Evaluation of the impact of inbreeding coefficient on milk production, lactation length and first calving age of Iranian dairy cows using Quantile regression

Inbreeding, which has been defined as the mating between relative animals, leads to increase homozygous genotypes and decrease heterozygous genotypes in a population. As a result, the progenies of such mating are inbred (Wakchaure and Genguly 2015). Reduction of the traits associated with physiological efficiency and reproductive potential are the most important impacts of inbreeding in the farm animals (Filho et al. 2015, Fleming et al. 2018). Traits in livestock have different heritabilities suggesting that they are not influenced by inbreeding in a similar pattern and that although animals’ fitness is generally deteriorated; the magnitude of inbreeding depends on the type of the trait (Roff 1998; Derose and Roff, 1999, Wright et al. 2008, Mikkelsen et al. 2010). Until now, all studies regarding effects of inbreeding on productive and reproductive traits of dairy cows have been focused on using the statistical models in which inbreeding coefficient was included as covariable (Behmaram et al. 2017) or as the classified variable (Amirzadeh 2012). As inbreeding coefficient is defined as a covariable in the model, only a regression coefficient is estimated describing average changes of the trait per increasing / decreasing inbreeding coefficient. As a matter of fact, inbreeding may unequally influence the shape of distribution of the trait. Based on this assumption, this research aimed to estimate inbreeding effects on some productive and reproductive traits of Iranian dairy cows using Quantile regression statistical method.     

The data set was provided by Animal Breeding Centre, Iran. Foxpro (version 2.6) and UEStudio (version 09) software were utilized for editing initial data. Final data consisted of 580,802 records belonging to 580,802 first-parity cows distributed in 1,185 herds (over 20 provinces of the country) and calved between years 1991 and 2015. The traits under consideration were lactation milk yield (TMILK), 305d, 2X milk yield (MILK3052X), average daily milk yield (ADM), lactation length (LL), and age at the first calving (AFC). The average of the traits in the final data set was 9,447 Kg, 7,792 Kg, 30 Kg, 315 d and 25.6 m, respectively. Holstein gene percentage (HGP) of the cows in the pedigree file was set to be in the range of 50 to 100 and AFC of the cows was set to be between 18 and 48 months. Inbreeding coefficient (IC) of individual animals was calculated by CFC software (Sargolzaei et al. 2006). Fitting a series of the Quantile regression models was conducted with the use of SAS (version 9.4) software. Quantile regression, which was introduced by Koenker and Bassett (1978), extends the regression model to conditional quantiles of the response variable, such as the 90th percentile. Quantile regression is particularly useful when the rate of change in the conditional Quantile, expressed by the regression coefficients, depends on the Quantile (Chen 2005). In all the models used in this research, fixed effects of province, year and month of calving, as well as linear co-variables of HGP, IC and AFC (except of the model for AFC as the trait) were included. For TMILK, lactation length was also included as linear co-variable. Moreover, in addition to the quantile models and for the sake of estimating usual regression coefficient, general linear model (GLM) was also fitted for each trait in which a single regression coefficient of the trait on IC was defined. Ordinary least-squares regression can be used to estimate conditional percentiles by making a distributional assumption such as normality for the error term in the model. The main advantage of Quantile regression over ordinary least-squares regression is its flexibility for modeling data with heterogeneous conditional distributions (Chen 2005).      

Based upon the analysis of main pedigree file, the total number of animals was 1,941,871 (16,169 sires and 895,376 dams) among which the number of base and non-base animals were 246,388 (3,936 sires and 120,287 dams) and 1,695483 (12,233 sires and 775,089 dams), respectively.Total number of inbred animals in the pedigree was 1,211,343. Average IC for total as well as inbred animals was found to be 0.9149% (minimum 0% and maximum 47.02%) and 1.4651% (minimum 0.00038% and maximum 47.02%), respectively. For the cows with records for all five traits, IC ranged from 0 to 38.45% with the average of 1.13% (SD=1.63%). Estimate of annual change of IC was found to be 0.017 (SE=0.005), which was statistically significant (P<0.01) indicating that there is a positive increase of inbreeding in Iranian dairy cows’ population over the time. Within each trait, different Quantiles were unequally influenced as animal’s IC increased. Vast majority of the estimated regression coefficients in different Quantiles were statistically significant (P<0.05). Based upon fitting Quantile regression model and the average estimated regression coefficients, it was found that TMILK, MILK3052X, ADM, LL, and AFC changed -5.5 (Kg), -2.6 (Kg), -18 (g), 0.35 (d) and 0.30 (d), respectively as the IC of the animal increased by 1%. Estimated simple regression coefficients based on fitting GLM models were found to be -9.83 Kg (SE=1.332 Kg), -6.9 Kg (SE=0.169 Kg), -32 gram (SE=4.2 gram), 0.2087 d (SE=0.08234 d) and 0.0158 m (SE=0.0024 m), respectively and all were statistically significant (P<0.05).     

This research indicated that different Quantiles of some productive and reproductive traits of Iranian dairy cows are not equally affected by inbreeding phenomenon suggesting that Quantile regression models are needed to be utilized in the future research for evaluating the impacts of inbreeding on the other traits, which are of great economic importance.