Many countries have pledged to reduce greenhouse gases. In this context, the dairy sector is one of the identified sectors to adapt production circumstances to address socio-environmental constraints due to its large carbon footprint related to CH₄ emission. This study aimed mainly to estimate (1) the genetic parameters of 2 milk mid-infrared-based CH₄ proxies [predicted daily CH₄ emission (PME, g/d), and log-transformed predicted CH₄ intensity (LMI)] and (2) their genetic correlations with milk production traits [milk (MY), fat (FY), and protein (PY) yields] from first- and second-parity Holstein cows. A total of 336,126 and 231,400 mid-infrared CH₄ phenotypes were collected from 56,957 and 34,992 first- and second-parity cows, respectively. The PME increased from the first to the second lactation (433 vs. 453 g/d) and the LMI decreased (2.93 vs. 2.86). We used 20 bivariate random regression test-day models to estimate the variance components. Moderate heritability values were observed for both CH₄ traits, and those values decreased slightly from the first to the second lactation (0.25 ± 0.01 and 0.22 ± 0.01 for PME; 0.18 ± 0.01 and 0.17 ± 0.02 for LMI). Lactation phenotypic and genetic correlations were negative between PME and MY in both first and second lactations (-0.07 vs. -0.07 and -0.19 vs. -0.24, respectively). More close scrutiny revealed that relative increase of PME was lower with high MY levels even reverting to decrease, and therefore explaining the negative correlations, indicating that higher producing cows could be a mitigation option for CH₄ emission. The PME phenotypic correlations were almost equal to 0 with FY and PY for both lactations. However, the genetic correlations between PME and FY were slightly positive (0.11 and 0.12), whereas with PY the correlations were slightly negative (-0.05 and -0.04). Both phenotypic and genetic correlations between LMI and MY or PY or FY were always relatively highly negative (from -0.21 to -0.88). As the genetic correlations between PME and LMI were strong (0.71 and 0.72 in first and second lactation), the selection of one trait would also strongly influence the other trait. However, in animal breeding context, PME, as a direct quantity CH₄ proxy, would be preferred to LMI, which is a ratio trait of PME with a trait already in the index. The range of PME sire estimated breeding values were 22.1 and 29.41 kg per lactation in first and second parity, respectively. Further studies must be conducted to evaluate the effect of the introduction of PME in a selection index on the other traits already included in this index, such as, for instance, fertility or longevity.

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