Prediction of Enteric Methane‐Related Traits From Body Weight and Milk Composition Traits, Including Ratios of De Novo, Mixed, and Preformed Fatty Acids in Holstein Cows

ABSTRACT

The aim of this study was to develop prediction equations for methane‐related traits in Holstein cows using body weight (BW) and milk composition traits, including the proportions of de novo (DEN), mixed (MIX), and preformed (PRF) fatty acids in milk fat. A total of 358 measurements from 92 Holstein cows were used in regression analyses for methane emission (CH₄, L/day), methane conversion factor (MCF), and the CH₄:CO₂ ratio. Independent variables included BW, energy‐corrected milk (ECM), milk yield, milk protein percentage (PRO), milk fat percentage, lactose percentage, protein‐to‐fat ratio (PFR), DEN, MIX, and PRF. Four well‐fitted equations were developed for CH₄ and MCF. The best fitted equation was as follows: CH₄ = −78.58 + 0.5632 × BW + 8.273 × ECM + 17.75 × PRO − 181.7 × PFR + 6.151 × DEN − 2.225 × MIX. When BW was excluded from the CH₄ equation, prediction bias was observed across parities and lactation stages. This bias was reduced by developing parity‐specific equations. These equations show moderate accuracy in validation. These findings demonstrate that methane‐related traits can be effectively predicted using routinely collected animal and milk composition data, offering the potential for improved methane monitoring and mitigation strategies in dairy production.

1. Introduction

Enteric methane (CH₄) emissions—produced through the anaerobic fermentation of feed in the rumen—have gained increasing attention as a major target for greenhouse gas reduction, as they significantly contribute to agricultural emissions (Gerber et al. 2013). Genetic selection is a permanent, cumulative strategy to enhance the sustainability of the dairy industry, while requiring minimal additional cost or labor for dairy farmers. Enteric CH₄ emissions are a heritable trait (e.g., Lassen and Løvendahl 2016; Pickering et al. 2015; Pszczola et al. 2017). Therefore, animal breeding offers a promising approach to reducing enteric CH₄ emissions in dairy cows.

Effective genetic selection requires large datasets of CH₄ emissions or related traits from individual cows. The reliability of genetic parameters is influenced by the dataset size. As noted by Richardson et al. (2021), expanding datasets is also crucial for estimating the genetic parameters of CH₄ related traits. On the other hand, establishing a methane measurement system at commercial farms can significantly contribute to expanding methane data. Several methods are available to measure enteric CH₄, including open‐circuit respiration chambers, the sulfur hexafluoride tracer technique, the GreenFeed system, and the sniffer method (Garnsworthy et al. 2019). Nevertheless, implementing these techniques on commercial farms is costly and impractical for large‐scale data collection.

The indirect prediction of enteric CH₄ emissions using routinely measured traits is an effective strategy for genetic selection. Several prediction equations for enteric CH₄ have been developed based on relationships with feed intake and rumen fermentation (e.g., Alemu et al. 2011; Moraes et al. 2014). However, direct measurement of feed intake and rumen fermentation traits is challenging. Therefore, alternative indicators such as body weight (BW) and milk traits have been used to predict enteric CH₄ emissions (Negussie et al. 2017). BW, milk yield, and milk composition serve as proxies for feed intake, as they reflect maintenance and production requirements (Negussie et al. 2017). In addition, BW is related to rumen capacity, which influences CH₄ production (Demment and Van Soest 1985). Milk fatty acids are valuable indicators of rumen fermentation. During ruminal synthesis, acetate and butyrate production generates hydrogen (H₂), a key substrate for CH₄ synthesis. Approximately half of milk fatty acids are synthesized de novo (DEN) from acetate and butyrate in the mammary gland (Bauman and Griinari 2003). CH₄ output has been reported to correlate with milk fatty acid composition (Chilliard et al. 2009), and several CH₄ prediction equations have been developed using individual fatty acids (Chilliard et al. 2009; Mohammed et al. 2011). Milk fatty acids can be classified into three categories based on their origin (Harvatine et al. 2009; Woolpert et al. 2017): DEN fatty acids (4–14 carbons), synthesized in the mammary glands; mixed (MIX) fatty acids (15–16 carbons), derived from both DEN synthesis and plasma uptake; and preformed (PRF) fatty acids (> 16 carbons), absorbed from circulating plasma originated from feed, adipose tissue mobilization, and partial synthesis in the rumen (Vlaeminck et al. 2006). The proportions of DEN, MIX, and PRF fatty acids in milk fat can be easily measured using Fourier transform infrared spectroscopy. In Japan, DEN and PRF data are routinely collected through monthly test‐day records. There are no prior studies that have predicted methane using these categorized fatty acids. These categorized fatty acids also have the potential to serve as indicators of rumen fermentation and contribute to the prediction of enteric CH₄ emissions using existing datasets in Japan.

The aim of this study was to develop prediction equations for CH₄ emissions and CH₄‐related traits in Holstein cows using BW and milk composition traits, including DEN, MIX, and PRF. Additionally, the study investigated the influence of BW on the accuracy of CH₄ emission predictions generated by the developed equations.

2. Materials and Methods

2.1. Animals

The study was conducted using Holstein cows from the Gunma Prefectural Livestock Experiment Station, Gunma, Japan (Farm 1); the Setouchi Field Science Center, Saijo Station, Hiroshima University, Japan (Farm 2); and a commercial dairy farm (Farm 3). All procedures complied with the animal care and use guidelines of the respective institutions. Experimental protocols were approved by the Gunma Prefectural Livestock Experiment Station (approval numbers: 2018.1(1), 2019.1(1), 2020.1(1), 2023‐2‐(1)) and the Animal Care and Use Committee of Hiroshima University (approval number: E17‐5‐2).

Experiments were conducted seven times at Farm 1 between October 2017 and November 2020, three times at Farm 2 between May 2017 and October 2019, and three times at Farm 3 between November 2023 and July 2024. Each experimental period lasted seven consecutive days. Cows were milked using free‐traffic automatic milking systems (AMS): Lely Astronaut A2 (Lely, Maassluis, the Netherlands) at Farm 1, Lely Astronaut A3 Next (Lely, Maassluis, the Netherlands) at Farm 2, and DeLaval VMS V300 (DeLaval, Tumba, Sweden). Cows were offered a partial mixed ration (PMR) 10, 4, and 2 times per day at Farm 1, Farm 2, and Farm 3, respectively. On all farms, a concentrate diet was supplied at each milking through the AMS. The total digestible nutrient (TDN) and crude protein (CP) contents of the PMR (on a dry matter basis) ranged from 69% to 76% and 15% to 16% at Farm 1 and were 69% and 14% at Farm 2, respectively. The TDN and CP contents of the AMS concentrate diet ranged from 79% to 91% and 14% to 22% at Farm 1 and were 86% and 19% at Farm 2, respectively. The information on feed could not be obtained at Farm 3.

2.2. Data Collection

Data collection procedures followed the methods described in our previous report (Uemoto et al. 2023). BW (kg) was measured during each experimental period on both farms. Daily milk yield was automatically recorded by the AMS over seven consecutive days, and the average daily milk yield (AMY, kg/day) was calculated. Milk samples were collected during each experimental period and analyzed for composition using Fourier transform infrared spectroscopy with a CombiFoss 6000 FC (FOSS, Hillerød, Denmark). Samples from Farm 1 and Farm 2 were analyzed at the milk inspection station of the milk marketing cooperatives in the Kinki region (Hyogo, Japan), whereas samples from Farm 3 were analyzed at the Tokachi Federation of Agricultural Cooperatives (Hokkaido, Japan) and Tokachi Federation of Agricultural Cooperatives (Hokkaido, Japan). The analyzed milk components included the milk fat percentage (FAT), milk protein percentage (PRO), and lactose percentage (LAC), as well as the ratios of DEN, MIX, and PRF fatty acids. Energy‐corrected milk (ECM, kg/day) was calculated using the equation proposed by Tyrrell and Reid (1965):

$$\mathrm{ECM}=\frac{\mathrm{AMY}\times \left(376\times \mathrm{FAT}+209\times \mathrm{PRO}+948\right)}{\mathrm{3,138}}.$$

The milk protein‐to‐fat ratio (PFR) was calculated as PRO divided by FAT.

Gas measurements were conducted using the sniffer method as described by Oikawa et al. (2022). Briefly, exhaled gas was sampled during each milking in the AMS milking box. The gas inlet was positioned at the rear of the feed trough, and gas was drawn through a pump at a flow rate of 6.5 L/min. Concentrations of CH₄ and CO₂ (ppm) in the sampled gas were measured daily for seven consecutive days using a Microportable Greenhouse Gas Analyzer (Model 909‐0050; LGR Ltd., CA, USA), with data logged at 1‐s intervals. Measured CH₄ and CO₂ concentrations were corrected for background levels. Data points with background‐corrected CO₂ concentrations below 500 ppm were excluded. For each milking, background‐corrected CH₄ and CO₂ concentrations were averaged, and the CH₄:CO₂ ratio was calculated. Data from each milking were retained only when the total duration of valid measurement points exceeded 3 min and at least 50% of logged points were usable. The mean CH₄:CO₂ ratio over seven consecutive days was calculated for cows with valid data from at least 5 days. CH₄ emission (L/day) and the methane conversion factor (MCF, J/100 J)—defined as the proportion of feed energy converted to CH₄—were calculated using the prediction equations reported by Suzuki et al. (2021):

$${\mathrm{CH}}_4=-507+0.536\times \mathrm{BW}+8.76\times \mathrm{ECM}+\mathrm{5,029}\times {\mathrm{CH}}_4:{\mathrm{CO}}_2$$ (1)

$$\mathit{MCF}=2.91-0.0498\times \mathit{ECM}+51.0\times {\mathrm{CH}}_4:{\mathrm{CO}}_2$$ (2)

MCF is the percentage of feed energy converted to CH₄.

In total, 386 records from 81 Holstein cows at Farm 1, 146 records from 26 Holstein cows at Farm 2, and 153 records from 105 Holstein cows at Farm 3 were collected. Records were filtered based on the following criteria: parity 1–3, 6–305 days in milk (DIM), and 90 ≤ (DEN + MIX + PRF) ≤ 105. After filtering, 248 records from 69 Holstein cows at Farm 1, 110 records from 23 Holstein cows at Farm 2, and 120 records from 91 cows at Farm 3 were retained for statistical analyses. Records at Farms 1 and 2 were used for the calculation of correlation coefficients and the development of prediction equations. Records at Farm 3 were used as test data for the developed prediction equations. Descriptive statistics of the observed traits are presented in Table 1.

TABLE 1.

Descriptive statistics of observed traits by each parity.

Traits	First				Second				Third
	Mean	SD	Min	Max	Mean	SD	Min	Max	Mean	SD	Min	Max
Farm 1 and Farm 2				(n = 195)				(n = 97)				(n = 66)
CH4 (L/day)	503.6	74.3	314.6	728.5	599.3	86.2	404.6	780.7	641.4	72.5	450.2	782.2
MCF (J/100 J)	5.26	0.68	3.64	7.13	4.80	0.68	3.08	6.20	5.00	0.58	3.35	6.00
CH4:CO2 (ppm/ppm)	0.0770	0.0111	0.0504	0.1095	0.0754	0.0106	0.0558	0.0970	0.0787	0.0081	0.0583	0.0949
BW (kg)	646	64	475	875	715	54	605	824	775	58	649	880
AMY (kg/day)	32.0	7.0	16.7	57.6	39.7	8.7	18.6	61.5	38.4	8.77	18.8	54.8
ECM (kg/day)	31.6	5.5	18.4	51.2	39.3	7.7	21.2	54.8	38.5	7.2	23.6	53.9
FAT (%)	3.98	0.65	2.56	6.29	3.92	0.62	2.64	5.45	4.06	0.65	2.68	5.99
PRO (%)	3.36	0.30	2.61	4.47	3.42	0.33	2.71	4.25	3.40	0.31	2.81	4.12
LAC (%)	4.63	0.16	3.44	4.99	4.56	0.16	3.90	4.88	4.50	0.19	3.90	4.92
PFR	0.863	0.123	0.512	1.260	0.888	0.130	0.576	1.325	0.851	0.104	0.612	1.119
DEN (%)	22.6	3.5	4.9	28.8	23.0	3.8	4.6	30.8	23.4	2.7	9.9	28.9
MIX (%)	38.5	3.83	27.6	50.3	39.2	4.0	30.9	48.0	40.5	4.6	30.7	50.8
PRF (%)	37.5	4.7	28.7	59.0	36.7	4.8	28.3	58.4	35.0	4.2	28.3	55.3
Farm 3				(n = 47)				(n = 41)				(n = 32)
CH4 (L/day)	539.5	85.7	317.3	704.4	621.0	99.9	414.3	880.4	631.8	109.6	329.4	832.1
MCF (J/100 J)	5.56	0.52	4.18	6.61	5.20	0.89	3.49	7.21	4.95	1.02	3.03	6.83
CH4:CO2 (ppm/ppm)	0.0851	0.096	0.0642	0.1065	0.0754	0.0106	0.0558	0.0970	0.0791	0.0164	0.0376	0.1076
BW (kg)	600	49	479	727	670	49	573	781	728	59	577	831
AMY (kg/day)	33.8	5.7	18.3	47.8	40.0	8.3	23.8	60.6	39.9	8.7	26.4	57.2
ECM (kg/day)	33.9	6.0	18.4	48.6	39.7	8.4	20.5	61.6	40.1	8.7	22.0	61.1
FAT (%)	4.01	0.57	1.58	5.20	3.93	0.61	2.46	5.82	4.09	0.82	2.71	5.70
PRO (%)	3.34	0.24	2.73	3.85	3.35	0.39	2.67	4.81	3.26	0.31	2.65	4.07
LAC (%)	4.69	0.17	4.10	5.00	4.67	0.15	4.27	4.97	4.66	0.13	4.41	4.92
PFR	0.853	0.159	0.690	1.797	0.862	0.099	0.665	1.155	0.824	0.150	0.597	1.192
DEN (%)	25.7	2.6	19.3	30.8	25.9	2.9	19.1	31.6	25.9	3.5	17.8	32.2
MIX (%)	32.3	2.56	25.6	37.8	31.6	3.5	19.0	39.4	31.8	2.8	25.4	36.6
PRF (%)	38.2	3.8	31.1	45.9	38.5	4.5	27.8	53.7	38.8	5.2	30.5	53.7

Abbreviations: AMY, average daily milk yield; BW, body weight; CH₄:CO₂, ratio of methane to carbon dioxide; DEN, ratio of de novo fatty acid in milk fat; ECM, energy‐corrected milk; FAT, milk fat rate; LAC, milk lactose rate; MCF, methane conversion factor; MIX, ratio of mixed fatty acid in milk fat; PFR, ratio of milk protein rate to milk fat rate; PRF, ratio of preformed fatty acid in milk fat; PRO, milk protein rate; SD, standard deviation.

2.3. Statistical Analyses

Multiple regression analyses were conducted using the R software (R Core Team 2022). Correlation coefficients among the observed traits were calculated. Multiple regression analyses were performed using the lm function to develop prediction equations. Dependent variables included CH₄ (L/day), MCF, and the CH₄:CO₂ ratio, while independent variables were BW, ECM, AMY, FAT, PRO, PFR, LAC, DEN, MIX, and PRF. Regression analyses were conducted for the three dependent variables using three sets of independent variables: PT1 (all independent variables), PT2 (independent variables except for BW, LAC, and MIX), and PT3 (independent variables except for BW, ECM, AMY, LAC, and MIX). In Japan, BW and LAC are recorded traits in test‐day data; however, actual measurements are limited and often estimated from other variables. MIX is not routinely recorded. Therefore, BW, LAC, and MIX were excluded from PT2. Because CH₄ and MCF were derived from equations that use ECM as an input (Equations 1 and 2), they tend to be highly correlated with AMY and ECM. PT3 was designed to develop prediction equations independent of ECM and AMY. Independent variables with a variance inflation factor greater than 10 were excluded to avoid multicollinearity. Variable selection was performed using the forward–backward stepwise method with the step function in R. The predictive performance of the developed equations was evaluated using the root‐mean‐square error (RMSE) and the adjusted coefficient of determination (Adj. R ²).

To assess model robustness, a fivefold cross‐validation was conducted following the procedure described by Picard and Cook (1984). The dataset was randomly divided into five subsets with an equal number of records. In each iteration, one subset was used for model evaluation, while the remaining four were used for model training. This process was repeated five times so that each subset served once as the evaluation set. For each validation round, RMSE and Adj. R ² were calculated, and the mean and standard deviation (SD) across the five repetitions were then computed.

Residuals between the observed and predicted values were plotted against the predicted values to evaluate potential prediction bias in the developed equations (St‐Pierre 2003). Outliers were tested by evaluating the studentized residuals. The contribution ratios of the independent variables were calculated using standardized datasets. Additionally, the mean observed and predicted values of CH₄, MCF, and CH₄:CO₂ were calculated for each parity and for every 60‐day interval from 6 DIM to assess bias by parity and lactation stage. DIM intervals were defined as follows: 65 (6–65 DIM), 125 (66–125 DIM), 185 (126–185 DIM), 245 (186–245 DIM), and 305 (246–305 DIM).

Multiple regression analyses were also conducted using the datasets divided by parity, with CH₄ (L/day) as the dependent variable and the same independent variables used in the CH₄ prediction equation developed under PT2. The mean observed and predicted CH₄ values were then calculated for each parity and 60‐day lactation interval to evaluate model performance across different parities.

The developed prediction equations were validated using test data from Farm 3, and the observed and predicted values were plotted. Regression equations, the coefficient of determination, and mean bias error (MBE) were calculated using the statsmodels package in Python (Seabold and Perktold 2010).

3. Results

3.1. Relationships of Methane‐Related Traits With Other Observed Traits

Pearson's correlation among observed traits were calculated (Figure 1). CH₄ (L/day) had significant positive correlations (p < 0.05) with BW (r = 0.61), AMY (r = 0.56), ECM (r = 0.70), FAT (r = 0.11), and DEN (r = 0.23). Conversely, CH₄ (L/day) had significant negative correlations (p < 0.05) with LAC (r = −0.13) and PRF (r = −0.23). MCF and CH₄:CO₂ were significant positively correlated (p < 0.05) with FAT (r = 0.39 and 0.35), PRO (r = 0.28 and 0.18), and DEN (r = 0.31 and 0.38). MCF and CH₄:CO₂ were AMY (r = −0.69 and −0.24), ECM (r = −0.64 and −0.13), PFR (r = −0.28 and −0.32), MIX (r = −0.14 and −0.16), and PRF (r = −0.13 and −0.19) were significantly negatively correlated (p < 0.05) with MCF and CH₄:CO₂.

FIGURE 1.

Correlation coefficient among dependent and independent variables. Red and blue colors indicate positive and negative correlations, respectively. AMY, average daily milk yield; BW, body weight; CH₄:CO₂, ratio of methane to carbon dioxide; DEN, ratio of de novo fatty acid in milk fat; ECM, energy‐corrected milk; FAT, milk fat rate; LAC, milk lactose rate; MCF, methane conversion factor; MIX, ratio of mixed fatty acid in milk fat; PFR, ratio of milk protein rate to milk fat rate; PRF, ratio of preformed fatty acid in milk fat; PRO, milk protein rate.

3.2. Development of Prediction Equations

Prediction equations for methane‐related traits were developed using multiple regression analysis with the three sets of independent variables (PT1–PT3). The resulting equations are presented in Table 2. For CH₄ (L/day), Equation (A1)—developed using selected variables from PT1—showed the best performance, with the lowest RMSE (42.7) and the highest Adj. R ² (0.801). The independent variables selected for Equation A1 were BW, ECM, PRO, PFR, DEN, and MIX. Equation A2, based on variables selected from PT2, also performed well, showing a relatively low RMSE (56.6) and a high Adj. R ² (0.651). ECM, PRO, PFR, and DEN were included as independent variables in Equation A2. In contrast, Equation A3, developed from PT3, had a high RMSE (92.3) and a low Adj. R ² value (0.074), indicating poor predictive accuracy. For MCF, Equations B1 and B2 yielded nearly identical results, with low RMSE values (0.435 and 0.437) and high Adj. R ² values (0.603 and 0.600), respectively. Both equations included AMY, PRO, PFR, and DEN as independent variables; however, Equation B1 additionally included MIX, whereas Equation B2 included PRF. Equation B3 showed weaker performance, with a higher RMSE (0.583) and a lower Adj. R ² value (0.285). For the CH₄:CO₂ ratio, Equations C1 and C2 demonstrated comparable accuracy, with RMSE values of 0.00856 and 0.00860 and Adj. R ² values of 0.334 and 0.326, respectively. The independent variables used in Equation C2 were selected from both PT2 and PT3.

TABLE 2.

Developed prediction equations for methane‐related traits.

Trait	Equation no.	Pattern of independent variables	Equation	RMSE	Adj. R 2
CH4 (L/day)	A1	PT1	−78.58 (39.85) + 0.5632 (0.0345) × BW + 8.273 (0.341) × ECM + 17.75 (8.83) × PRO − 181.7 (19.2) × PFR + 6.151 (0.701) × DEN − 2.225 (0.592) × MIX	42.7	0.801
	A2	PT2	−74.21 (45.11) + 10.23 (0.42) × ECM + 78.58 (10.38) × PRO − 170.2 (25.3) × PFR + 6.673 (0.914) × DEN	56.6	0.651
	A3	PT3	627.7 (92.7) − 114.3 (41.1) × PFR + 4.981 (1.992) × DEN − 2.376 (1.436) × PRF	92.3	0.074
MCF (J/100 J)	B1	PT1	7.646 (0.411) − 0.05419 (0.00323) × AMY − 0.1626 (0.0892) × PRO − 0.8690 (0.2070) × PFR + 0.06470 (0.00707) × DEN − 0.02110 (0.00584) × MIX	0.435	0.603
	B2	PT2	5.498 (0.569) − 0.05416 (0.00325) × AMY − 0.1764 (0.0892) × PRO − 0.8485 (0.2076) × PFR + 0.08871 (0.00940) × DEN + 0.02175 (0.00687) × PRF	0.437	0.600
	B3	PT3	1.561 (0.692) + 0.5563 (0.1037) × PRO − 2.105 (0.258) × PFR + 0.09657 (0.01254) × DEN + 0.03414 (0.00912) × PRF	0.583	0.285
CH4:CO2 (ppm/ppm)	C1	PT1	0.08642 (0.00808) − 0.00008949 (0.00006353) × AMY + 0.003433 (0.001755) × PRO − 0.03437 (0.00408) × PFR + 0.001232 (0.000139) × DEN − 0.0004208 (0.0001149) × MIX	0.00856	0.334
	C2	PT2, PT3	0.03705 (0.01020) + 0.004362 (0.001530) × PRO − 0.03602 (0.00381) × PFR + 0.001725 (0.000185) × DEN + 0.0004555 (0.0001345) × PRF	0.00860	0.326

Note: Abbreviations of traits are defined in Table 1. Subscripted values in parentheses indicate standard errors. Patterns of independent variables used in the multiple regression analyses are as follows: all independent variables (PT1); independent variables excluding BW, LAC, and MIX (PT2); independent variables excluding BW, ECM, AMY, LAC, and MIX (PT3).

Abbreviations: Adj. R ², adjusted coefficient of determination; RMSE, root‐mean‐square error.

The effectiveness of the independent variables in the developed prediction equations was assessed through fivefold cross‐validation. The cross‐validation results are presented in Table 3. Equations A1, A2, B1, and B2 demonstrated low mean RMSE values (43.1, 57.3, 0.433, and 0.435, respectively) and high mean Adj. R ² values (0.771, 0.606, 0.565, and 0.562, respectively). These equations also showed low SD of Adj. R ² (0.036, 0.081, 0.064, and 0.065), indicating stable predictive performance. These results suggest that the independent variables used in Equations A1, A2, B1, and B2 were robust and provided reliable predictions of CH₄ and MCF. Equations C1 and C2, developed for predicting the CH₄:CO₂ ratio, produced nearly identical results, with RMSE values of 0.00853 and 0.00857 and Adj. R ² values of 0.274 and 0.278, respectively. Residuals between the observed and predicted values for Equations A1, A2, B1, B2, C1, and C2 are presented in Figure 2. The residuals were evenly distributed across the predicted values, and no outliers were observed (|studentized residuals| < 3), indicating that the equations adequately fit the dataset and met the assumptions of linear regression.

TABLE 3.

Cross‐validation results of the developed prediction equations for methane‐related traits.

Trait	Equation no.	RMSE		Adj. R 2
		Mean	SD	Mean	SD
CH4 (L/day)	A1	43.1	4.1	0.771	0.036
	A2	57.3	6.9	0.606	0.081
	A3	93.1	10.1	−0.007	0.066
MCF (J/100 J)	B1	0.433	0.044	0.565	0.064
	B2	0.435	0.044	0.562	0.065
	B3	0.585	0.036	0.222	0.060
CH4:CO2 (ppm/ppm)	C1	0.00853	0.00087	0.274	0.070
	C2	0.00857	0.00086	0.278	0.067

Abbreviations: Adj. R ², adjusted coefficient of determination; MCF, methane conversion factor; RMSE, root‐mean‐square error; SD, standard deviation.

FIGURE 2.

Residual plots for predicted values using Equations A1 (A), A2 (B), B1 (C), B2 (D), C1 (E), and C2 (F). Gray lines indicate the zero‐residual reference. CH₄:CO₂, ratio of methane to carbon dioxide; MCF, methane conversion factor.

The proportions of variance explained by each independent variable were calculated from standardized regression coefficients (Figure 3). ECM contributed the highest proportion of variance in Equations A1 and A2 (0.376 and 0.528, respectively), while AMY was the largest contributor in Equations B1 and B2 (0.500 and 0.451, respectively). BW accounted for a substantial proportion of variance in Equation A1 (0.270). Both PFR and DEN contributed more than 0.1 across all equations. Notably, in Equations C1 and C2, the CH₄:CO₂ ratio was strongly influenced by PFR (0.350 and 0.318) and DEN (0.354 and 0.430), respectively.

FIGURE 3.

Proportions of variance in selected independent variables for Equations A1, A2, B1, B2, C1, and C2. Proportions of variance were calculated using multiple regression analysis with standardized variables. Abbreviations of traits are defined in Table 1.

3.3. Confirmation of Prediction Bias by Parity and Days in Milk

Predicted values from Equations A1, A2, B1, B2, C1, and C2 were averaged for each parity and every 60‐day interval from 6 DIM to evaluate potential bias by parity and lactation stage (Figure 4). The mean predicted CH₄ values in Equation A1 closely matched the observed CH₄ values across all time points (Figures 4A–C). In contrast, Equation A2 slightly overestimated CH₄ at the first parity and during the early lactation stages (65 and 125 DIM) of the second parity. Conversely, Equation A2 tended to underestimate CH₄ during the late lactation stages (245 and 305 DIM) of the second parity and across all stages of the third parity. Predicted MCF values from Equations B1 and B2 were nearly identical and closely aligned with the observed MCF values at all time points (Figures 4D–F). Similarly, the predicted CH₄:CO₂ ratios from Equations C1 and C2 were almost identical and generally consistent with observed values, except for a slight deviation at 65 DIM in the second parity (Figures 4G–I).

FIGURE 4.

Averages of observed and predicted CH₄ (A–C), MCF (D–F), and CH₄:CO₂ (G–I) by days in milk (DIM) for first (A, D, and G), second (B, E, and H), and third (C, F, and I) parities. Solid lines indicate averages of observed values; dashed lines indicate averages of predicted values by Equations A1, B1, and C1, and dotted lines indicate averages of predicted values by Equations A2, B2, and C2. DIM intervals are as follows: 65 = 6–65 DIM, 125 = 66–125 DIM, 185 = 126–185 DIM, 245 = 186–245 DIM, and 305 = 246–305 DIM. CH₄:CO₂, ratio of methane to carbon dioxide; MCF = methane conversion factor.

3.4. Development of CH₄ Prediction Equations by Parity

The bias observed in the predicted values of Equation A2 was likely due to the exclusion of BW as an independent variable. To reduce this bias, CH₄ prediction equations were developed separately for each parity using the same variables as in Equation A2. The resulting equations are presented in Table 4. The RMSE for the first (P1), second (P2), and third (P3) parity equations were 52.2, 51.7, and 44.0, respectively. The Adj. R ² values were 0.494 for P1, 0.620 for P2, and 0.601 for P3. The mean predicted CH₄ values generated by Equations P1, P2, and P3 are shown in Figure 5. These predictions were closer to the observed CH₄ mean than those obtained from Equation A2, indicating improved accuracy. However, for the first and second parities, Equations P1 and P2 slightly overestimated CH₄ during early lactation (65 and 125 DIM) and underestimated CH₄ during late lactation (245 and 305 DIM).

TABLE 4.

Developed prediction equations for each parity.

Trait	Equation no.	Parity	Equation	RMSE	Adj. R 2
CH4 (L/day)	P1	First	32.98 (58.70) + 8.993 (0.732) × ECM + 46.11 (14.42) × PRO − 137.0 (31.9) × PFR + 6.578 (1.195) × DEN	52.2	0.494
	P2	Second	36.05 (94.66) + 8.526 (0.732) × ECM + 79.72 (18.41) × PRO − 235.0 (43.5) × PFR + 7.154 (1.500) × DEN	51.7	0.620
	P3	Third	−27.50 (102.2) + 8.051 (0.846) × ECM + 91.70 (19.23) × PRO − 68.79 (56.64) × PFR + 4.493 (2.209) × DEN	44.0	0.601

Note: Abbreviations of traits are defined in Table 1. Subscripted values in parentheses indicate standard error.

Abbreviations: Adj. R ², adjusted coefficient of determination; RMSE, root‐mean‐square error.

FIGURE 5.

Averages of observed CH₄ and predicted CH₄ from Equations P1–P3 and A2 for first (A), second (B), and third (C) parities. Solid lines indicate averages of observed CH4, dash–chained lines indicate averages of predicted CH₄ from P1–P3, and dotted lines indicate averages of predicted CH₄ from Equation A2. Days in milk (DIM) intervals are as follows: 65 = 6–65 DIM; 125 = 66–125 DIM; 185 = 126–185 DIM; 245 = 186–245 DIM; 305 = 246–305 DIM.

3.5. Validation of Developed Prediction Equations Using Test Data

Next, we validated the prediction equations using data from a commercial farm (Figure 6). Equation A1 showed the highest coefficient of determination (0.51), with Equation A2 and P1–P3 showing values of 0.36 and 0.45, respectively. The coefficient of determination by both Equations B1 and B2 was 0.24. The prediction equations for CH₄/CO₂ had 0.00. The MBE values for Equations A1, A2, and P1–P3 were 0.026, 0.058, and 0.075, respectively. The MBE values for Equations B1, B2, C1, and C2 were 0.00047, 0.000095, 0.0000055, and 0.00000030, respectively.

FIGURE 6.

Scatter plots of observed and predicted methane‐related traits from Equations A1 (A), A2 (B), P1‐3 (C), B1 (D), B2 (E), C1 (F), and C2 (G) using test data. Solid lines indicate the regression equations shown in each figure. CH₄:CO₂, ratio of methane to carbon dioxide; MCF, methane conversion factor; R ², coefficient of determination.

4. Discussion

This study demonstrated that the ratios of DEN, MIX, and PRF fatty acids contribute to the prediction of methane‐related traits. In this study, DEN and PRF showed positive and negative correlations with CH₄, MCF, and CH_4:CO₂, respectively, while MIX showed a negative correlation with MCF and CH_4:CO₂, but not with CH₄. In general, individual DEN synthesized milk fatty acids were positively correlated with CH₄, given the common biochemical pathways between methane, acetate, and butyrate in the rumen (Chilliard et al. 2009; van Gastelen et al. 2017). PRF, especially unsaturated milk fatty acid, was negatively correlated with CH₄ (Rico et al. 2016; van Gastelen et al. 2017). The correlations between CH₄, MCF, and CH₄:CO₂ and categorized milk fatty acids in this study are consistent with these relationships. Previous results on MIX differed across studies. The findings for CH₄ in this study were consistent with those of Rico et al. (2016). Conversely, Chilliard et al. (2009) have reported a positive correlation between CH₄ and MIX. Although we could not find evidences regarding the correlation between MCF and CH₄:CO₂ and MIX, a positive correlation with C16:0 has been previously reported for methane yield (g/kg daily matter intake), a trait similar to MCF (Dijkstra et al. 2011; van Lingen et al. 2014). Notably, DEN was consistently selected as an independent variable in all developed equations through stepwise selection. Its correlations with methane‐related traits were equal to or stronger than those of MIX and PRF. In addition, DEN accounted for a higher proportion of variance across all developed equations (A1, A2, B1, B2, C1, and C2), suggesting that DEN is a more effective predictor of methane‐related traits than MIX or PRF.

Equations A1 and A2 demonstrated high Adj. R ² for CH₄ emissions in Tables 2 and 3. However, Equation A2 exhibited bias across parities and lactation stages. This bias likely resulted from the exclusion of BW, which may have limited the ability of the equation to reflect increases in CH₄ emissions associated with higher feed intake as cows grow. To address this, parity‐specific equations (P1, P2, and P3) were developed, which reduced parity‐related bias but did not eliminate the bias associated with lactation stage. Similarly, Castro‐Montoya et al. (2017) reported that incorporating daily matter intake data improves methane prediction equations based on milk fatty acid compositions. This finding supports the importance of including feed intake–related variables such as BW in predictive models. We did not include BW in the development of Equation A2 and parity‐specific equations because it is not routinely recorded in many commercial farms. Therefore, these equations have a major advantage in their applicability to routinely recorded test‐day data without BW information, while the resulting bias should be carefully considered. Recently, image‐based techniques for predicting bovine BW have been reported (e.g., Gebreyesus et al. 2023; Xavier et al. 2022). The advancement of such technologies may enable more regular and accurate BW collection in the future.

Figure 6 shows that the coefficients of determination of the equations for CH₄ and MCF ranged from 0.24 to 0.51 when validating data from another farm. Equation A1 exhibited the highest coefficient of determination, and Equations P1–P3 had higher coefficients of determination than Equation A2. This suggests that developing equations specific to parity was effective for methane prediction. Despite the modest accuracy of these equations, they could roughly rank and classify cows into high‐ and low‐methane‐emitting groups. Therefore, they can be useful for genetic selection based on methane emissions but are not suitable for predictions at the cow level. Bougouin et al. (2019) found that predicting methane emissions for individual cows using milk fatty acids yielded limited accuracy; however, performance improved when considering herd‐level averages. In alignment with those findings, the equations presented in this study indicate MBE values close to zero, suggesting enhanced accuracy in herd‐level predictions.

Equations A1, A2, B1, and B2 include ECM or AMY as independent variables; thus, they should be applied in breeding programs with caution. Genetic improvement of methane‐related traits based on these equations may inadvertently reduce productivity, as predicted values are influenced by milk yield. To address this, residual methane production has been proposed as a derived trait that minimizes correlations between methane production and other productive traits. Residual methane production is defined as the difference between observed methane production and the value predicted from related variables. Several studies have investigated the genetic parameters of residual methane production while excluding correlations with ECM, dry matter intake, BW, and similar traits (e.g., Manzanilla‐Pech et al. 2016; Richardson et al. 2021). Therefore, residual methane production represents a useful approach for genetic improvement aimed at reducing methane emissions using the developed equations.

This study attempted to develop prediction equations that excluded BW, ECM, and AMY as independent variables because these traits are used in Suzuki et al.’s (2021) equations and are highly correlated with methane‐related traits. However, Equations A3 and B3 showed low Adj. R ², indicating weak predictive ability. Although Equation C2 for CH₄:CO₂ also had a relatively low Adj. R ², it achieved the highest among equations that did not include BW, ECM, or AMY in Tables 2 and 3. However, the developed equations for CH₄:CO₂ showed a low coefficient of determination in the validation. CH₄:CO₂ was directly measured using the sniffer method and did not involve predictions based on other traits. To date, no previous studies have used the CH₄/CO₂ ratio as the target variable to predict its value based on milk components or similar factors. However, differences in feed composition affect the predictive accuracy for CH₄ based on milk fatty acids (Engelke et al. 2019). Therefore, clarifying the factors influencing the predictive accuracy of CH₄/CO₂ may improve predictive accuracy.

Observed CH₄ in the present study was obtained from the CH₄:CO₂ ratio, ECM, and BW. Huhtanen et al. (2020) mentioned the possibility that predicting CO₂ emission from production traits such as BW and milk yield results in the over/under estimation due to feed efficiency, and predicted CH₄ from multiplying estimated CO₂ by CH₄:CO₂ is also affected. Observed CH₄ in this study was calculated using a different equation from Huhtanen et al. (2020), but similar biases may exist. However, Suzuki et al. (2021) noted that the relative ranking of calculated CH₄ and MCF values closely matches that of directly measured data. Therefore, such bias is unlikely to substantially affect genetic evaluations or breeding decisions.

One of the major challenges in implementing breeding strategies for methane reduction is the lack of methods for large‐scale, continuous methane measurement. Predicting methane emissions from milk traits—particularly milk fatty acid composition—offers a promising solution. Genetic parameter estimation has been successfully conducted using methane prediction based on specific milk fatty acids (Kandel et al. 2012; van Engelen et al. 2015), and mid‐infrared milk spectra (Atashi et al. 2025; Fresco et al. 2024; Kandel et al. 2017). However, in Japan, data on specific milk fatty acids are not routinely collected, and the use of mid‐infrared spectra for methane prediction remains under development. The equations developed in this study were designed to utilize traits already recorded in Japanese test‐day data. Therefore, these equations have strong potential to support methane reduction through genetic improvement within the Japanese dairy industry.

This study developed prediction equations for methane‐related traits using BW and milk composition traits, including the ratio of DEN, MIX, and PRF fatty acids. Several multiple regression equations demonstrated the potential to predict methane‐related traits from routinely collected data in Japan. Furthermore, DEN, MIX, and PRF significantly contributed to methane‐related prediction accuracy. The CH₄ prediction equation that excluded BW exhibited bias across parities and lactation stages, indicating that BW is an important variable reflecting both cow growth and feed intake variation.

Funding

This work was supported by the Ministry of Agriculture, Forestry, and Fisheries of Japan through the commissioned projects Development of the Climate Change Mitigation Technology in the Livestock Sector, JP17935124, and the Ministry of Agriculture, Forestry, and Fisheries of Japan through the commissioned projects Development of GHG Mitigation Technology in the Livestock Sector, JPJ011299.

Conflicts of Interest

The authors declare no conflicts of interest.