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.

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:

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.

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 correlations between countries (r _g) 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):

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).

Average AFC for Mexican heifers was 771 days (SD = 90), similar to the 778 days (SD = 89) found in US Holsteins (Cole & Null, 2010). Average CI for Mexican Holsteins was 424 days (SD = 90), which is only slightly higher than the value of 404 days (SD = 66) for US Holsteins for the period 1980-2004, but with a positive time trend (Hare et al., 2006). Average AFC for Canadian Holsteins born in 2008 was 782 days (SD = 64) and average CI for primiparous Canadian Holstein cows born in 2008 was 399 days (SD = 54) (Jamrozik et al., 2005).

Means for milk yield, fat yield, protein yield, and fat content were lower than the corresponding means for registered US Holsteins for the same period (USDA-ARS, 2009). by 6, 10, 1, and 6%, respectively, while for protein content it was 3% larger. This relatively small difference is consequence of the good management in registered Holstein herds in Mexico. Breeding decisions may also have contributed to the small difference in production level between the Mexican and the Canadian and US populations. Mexican means for milk yield, fat yield, protein yield, and fat content were larger than the corresponding means for registered Canadian Holsteins for the period 2001-2008 by 13, 6, and 11%, respectively, and were 8 and 3% less for fat and protein content, respectively (ICAR, 2013), indicating that small differences exist with respect to Canada as well, albeit slightly larger compared to those for the US.

Heritability for AFC (0.06 ± 0.01) was close to the estimate for US (0.03) (Cole & Null, 2010) and Canadian Holsteins (0.09) (Jamrozik et al., 2005). Nevertheless, it was lower than a previous estimate (0.28) for the same Mexican Holstein population (Montaldo et al., 2009). as well as to estimates from the US (0.20 - 0.33) (Ruiz-Sánchez et al., 2007). Differences for published AFC heritabilities may be due to within-herd confounded genetic and environmental effects (Cienfuegos et al., 2006), implying that it is necessary to include the herd by sire interaction effect in the statistical models used to analyze this trait to avoid inflated heritability estimates (Mark, 2004).

Heritability for CI (0.03 ± 0.01) confirmed the low (but above zero) value previously estimated for this population (Montaldo et al., 2009). This estimate is similar to estimates for CI or days open from studies from several countries in the range of 0.02 to 0.04 (Haile-Mariam et al., 2003, 2008; Wall et al., 2003; VanRaden et al., 2004; Jorjani, 2006a), but it was smaller than an estimate from Canada (0.10) (Jamrozik et al., 2005). These differences in heritability values may be related to differences in herd reproduction management, climate, and recording of these traits across countries.

Heritability estimates for milk, fat, and protein yields (0.18 ± 0.01, 0.20 ± 0.01, and 0.19 ± 0.01, respectively) (Table 2) were close to the lower boundary of the range of published values for Interbull countries (0.19-0.59) for milk production traits (Mark, 2004). Heritabilities in the current study were similar to estimates using data from Spain (González-Recio et al., 2006). Our heritability estimate for fat yield (0.20 ± 0.01) was similar to that estimated for Australian cows (0.17 to 0.22) (Calus et al., 2005; Haile-Mariam et al., 2008). Management and climatic effects likely modify the way Holstein cows react to these influences.

In a study using three US regions, heritability for fat content was estimated varying from 0.32 to 0.41 (Carabaño et al., 1990), which was slightly lower than that observed in our study (0.46). Our estimate is within the range (0.40 to 0.52) estimated for Australian dairy cattle and different herd production levels (Calus et al., 2005). In Canadian Holsteins, heritability for fat and protein contents ranged from 0.53 to 0.59 across parities (Miglior et al., 2007). Heritabilities estimated for US Holstein first calving cows for fat and protein contents were both 0.56 (Castillo-Juárez et al., 2000), slightly above that observed in our study of 0.46 ± 0.01 and 0.49 ± 0.01, respectively.

Fertility traits. Although relatively low PTA reliabilities were used to estimate genetic correlations for AFC and CI, estimated genetic correlations may not be seriously underestimated, since there is no strong selection or correlated responses for these traits (Powell et al., 2003; Cole & Null, 2010). Therefore, the observed values < 1 and significantly lower than correlations obtained from simulated data indicate the existence of important and moderate G×E effects for AFC, and CI, respectively. These values are also in contrast to higher estimates obtained for yield traits.

There are few estimates of the genetic correlation for AFC between countries. This correlation between Colombia and Brazil was estimated as 0.78 Cerón-Muñoz et al. (2004) which indicates G×E effects of moderate magnitude for AFC between these countries.

We can assume that the larger G×E effects for AFC between Mexico and Canada may be related to differences in heifer rearing systems or climatic factors between the two countries, even if averages for AFC were approximately similar in the two populations. Climatic and management differences may explain also the moderate G×E effects found between CI in Mexico and Canada and with daughter pregnancy rate in the US.

The genetic correlation between DPR in the US and CI in Canada estimated in our study (= 0.93), was similar to that obtained between DPR in the US and days open (multiplied by -1) in Spain (0.94) but greater than the genetic correlation between DPR in the US and first service to conception (multiplied by -1) in Canada (0.72) (Nilforooshan et al., 2010). These results suggest that some genetic correlation estimates lower than 1 observed between countries for fertility traits are likely due to different trait definitions, rather than evidence of G×E effects (Jorjani, 2005). Differences in trait definition however is unlikely a reason for the small and mostly not-significant ( p>0.10) differences found in this paper between the estimated correlations Mexico-Canada and Mexico-US for CI or DPR.

The range of estimates of genetic correlations of reproductive interval traits (CI, days open) between 14 and 17 countries used in international genetic evaluations for Holsteins (Interbull, 2013c), varied from 0.60 to 0.97 with an average of 0.84. Specifically, the genetic correlation between days open in Canada (multiplied by -1) with DPR in US used by Interbull is 0.88, not far from the estimate of 0.94 obtained in this study. Published genetic correlation estimates across countries for CI in a range of 0.82 to 0.96 (Jorjani, 2006b) are higher, in general, than our higher values observed between Mexico and Canada (0.69 ± 0.13) and between CI in Mexico and DPR in the US (0.73 ± 0.16). Moderate G×E effects found between CI in Mexico and CI in Canada, or between CI in Mexico and DPR in the US, may be caused by differences in reproductive herd management and climatic effects in the three populations studied.

Milk yield traits. Genetic correlations were estimated as 0.88, 0.87, and 0.87 for milk, fat and protein yields, respectively, as an average for the 27 countries members of Interbull. The average correlation for the 7 core populations with information for all traits, excluding clinical mastitis and stillbirth, was 0.92 for milk, fat, and protein yields, with a range of ± 0.07-0.08 (Mark, 2004). More recent estimates indicate lower genetic correlations for yield traits between grazing systems in New Zealand with other countries (0.75-0.76) compared to those for Canada-USA (0.92-0.94) (Interbull, 2013a). The range of genetic correlations for all countries for milk, fat and protein yields was 0.75-0.96. Interbull estimates of genetic correlations between Argentina or Uruguay and Canada, and between Argentina or Uruguay and US for yield traits are all equal to 0.85 (Interbull, 2013a).

Comparison with simulated values under the hypothesis of no G×E, indicates that G×E effects between Mexico-Canada and Mexico-US are probably small for these traits. Lack of G×E for milk yield traits may be related to the high production levels, which have increased over time (Montaldo et al., 2009, 2010), making the production environment for this population gradually closer to that in the US, and the mostly temperate climate of the studied registered Mexican Holstein population in herds managed under a conventional production system (Montaldo et al., 2010). Genetic correlations for Mexico-Canada and Mexico-US for milk yield traits were greater than estimates found for New Zealand-US which support the idea that higher r _g values are associated with more similar conventional production systems between Mexico and the US for Holsteins. As most of the herds in the analyzed Mexican population are located in high plateaus with temperate climates, we may conclude that altitude above sea level (lower than 3000 m), is not associated with strong G×E effects for milk yield traits in Holsteins. Small G×E effects for fat and protein contents may be related to differences in feeding and management systems across countries.

Genetic correlation for milk traits between Canada or the US with the remaining portion of the dairy population of Mexico (grade Holsteins, crossbreeds) or for lower input production systems may be different and is a topic for future studies.

In conclusion, strong G×E interaction effects between Mexico and Canada were found for AFC, and moderate G×E interaction effects were found between Mexico and Canada for CI, and between CI in Mexico with DPR in the US. No G×E interaction effects between Mexico with Canada and the US for milk yield traits were found. There were small but significant G×E interaction effects for fat and protein contents. These findings need to be taken into account when selecting sires evaluated in Canada and the US to be used in Mexican Holstein herds.