Evaluation of the relationship between residual methane emission and residual feed intake in lactating dairy cows using frequentist and Bayesian models.

Residual methane (CH4) emission (RCH4) has been proposed as a promising indicator trait to identify dairy cows with inherently low enteric CH4 emissions without compromising production. We compiled a database of 1,060 individual records from 546 lactating dairy cows from 37 respiration chamber studies representing multiple breeds, diets, and production levels. Residual CH4 was calculated as the difference between observed and predicted CH4 emission (g/d) from a model including DMI and BW as predictors, whereas RFI was derived as observed minus predicted DMI using ECM, metabolic BW, and energy balance (EB) as predictors. Because EB in the present RFI implementation was derived partly from DMI, while DMI was also a predictor of RCH4, this specific implementation introduces a shared mathematical dependency that may contribute to the observed RCH4-RFI association. This dependency is specific to the present trait formulation and is not an inherent property of RFI methodology. Mixed-effects models indicated weak but statistically significant associations between RCH4 and RFI or residual ECM (observed minus predicted ECM). Cows classified as low RCH4 emitted less CH4 (g/d) and had lower CH4 yield (g/kg DMI) and emission intensity (g/kg ECM) than medium- and high-RCH4 cows; however, OM digestibility did not differ among groups. In contrast, cows classified as low-RFI were associated with higher apparent OM digestibility, greater production efficiency, and lower CH4 production and intensity compared with cows classified as medium- and high-RFI. Bayesian multivariate modeling indicated that the association between RCH4 and RFI resided primarily in the residual covariance rather than in structured between-study covariance. The covariance-partitioning model estimated a modest positive residual correlation (ρ = 0.27), whereas the regression-based hierarchical model estimated a smaller and uncertain residual correlation (ρ = 0.11, 95% CrI: -0.49 to +0.64). Structured between-study variation was minimal in both approaches. Collectively, these findings provide limited evidence that RCH4 represents a biologically independent efficiency trait. After accounting for hierarchical covariance, the association between RCH4 and RFI was weak, with considerable uncertainty in its estimated magnitude. In contrast, cows classified as low RFI were associated with higher apparent digestibility, lower estimated maintenance ME requirements, and lower CH4 production and intensity than cows classified as medium- and high-RFI. These results highlight the need for caution when interpreting RCH4 as an indicator of biological efficiency. Importantly, this study provides a biological and statistical evaluation of RCH4 rather than an assessment of genetic responses to selection.