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 CH emission. This study aimed mainly to estimate (1) the genetic parameters of 2 milk mid-infrared-based CH proxies [predicted daily CH emission (PME, g/d), and log-transformed predicted CH 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 CH 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 CH 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 CH 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 CH 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.

The authors advise that during the study period the definition (not the evaluation) of reported udder health (UDH) changed and the scale was reversed (i.e. the negative (-) associated with UDH should be positive (+) and vice versa). However, this correction was omitted in a few places in the published paper. Therefore, the correct text in the 'Expected genetic changes under selection scenarios' section should read:A relative weight of 25% of PME (selection scenario IV) generated a response of PME by -6%, MY by 15%, FY by 6%, PY by 11%, fertility by -4%, BCS by -11%, UDH by 13% and longevity by 22%. For example by the addition of 25% of LMI, the resulting response would be for LMI by -24%, MY by 29%, FY by 16%, PY by 28%, fertility by -10%, BCS by -13%, UDH by 13% and longevity by 23%.The correct versions of Tables 5 and 6 are as follows: Table 6. Selection responses (percentage of change) of environmental, production and functional traits to LMI selection scenarios LMI, log-transformed methane intensity; MY, milk yield; FY, fat yield; PY, protein yield; Fertility, Combined female fertility; BCS, body condition score; UDH, udder health (reversed somatic cell score); Selection scenario 1 = current Walloon dairy cattle selection program, from second to fifth selection scenarios were addition of PME by 5%, 12.5%, 25% and 50% and proportional decrease on other traits respectively Table 5. Selection responses (percentage of change) of environmental, production and functional traits to PME selection scenarios PME, predicted methane emissions; MY, milk yield; FY, fat yield; PY, protein yield; Fertility, Combined female fertility; BCS, body condition score; UDH, udder health (reversed somatic cell score); Selection scenario 1 = current Walloon dairy cattle index (VeG), from second to fifth selection scenarios were addition of PME by 5%, 12.5%, 25% and 50% and proportional decrease on other traits respectively Abstract. Methane (CH 4 ) emission is an important environmental trait in dairy cows. Breeding aiming to mitigate CH 4 emissions require the estimation of genetic correlations with other economically important traits and the prediction of their selection response. In this study, test-day CH 4 emissions were predicted from milk mid-infrared spectra of Holstein cows. Predicted CH 4 emissions (PME) and log-transformed CH 4 intensity (LMI) computed as the natural logarithm of PME divided by milk yield (MY). Genetic correlations of PME and LMI with traits used currently were approximated from correlations between estimated breeding values of sires. Values were for PME with MY 0.06, fat yield (FY) 0.09, protein yield (PY) 0.13, fertility 0.17; body condition score (BCS) -0.02; udder health (UDH) 0.22; and longevity 0.22. As expected by its definition, values were negative for LMI with production traits (MY -0.61; FY -0.15 and PY -0.40) and positive with fertility (0.36); BCS (0.20); UDH (0.08) and longevity (0.06). The genetic correlations of 33 type traits with PME ranged from -0.12 to 0.25 and for LMI ranged from -0.22...

The authors advise that during the study period the definition (not the evaluation) of reported udder health (UDH) changed and the scale was reversed (i.e. the negative (-) associated with UDH should be positive (+) and vice versa). However, this correction was omitted in a few places in the published paper. Therefore, the correct text in the 'Expected genetic changes under selection scenarios' section should read:A relative weight of 25% of PME (selection scenario IV) generated a response of PME by -6%, MY by 15%, FY by 6%, PY by 11%, fertility by -4%, BCS by -11%, UDH by 13% and longevity by 22%. For example by the addition of 25% of LMI, the resulting response would be for LMI by -24%, MY by 29%, FY by 16%, PY by 28%, fertility by -10%, BCS by -13%, UDH by 13% and longevity by 23%.The correct versions of Tables 5 and 6 are as follows: Table 6. Selection responses (percentage of change) of environmental, production and functional traits to LMI selection scenarios LMI, log-transformed methane intensity; MY, milk yield; FY, fat yield; PY, protein yield; Fertility, Combined female fertility; BCS, body condition score; UDH, udder health (reversed somatic cell score); Selection scenario 1 = current Walloon dairy cattle selection program, from second to fifth selection scenarios were addition of PME by 5%, 12.5%, 25% and 50% and proportional decrease on other traits respectively Table 5. Selection responses (percentage of change) of environmental, production and functional traits to PME selection scenarios PME, predicted methane emissions; MY, milk yield; FY, fat yield; PY, protein yield; Fertility, Combined female fertility; BCS, body condition score; UDH, udder health (reversed somatic cell score); Selection scenario 1 = current Walloon dairy cattle index (VeG), from second to fifth selection scenarios were addition of PME by 5%, 12.5%, 25% and 50% and proportional decrease on other traits respectively Abstract. Methane (CH 4 ) emission is an important environmental trait in dairy cows. Breeding aiming to mitigate CH 4 emissions require the estimation of genetic correlations with other economically important traits and the prediction of their selection response. In this study, test-day CH 4 emissions were predicted from milk mid-infrared spectra of Holstein cows. Predicted CH 4 emissions (PME) and log-transformed CH 4 intensity (LMI) computed as the natural logarithm of PME divided by milk yield (MY). Genetic correlations of PME and LMI with traits used currently were approximated from correlations between estimated breeding values of sires. Values were for PME with MY 0.06, fat yield (FY) 0.09, protein yield (PY) 0.13, fertility 0.17; body condition score (BCS) -0.02; udder health (UDH) 0.22; and longevity 0.22. As expected by its definition, values were negative for LMI with production traits (MY -0.61; FY -0.15 and PY -0.40) and positive with fertility (0.36); BCS (0.20); UDH (0.08) and longevity (0.06). The genetic correlations of 33 type traits with PME ranged from -0.12 to 0.25 and for LMI ranged from -0.22...