, Sartori C, Guzzo N, Mantovani R.
Genomic Prediction in Local Breeds: The Rendena Cattle as a Case Study. *Animals*. 2021; 11(6):1815.
https://doi.org/10.3390/ani11061815

**Chicago/Turabian Style**

Mancin, Enrico, Beniamino Tuliozi, Cristina Sartori, Nadia Guzzo, and Roberto Mantovani.
2021. "Genomic Prediction in Local Breeds: The Rendena Cattle as a Case Study" *Animals* 11, no. 6: 1815.
https://doi.org/10.3390/ani11061815