# Comparison of Statistical Models for Days to 114 kg and Backfat Depth

North Carolina State University Swine Genetics Research from 2001.

By Todd See

Five models were studied for the genetic evaluation of backfat depth and days to 114 kg in Duroc swine. Models were compared using likelihood ratio tests on a chi-square distribution. The results clearly indicated the importance of including the litter effect. Results also indicated that for days to 114 kg the model providing the best fit (p < .001) included all random effects, while for backfat (p < .005) pe was not included. However, permanent environmental effects account for only 1% of the variation for days and can probably be safely ignored. In addition, the complete model resulted in markedly larger heritability estimates due in part to the large negative genetic correlations observed between direct and maternal effects. The data structure associated with the estimation of this correlation should be considered when selecting a model for genetic evaluations.

**Introduction**

The objective of this project was to evaluate the suitability of differing animal models for the genetic evaluation of growth rate and backfat depth in swine. Most evaluations of backfat depth and days to 114 kg from swine utilize a model that includes direct genetic and litter as random effects. Applying the model with the best fit should result in the most accurate genetic evaluation. Therefore more complete models should be considered. However, inaccuracies due to data structure and computational complexity should be considered.

**Material and Methods**

Data were provided by the United Duroc Swine Registry. The analysis dataset consisted of 44,223 records, 1677 contemporary groups and 220 levels for sex(herd). Five single trait animal models (Table 1) were compared for days and backfat depth. The fixed part of the model (contemporary group and sex(herd) was constant across all five models (Table 1).

(Co)variance components were estimated using the MTDFREML computer programs. This set of programs determines the best set of parameter estimates by minimizing -2 times the restricted log likelihood function (L), that is, -2L = constant + log|R| + log|C| + y’Py where C is the full-rank coefficient matrix for the mixed model equations and y’Py is the weighted sums of squares for the residuals. A likelihood ratio test was used to compare the six models. This statistical procedure consists of subtracting the value of – 2L from the model with more parameters from -2L corresponding to the model with fewer parameters. The difference was compared to a chi-square distribution with degrees of freedom equal to the difference in the number of parameters estimated for the two models. The restricted log likelihood function, order and number of iterations (Table 2) were obtained at convergence of the MTDFREML iterative process.

#### Table 1. Models

Model^{1} |
s^{2}g |
s^{2}m |
sg,m | s^{2}c |
s^{2}pe |
s^{2}e |
---|---|---|---|---|---|---|

1 g+e | x | x | ||||

2 g+c+e | x | x | x | |||

3 g+m+c+e | x | x | x | x | ||

4 g+m+r+c+e | x | x | x | x | x | |

5 g+m+r+c+pe+e | x | x | x | x | x | x |

^{1}g=random genetic effect, m=random maternal genetic effect, c=random litter effect, pe=random effect of permanent maternal environment, and e=random residual effect.

#### Table 2. Model information and likelihood estimates.

Iterations | -2 log likelihood | ||||
---|---|---|---|---|---|

Order | BF | Days | BF | Days | Parameters |

1 52338 | 26 | 31 | 142717.0 | 271586 | 2 |

2 64627 | 49 | 43 | 142420.6 | 268962 | 3 |

3 115068 | 73 | 79 | 142420.3 | 268960 | 4 |

4 115068 | 140 | 198 | 142403.1 | 268869 | 5 |

5 121983 | 278 | 410 | 142403.1 | 268770 | 6 |

**Results and Discussion**

Likelihood ratio tests (Table 3) indicate that for days to 114 kg the model providing the best fit (p < .001) included all random effects, while for backfat (p < .005) pe was not included. However, permanent environmental effects account for only 1% of the variation for days and can probably be safely ignored. Genetic parameters estimated from all models are shown in Table 4 for days and Table 5 for backfat depth. Heritability estimates from the best fitting models were .45 for days and .43 for backfat depth. Heritability for maternal genetic effects was .10 and .03 for days and backfat depth. Heritability estimates from the Model 2 that balances fit with computational ease and data structure were .29 for days and .35 for backfat.

#### Table 3. Likelihood ratio test (LRT) between models for days (upper off-diagonals) and backfat depth (lower off-diagonals) models.

Model | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

1 g+e | – | ** | ** | ** | ** |

2 g+c+e | ** | – | NS | ** | ** |

3 g+m+c+e | ** | NS | – | ** | ** |

4 g+m+r+c+e | ** | * | ** | – | ** |

5 g+m+r+c+pe+e | ** | * | * | NS | – |

NS p > .1 *p < .005 **p < .001

#### Table 4. Genetic parameters for days to 114 kg in Duroc swine.

Model | h^{2} |
m^{2} |
c^{2} |
pe^{2} |
r_{gm} |
---|---|---|---|---|---|

1 g+e | .55 | ||||

2 g+c+e | .29 | .23 | |||

3 g+m+c+e | .29 | .01 | .23 | ||

4 g+m+r+c+e | .45 | .11 | .23 | -.76 | |

5 g+m+r+c+pe+e | .45 | .10 | .23 | .01 | -.78 |

#### Table 5. Genetic parameters for adjusted backfat depth in Duroc swine.

Model | h^{2} |
m^{2} |
c^{2} |
pe^{2} |
r_{gm} |
---|---|---|---|---|---|

1 g+e | .46 | ||||

2 g+c+e | .35 | .08 | |||

3 g+m+c+e | .34 | .003 | .07 | ||

4 g+m+r+c+e | .43 | .03 | .07 | -.53 | |

5 g+m+r+c+pe+e | .43 | .03 | .07 | .00 | -.53 |

When maternal effects are included in the model the heritability is greatly increased, 55% for days and 23% for backfat. This increase in heritability estimate would be expected to create a wider distribution among EPDs, resulting in more desirable numbers for trait leaders.

The results clearly indicated the importance of including the litter effect (Model 2). However, to accurately estimate litter effects sows should have more than 1 litter. In this data 60% of the sows were represented by 1 litter. Consideration needs to be given to data structure and multiple litters per nucleus female. Model 3 was fit only to describe the observed increase in heritability from adding maternal genetic effects and the result do not significantly differ from model 2. The results indicate that the large negative genetic correlation between direct and maternal effects causes the increase in both direct and maternal heritabilites. To accurately estimate maternal genetic effects and correlation between direct and maternal effects sires should have multiple daughters with measured progeny and daughters should have multiple litters with measured offspring. This also raises concerns over contemporary group structure and numbers of records per female and sire.

It should also be considered that Model 2 is more conservative by not taking into account maternal and permanent environmental effects that are prone to errors due to data structure. In addition, Model 2 is easier computationally. Therefore careful consideration should be given to both Model 2 and Model 4 when selecting a model for genetic evaluations of post-weaning traits in swine.

**Implications**

Applying the model with the best fit should result in the most accurate genetic evaluation. However, inaccuracies due to data structure and computational complexity should be considered. When maternal effects are included in the model the heritability is greatly increased, 55% for days and 23% for backfat. This result is due in part to a large negative genetic correlation between direct and maternal effects. The accuracy of the estimation of this correlation should be considered when selecting a model