Material and methodsTop

Mexican genetic evaluations

Records for milk, fat and protein yields, fat and protein contents, CI, and AFC for Mexican Holstein cattle recorded from 1997 to 2008 were obtained from the Mexican Holstein Association (Querétaro, Mexico). Data for milk, fat, and protein yields were adjusted to 305 days mature equivalent by the Mexican Holstein Association (Montaldo et al., 2010). Data were edited to include only records from cows with known sire, dam, and date of birth. Only records with 100 or more days in milk were included, with a minimum CI of 293 days (biological limit) and a maximum of 790 days (3 standard deviations of the mean). Age at first calving lower than 549 days (biological limit), or higher than 1,271 days (three standard deviations from the mean), were also excluded from the analyses. Contemporary groups were required to provide at least 3 records for milk yield trait analyses. For production and milk composition traits, values beyond 3 standard deviations from the mean were also excluded from the analyses. Additionally, for fat and protein contents, minimum and maximum included values were determined from their distributions and from the usual admissible values allowed for these traits (Montaldo et al., 2010). Admissible values ranged from 1.9 to 5.0% for fat content, and from 2.4 to 3.8% for protein content. Values outside these ranges were considered missing values for both contents, as well as for the fat and protein yields data for the same lactation record. The number of observations per trait included in the analyses after edits is shown in Table 1. The pedigree file included 323,638 animals born between 1950 and 2007, which included 14,482 sires and 158,363 dams. Three calving seasons (or birth seasons for AFC) were defined according to their effect on the studied traits and to the distribution of the observations as (1) January-April, (2) May-August, and (3) September-December.

Table 1. Descriptive statistics for fertility, production and milk composition traits in Holstein cattle in Mexico. SD: standard deviation.

In order to estimate genetic parameters, data were analyzed using single-trait repeatability models, which included calving season by parity number, and herd-year-season of calving as fixed effects, and animal, sire by herd, and permanent environment as random effects. In order to analyze AFC, an animal model that included herd-year-birth season as a fixed effect, and the random effects of animal, and sire by herd, was used. Analyses were performed using AI-REML procedure using ASReml software (Gilmour et al., 2009).

The model expressed in matrix notation was as follows:

y = Xb + Za + Wp + Ks + e

in the case of AFC it was:

y = Xb + Za + Ks + e

where y is the vector of observations for the trait; b is the vector of fixed effects; a is the vector of animal random effects; p is the vector of the random permanent environmental effects; s is the vector of sire-herd effects; e is the vector of random residual effects; and X, Z, W and K are the incidence matrices assigning observations to fixed, random animal, random permanent environmental, and sire by herd random effects, respectively.

Expectations (E) and covariance matrices (V) of random vectors are described in the following equations:

where σ²_a, σ²_p, σ²_s, σ²_e and are scalars, A is the numerator relationship matrix and I is an identity matrix.

United States genetic evaluations

Genetic evaluations for the US were obtained directly from the USDA AIPL web site (USDA-ARS, 2009). This file contained information from 202,630 sires born from 1950 to 2001, of which 8,991 also had Mexican genetic evaluations; while only between 121 and 462 sires out of this subset (depending on the analyzed trait) had Mexican genetic evaluations with a reliability = 0.5, and also had genetic evaluations in Canada for yield and milk content traits. Insofar as the US neither generates generate genetic evaluations for CI nor AFC, the correlation between CI in Mexico and daughter pregnancy rate (DPR) in the US was calculated. A total of 747 sires with DPR genetic evaluations in the US with a minimum reliability of 0.20 for the Mexican CI genetic evaluations were used.

Canadian genetic evaluations

For AFC and CI, the Canadian genetic evaluations were obtained directly from the Canadian Dairy Network (Guelph, ON, Canada), which included the genetic evaluations of 4,658 sires, of which 747 and 682 also had Mexican genetic evaluations with a reliability = 0.20 for AFC and CI, respectively. The Canadian genetic evaluations for yield and milk composite traits were obtained from the Canadian Dairy Network web site (Canadian Dairy Network, 2009) which contained information from 9,084 sires born from 1969 to 2006, of which 2,575 also had Mexican genetic evaluations.

Genetic correlation estimates

Genetic correlations between countries (rg) were obtained from the observed correlations between the predicted transmitting ability (PTA) of each bull in two countries divided by the square root of the product of their average reliabilities according to the following formula (Calo et al., 1973):

where rg = estimated genetic correlation, ro = estimated correlation among PTAs, areli = average reliability of PTAs on country i, arelj = average reliability of PTAs on country j.

Simulation of genetic correlations

In order to account for a possible underestimation of the genetic correlation due to selection of the sires from the country of origin, estimates of genetic correlations between PTAs in Mexico-Canada and Mexico-US obtained by [1] were compared to genetic correlations obtained from simulated PTAs in two environments assuming no G×E interaction effects and using the same number of sires and PTA reliability from the real populations (see Montaldo & Pelastre-Cruz, 2012, for more details about the simulation procedure). Thus, correlations from simulated data provide an upper limit for the estimated genetic correlation if no genotype x environment interaction effects were present. Simulated PTAs were obtained using a sire model with 10,000 replicates. The PTAs from the top 50 and 90% sires (selection intensity 0.80 and 0.20) in their country of origin for milk yield traits and fat or protein contents and reproductive traits (Powell et al., 2003), respectively, were sampled to obtain the simulated data. Heritabilities used for simulation for Mexican Holsteins are shown in Table 2. The number of sampled sires and corresponding reliabilities are shown in Tables 3 to 5 for each trait. Heritabilities for yield traits and DPR for USA were obtained from published estimates (VanRaden et al., 2004). Heritabilities for Canada were assumed as 0.43 for milk yield, 0.34 for fat yield, 0.40 for protein yield (Interbull, 2013b), 0.088 for AFC, and 0.099 for CI (Jamrozik et al., 2005). Heritabilities for fat and protein contents were assumed as 0.56 both for Canada and US (Castillo-Juárez et al., 2000).

Table 2. Parameters estimated for the studied traits for Mexican Holstein cattle.

Results

Descriptive statistics for the Mexican population for the studied traits are shown in Table 1. Genetic parameters estimated for the studied traits for Mexican Holstein cattle are shown in Table 2. Heritabilities for production traits were in the range of 0.18 ± 0.01 to 0.20 ± 0.01. Estimates for fat and protein content were 0.46 ± 0.01 and 0.49 ± 0.01, respectively, and those for AFC and CI were 0.06 ± 0.01 and 0.03 ± 0.01, respectively. Estimated and genetic correlations from simulated data between Mexico and Canada for AFC, using different minimum reliability levels of Mexican PTA, are shown in Table 3. The minimum reliability for Mexican PTAs considered varied from 0.20 to 0.50 which included different numbers of sires (from 61 to 747). Genetic correlations varied from 0.33 ± 0.13 to 0.48 ± 0.16. Genetic correlations were lower than those calculated using a similar simulated data structure, which suggests the presence of G×E effects. All 1-tailed z-tests to compare if genetic correlations from actual data were smaller than the genetic correlations from simulated data for AFC were significant (p<0.01).

Table 3. Genetic correlations estimated and from simulated data between Mexico and Canada for age at first calving, according to different minimum reliability levels of Mexican predicted transmitting abilities (PTAs).

Genetic correlations between Mexican CI and US DPR (Table 4) which are shown multiplied by -1 to facilitate interpretation, varied from 0.64 ± 0.07 to 0.73 ± 0.16. Genetic correlations for CI between Mexico and Canada (Table 4) varied between 0.48 ± 0.07 and 0.69 ± 0.13. Estimated and genetic correlations from simulated data between Canada and the US were very close to 1, irrespective of the difference in trait definition between these countries (Table 4). These results suggest the presence of moderate G×E effects for CI between Mexico-Canada and Mexico-US, but not between Canada-US. All 1-tailed z-tests to compare if genetic correlations from actual data were smaller than the genetic correlations from simulated data for CI were significant (p<0.01).

Table 4. Genetic correlations estimated and from simulated data for calving interval in Mexico (MEX) and Canada (CAN) and daughter pregnancy rate in the United States (US), based on different minimum reliability levels of Mexican predicted transmitting abilities (PTAs).

Genetic correlations between Canada and the US for milk (0.97 ± 0.03), fat (0.95 ± 0.03), and protein (0.96 ± 0.03) yields (Table 5) were near unity, and were not statistically different from those obtained between Mexico and Canada (0.85 ± 0.06, 0.84 ± 0.06, and 0.92 ± 0.06) nor to those obtained between Mexico and US (0.86 ± 0.03, 0.85 ± 0.06, and 0.90 ± 0.06) for PTAs with reliabilities = 75%. Correlations from simulated data for yield traits with a minimum reliability of 75% in Mexico and assuming a selection intensity of 0.80 for these traits, were notably similar to the estimated values. Correlations from simulated data using a minimum reliability of 50% and similar selection intensity were lower than the estimated correlations, probably because the selection intensity assumed in simulations was too high in this case. Overall, these results suggest that there are no, or very small G×E effects for these traits between the countries studied.

Table 5. Genetic correlations estimated and from simulated data for milk, fat and protein yield, and fat and protein contents between Mexico (MEX), Canada (CAN) and the United States (US) for sires evaluated in the three countries according to different minimum reliability of Mexican predicted transmitting abilities (PTAs).

For fat and protein contents (Table 5) genetic correlations between Mexico-Canada (0.87 ± 0.04 to 0.89 ± 0.04) and Mexico-US (0.89 ± 0.04 to 0.91 ± 0.04) were moderately lower than those between Canada-US (0.99 ± 0.01) and to their corresponding simulated values, using a selection intensity of 0.20 (0.95 ± 0.02 to 0.97 ± 0.01). These results suggest small GxE effects for these traits between Mexico-Canada and Mexico-US. All 1-tailed z-tests to compare if genetic correlations from actual data were smaller than the genetic correlations from simulated data for fat and protein contents were significant (p<0.01).