Rafael Muñoz-Tamayo
email: rafael.munoz-tamayo@inra.fr

J F Ramírez Agudelo

R J Dewhurst

G Miller

T Vernon

H Kettle

A parsimonious software sensor for estimating the individual dynamic pattern of methane emissions from cattle

Keywords: greenhouse gas, methane, modelling, ruminant, precision farming

Large efforts have been deployed in developing methods to estimate methane emissions from cattle. For large scale applications, accurate and inexpensive methane predictors are required. Within a livestock precision farming context, the objective of this work was to integrate real-time data on animal feeding behaviour with an in silico model for predicting the individual dynamic pattern of methane emission in cattle. The integration of real-time data with a mathematical model to predict variables that are not directly measured constitutes a software sensor. We developed a dynamic parsimonious grey-box model that uses as predictor variables either dry matter intake (DMI) or the intake time (IT). The model is described by ordinary differential equations. Model building was supported by experimental data of methane emissions from respiration chambers. The data set comes from a study with finishing beef steers (cross-bred Charolais and purebred Luing finishing). DMI and IT were recorded with load cells. A total of 37 individual dynamic patterns of methane production were analysed. Model performance was assessed by concordance analysis between the predicted methane output and the methane measured in respiration chambers. The model predictors DMI and IT performed similarly with a Lin's concordance correlation coefficient (CCC) of 0.78 on average. When predicting the daily methane production, the CCC was 0.99 for both DMI and IT predictors. Consequently, on the basis of concordance analysis, our model performs very well compared with reported literature results for methane proxies and predictive models. Since IT measurements are easier to obtain than DMI measurements, this study suggests that a software sensor that integrates our in silico model with a real-time sensor providing accurate IT measurements is a viable solution for predicting methane output in a large scale context.

Introduction

Methane emission from cattle is an output associated to animal efficiency that impacts the environmental footprint of livestock farming. Accordingly, reducing enteric methane production is a major target for ruminant production systems [START_REF] Martin | Methane mitigation in ruminants: from microbe to the farm scale[END_REF][START_REF] Hristov | Special topics--Mitigation of methane and nitrous oxide emissions from animal operations: I. A review of enteric methane mitigation options[END_REF]. Large efforts have been deployed to develop methods and devices to measure and estimate methane emissions from ruminants, with respiration chambers being the gold standard under rigorous operation (Gardiner et al., 2015[START_REF] Hammond | Review of current in vivo measurement techniques for quantifying enteric methane emission from ruminants[END_REF]. However, some of these techniques are usually costly and not suitable to be applied for on farm application at large scale for the development of mitigation strategies of greenhouse gas emissions. An ideal technique for large scale application should provide, at low cost, individual accurate estimations of methane produced by ruminants (Negussie et al., 2017b). In complement to the development of methane proxies, mathematical modelling offers a useful tool for methane prediction. Mathematical models are often categorized as white box (phenomenological, mechanistic) or black box (empirical) models. A model with mechanistic and empirical components is termed as a grey box model. With respect to the models developed for predicting methane production by ruminants, white box models aim at describing the biological phenomena associated to rumen fermentation and methanogenesis [START_REF] Mills | A mechanistic model of whole-tract digestion and methanogenesis in the lactating dairy cow: model development, evaluation, and application[END_REF][START_REF] Huhtanen | Nordic dairy cow model Karoline in predicting methane emissions: 1. model description and sensitivity analysis[END_REF][START_REF] Vetharaniam | A modified version of the Molly rumen model to quantify methane emissions from sheep[END_REF]. These phenomena may include for instance the microbial activity of archaea methanogens [START_REF] Wang | A mathematical model to describe the diurnal pattern of enteric methane emissions from non-lactating dairy cows post-feeding[END_REF][START_REF] Muñoz-Tamayo | Mechanistic modelling of in vitro fermentation by rumen microbiota[END_REF]. Alternatively, black box models aim at deriving regression equations that quantify relationships between variable predictors and methane emissions (Sauvant et al., 2011, Ramin and[START_REF] Ramin | Development of equations for predicting methane emissions from ruminants[END_REF]. In general, white box models offer the possibility of quantifying the dynamics of key variables while black box models are often static. On the other hand, black box models are less complex than white box model which favours their implementation for practical purposes (e.g., on-farm monitoring). Existing black box models for methane predictions are algebraic equations that use an average measure of dry matter intake (DMI) as primary predictor [START_REF] Giger-Reverdin | Literature survey of the influence of dietary fat composition on methane production in dairy cattle[END_REF][START_REF] Charmley | A universal equation to predict methane production of forage-fed cattle in Australia[END_REF][START_REF] Niu | Prediction of enteric methane production, yield and intensity in dairy cattle using an intercontinental database[END_REF]. Generally, models and techniques have been applied to estimate the daily average methane emission. Few studies report predictions of the dynamic pattern of methane production [START_REF] Wang | A mathematical model to describe the diurnal pattern of enteric methane emissions from non-lactating dairy cows post-feeding[END_REF]. Integrating dynamic data from dedicated sensors with mathematical models to support livestock management decisions, and guide timely interventions is the great promise of precision livestock farming [START_REF] Wathes | Is precision livestock farming an engineer's daydream or nightmare, an animal's friend or foe, and a farmer's panacea or pitfall?[END_REF][START_REF] Rutten | Invited review: Sensors to support health management on dairy farms[END_REF][START_REF] Friggens | Review: Deciphering animal robustness. A synthesis to facilitate its use in livestock breeding and management[END_REF]. The integration of real-time data with a mathematical model to predict variables that are not directly measured constitutes what is called as software sensor (observer) in the automatic control scientific literature [START_REF] Dochain | State and parameter estimation in chemical and biochemical processes: a tutorial[END_REF]. Software sensors have been broadly applied to monitor and control biotechnological processes. A highly performant software sensor is composed of (i) real-time sensors that accurately measure variables of interest and (ii) a reliable model that provides accurate predictions and has a simple structure to facilitate its implementation. In this context, the objective of this work was to develop a software sensor for predicting the individual dynamic pattern of methane emissions in cattle. While, a software sensor operates in real-time using online sensor measurements, for a research purpose, our development was applied to off-line data as preliminary step for further on-line applications. Our software sensor is composed of a dynamic grey box model and dynamic data on animal feeding behaviour measured either as dry matter intake (DMI) or simply as intake time (IT). Our developments provide a promising and viable solution for predicting methane output for on farm applications at large scale.

Material and methods

Experimental data

Model building was supported by the analysis of experimental data obtained from studies conducted at Scotland's Rural College (SRUC, United Kingdom) with finishing beef steers from two breeds (cross-bred Charolais and purebred Luing) [START_REF] Troy | Effectiveness of nitrate addition and increased oil content as methane mitigation strategies for beef cattle fed two contrasting basal diets[END_REF]. Animals received two contrasting basal diets consisting (g/kg DM) of 500:500 and 80:920 forage to concentrate ratios. Within each basal diet, there were two treatments: a control treatment with rapeseed meal as protein source, and an oil treatment with rapeseed cake as protein source to increase dietary oil from 27 (control) to 53 g/kg DM. Methane emissions were measured in a respiration chamber facility with a turnover rate constant of 0.04 min -1 and a gas recovery of 98% [START_REF] Rooke | Hydrogen and methane emissions from beef cattle and their rumen microbial community vary with diet, time after feeding and genotype[END_REF]. The gas sampling time was 6 min. DMI and IT were recorded with load cells. A total of 37 individual dynamic patterns of methane production was analysed.

Mathematical model development

A mass balance applied to the respiration chamber for methane gives the following ordinary differential equation (ODE)

𝑑𝑥 c (𝑡) 𝑑𝑡 = 𝑎 • 𝑥 a (𝑡) -𝑏 • (𝑥 c (𝑡) -𝑥 i (𝑡)) (1)
Where 𝑥 c , 𝑥 i are the amount (in grams) of methane inside the chamber and at the inlet of the chamber respectively, and 𝑥 a is the amount of methane in the gas flow released by the animal (exhalation+ eructation). The parameter 𝑎 (min -1 ) is the rate constant of the animal gas emission and 𝑏 (min -1 ) is the turnover rate of the chamber. Note that in reality, 𝑎 may be time varying. If 𝑥 i is almost constant over time and 𝑥 i ≪ 𝑥 c , then Eq. ( 1) is simplified to

d𝑥 c (𝑡) d𝑡 = 𝑎 • 𝑥 a (𝑡) -𝑏 • 𝑥 c (𝑡) (2)
The quantity 𝑎 • 𝑥 a is the gas produced (g/min) by the animal while 𝑏 • 𝑥 c is the gas production (g/min) measured in the chamber. For mathematical convenience, we denote 𝑦 a = 𝑎 • 𝑥 a and 𝑦 c = 𝑏 • 𝑥 c . Equation ( 2) is thus translated to

d𝑦 c (𝑡) d𝑡 = 𝑏 • (𝑦 a (𝑡) -𝑦 c (𝑡)) (3)
If the turnover rate of the chamber is optimally chosen, it can be shown that 𝑦 c follows almost the same dynamics of 𝑦 a (See Supplementary material S1). In the remaining of the text, we will assume that 𝑦 c = 𝑦 a . Based on this clarification, we proposed the following ODE model for predicting the animal methane emission 𝑦 a d𝑦 a (𝑡)

d𝑡 = 𝑐 • 𝑢(𝑡) -𝑑 • 𝑦 a (𝑡) (4)
where 𝑢 is either the DMI or IT. DMI is in g/min and IT is a Boolean variable having the value one to indicate intake (eating) activity and zero otherwise. The parameters 𝑐, 𝑑 are specific to the animal and diet and must be estimated from the experimental data.

The parameter 𝑑 is in min -1 . The parameter 𝑐 is in g CH4/(g DM•min) or in g CH4/min 2 when using DMI or IT as predictors respectively. The model in Eq. ( 4) has a parsimonious structure with only two parameters. Although very simple, it follows the structure of a mass balance model (as Eq. ( 2)) in aggregated form. Indeed, the quantity parameter 𝑐/𝑑 can be interpreted as a yield factor i.e, the mass of methane produced per mass of DM (when using DMI as a predictor). Given this phenomenological characteristic, the model is referred to as a grey box model. Additionally, the model has the property of being identifiable, that is that the parameters 𝑐, 𝑑 can, in theory, be uniquely estimated if noise-free dynamic data of 𝑦 a and 𝑢 are available (see, e.g., Muñoz-Tamayo et al., 2018 for a discussion on parameter identifiability). The model in Eq. ( 4) can also be written in finite differential form. By applying backward differentiation with a constant time step ∆𝑡, we obtain

𝑦 a (𝑡) = 𝑐•∆𝑡 1+𝑑•∆𝑡 • 𝑢(𝑡) + 1 1+𝑑•∆𝑡 • 𝑦 a (𝑡 -∆𝑡) (5)
Equation ( 5) is an exponential smoothing filter. After a sensitivity analysis (not shown) the step time was fixed to ∆𝑡 = 1.0 min. The model was implemented in the open source software Scilab (https://www.scilab.org). Model calibration was performed by minimizing the sum of squared errors beween experimental data and predicted output for each of the 37 dynamic methane patterns. The minimization was performed using the Nelder-Mead algorithm implemented in the fminsearch function of Scilab. Our grey box model has the simplest structure to represent the dynamics of methane emissions from time series data of DMI or IT. To assess if increasing model complexity could lead to gains in goodness of fitting, we tested the performance of different linear models (described by Laplace transfer functions) with higher number of parameters than our model using the Matlab® System Identification Toolbox [START_REF] Ljung | System Identification Toolbox for use with Matlab[END_REF]. Our model was the best linear candidate model with respect to the Akaike's information criterion which provides an indicator of model parsimony based on a trade-off between goodness of fit and model complexity (quantified by the number of model parameters). The Lin's concordance correlation coefficient [START_REF] Lin | A concordance correlation coefficient to evaluate reproducibility[END_REF] was computed to quantify the agreement between the methane estimation provided by the software sensor and the methane measured in respiration chambers (the gold standard).

Results

Figure 1 shows typical data extracted from the experimental study. The dynamics of methane production is modulated by the feeding pattern (DMI or IT). Methane emissions increased following feeding and declines towards a basal value before the next feeding as observed in other studies [START_REF] Crompton | Fluctuations in methane emission in response to feeding pattern in lactating dairy cows[END_REF][START_REF] Wang | A mathematical model to describe the diurnal pattern of enteric methane emissions from non-lactating dairy cows post-feeding[END_REF][START_REF] Olijhoek | Effect of dietary nitrate level on enteric methane production, hydrogen emission, rumen fermentation, and nutrient digestibility in dairy cows[END_REF]. Figure 4 shows the individual daily average methane emission (n=37 steers) against predicted methane production. It is observed that individuals fed with the mixed basal diet produce more methane than those fed with the control basal diet [START_REF] Troy | Effectiveness of nitrate addition and increased oil content as methane mitigation strategies for beef cattle fed two contrasting basal diets[END_REF]. Results are presented for the model using either DMI or IT as predictors Tables 1 and2 show the results of the model calibration for the individual dynamics of methane production using either DMI or IT as predictors for the control and oil treatments respectively. Classical statistical indicators are also given. The statistical analysis about the effects of genotype, basal diet and treatment on methane production has already been published [START_REF] Troy | Effectiveness of nitrate addition and increased oil content as methane mitigation strategies for beef cattle fed two contrasting basal diets[END_REF]. To avoid redundancy, we focus here on the analysis of model parameters. Figure 5 shows the boxplots for the model parameters by treatment and basal diet.

Table 3 shows the results of unpaired t tests at the 5% level testing for a difference in parameter means in concentrate vs mixed basal diets and rapeseed meal vs rapeseed cake. The model parameter 𝑐 is significantly lower for a concentrate diet compared to a mixed basal diet, but parameter 𝑑 is not significantly different (at the 5% level) for each diet. This is to be expected as 𝑐 includes the methane yield factor that converts 𝑢(𝑡) (DMI or IT) to 𝑦 𝑎 (𝑡) , whereas 𝑑 is simply a specific rate constant related to gas release. While the methane yield depends on the level of concentrate in the diet, the concentrate level might not have impact on the rate of gas release (exhalation+ eructation). The level of dietary oil (oil and control) did not have significant effect on any parameters. Our software sensor provides satisfactory results for predicting the dynamics of methane production with similar levels of performance between DMI and IT as predictors. For DMI, the average CCC was of 0.79. For IT, the average CCC was 0.76. Interestingly, for 14 out of 37 dynamic data, the CCC for IT was higher than the CCC for DMI, indicating the great potential of using IT as predictor. When the software sensor was applied for predicting the daily average methane emission (Figure 4), the CCC was 0.99. On the basis of concordance analysis, our software sensor performs very well compared with reported literature results for methane proxies and predictive models [START_REF] Wang | A mathematical model to describe the diurnal pattern of enteric methane emissions from non-lactating dairy cows post-feeding[END_REF], Negussie et al., 2017a[START_REF] Niu | Prediction of enteric methane production, yield and intensity in dairy cattle using an intercontinental database[END_REF].

Discussion

The primary role of the feeding pattern on methane emissions in cattle [START_REF] Crompton | Fluctuations in methane emission in response to feeding pattern in lactating dairy cows[END_REF] motivated us to investigate the capability of predicting the dynamics of methane production from cattle using only time-series data of feeding behaviour (DMI or IT) via the construction of a software sensor. The objective of this construction was to develop a suitable tool for estimating methane that could be applied at large scale. The outcome of our work is encouraging to envisage a real-time implementation provided that accurate measurements or estimations of feeding behaviour are guaranteed, which is in compliance with other studies [START_REF] Appuhamy | Models for predicting enteric methane emissions from dairy cows in North America, Europe, and Australia and New Zealand[END_REF]. Since the pattern of feeding behaviour is an individual trait among ruminants [START_REF] Morita | Effects of concentrate intake on subsequent roughage intake and eating behavior of cows in an automatic milking system[END_REF][START_REF] Giger-Reverdin | A new segmentation-clustering method to analyse feeding behaviour of ruminants from withinday cumulative intake patterns[END_REF], individual characterisation of feeding patterns is central for producing individual estimations of methane by ruminants in a large scale context. Our study suggest that IT is a good predictor of methane emissions. The use of IT as predictor in our model relies on the assumption that the intake rate is constant across the day. This assumption applied to the data analysed here was shown to be adequate for methane prediction purposes, but additional data should be further analysed to assess the assumption robustness. For a real implementation at large scale, using IT as predictor instead of DMI has great advantages in terms of costs and setting. Successful results on real-time determination of IT by means of accelerometers [START_REF] Oudshoorn | Estimation of grass intake on pasture for dairy cows using tightly and loosely mounted di-and tri-axial accelerometers combined with bite count[END_REF][START_REF] Arcidiacono | Development of a thresholdbased classifier for real-time recognition of cow feeding and standing behavioural activities from accelerometer data[END_REF] are encouraging to make of our software sensor a feasible and low cost solution for on farm applications in the future. Recently, it has been suggested that, for a stable management of feed allocation, the diurnal pattern of methane is constant over time [START_REF] Bell | Does the diurnal pattern of enteric methane emissions from dairy cows change over time? Animal[END_REF], which, with respect to our modelling work, translates into a constant diurnal feeding behaviour pattern. Accordingly, monitoring IT offers an opportunity not only to predict methane emissions but also a tool to characterise individual normal feeding patterns.

By this, it will be possible to signal when an animal exhibits a different pattern from its normal pattern. This change of pattern could be associated to a perturbation, providing useful information for timely interventions. Finally, a software sensor is meant to operate in real time using on-line measurements.

In this work, however, our analysis was developed off-line. Further work needs to be carried out to evaluate the developed software sensor in real-time by integrating accelerometers for IT estimation. Running the software sensor requires prior calibration of the model parameters. This calibration can be performed, for example, by the GreenFeed system given its reliability for determining methane emissions on farm [START_REF] Doreau | Comparison of 3 Methods for Estimating Enteric Methane and Carbon Dioxide Emission in Nonlactating Cows[END_REF], provided an adequate setting [START_REF] Renand | Assessing individual differences in enteric methane emission among beef heifers using the GreenFeed Emission Monitoring system: effect of the length of testing period on precision[END_REF].

Once the model parameters are estimated, the software sensor can be applied by setting an initial condition for methane production. This initial condition has a strong impact on the amplitude of the methane emissions pattern. In our study, we extracted the initial condition from the experimental data. For real implementation, it would be recommended to start the software sensor at a moment when the methane production is close to the basal production of methane (e.g. before a meal). From the experiments analysed in this study, the basal production of methane was between 0.015 and 0.13 g/min. The strategy of starting the software sensor at a moment where the methane production is close to basal production reduces the impact of a wrong choice of initial condition. Since the methane emission pattern might change over age and physiological state of animals (e.g., lactation stage for dairy cattle), adjustment of model parameters might be required when appropriate.

Figure S1

Simulation study. Virtual data of methane production by the animal (*) are compared with the output from a respiration chamber using Eq. ( 1) at three turnover rates: 0.004 min -1 (blue -.), 0.4 min -1 (red --), 0.04 min -1 (solid black line).

The turnover rate of the respiration chambers used in this study was 0.04 min -1 .

Figure 1

 1 Figure 1 Example of dynamic data of methane production (top) and feeding behaviour measured as DMI (*) and IT (solid line)

Figure 2 Figure 3

 23 Figure 2 Experimental (*) versus predicted methane emissions using DMI (red solid line) and IT (dashed black line) as predictors for control and oil treatments. Top plots are the experiments where model fits were the best. Bottom plots are the experiments where model fits were the poorest. IT is as good predictor as DMI

Figure 4

 4 Figure 4 Experimental data vs predicted output of daily average methane emission production for control (o) and oil () treatments . Filled marks are for the mixed basal diet, unfilled marks are for the concentrate basal diet. The isocline is the solid line. Results are presented for the model using either DMI or IT as predictors

Figure 5

 5 Figure 5 Estimated parameters of the model by treatment (control and oil). Grey boxes are for the concentrate basal diet and white boxes are for the mixed basal diet

Table 1

 1 Model calibration results of individuals for the control treatment

		Model with DMI as predictor			Model with IT as predictor
	Animal * 𝑐 • 10 -5 𝑑 • 10 -3 CCC ** 𝑟 2 CV RMSE	***	𝑐 • 10 -3	𝑑 • 10 -3 CCC	𝑟 2	CV RMSE
		gCH4/(g	min -1				gCH4/min 2	min -1
		DM•min)
	ChC1	2.93	2.35	0.74 0.51	22.53	3.47	2.12	0.78 0.61 20.07
	ChC2	2.51	2.53	0.78 0.58	23.29	2.04	2.32	0.72 0.50 25.50
	ChC4	3.63	2.31	0.80 0.64	18.71	3.19	2.33	0.72 0.54 21.27
	ChC5	3.55	1.38	0.85 0.72	13.81	2.36	1.49	0.80 0.61 16.38
	ChC6	2.84	1.90	0.66 0.46	14.41	2.83	1.68	0.61 0.42 14.89
	ChM1	4.80	2.12	0.92 0.83	12.90	3.78	1.90	0.89 0.77 14.89
	ChM3	3.08	1.17	0.82 0.63	16.55	0.79	0.47	0.70 0.50 19.21
	ChM4	4.53	1.49	0.81 0.63	12.03	7.22	1.87	0.85 0.69 10.96
	ChM5	4.17	1.62	0.77 0.59	16.70	3.60	1.46	0.77 0.57 17.07
	LuC1	3.21	2.26	0.88 0.76	13.47	2.51	1.78	0.81 0.69 15.38
	LuC3	3.50	1.76	0.83 0.72	13.26	2.51	1.57	0.71 0.52 17.35
	LuC4	3.41	1.60	0.83 0.67	10.61	1.88	0.98	0.77 0.63 11.26
	LuC6	2.00	1.58	0.52 0.26	24.35	2.06	1.58	0.53 0.31 23.64
	LuM1	4.59	1.87	0.91 0.79	13.92	3.93	1.88	0.90 0.78 14.37
	LuM3	2.21	1.24	0.61 0.43	20.09	1.74	1.08	0.59 0.41 20.35
	LuM4	4.37	1.37	0.81 0.65	16.02	5.29	1.85	0.74 0.52 18.90
	LuM5	5.30	1.90	0.87 0.71	13.54	3.42	1.91	0.91 0.82 10.71
	LuM6	3.52	1.41	0.89 0.79	12.70	2.48	1.46	0.87 0.74 13.93
	Mean	3.56	1.77	0.79 0.63	16.05	3.06	1.65	0.76 0.59 17.01

Table 2

 2 Model calibration results of individuals for the oil treatment

		Model with DMI as predictor			Model with IT as predictor
	Animal*	𝑐 • 10 -5	𝑑 • 10 -3 CCC **	𝑟 2	CV RMSE	***	𝑐 • 10 -3	𝑑 • 10 -3 CCC	𝑟 2	CV RMSE
		gCH4/(g	min -1					gCH4/min 2	min -1
		DM•min)
	ChC1	2.90	2.08	0.88 0.77	21.01	4.20	2.36	0.89 0.79 20.33
	ChC3	2.52	1.13	0.84 0.72	12.71	1.54	1.15	0.85 0.73 12.34
	ChC5	3.21	2.65	0.80 0.63	18.06	2.20	2.61	0.84 0.72 15.66
	ChC6	2.94	1.54	0.76 0.52	15.94	2.12	1.49	0.87 0.76 11.20
	ChM1	2.14	0.95	0.53 0.31	14.05	2.49	1.54	0.82 0.66	9.82
	ChM2	3.48	1.45	0.80 0.61	11.38	2.29	1.39	0.81 0.64 10.99
	ChM3	3.28	1.39	0.82 0.66	12.45	2.88	1.10	0.69 0.46 15.73
	ChM4	3.79	1.54	0.84 0.70	13.20	3.59	1.33	0.73 0.51 16.97
	ChM5	4.49	2.06	0.91 0.80	11.70	3.53	1.95	0.76 0.47 19.05
	ChM6	2.77	1.40	0.86 0.77	12.75	1.85	1.19	0.83 0.73 13.89
	LuC2	1.74	1.25	0.53 0.26	14.67	0.19	0.33	0.15 0.05 16.58
	LuC3	3.17	2.40	0.78 0.60	23.11	4.21	2.27	0.77 0.59 23.26
	LuC4	2.73	1.77	0.87 0.76	18.44	2.27	1.79	0.89 0.80 16.62
	LuC5	3.29	2.63	0.71 0.53	18.72	2.24	2.39	0.69 0.48 19.57
	LuM1	4.58	2.01	0.90 0.81	10.49	4.86	1.97	0.86 0.74 12.32
	LuM2	4.74	1.95	0.91 0.82	14.59	3.57	1.88	0.93 0.86 12.93
	LuM4	4.88	2.55	0.65 0.35	20.04	7.34	2.43	0.62 0.31 20.69
	LuM5	3.56	1.45	0.79 0.47	11.48	2.47	1.22	0.90 0.82	6.69
	LuM6	4.34	2.17	0.75 0.61	11.97	2.36	1.57	0.90 0.82	8.15
	Mean	3.40	1.81	0.79 0.62	15.09	2.96	1.68	0.78 0.63 14.88
	* Animals are identified by the type of breed: Charolais (Ch) or Luing (Lu), and the type of basal diet:
	mixed (M) or concentrate (C).

** CCC: Lin's concordance correlation coefficient. *** CV RMSE : coefficient of variation of the root mean squared error.

Table 3 P

 3 -values when testing for a difference in parameter means between basal diet and level of dietary oil groups

	P-values	Basal diet	Level of dietary oil
	DMI 𝑐	<0.001	0.5807
	DMI 𝑑	0.0603	0.8048
	IT 𝑐	0.0287	0.8349
	IT 𝑑	0.2508	0.8596

Acknowledgements

We thank Dr. John A. Rooke for helpful explanations on the respiration data from the study conducted at SRUC. We thank Dr. Glenn Marion (BioSS) for his valuable comments for improving the clarity of the manuscript. John Fredy Ramírez Agudelo is supported by a PhD grant of Colciencias (Colombia). BioSS and SRUC are funded by the Scottish Government through the Strategic Research programme of the Scottish Government's Rural and Environment Science and Analytical Services Division (RESAS). Helen Kettle was also funded under the Scottish Government's Strategic Partnership in Animal Science Excellence.

Rere

Supplementary material S1 Influence of the turnover rate of a respiration chamber on methane output

In a respiration chamber, the rate of methane produced (g/min) by the animal (𝑦 a ) and the rate of methane production measured in the chamber (𝑦 c ) are related by the following mass balance model

where 𝑏 (min -1 ) is the turnover rate of the chamber. The magnitude of 𝑏 determines how fast the trajectory of 𝑦 c will follow the trajectory of 𝑦 a . The higher 𝑏, the faster 𝑦 c converges to the trajectory of 𝑦 a . As displayed in Figure S1, a wrong choice of the turnover rate will imply an important mismatch between the dynamics of methane produced by the animal and the dynamics of the methane flux of the chamber. An adequate turnover rate guarantees that the dynamic of 𝑦 a is mirrored by the dynamics of 𝑦 c , that is that the approximation 𝑦 c ≈ 𝑦 a (used in this work) is consistent.

In theory, a very high turnover rate of the respiration chamber is ideal to capture the dynamics of methane produced by the animal. In practice, however, attention should be paid to very high turnover rates, since the gas flux at the outlet of the camber might be too fast for the gas analyser to produce consistent measurements.

The rate of sampling of the gas analyser must be considered to select the optimal turnover rate. Since the overall efficiency of a respiration chamber depends on the extraction, conduction, and gas analysis (Gardiner et al., 2015), both turnover rate and sampling rate are determining elements of the accuracy of respiration chambers for measuring methane emissions from livestock.

Figure S1 Experimen


Rafael Mu Ñoz-Tamayo
email: rafael.munoz-tamayo@inra.fr

A brief tribute to slowness in science *

November 2018 P ublish or perish: is it the right motto? The answer to this question should be a strong NO. But we already know that this is not the case. I look at the different research calls in which I have participated to get funding. In the CV section, I find the following phrase: I have a solid track record with W publications, of which X% are published in Q1 journals. I have Y citations and my h-index is Z. Is this the right information that defines my path? Are these the correct measurements of my research? I hope not. Even so, I am the one who has written these phrases and nobody has forced me to write them like that. The why goes with the following essay.

Let's imagine for a moment the following cliché of the scientist: a man with dishevelled hair, wide trousers, the collar of the shirt badly put, the glasses are somewhat fogged. The lenses reflect a lost look towards an apple tree. Time passes slowly. Ideas are carefully woven in a galaxy of neurons. The sun has hidden and our scientist takes the bicycle to go home. The next morning, when passing close to the river, the song of a bird makes him think in certain harmonics.

Well, this image encloses the implicit sense of a spiritual work, guided by the essence of asking, perhaps, by the utopian idea of finding a treasure that might change humankind. For some scientists, the utopia will come true. For others, the utopia will remain as a driving force. However, the reality faced by the scientist, in particular the young (early-career) scientist, is another one.

Metrics and misadventures

As it has occurred in the evaluation process of various public sector institutions [Ogien(2013)], the number has gained an overwhelming importance in the evaluation of research. In principle, the concept of measuring the research work responds to the natural need to have evaluation standards, which is absolutely valid and pertinent. The great difficulty in this procedure is that the measure implies science to be defined as a product and, in this transformation of sense, the legitimacy of science (and of the scientist who performs it) is hereof validated by the measure, in a process that is unscientific, subjective, and secretive [PLoSMedicine-Editors(2006)]. But science is not a product.

Currently, the performance of a scientist is mainly measured by their publications: the number of articles published, the number of times their articles are cited by peers, and the prestige of the journals where the articles have been published. The prestige of a journal is often assessed by an indicator known as the impact factor (IF) that measures the average number of citations for each article published in the journal. In addition to the IF, the scientist performance is measured by the H index that attempts to measure the impact of the work published in the scientific community. An index H of value n implies that the scientist has at least n published articles that have been cited at least n times.

The IF, the index H, the number of articles and citations are currently the main criteria for promotion and evaluation both in competitions to obtain research positions and in the calls for research projects and scholarships at national and international level. Although these indicators might correlate with the quality of scientific work, several authors have identified the limitations and dangers of these indicators to assess the value of published research work [Seglen(1997), PLoSMedicine-Editors(2006), Lawrence(2007), [START_REF] Brembs | Deep impact: unintended consequences of journal rank[END_REF], [START_REF] Paulus | The impact factor fallacy[END_REF]].

From these criticisms, it is worth to mention the San Francisco Declaration on Research Assessment (DORA, https://sfdora.org/read/) [Cagan(2013)] initiative to discourage and combat the misuse of IF to evaluate the work of individual scientists.

Evaluation is necessary to guarantee the quality of science, and publishing is undoubtedly a central aspect of the scientific work, which also implies a source of satisfaction and recognition. However, publication is not the raison d'être of science. The disproportionate importance of publications in the scientific career is a dangerous threat that promotes a science where the discovery of truth is diminished by the desire of publishing [Lawrence(2007), [START_REF] Park | Modelling the effects of subjective and objective decision making in scientific peer review[END_REF]].

This phenomenon is recognized in the scientific community under the broadly spread materialistic motto publish or perish, and is accompanied by the IF obsession (impactitis) [START_REF] Casadevall | Impacted science: Impact is not importance[END_REF]]. And in this race towards publication, the integrity of science has been jeopardized by ethical misconduct from the scientific community (including Nobel prizes) [START_REF] Martinson | Scientists behaving badly[END_REF]]. In fact, a significant number of cases of falsification [START_REF] Nosek | Scientific utopia: Ii. restructuring incentives and practices to promote truth over publishability[END_REF]] and data fabrication have been reported in various scientific domains such as the Schön case (2002) in physics, the Stapel case (2011) in psychology and the Voinnet case (2015) in biology (communication by Patricia Volland-Nail http://fr.slideshare.net/pvolland). A gray cloud covers a profession that should enlighten our knowledge of the world.

The pressure exerted by the eagerness to publish affects the entire scientific community, but it shows a marked importance for the young researcher, who must face a hypercompetition to be consolidated as a scientist through funding grants and job competitions in a selection system strongly based on article publication indicators [START_REF] Schäfer | Perspectives from early career researchers on the publication process in ecology -a response to Statzner & Resh[END_REF], [START_REF] Farlin | Performance indicators: The educational effect of publication pressure on young researchers in environmental sciences[END_REF], Schekman(2013)]. This system tends to favour short-term applied research projects over long-term basic research projects [Haroche(2012)]. The pressure to publish at any price is undoubtedly detrimental to the quality of science and the development of the profile of the researcher, who from the early stage of their career sees how the first utopia becomes overshadowed by mercantile factors. In the silence, the imposter syndrome [Woolston(2016)] comes to disturb our thoughts. In this context, it is very valuable, as statement of principle, the decisions of the ASM journals and eLife of removing the information of the IF on their websites as a declaration of the IF inappropriate use and of the need of alternative research metrics [START_REF] Schekman | Reforming research assessment[END_REF], [START_REF] Casadevall | Asm journals eliminate impact factor information from journal websites[END_REF]]. It must be kept in mind, however, that any kind of journal-based assessment will remain flawed in some way and not exempted of the impact factor fallacies discussed by [START_REF] Paulus | The impact factor fallacy[END_REF]].

A look at the slowness

The responsibility of changing the engine that drives the scientific activity is not only the resultant of the bureaucratic and political strategies of research centres, and the funding and evaluation agencies of research institutions in each country. The responsibility is also ours who have allowed the implantation of the tremendous reliance on journal citation metrics as indicators of the importance of our research [START_REF] Casadevall | Impacted science: Impact is not importance[END_REF]]. Although this essay illustrates a tendency that is detrimental to the integrity of science, it would be irresponsible to affirm that all scientists follow the doctrine of publishing or perishing and that the conquest of knowledge, as the first motivation, occupies a marginal place. Many researchers continue defending the integrity of science, and resist to the view of science as a mercantile product.

Science will continue its primary role of advancing knowledge and serve society. Modern times call for engaged scientists that, as proposed by the French collective Sciences en Marche (http://sciencesenmarche.org), defend the scientific method against preconceived opinions and ideologies, and strengthen the dialogue between science and society. Within this context, a switch of direction is needed for promoting beauty and integrity in science. In addition to the actions necessary in the hiring, promotion and funding decisions adopted in scientific institutions, a change of attitude on the part of the scientific community is necessary. We must return to the essential scientific values over the accumulation of publications, and thus be able to eradicate the impactitis medical condition [START_REF] Casadevall | Causes for the persistence of impact factor mania[END_REF]]. We must defend the principles of scientific integrity [Letellier(2016)] and engage in conducting a responsible, reliable and traceable research. And for that, we must beat the rush, not to fall into lethargy, but to strengthen our thinking. Science and the scientist need time. Time even to misunderstand each other (http://slow-science.org/). Time to read, not only the work of our scientific peers, but also to read and re-read Aristotle, Khant, Khun, Popper, Russell and modern philosophers. Time to read Mafalda, Calvin and Hobbes.

We need to beat the rush, to position utopia as the first place. Promote ethical behaviour through training and discussion spaces for consolidating, at the early stage of the scientist career, an awareness of what the essential scientific values are. An awareness that translates into action of resistance to defend the humanistic role of science.

Beat the rush, to look at science as well as art [ Barnes(1995)]. Beat the rush, to make the irrational emerge, to give way to creative thinking and give rise to serendipity: that of Alexander Flemming and Isaac Newton, and be able to shout Eureka all over the world.

Beat the rush, to strengthen the genius and keep alive the spirit of a child who asks questions over and over 1 . Beat the rush, to experience the joy of understanding: what is gone, what is on the way. 2 .

1 As the child of the song Escaramujo by Silvio Rodríguez. 2 From the poem Five Lines by Nazim Hikmet.