Aridity index and rain season classifications

Definition of CG using the RC criterion considered the average of pluvial precipitation of the herd site and considering only rainy and dry categories to classify each month-season according to their weather classification (Magaña and Segura, Reference Magaña and Segura1997; Rivera et al., Reference Rivera, Ramírez, Moncada and Trujillo2013; Nuñez et al., Reference Núñez, Ramírez, García, Larios and Hidalgo2021). The RC criterion is currently used for national GE of Braunvieh cattle (Nuñez et al., Reference Núñez, Ramírez, García, Larios and Hidalgo2021).

In the other hand, a new approach based on an AI estimates, was used to classify season for inclusion into contemporary grouping for BW and WW dates based on herd localization using Pro.Clima V.1.0 App (Parra et al., Reference Parra, Ortiz, Herrera and Vega2020). This approach is described as follows:

Climatological information from the historical data bank of the National Water Commission (Comisión Nacional del Agua, by its Spanish letters) was extracted by the daily information quick extractor (ERICIII) and adapted to an R script for further analysis (R Core Team, 2018).

Meteorological data from 4500 weather stations from 1985 to 2015 were extracted, including daily rain, temperatures (minimum, maximum and means), solar radiation, relative humidity and wind velocity records. The information included all meteorological stations from Mexico. The evapotranspiration (ETo) was estimated and recalibrated by the formula suggested by Lobit et al. (Reference Lobit, Gómez, Bautista and Lhome2018), which was based on the Penman–Monteith method as follows:

$$\eqalign{ {\rm ETo} &= 0.1555{\rm \;Ra\;}\sqrt {( {T{\rm max}-T{\rm min}} ) } \cr &\quad \times \! \left({9.967{\rm \;}\,{10}^{{-}2} + 4.280{\rm \;}\,{10}^{{-}3}{\rm \;}\displaystyle{{T{\rm max} + T{\rm min}} \over 2}} \right)}$$

where Ra = solar radiation, Tmax = maximum temperature, Tmin = minimum temperature.

After the ETo recalibration, the AI was calculated for each day and meteorological station according to the formula proposed by Middleton and Thomas (Reference Middleton and Thomas1992) and Spinoni et al. (Reference Spinoni, Vogt, Naumann, Carrao and Barbosa2015) as follows:

$${\rm AI} = \displaystyle{{\sum\nolimits_{i = 1}^m {\left({\displaystyle{{P_i} \over {{\rm ET}{\rm o}_i}}} \right)} } \over m}$$

where AI = aridity index, P = daily pluvial precipitation and ETo = recalibrated ETo, for i = 1 to the mth day of the month.

Posteriorly, average estimates by month were used to classify each season in four categories suggested by Middleton and Thomas (Reference Middleton and Thomas1992), 0–0.20 = arid, 0.21–0.50 = semiarid, 0.51–0.65 = subhumid and > 0.65 = humid.

Model comparisons

Two approaches were used to compare the effect of season classification for the definition of CG. First, four linear mixed models were fitted, one for each trait studied (BW; WW). Models included the fixed effects of herd, year, sex and season, the linear and quadratic covariate effect of dam age, the linear covariate effect of Braunvieh purity percentage and the random effects of sire and dam. The only difference between the two models was the classification of the season according to the RC and AI criteria. The solutions of the mixed-model equations were obtained using maximum likelihood, as implemented in the MIXED procedure of the SAS package version 9.1 (SAS Institute Inc., Cary, NC, USA). The goodness of fit measures of the models was evaluated through: −2LogL (log-likelihood), AIC (Akaike information criterion; Akaike, Reference Akaike1973), corrected AIC and BIC (Bayesian information criterion; Schwarz, Reference Schwarz1978). The AIC and BIC goodness of fit measures were estimated as follows: AIC = −2LogL + 2k, and BIC = −2LogL + Log(n) × k, where LogL is the log-likelihood estimated from each assessed genetic model, k is the number of parameters (Akaike, Reference Akaike1973) and n is the number of records. The lower these statistics the better the models.

The second approach considered fitting a bivariate model including the season classifications into the CG herd-year-season structure, this structure was selected considering the current structure of GE for Braunvieh cattle in Mexico. The bivariate animal model used a pedigree size of 46 233 animals and included the random effects of sire and dam and covariance between them. For each model, fixed effects of CG (herd-year-season) and sex, the linear and quadratic covariate effect of dam age, and the linear covariate effect of purity percentage were included. These analyses were carried out using the software MTDFREML (Van Vleck and Boldman, Reference Van Vleck and Boldman1993).

Since the difference among models was the RC and AI in the CG structure, and the number of parameters for each model was the same, an exploratory comparison between models was considered using, −2LogL and computing AIC and BIC goodness of fit measures, to choose best model as previously described.

Estimates of (co)variance components, direct and maternal heritabilities, the genetic correlation between direct and maternal genetic effects, and environmental proportion effects were computed. Genetic correlations between direct and maternal effects for both traits were also estimated.

The effect of criteria to define season on the GE was evaluated on the changes of expected progeny differences (EPD), accuracies (ACC) and prediction error variances (PEV) for BW and WW of the top 10% animals selected based on EPD for WW. A paired t test analysis was performed between EPD, ACC and PEV of both models, considering the 10% top animals selected independently by WW direct (WWd) EPD or ACC, using the TTEST procedure of SAS version 9.1 (SAS, 2017). Finally, the regression of WWd EPD and ACC from those sires with more than 15 offspring was fitted to graphically illustrate those changes.