Genetic parameters for repeatedly recorded enteric methane concentrations of dairy cows

Animal breeding techniques offer potential to reduce enteric emissions of ruminants to lower the environmental impact of dairy farming. The aim of this study was to estimate the heritability and repeatability of methane (CH 4 ) concentrations, using the largest data set from long-term repeatedly recorded CH 4 on cows to date, and to evaluate (1) the accuracy of breeding values for different CH 4 traits, including using visits or weekly means, and (2) recording strategies (with varying numbers of records and recorded daughters per sire). The data comprised of long-term recording of CH 4 and carbon dioxide (CO 2 ), from 1,746 Holstein Friesian cows, on 14 commercial dairy farms throughout the Netherlands. Emissions were recorded in 10-to 35-s intervals, between 64 and 436 d, depending on farms. From each robot visit, CH 4 and CO 2 concentrations were summarized into various traits, averaged per visit and per week: mean, median, mean log, and mean CH 4 / CO 2 ratio. Genetic parameters were estimated with animal repeatability models, using a restricted maximum likelihood procedure, and a relationship matrix based on genotypes and pedigree. The heritability was equal for mean and median CH 4 per visit (0.13) but lower for logCH 4 and CH 4 /CO 2 (0.07 and 0.01, respectively). Phenotypic and genetic correlations were high (≥0.78) between the CH 4 traits, apart from the genetic correlations with the CH 4 /CO 2 trait, which were negative. To achieve a minimum reliability of 50% for the estimated breeding value of a bull, 25 records on mean CH 4 , measured on 10 different daughters, were sufficient. Although the heritability and repeatability were higher for weekly (0.32 and 0.68, respectively) than for visit mean CH 4 (0.13 and 0.30, respectively), the reliabilities of estimated breeding values from visit or weekly means were equal; thus, we found no advantage in averaging records to weekly means for genetic evaluations.


INTRODUCTION
Ruminants produce methane (CH 4 ) by anaerobic fermentation in the rumen, which is emitted in the air mostly through breathing and belching (Herrero et al., 2016).Reducing these emissions can help to lower the environmental impact of dairy farming.Although enteric CH 4 emissions have been hypothesized to be carbon neutral (Mitloehner et al., 2020), mitigation still contributes to reducing the total emissions of the sector.Animal breeding offers an opportunity to achieve a permanent, cost-effective, and cumulative reduction in enteric CH 4 emissions, which can be implemented in addition to changes in nutrition and manure management (Knapp et al., 2014).To apply breeding techniques, large-scale recording of individual enteric CH 4 emissions is essential (de Haas et al., 2017).
Large-scale and cost-effective recording of individual cows is possible by using "sniffers" (Madsen et al., 2010;Garnsworthy et al., 2019).Sniffers use infrared spectroscopy to measure gas concentrations from the breath and belching of cows.The devices are installed in the feed bin of automated milking stations (AMS), where continuous measurements of the CH 4 concentration (ppm) in the air are taken.Sniffers do not use an air flux measurement, and therefore they cannot measure the CH 4 production in grams per cow per day.However, studies have shown high correlations (0.75 ± 0.20 and 0.89 ± 0.07) between on-farm sniffer measurements in parts per million and respiration chamber measurements, in which the exact CH 4 emission of an individual cow was measured (Difford et al., 2019;Garnsworthy et al., 2019).This suggested potential in using sniffers to quantify the variation in enteric CH 4 emissions between cows, and that the measurements could be used to rank cows from low to high emitters for animal breeding practices.
From CH 4 concentrations measured by sniffers, genetic parameters for several traits have previously been estimated.Many studies have used averages of measured CH 4 concentrations (ppm), for which the heritability ranged between 0.11 ± 0.02 and 0.26 ± 0.11 (van Engelen et al., 2018;Difford et al., 2020;Saborío-Montero et al., 2020).Other studies have predicted CH 4 production (g/d) from CH 4 concentrations (ppm) by using CO 2 as tracer gas, combined with the CH 4 /CO 2 ratio, as described in Madsen et al. (2010).The heritability for this predicted CH 4 production ranged between 0.12 ± 0.16 and 0.45 ± 0.11 (Lassen and Lovendahl, 2016;Pszczola et al., 2017;Difford et al., 2018;Zetouni et al., 2018;Breider et al., 2019).Some studies have discussed CH 4 traits in relation to other relevant breeding goal traits, such as milk production (CH 4 intensity), DMI (CH 4 yield), or residual CH 4 (de Haas et al., 2017).Of those 3 traits, only CH 4 intensity has a published heritability for dairy cows, estimated as 0.21 ± 0.06 (Lassen and Lovendahl, 2016).Trait definition affects estimates of heritabilities and genetic correlations, although in the literature differences between estimated genetic parameters have also been large when the same trait definition was used.Large differences in parameter estimates might also be due to different recording strategies and circumstances between studies.Furthermore, many currently published estimates are associated with large uncertainties shown by high standard errors.Most initial studies have either a small number of records per cow, a small number of recorded cows, or a small number of recorded farms.However, accurate estimates are needed to derive the expected accuracy of breeding values for different trait definitions and recording strategies, important aspects of setting up a breeding program (Falconer and Mackay, 1996).
In the Netherlands, a breeding goal will be developed to reduce enteric CH 4 emissions of dairy cows, for which phenotypes are being collected in AMS by sniffers.The aim of this study was to estimate the heritability and repeatability of CH 4 concentrations, using the largest data set from long-term repeatedly recorded cows to date, and to use the data and the corresponding estimates to evaluate (1) the accuracy of breeding values for different traits (and visits or weekly means) and (2) recording strategies (with varying number of records and recorded daughters per sire).The heritability and genetic correlation of alternative CH 4 and CO 2 traits were also estimated.Data were available for continuous and repeated recording of CH 4 and CO 2 concentrations by sniffers between 64 and 436 d, on 14 commercial dairy farms throughout the Netherlands, with a total of 1,746 dairy cows.The heritabilities and genetic correlations between different CH 4 traits and the described recording strategies provide tools to aid discussions that are needed to construct new breeding goals aiming to reduce enteric CH 4 emissions of dairy cows.

Data
Enteric CH 4 emissions were recorded in AMS on 14 commercial dairy farms located throughout the Netherlands, between March 2019 and September 2020.On these farms, a total of 475,555 AMS visits from 2,414 dairy cows were recorded.Emissions were recorded by sniffers (WD-WUR version 1.0, Carltech BV).On each farm, a unique device was installed in close proximity to the AMS, with an air inlet leading from the feed bin of the AMS.Various types of AMS systems were used in the study, manufactured by Lely Industries NV, GEA Group, DeLaval BV, and Fullwood Packo BV.On each farm, at most 1 AMS was equipped with a sniffer, even if multiple AMS were used within a herd.Before installation in the AMS, sniffers were calibrated using flacons of CH 4 , CO 2 , and nitrogen.The sniffers could measure CH 4 concentrations in a range of 0 to 2,000 ppm and CO 2 concentrations in a range of 0 to 10,000 ppm.
On each farm, air was sampled continuously, and every 10 to 35 s (varying between devices) a mean was uploaded to the cloud using Arduinos (SODAQ SARA SFF R410M developer board).A data check was performed twice a week to ensure that the sniffers had no sudden change in the mean or variation in emissions.Genotype data, pedigree data, and other phenotypic data were made available by the cooperative cattle improvement organization CRV (Arnhem, the Netherlands).Animals were genotyped with the Eurogenomics 10K chip.The genotype data comprised 1,817 animals with 76,438 SNPs (imputation was routinely performed by CRV), of which 1,611 cows were phenotyped for CH 4 emissions.The additional 206 cows that were genotyped but not phenotyped were included to maintain linkage between the small number of herds and the large number of bulls with few daughters.Phenotypic data provided by CRV included test-day milk yield, breed composition, and calving dates.

Matching Records to Cow Identification Numbers
Sniffers are not able to record cow identification numbers.Therefore, to match a sniffer measurement with an identification number, the CH 4 measurements were aligned with identification numbers recorded by the AMS.The records could not be merged based merely on timestamps, because the times of sniffers were set manually, whereby inaccuracies may have occurred, and changes to and from daylight saving time were not registered.Therefore, we used an algorithm that matches the sniffer and AMS records, based on the AMS entry van Breukelen et al.: RECORDING ENTERIC METHANE FOR BREEDING time and peaks of CH 4 emissions in the sniffer data, which were located with the function "findpeaks" from the package "pracma" in R version 3.6.1 (R Foundation for Statistical Computing; Borchers, 2019).This method is similar to that described by Garnsworthy et al. (2012).A peak was detected based on an increase of 500 ppm of CH 4 , with at least 3 increasing datapoints before the peak, followed by 3 decreasing datapoints.A match was defined as a peak that occurred within 30 s before or after the AMS entry time.A 30-s timeframe around the AMS entry was necessary (±time), because the AMS only recorded entry time to the minute, whereas sniffers recorded time at the level of seconds.The time difference with the most matches between sniffer CH 4 peaks and AMS entry times was considered to be the true time difference.Time differences were confirmed by visual inspection before matching the data set.When data were not matched correctly, many milkings would not result in increases of CH 4 , whereas for correctly matched data it could clearly be observed that CH 4 concentrations peaked at the start of milkings and would be low and stable when the robot was empty.

Data Editing
The continuous CH 4 measurements within an AMS visit were used to define various CH 4 and CO 2 traits, of which details are described subsequently in the section "Methane Traits."Milking robot visits that did not result in a milking were discarded, as these cows would not receive pellets and would therefore not put the nose in the feed bin close to the air inlet for a longer period of time.Within AMS visits, records taken during the first minute of milking were discarded.This was to ensure that the cow had reached the feed bin and to account for a delay in the air sample entering the air inlet and reaching the sensor.The CH 4 recording period was defined to last at least 2.5 min, to capture not only breathing but also the belching of cows (van Soest, 1994).Last, records after 5 min of milking were discarded, because after 6 min a decrease in the mean CH 4 emission of all visits combined was observed.This is most likely because, on average, after the first 6 min of milking, cows have finished eating the pellets and would move the nose away from the air inlet, resulting in a decrease of mean emissions.
Background emissions were filtered by subtracting the lowest 1% quantile of records during milking on the day of the measurement from all individual CH 4 and CO 2 measurements of that day.Records from cows up to 305 DIM were analyzed, to correctly match the CH 4 records to calving dates and the corresponding parity.Cows whose breeds were less than 75% Holstein were removed from the data set.The final data set comprised 308,968 visits from 1,746 individual cows, which all had pedigree data, and 1,611 of these cows also had genotype information.

Methane Traits
For each AMS visit, a mean, a median, a mean of the log of CH 4 and CO 2 emissions, and a mean CH 4 /CO 2 ratio were estimated from the concentrations (ppm) measured every 10 to 35 s (Table 1).Furthermore, a second data set was created, from which a mean per week trait was calculated from all visit traits.The mean per week trait included only weeks with a minimum of 7 robot visits per cow recorded.The data set with weekly means comprised 17,320 records on 1,579 cows.The traits (mean, median, log, and CH 4 /CO 2 ratio) were selected based on what has been used previously in the literature (Difford et al., 2016;Lassen and Lovendahl, 2016;van Engelen et al., 2018), which typically include 1 or 2 of these traits but never all 4 as a mean per visit and per week.Traits based on predictions of CH 4 production were not included in the analyses.Recently it has been shown that the method commonly used to predict CH 4 production from CH 4 and CO 2 concentrations (as described by Madsen et al., 2010, is likely to favor inefficient cows over efficient cows in ranking them from low to high CH 4 emitting (Huhtanen et al., 2020).This is most likely a result of biased estimates of CO 2 production, due to differences between cows in their efficiency of energy utilization for maintenance or milk production.Additionally, CH 4 traits defined as a ratio to other relevant breeding goal traits, such as milk production (CH 4 intensity) and DMI (CH 4 yield), or as a residual CH 4 trait, were not included in the analyses, because information on milk yield and DMI were not available.

Genetic Parameter Estimation
Genetic parameters were estimated with univariate animal models, which included repeated records, using the REML procedure in ASReml version 4.2 (Gilmour et al., 2015).From the pedigree and genotype data, a combined genetic relationship matrix (H −1 matrix) was constructed following the method of Aguilar et al. (2010) and Christensen and Lund (2010), using calc_grm version r1.143 (Calus and Vandenplas, 2016).Before constructing the H −1 matrix, the pedigree was pruned to include only phenotyped animals and their ancestors, using the statistical programming software R version 3.6.1 and the R package "optiSel" (Wellmann, 2020).The pruned pedigree comprised 34,394 animals, The significance of fixed effects on the defined CH 4 traits was analyzed in ASReml.The random effects included were the additive genetic, parity by permanent environmental, and residual effect.The following model was defined: where y is the phenotype for a CH 4 trait; µ is the mean; HYW is the fixed effect of herd × year × week where the measurement was taken (i = 1-1,120); Farm•Hour is the fixed interaction between farm (j = 1-14) and hour of the day (k = 1-24) and was only used on the visit data; Dur is the fixed effect for duration of the visit and was only used on the visit data (excluded for weekly); DIM is the fixed regression coefficient for days in milk; β l is the term of the third-order Legendre polynomial for DIM; Par is the fixed effect of parity (m = 1-4, where 4 is parity 4 or higher); a is the random additive genetic effect of the nth animal, a where H is the combined relationship matrix, and σ a 2 is the additive genetic variance; Parity•PE is the permanent environmental effect of the cows per parity

Iσ
where I is the incidence matrix and σ pe 2 is the permanent environmental variance per parity; and e is the residual error, ( ) where σ e 2 is the error variance.
To estimate phenotypic and genetic correlations between the various CH 4 and CO 2 traits, a series of bivariate analyses were carried out.The same animal model as described previously, including covariances between the residual, genetic, and permanent environmental effects, was used to carry out the analysis for each pair of traits.
From the variance estimates, the heritability and repeatability of the various CH 4 and CO 2 traits were estimated (Mrode, 2005).Heritability was defined as follows: and repeatability was defined thus: where σ a 2 is the additive genetic variance, σ pe 2 is the permanent environmental variance, and σ e 2 is the error variance.

Reliability of Estimated Breeding Values
Two types of reliabilities were compared in this study.The model reliabilities of EBV were obtained directly from the previous model, and were defined as follows (Gilmour et al., 2015): where SE is the ASReml standard error of the EBV, and σ a 2 is the estimated additive genetic variance.These model reliabilities, derived directly from the data, take into account the true relationships that exist between all animals.Furthermore, predicted reliabilities of EBV were derived from quantitative genetics theory, based on the number of repeated records or the number of daughters per sire (Table 2; Mrode, 2005).These reliabilities assume that records are only available for an individual cow or records are only available on halfsib daughters of a bull, and no other relationships exist in the data.The predicted reliabilities for phenotyped cows with repeated records were calculated as where n is the number of records, h 2 is the heritability, and t is the repeatability.The predicted reliabilities for sires of phenotyped cows with a predefined number of daughters were then calculated thus: , where d is the number of daughters, and r cow 2 is the derived reliability for the breeding value of the phenotyped daughters; that is, equivalent to h 2 when only one visit or weekly record is available per cow.

Average Methane Emissions
The overall mean CH 4 emission per visit was 367 ppm, with a standard deviation of 216 ppm (CV = 59%; Table 1, Appendix Figures A1 and A2).The number of days with records ranged from 64 to 436 d for different farms, and depended on the moment of installation and downtime due to maintenance on the sniffers.Mean CH 4 and CO 2 emissions varied between farms and ranged from 99 to 562 ppm, and from 1,161 to 5,186 ppm, respectively (Table 3).
On average, the mean CH 4 emissions peaked at the start of the lactation, after which the emissions gradually decreased, and so the CH 4 emissions follow the standard lactation curve of milk yield (Figure 1).By visual inspection of the phenotypic data, diurnal patters were observed on most farms.In general, the mean CH 4 emissions were observed to decline during the night, increase in the morning, and stay high throughout the day.On 4 farms, a diurnal pattern could not be observed, for which the CH 4 emissions remained constant throughout the day.

Genetic Parameter Estimation
The estimated heritability and repeatability from mean visit emissions were 0.13 ± 0.01 and 0.30 ± 0.01, respectively (Table 4).After averaging the records per week, the heritability and repeatability for mean CH 4 significantly increased for all traits and became moderate (0.32 ± 0.03 and 0.68 ± 0.01, respectively; Table 4).Averaging the recorded visits per week, resulted in a large decrease of the residual variance (Table 5).Mean and median CH 4 emissions had the highest heritability and repeatability.The trait log-transformed CH 4 emissions had a lower heritability than the mean CH 4 emissions (0.23 ± 0.03 for weekly logCH 4 emissions).The ratio trait had the lowest heritability and a low repeatability (0.02 ± 0.01 and 0.15 ± 0.01, respectively, for weekly CH 4 /CO 2 emissions).

Genetic Correlations Between Methane Traits
Phenotypic and genetic correlations were estimated between the weekly emission traits.The estimated genetic correlations between the mean, median, and logCH 4 traits were high (0.78-1.00;Table 6).On the contrary, the phenotypic and genetic correlations between the CH 4 /CO 2 ratio trait and all other traits were negative (−0.08 to −0.45 and −0.27 to −0.99, respectively), and the genetic correlations had high standard errors (0.16-0.29).Furthermore, the phenotypic corre-lations between CH 4 and CO 2 emission traits were high (0.70-0.85).

Reliability of Estimated Breeding Values
Predicted reliabilities for EBV were estimated based on the heritability and repeatability estimates for mean visit and weekly emissions.The predicted reliability for EBV of phenotyped cows with repeated records increased steeply for the first 10 weekly records of mean CH 4 emissions, after which the gain per additional recording per cow became smaller (Figure 2).For visits, the increase in reliability was slightly less steep, and the gain per additional recording became smaller after around 25 recorded visits.For phenotyped cows, one weekly mean gave a higher reliability than one visit, which is a result of the higher heritability for weekly means (Figure 2 and Table 7).However, when considering an average of 7 visits per week, the 2 reliabilities  were approximately equal (7 visits per week versus 1 weekly).This was calculated from the parameter estimates and applying a sensitivity analysis based on their standard errors.
The predicted reliability of EBV for sires increased when a larger number of daughters were recorded per sire, and the level of reliability depended on the number of records for mean CH 4 emission per daughter (Figure 3).With a larger number of records per daughter, the reliability of sires was higher, although after 10 recorded weeks or 25 recorded visits, the gain in adding extra records became negligible.For sires with a large number of recorded daughters that all have a large number of records, the difference between the reliability for visit emissions and weekly emissions decreased (Table 7).
For cows with own performance information, including repeated records, the realized reliability for mean CH 4 emission was higher than that expected based on the predicted reliability (Figure 4A).For sires, the realized reliability, which included all records, followed the expected pattern from predicted reliabilities (Figure 4B). Figure 4A confirms that the largest increase in reliability came from the inclusion of approximately the first 25 repeated records.By including more repeated records, the reliability for cows only marginally increased.

DISCUSSION
The aim of this study was to estimate the heritability and repeatability of CH 4 concentrations, using the largest data set from long-term repeatedly recorded cows to date, and to use the data and corresponding estimates to evaluate (1) the accuracy of breeding values for different traits (visits or weekly means) and (2) recording strategies (with varying numbers of records and recorded daughters per sire).Data were available on continuous and repeated recording of CH 4 and CO 2 emissions, from 1,746 dairy cows, on 14 commercial dairy farms throughout the Netherlands.From the data, genetic parameters were estimated with univariate and bivariate animal models, using a restricted maximum likelihood procedure.The results show that mean CH 4 emissions had moderate heritability and repeatability, but that there was no advantage in averaging the mean emissions per week to estimate breeding values for sires.From the mean emissions per visit, 25 records measured on 10 different daughters gave reliabilities of breeding values above the Dutch publication threshold of 50%.

Phenotypic Analysis
The mean CH 4 emissions recorded in this study was 367 ppm, which is within the low range of previously estimated means from similar sniffer devices (between 254 and 1,288 ppm; van Engelen et al., 2018;Bell et al., 2019;Difford et al., 2019;López-Paredes et al., 2020;Saborío-Montero et al., 2020).Low records can be a result of variations in measurement conditions and drifting of sensors toward zero.This may also have caused the coefficient of variation (CV) to increase to higher levels than expected and caused differences in the CV between farms.By correcting for differences between farms and between measuring weeks within farms in the genetic analysis, we assume that these factors have minimal influence on the estimates of the genetic parameters.Another concern that is often raised is that CH 4 measurements by sniffers are inaccurate or biased and are influenced by systematic environmental effects, random errors, and systematic errors (Huhtanen and Hristov, 2018).Systematic environmental effects, such as conditions during the day or farm, are not problematic for genetic analysis and can be separated from genetic effects by the separation of environmental effects in mixed model analysis.Similarly, random errors, which can be a result of movement of the cow's nose and the position of the nose in the feed bin (Wu et al., 2018), do not have to be problematic and can be reduced by taking multiple repeated measurements of each cow.Furthermore, the effect of the position of the nose and head lifting was expected to be reduced by only considering the first 5 min of milking, where we expect most cows were eating concentrates.Systematic errors, such as behavior during milking, are more serious if the errors are also partly genetic in nature.For example, cows that are restless in nature might look around in the milking robot more frequently, causing the measured concentrations to decline.It should be further studied whether this behavior is repeatable and heritable, as has also been pointed out by Wu et al. (2018).Nonetheless, even if sniffer measurements party reflect differences in other traits, CH 4 measured by sniffers could still serve as in indicator for true CH 4 emissions (Bovenhuis et al., 2018).The pattern of CH 4 emissions over DIM (Figure 1) and the diurnal pattern indicate that sniffers are able to detect variation in emissions.Diurnal patterns have been reported previously (Bell et al., 2014b;Pszczola et al., 2017;van Engelen et al., 2018), and in these studies the CH 4 emissions increased during the day and decreased during the night, which is similar to patterns observed in this study.Crompton et al. (2011) showed that these diurnal patterns in CH 4 emissions can be caused by changes in feed intake during the day.In our study, the relationship between CH 4 emissions and feed intake was not further investigated, as data on feed intake was not available.
For DIM, earlier studies have reported a steep increase of CH 4 emissions in the first weeks of lactation, with emissions remaining stable or gradually decreasing thereafter (Garnsworthy et al., 2012;Bell et al., 2014a;Pszczola et al., 2017).This is in agreement with the pattern for DIM observed in this study (Figure 1).Also, feed intake may play a role; daily DMI is typically lower in early lactation compared with mid and late lactation (Krattenmacher et al., 2019).

Methane Traits
In this study we have analyzed average CH 4 concentrations (ppm) measured in the feed bin of milking robots.High individual-level correlations have been reported (0.75 ± 0.20) between sniffer CH 4 breath concentration (ppm) measurements and respiration chamber CH 4 production (g/d) measurements; this was published by a study that installed sniffers in milking robots for 3 wk of lactation and subsequently in respiration chambers (Difford et al., 2019).Therefore, we assumed that analyzing concentrations measured in parts per million gives sufficient information about relative differences between cows, which is required to select the best-performing animals for breeding practices.Additionally, we analyzed CH 4 /CO 2 as a ratio trait that is generally used in quantifying CH 4 production (Madsen et al., 2010).Nonetheless, to gain confidence in using CH 4 concentration measurements from sniffers for genetic evaluations, the relationship with measurements of emissions in grams per day, as is done with the GreenFeed (C-Lock Inc.; Hammond et al., 2016), should be investigated further.This is needed to confirm that the total emissions in grams per day will be   In the literature, CH 4 measurements in parts per million are often converted to grams per day to approximate a cow's total emission.To predict emissions in grams per day from concentration measurements by sniffers, CO 2 emissions are used as a tracer gas through a formula that assumes a constant efficiency of energy utilization for different metabolic functions (Madsen et al., 2010).This assumption is not always met and can result in CH 4 emissions to be overestimated, on average by 17% for efficient compared with inefficient cows, favoring the inefficient cows (Huhtanen et al., 2020).Other traits that have received interest in the literature are CH 4 intensity (g of CH 4 /kg of milk), CH 4 yield (g of CH 4 /kg of DMI), and residual CH 4 (observed CH 4 minus predicted, from, e.g., milk yield, CH 4 ; de Haas et al., 2017).These traits would account for the highly conserved relationships between CH 4 , milk yield, and feed intake, and thus rank cows from low to high emitting, regardless of their level of production or feed intake.However, these relationships can also be addressed by including correlation structures between CH 4 , milk yield, and feed intake in the selection index.In a simulation study, Zetouni et al. (2017) showed that a multitrait approach resulted in higher genetic gain than by selecting for ratio traits.Additionally, responses to selection for a multitrait index, compared with including a ratio trait, will be easier to interpret, which makes the index more approachable for farmers.Because the interest was in analyzing traits that would be suitable to add to a breeding goal, we did not include analyses on CH 4 as a ratio to other breeding goal traits, although more research is needed to verify the effect of using a ratio trait for CH 4 in breeding goals.
Many traits had minimum records of 0 ppm CH 4 (rounded to zero), which is below what is biologically expected (Table 1, Appendix Figures A1 and A2).The low records were most likely a result of drifting of the sensor calibration that occurred during the study, where the sensor calibration drifted toward zero.As a  result, the CH 4 data were not normally distributed, and therefore a log-transformation on the CH 4 records was performed.Nonetheless, because CH 4 emissions are expected to be normally distributed by nature and moved toward normality after averaging the records to means per week (Appendix Figure A2), we do not recommend using log-transformations of a CH 4 trait in the breeding objective.Furthermore, log-transformation did not solve non-normality of CH 4 in this data set.Therefore, we recommend investigating other options to correct for drift of sensors in future studies; for example, by using censored models or multiple imputation, or by standardization of the data based on the week of the measurement.
Other traits derived from sniffer measurements that are often mentioned in the literature are CH 4 emissions estimated from eructation peak traits (Garnsworthy et al., 2012;Bell et al., 2019;López-Paredes et al., 2020).Peak traits were not included in this study, because the recording interval of up to 35 s does not provide sufficiently detailed information.However, estimations of the CH 4 emissions from peaks have been shown to be moderately to highly correlated with the average CH 4 concentration during milking (0.62 and 0.86, on different diets; Bell et al., 2014b).Therefore, peak traits may still be of interest for breeding when using different recording practices, where concentrations are measured, for example, every second.

Genetic Parameters
The estimated heritabilities were highest for mean and median CH 4 emissions averaged per week (both were 0.32 ± 0.03; Table 4).As expected, averaging the recorded visits to records per week resulted in an increased heritability.Earlier studies reported heritabilities for the mean CH 4 concentration (ppm) and mean logCH 4 concentration per week, measured by sniffers, ranging from 0.11 ± 0.03 to 0.26 ± 0.11 (Difford et al., 2020;López-Paredes et al., 2020), and for mean CH 4 production per week of 0.12 ± 0.16 in a repeatability model (Breider et al., 2019), and of 0.25 ± 0.07 from one weekly record (Zetouni et al., 2018).Thus, the heritability estimated for weekly mean emissions in this study is somewhat higher than what has been observed in literature.This could have been a result of the large quantity of data used and the inclusion of genomic information, as well as of the requirement of a minimum number of 7 records per weekly mean to come to a more reliable average.The heritability for mean CH 4 concentration per visit (0.13 ± 0.01 for mean CH 4 and 0.09 ± 0.01 for logCH 4 ) is similar to the heritability reported by van Engelen et al. (2018) for logCH 4 concentration (0.11 ± 0.02) and by Saborío-Montero et al. (2020) for average CH 4 concentration over a period of 2 to 3 wk (0.12 ± 0.01).Estimates that have been reported in the literature for the heritability of mean CH 4 production per visit were somewhat higher, at 0.21 ± 0.06 and 0.19 ± 0.09 (Lassen and Lovendahl, 2016;Difford et al., 2018).Residual variances may differ between farms; therefore it is of interest to estimate intra-herd variances.However, we were not able to estimate genetic parameters within farms, because most farms had a limited number of cows recorded, with only one farm having recorded over 200 cows (n = 293; Table 3).
The repeatabilities estimated in this study for mean and median CH 4 emissions were moderate and, again, higher for weekly than for visit mean emissions (0.68 ± 0.01 and 0.30 ± 0.01, respectively; Table 4).Repeatability estimates for CH 4 concentrations recorded by sniffers have been published previously.In the literature, repeatabilities of mean CH 4 concentrations per visit were 0.42 and 0.45 ± 0.07 (Rey et al., 2019;Sypniewski et al., 2019), and 0.27 ± <0.01 and 0.33 for logCH 4 (Difford et al., 2016;van Engelen et al., 2018).Thus, the repeatabilities estimated in this study for mean CH 4 emissions per visit were lower than previously published estimates (0.30 and 0.18 for mean CH 4 and logCH 4 , respectively).For CH 4 production per visit or per day, repeatability estimates have been reported that ranged from 0.36 to 0.66 ± 0.11 (Haque et al., 2015;Negussie et al., 2017;Sorg et al., 2018), which is in the same range as or higher than the repeatabilities reported for CH 4 concentrations.Estimates of the repeatability for log CH 4 concentrations averaged per week ranged from 0.47 to 0.84 (Difford et al., 2016;Difford et al., 2019;Difford et al., 2020).The repeatability estimated in this study for weekly logCH 4 emissions (0.65 ± 0.01) falls within this range.
In this study, the CH 4 /CO 2 ratio trait had a low heritability (0.01 ± <0.01 to 0.02 ± 0.01) and a low repeatability (0.08 ± <0.01 to 0.15 ± 0.01).Low estimates have also been reported in the study by van Engelen et al. (2018), where the heritability was 0.03 ± 0.01 and the repeatability was 0.14 ± <0.01.However, for the CH 4 /CO 2 ratio trait, Lassen and Lovendahl (2016) reported a higher estimate of heritability of 0.16 ± 0.04, although in that study emissions were measured for 7 d and averaged over the full recording period.A low heritability indicates that a larger number of records per cow is needed for the CH 4 /CO 2 ratio trait to accurately estimate EBV, compared with direct measurements of CH 4 concentration, which were shown to be moderately heritable in this study.Using CH 4 in a ratio trait has other disadvantages.First, as has been addressed previously, direct selection on the trait of interest is more advantageous, as it realizes a higher genetic response than indirect selection on a ratio trait (Zetouni et al., 2017).Second, interpretation would be more difficult, as the level of feed intake, efficiency of energy utilization, and body energy balance can also influence the gas ratio (Huhtanen et al., 2015).Finally, Huhtanen et al. (2015) suggest that air-mixing conditions, caused by the geometry of the feed bin, might influence the CH 4 / CO 2 ratio.
Genetic correlations between the mean, median, and logCH 4 traits were high (0.78-1.00), indicating that these traits can be used interchangeably after standardization (Table 6).In contrast, the phenotypic and genetic correlations between the CH 4 /CO 2 ratio trait and all other traits were negative.Again, this shows that the CH 4 /CO 2 ratio is most likely less suitable for application in selection indices and not a good indicator of a cow's CH 4 emission.However, in our study the ratio may have been influenced by the drift of CH 4 sensors while the CO 2 sensor remained stable, making the relationship between the ratio and its component traits nonlinear, and therefore could be more informative when sensors are calibrated regularly.
The phenotypic and genetic correlations between CH 4 and CO 2 concentrations were positive.The phenotypic correlations ranged from 0.70 ± 0.01 to 0.85 ± <0.01, and the genetic correlations ranged from 0.75 ± 0.02 to 0.90 ± 0.01.This is agreement with what has been reported in an earlier study, where the phenotypic correlations ranged from 0.87 ± <0.01 to 0.96 ± <0.01, and the genetic correlations ranged from 0.96 ± 0.03 to 0.97 ± 0.03 (Difford et al., 2020).Furthermore, a study that used respiration chamber measurements also reported a high phenotypic correlation between CH 4 and CO 2 production (0.93; Aubry and Yan, 2015).The high correlations suggest that a strong relationship exists between the quantity of emitted CH 4 and CO 2 .

Recording Strategies
For cows with own performance information, the predicted reliability appears higher when estimated from the mean CH 4 emission per week compared with the reliability estimated from visits, for the same number of records per cow (0.46 and 0.40, for 25 recorded weeks or visits respectively).However, in this scenario a weekly mean is expected to be calculated from at least 7 recorded visits, and, when comparing the reliability from 7 visits to one week, no gain in reliability is detectable for either scenario.Therefore, to estimate reliable EBV, we found no gain in averaging the recorded visits per week.Similarly, for sires the reliabilities of EBV were approximately equal for one weekly record versus 7 recorded visits.This also illustrates that heritability should always be interpreted in context of the trait definition.
The reliability of EBV estimated from own performance information is constrained by the large difference between the heritability and the repeatability, which is the permanent environmental effect (Falconer and Mackay, 1996).This effect can also be observed in Figure 4A, where the predicted reliabilities, derived from quantitative genetics theory, are plotted based on the number of repeated measurements.By taking measurements further apart in time, the permanent environmental variance could possibly be reduced.When the time gap between records increases, the environmental correlation between records may decay faster than the genetic correlation, which could result in a higher reliability for cows.Although this effect was not investigated in this study, it might be useful in optimizing recording strategies and for efficient use of recording equipment, but should be investigated further.Given that CH 4 emissions have been shown to have a different genetic background over DIM (Pszczola et al., 2017), it is important to consider lactation stages.Nonetheless, for a large number of animals, the realized reliabilities by ASReml were higher expected based on the predicted reliabilities (Figure 4).The higher reliability can be explained by the inclusion of extra information on relatives.The predicted reliabilities assume that only CH 4 records on the individual animal are available, whereas in the data daughters, half-sibs and full sibs may also have phenotypic records, which provide additional information about the individual animal.
From Figure 4B, we can derive the number of daughters that should be phenotyped in practice to be able to reliably estimate breeding values for the mean CH 4 emissions for bulls.The Dutch cattle improvement organization CRV publishes breeding values for milk production traits when the reliability is above 50%, and for all other traits when the reliability is above 25% (CRV, 2020).Using these numbers, in Figure 4 we can observe that around 10 daughters per sire, with at least 10 visits recorded on mean CH 4 emissions per daughter, would need to be recorded to reach an accuracy of 50% for sires.However, only a handful of daughters, with at least 10 repeated records per daughter, would need to be recorded to achieve a reliability of 25%.These numbers of records are determined by the estimated heritability and repeatability and assume that these are estimated without error.However, in our study the standard errors (SE) were between <0.01 and 0.04, and therefore a sensitivity analysis was performed, which assumed that the heritability or the reliability (or both) were ± 2 SE.This analysis showed that the required minimum number of records did not change within the expected range of error of the heritability and repeatability estimates.From the results, we suggest that at least 25 visits should be recorded on cows to accurately calculate EBV for mean visit CH 4 emissions for the phenotyped cows or their sires in a repeatability model (Figures 2  and 3).A study using the GreenFeed system, showing the computation of a cow's CH 4 or CO 2 production rate, required a minimum of 30 recorded visits, each lasting more than 3 min, to obtain a reliable average of multiple short-term breath measurements (Arthur et al., 2017).This indicates that, despite the Green-Feed system's more accurate recording, by correcting the measurements for areal conditions and movement of the head of the cow (Huhtanen et al., 2015), the minimum recording period of the system is similar to the minimum recording period of the sniffer.Additionally, sniffers have the advantage of the ability to record a larger number of cows per recording period, equal to the capacity of the AMS, which is a prerequisite for genetic evaluations for which hundreds to thousands of animals need to be phenotyped.Nonetheless, it is important to realize that these recommendations relate to mean CH 4 concentrations with heritability and repeatability in the magnitude of what has been estimated in this study.When new traits are defined, with different parameter estimates, or different models are applied, the recording strategies have to be re-evaluated.

Implications
This study confirms that there is promise in using CH 4 emissions measured by sniffers in genetic evaluations.Mean CH 4 emissions (ppm) per visit and per week have moderate to high heritability and repeatability, are easy to record and easy to interpret as absolute differences between cows, and could most likely serve as an indicator for total CH 4 emissions (g/d), as is suggested by the high correlations between sniffer and respiration chamber measurements (Difford et al., 2019;Garnsworthy et al., 2019).Methane emissions are currently not included in dairy selection indices around the world.Large-scale phenotyping is required first, to investigate the relationships between CH 4 emissions and other selection index traits.However, currently not enough measurements were available to derive the relationships between CH 4 emissions and other breeding goal traits, which are required before inclusion in a selection index.
It has to be further investigated which trait or traits defined from CH 4 emissions measured by sniffers should be added to a breeding goal that aims to reduce enteric CH 4 emissions per animal.Previous studies have shown that the heritability of CH 4 emissions changes over a lactation, and that the genetic correlation between different DIM was on average 0.74 and could decrease to 0 for DIM further apart (5 vs. 305 DIM; Pszczola et al., 2017;Breider et al., 2019;Sypniewski et al., 2021).This shows that it is important to consider the period in which CH 4 was recorded, and not simply to assume a genetic correlation of one between different DIM, as was done with the repeatability model in this study.Random regression models have the advantage of allowing for heterogeneous genetic and residual variances between lactation stages, and can model underlying genetic correlations, similar to models that are used for milk yield in the Netherlands (CRV, 2018).Additionally, correction for heterogeneity of variances might be required to adjust for different variances across herds.Better modeling of the underlying genetic structure will most likely improve the reliability of breeding value estimations and reduce the need for recording in different lactation periods.Random regression models will be investigated with this data set when more data has been collected.Nonetheless, the current estimates of heritability clearly indicate that, also by using a simpler repeatability model, genetic progress can be made.

CONCLUSIONS
In this study, genetic parameters were estimated for CH 4 concentrations continuously measured in the feed bin of milking robots.Moderate heritability and repeatability were estimated for mean and median CH 4 emissions.Low heritability was estimated for the ratio trait of CH 4 /CO 2 .Phenotypic and genetic correlations were high between the mean, median, and logCH 4 traits, excluding the CH 4 /CO 2 ratio trait, which was negative.From the mean CH 4 emissions per visit, 25 records on mean CH 4 , measured on 10 different daughters, gave reliabilities of breeding values above the Dutch breeding value publication threshold of 50%.Although the heritability and repeatability for the mean emissions per week were higher than for the mean emissions per robot visit, the reliabilities of estimated breeding values derived from the 2 recording strategies are equal.

vanFigure 1 .
Figure 1.Mean methane (CH 4 ) emissions (ppm) per automated milking station visit on each day in milk.

Figure 2 .
Figure2.Predicted reliability for the mean CH 4 emission for cows with own performance information, based on the number of phenotypic records per cow.Calculated for the number of recorded visits (solid line) and the number of recorded weeks (dotted line).Lines were derived from the corresponding estimates of heritability and repeatability (0.13 and 0.30 for visits, and 0.32 and 0.68 for weeks, respectively).

vanFigure 4 .
Figure 4. Realized reliability of EBV (dots) and expected predicted reliability (lines) for cows with own performance information on the mean CH 4 emissions per robot visit, by their number of recorded visits (A), and for sires of phenotyped cows by their number of daughters, which assumes each cow has 1 (solid line), 10 (small-dashed line), or 100 (large-dashed line) repeated records (B).

Figure 3 .
Figure3.Predicted reliability for sires with phenotyped daughters, based on the number of records on mean CH 4 emission per daughter and the number of daughters per sire.The reliability was derived for both visit means (light gray) and weekly means (dark gray) from the corresponding estimates of heritability and repeatability (0.13 and 0.30 for visits, and 0.32 and 0.68 for weeks, respectively).

van
Breukelen et al.: RECORDING ENTERIC METHANE FOR BREEDING

Table 1 .
van Breukelen et al.: RECORDING ENTERIC METHANE FOR BREEDING Mean (±SD), minimum (Min), and maximum (Max) of the traits defined for enteric methane (CH 4 ) and carbon dioxide (CO 2 ) emissions as visit means (308,968 records on 1,746 cows) or weekly means (17,320 records on 1,579 cows)

Table 2 .
van Breukelen et al.: RECORDING ENTERIC METHANE FOR BREEDING Number of bulls having 1 to 130 daughters in the data set, in classes of 10

Table 3 .
Descriptive statistics per farm for number of cows, total number of days with records (there can be gaps in the recording period), total number of visits recorded, and mean methane (CH 4 , ppm) and carbon dioxide (CO 2 , ppm) emissions (±SD)

Table 5 .
van Breukelen et al.: RECORDING ENTERIC METHANE FOR BREEDING Genetic σ a

Table 6 .
van Breukelen et al.: RECORDING ENTERIC METHANE FOR BREEDING Phenotypic (above the diagonal) and genetic correlations (below the diagonal) between weekly CH

Table 7 .
Predicted reliabilities for cows with own performance information and sires with phenotyped daughters 1 reduced by breeding for reduced CH 4 concentrations measured in parts per million.