Methane is a greenhouse gas of high interest to the dairy industry, with 57% of Australia's dairy emissions attributed to enteric methane. Enteric methane emissions also constitute a loss of approximately 6.5% of ingested energy. Genetic selection offers a unique mitigation strategy to decrease the methane emissions of dairy cattle, while simultaneously improving their energy efficiency. Breeding objectives should focus on improving the overall sustainability of dairy cattle by reducing methane emissions without negatively affecting important economic traits. Common definitions for methane production, methane yield, and methane intensity are widely accepted, but there is not yet consensus for the most appropriate method to calculate residual methane production, as the different methods have not been compared. In this study, we examined 9 definitions of residual methane production. Records of individual cow methane, dry matter intake (DMI), and energy corrected milk (ECM) were obtained from 379 animals and measured over a 5-d period from 12 batches across 5 yr using the SF 6 tracer method and an electronic feed recording system, respectively. The 9 methods of calculating residual methane involved genetic and phenotypic regression of methane production on a combination of DMI and ECM corrected for days in milk, parity, and experimental batch using phenotypes or direct genomic values. As direct genomic values (DGV) for DMI are not routinely evaluated in Australia at this time, DGV for FeedSaved, which is derived from DGV for residual feed intake and estimated breeding value for bodyweight, were used. Heritability estimates were calculated using univariate models, and correla-tions were estimated using bivariate models corrected for the fixed effects of year-batch, days in milk, and lactation number, and fitted using a genomic relationship matrix. Residual methane production candidate traits had low to moderate heritability (0.10 ± 0.09 to 0.21 ± 0.10), with residual methane production corrected for ECM being the highest. All definitions of residual methane were highly correlated phenotypically (>0.87) and genetically (>0.79) with one another and moderately to highly with other methane candidate traits (>0.59), with high standard errors. The results suggest that direct selection for a residual methane production trait would result in indirect, favorable improvement in all other methane traits. The high standard errors highlight the importance of expanding data sets by measuring more animals for their methane emissions and DMI, or through exploration of proxy traits and combining data via international collaboration.

Selecting for lower methane (CH 4 ) emitting animals is one of the best approaches to reduce CH 4 given that genetic progress is permanent and cumulative over generations. As genetic selection requires a large number of animals with records and few countries actively record CH 4 , combining data from different countries could help to expedite accurate genetic parameters for CH 4 traits and build a future genomic reference population. Additionally, if we want to include CH 4 in the breeding goal, it is important to know the genetic correlations of CH 4 traits with other economically important traits. Therefore, the aim of this study was first to estimate genetic parameters of 7 suggested methane traits, as well as genetic correlations between methane traits and production, maintenance, and efficiency traits using a multicountry database. The second aim was to estimate genetic correlations within parities and stages of lactation for CH 4 . The third aim was to evaluate the expected response of economically important traits by including CH 4 traits in the breeding goal. A total of 15,320 methane production (MeP, g/d) records from 2,990 cows belonging to 4 countries (Canada, Australia, Switzerland, and Denmark) were analyzed. Records on dry matter intake (DMI), body weight (BW), body condition score, and milk yield (MY) were also available. Additional traits such as methane yield (MeY; g/kg DMI), methane intensity (MeI; g/kg energy-cor-rected milk), a genetic standardized methane production, and 3 definitions of residual methane production (g/d), residual feed intake, metabolic BW (MBW), BW change, and energy-corrected milk were calculated. The estimated heritability of MeP was 0.21, whereas heritability estimates for MeY and MeI were 0.30 and 0.38, and for the residual methane traits heritability ranged from 0.13 to 0.16. Genetic correlations between different methane traits were moderate to high (0.41 to 0.97). Genetic correlations between MeP and economically important traits ranged from 0.29 (MY) to 0.65 (BW and MBW), being 0.41 for DMI. Selection index calculations showed that residual methane had the most potential for inclusion in the breeding goal when compared with MeP, MeY, and MeI, as residual methane allows for selection of low methane emitting animals without compromising other economically important traits. Inclusion of residual feed intake in the breeding goal could further reduce methane, as the correlation with residual methane is moderate and elicits a favorable correlated response. Adding a negative economic value for methane could facilitate a substantial reduction in methane emissions while maintaining an increase in milk production.