# Comparison of country-specific predictions of feed intake and methane emissions in sheep using different proxies

Q. Le Graverand, N. Lambe, F. Mcgovern, E.A. Navajas, P. Johnson, N.

Mchugh, I. de Barbieri, G. Ciappesoni, S. Rowe, B.A. Åby, et al.

► To cite this version:

Q. Le Graverand, N. Lambe, F. Mcgovern, E.A. Navajas, P. Johnson, et al. Comparison of country-specific predictions of feed intake and methane emissions in sheep using different proxies. Livestock Science, 2025, 296 (105716), pp.105716. 10.1016/j.livsci.2025.105716. hal-05100622

HAL Id: hal-05100622

https://hal.inrae.fr/hal-05100622v1

Submitted on 6 Jun 2025

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# Comparison of country-specific predictions of feed intake and methane emissions in sheep using different proxies

Q. Le Graverand<sup>a, ID</sup>, N. Lambe<sup>b, ID</sup>, F. McGovern<sup>c</sup>, E.A. Navajas<sup>d</sup>, P. Johnson<sup>e</sup>, N. McHugh<sup>c</sup>, I. De Barbieri<sup>d</sup>, G. Ciappesoni<sup>d, ID</sup>, S. Rowe<sup>e</sup>, B.A. Åby<sup>f, ID</sup>, J. Conington<sup>b, ID</sup>, C. Marie-Etancelin<sup>a, ID</sup>, F. Tortereau<sup>a, * ID</sup>

## HIGHLIGHTS

* Feed intake is more accurately predicted than feed efficiency traits.

* Body weight and feeding behaviour are the best proxy measurements for feed intake.

* Methane emissions are predicted with low to moderate accuracy.

## ARTICLE INFO

**Keywords:**

Sheep

Residual feed intake

Methane

Prediction

Proxies

Feed conversion ratio

## ABSTRACT

Ruminants are often singled out as being the main culprits when it comes to greenhouse gas (GHG) emissions, for methane (CH₄) in particular. However, with their diets based on forage and grazing, ruminants have a role to play to limit the feed-food competition. Sheep breeders are open to the prospect of including both feed efficiency and GHG emissions in their breeding programmes and whether or not it is for the purpose of genetic (or genomic) selection, the acquisition of new phenotypes for feed efficiency and GHG emissions are essential. Currently, devices recording GHG emissions and individual feed intake of animals reared indoors remains too expensive for most sheep breeders worldwide. In this study, research groups from six countries (UK (Scotland), France, Norway, Ireland, New Zealand and Uruguay) gathered their results obtained in different breeds to identify the most promising proxy measurements of feed intake and methane emissions. Despite the fact that each group set up their own protocol, there were several points in common: most feed intake trials were performed during 6 weeks on growing animals, and GHG emissions were all recorded with portable accumulation chambers (PACs). Different traits, in addition to feed intake and GHG emissions, were recorded and considered as putative proxies (body composition, growth, bodyweight, feeding behaviour, body condition score), as well as sheep genotypes and ruminal microbiota. Models' goodness of fit were estimated on training sets, whereas their prediction accuracy was assessed on actual validation datasets. The comparison of training and validation accuracies obtained with each dataset highlighted the well-documented problem of overfitting, particularly with microbiota data. In general, validation prediction accuracies were higher for feed intake than for the two feed efficiency criteria (residual feed intake and feed conversion ratio) investigated. The best predictions for feed intake were obtained when body weight and the average number of feeding events per day were included in the models (R²<sup>valid</sup>=0.78). Methane emissions were predicted with the highest accuracy when feed intake was considered among the proxies. Prediction accuracies for methane emissions obtained with the metagenome were higher than with sheep genome, although this accuracy remains quite low (R<sup>valid</sup>=0.32).

<footnote><sup>a</sup> GenPhySE, INRAE, ENVT, Université de Toulouse, 31326, Castanet Tolosan, France</footnote>

<footnote><sup>b</sup> Scotland's Rural College, W. Mains Rd., Edinburgh, Scotland EH9 3JG, UK</footnote>

<footnote><sup>c</sup> Teagasc, Animal and Grassland Research and Innovation Centre, Co., Galway, Athenry, Ireland</footnote>

<footnote><sup>d</sup> INIA Las Brujas, Instituto Nacional de Investigación Agropecuaria, Rincón del Colorado, Canelones 90100, Uruguay</footnote>

<footnote><sup>e</sup> AgResearch Invermay, Puddle Alley, Mosgiel, New Zealand</footnote>

<footnote><sup>f</sup> Norwegian University of Life Sciences, Universitetstunet 3, Ås 1433, Norway</footnote>

<footnote>* Corresponding author.
E-mail address: flavie.tortereau@inrae.fr (F. Tortereau).</footnote>
By comparing independent results from six countries, we highlighted that the recording of body weights, feeding behaviour and fixed effects are crucial for the prediction of feed intake. However, feed efficiency and methane emissions are relatively difficult to predict well, with the proxy measurements assessed here.

# 1. Introduction

Livestock production must overcome major challenges related to climate change, such as feed-food competition, use of arable lands and the environmental footprint. Ruminants have a key role to overcome these challenges: thanks to their digestive process, they are able to transform fibrous vegetation into high-quality food edible for humans. If this is a major asset to limit feed-food competition, there is a very unfavourable counterpart: methane emissions from the rumen microbiota. Methane (CH₄) is one of the main greenhouse gases (GHG), and enteric fermentation is responsible for 30% of agricultural emissions (FAO, 2023).

A current objective is to breed animals that more efficiently convert forage into food products (meat, milk) and fibre, while emitting low amounts of methane. Feed efficiency and GHG emissions are two relatively recent traits that are being considered in sheep breeding programmes although the former is well-established for other livestock species. Phenotyping of feed intake (required to calculate feed efficiency criteria, (Koch et al., 1963)) and GHG emissions at the animal level is currently too expensive to be taken on a large number of individuals, therefore identifying predictors of these that can be technically and economically recorded on large cohorts of animals should be considered.

Previous studies have highlighted phenotypic and/or genetic links amongst feed efficiency, feed intake and CH₄ emissions as well as other traits in sheep such as body weight, growth, body composition, feeding behaviour (Johnson et al. 2022; Marie-Etancelin et al. 2019; Marques et al. 2022; Paganoni et al. 2017; Tortereau et al. 2020), ruminal microbiota (Ellison et al. 2019; Marie-Etancelin et al. 2021; McGovern et al. 2020) and plasma metabolites (Goldansaz et al., 2020; Touitou et al., 2022). Ruminal microbiome and ruminal metabolome have been shown to improve the prediction of methane-related traits (Ross et al., 2020) but it has also been shown that ruminal microbiota does not improve phenotypic prediction of feed intake-related traits with animals phenotyped and sampled over several years (Le Graverand et al., 2023). Therefore, it is still uncertain whether these traits can predict feed intake, feed efficiency and CH₄ emissions with sufficient accuracy to allow these measures to be deployed on a larger scale, and thus make it possible to select sheep with reduced environmental footprint.

In this paper, feed efficiency, feed intake and CH₄ emission data were collected in six different countries. Each country analysed data separately to highlight which proxies could predict feeding and emissions traits under various recording conditions. The predictive ability of the best identified proxies was also compared according to animal physiological characteristics.

# 2. Material and methods

## 2.1. Animals, protocols and predicted traits

Animals were part of studies, carried out in six different countries (Table 1). The studies were designed to record individual feed intake and/or GHG emissions.

In France, the protocol was approved by a regional ethics committee (APAFIS #12682-2017121509105248 v3) on behalf of the French Ministry for Higher Education, Research and Innovation and carried out at the INRAE P3R unit (https://doi.org/10.15454/1.5483259352597417E12). In Scotland, the protocol was approved by UK Home Office license, following the regulations of the Animals (Scientific Procedures) Act 1986. In Uruguay, the protocol was approved by INIA Animal Ethics Committee (INIA 2018.2). In New Zealand, the protocol was approved

by AgResearch Animal Ethics Committee (AEC13563, AEC13892 and AEC14221). In Ireland, the protocol was approved by the health protection regulatory authority (AE19132/P098 & P112). In Norway, the protocol was approved by the Norwegian committee for the protection of animals used for scientific purposes (FOTS ID 24,196).

### 2.1.1. Feed intake and efficiency

Feed intake (FI) was recorded in all the studies. In France, Uruguay, Scotland and New Zealand, sheep were housed collectively and fed with automatic feeders which record each individual animal visit (duration and quantity) via electronic identification. For these four countries, the same phenotyping strategy was applied: six weeks of FI recording after two weeks of adaptation. In Ireland, feed intake was recorded differently depending on whether lambs were fed indoors or at pasture: when fed indoors, lambs were housed and fed individually, whereas outdoors, the n-alkane technique was used to estimate individual pasture intake as described by (McGovern et al. 2021). In Norway, ewes were housed and fed individually during the duration of the feed intake trials, two periods of three weeks each (including one week of adaptation). In all six studies, daily feed intake was averaged over the period of recording and expressed as daily dry matter intake (DMI) or daily energy intake (DEI) expressed in kcal/day in the Uruguayan dataset.

Apart from the measurement of feed intake, animals were weighed without prior fasting. In France, body weights (BW) were recorded at the beginning, at the middle and at the end of the six-week period, and average daily gain (ADG) was calculated over the six-week period. In Scotland, lambs were weighed on a weekly-basis, and ADG was calculated from the regression slope of weekly BW during the six-week feed intake trial. In Ireland, all animals were weighed fortnightly including directly before entering the Portable Accumulation Chambers (PACs) for methane measurements, or directly before the start of the feed intake trial, and ADG was calculated from the regression slope of the fortnightly weights from birth to the point of measurement (either for feed intake or methane). In Uruguay, BW were recorded by automatic weighing platforms, equipped with an electronic tag reader. Platforms were placed in front of the drinker to weigh animals automatically each time they came to drink water. ADG was defined as the slope of the regression of daily BW over the days in the trial. In New Zealand, BW were recorded twice weekly. Growth rates were calculated by using interpolation (weights on days between measurements estimated as the daily gain between two consecutive BW). In Norway, BW were recorded twice during the adaptation week, and every day during two periods (each period corresponded to a different silage quality) of two weeks, shortly before every PACs measurement. No ADG was calculated for the adult ewes in this trial.

Body composition was measured with ultrasound (US) in France, Ireland, Scotland, Uruguay and New Zealand. In France, ultrasound scans were performed at the level of the last floating rib at 1 cm from the spine, at the middle and end of the feed intake test period to estimate muscle depth (MD) of the *M. longissimus dorsi* and backfat thickness (BFT). In Ireland, MD and BFT of the *longissimus dorsi* muscle were measured with ultrasound by a trained technician at the third lumbar vertebrae. Ultrasound muscle and fat depth were measured on most lambs coinciding with the feed intake measurement. In New Zealand and Scotland, lambs were scanned using B-mode ultrasound by a commercial ultrasound assessor before the start and at the end of the feed intake test period to measure the depth of subcutaneous fat and muscle over the *M. longissimus dorsi*, also positioned at the third lumbar vertebra (Pálsson, 1939). In Uruguay, rib eye area (REA) and BFT were measured between the thoracic vertebrae 12 and 13, perpendicular to the spine
<table><caption>**Table 1**

Description of protocols according to each country.</caption><thead><tr><th></th><th>France</th><th>Scotland</th><th>Uruguay</th><th>New Zealand</th><th>Ireland</th><th>Norway</th></tr></thead><tbody><tr><td>Breed(s),<br>population(s),<br>line(s)<br>Start Age</td><td>Romane (two lines<br>divergently selected on<br>residual feed intake)<br>~ 90 days</td><td>Texel x Scotch<br>Mule lambs (Texel<br>sires)<br>~ 100 days</td><td>Australian Merino, Dohne Merino and<br>Corriedale<br>~10 months (Australian Merino), ~14<br>months (Dohne Merino), ~6 months<br>(Corriedale)</td><td>Beef + Lamb New Zealand Central Progeny<br>Test, the AgResearch Progeny Test flock or<br>the AgResearch Methane selection lines<br>~ 9 months</td><td>Representative of the national population<br>with four main breed types (Suffolk, Texel,<br>Belclare and Charollais)<br>Immature<br>(&lt;12 months)<br>and mature<br>(&gt;12 months)<br>Females</td><td>Old Norwegian Spæl and<br>Norwegian White Sheep<br>Mature<br>(&gt; 12 months)<br>Females<br>40 (20 per breed)</td></tr><tr><td>Sex</td><td>Males</td><td>Castrated males<br>and females<br>239</td><td>Males and females</td><td>Females</td><td>523</td><td>2 periods of 3 weeks,<br>including one-week<br>adaptation per period</td></tr><tr><td>Number of<br>animals - FI<br>Duration of feed<br>intake<br>recording<br>Diet for FI trial</td><td>277<br>6 weeks (after 2 weeks of<br>adaptation)</td><td>6 weeks (after 2<br>weeks of<br>adaptation)<br>Pelleted grass nuts</td><td>1287 (for the three breeds)<br>6 weeks (after 2 weeks of adaptation)</td><td>6 weeks (after 2 weeks of adaptation)</td><td>12 days indoor or 6 days at pasture</td><td>Two grass silage qualities<br>('early' and 'average' cut)<br>40 (20 per breed)<br>40 (20 per breed)</td></tr><tr><td>Number of<br>animals - GHG<br>Number of<br>animals with FI<br>and GHG<br>Reference</td><td>-<br>-<br>(Tortereau et al., 2020)</td><td>Low energy concentrate</td><td>Two types of Lucerne haylage</td><td>Lucerne pellets</td><td>Pasture/outdoor: perennial ryegrass<br>Indoor: grass silage<br>4869<br>180</td><td>(Åby et al., 2023)</td></tr><tr><td></td><td></td><td></td><td>1741 (Australian Merino)<br>1741</td><td>986<br>986</td><td>(O'Connor et al., 2023)</td><td>(Åby et al., 2023)</td></tr></tbody></table>

(De Barbieri et al., 2021), at the end of the feed intake test period.

In New Zealand and Scotland, computed tomography (CT) scanning was performed to have a more comprehensive body composition estimation. In New Zealand, a subset of lambs already measured with back ultrasounds were analysed with CT scanning after the feed intake test period. Five body composition traits were derived from CT-scan images: subcutaneous fat, intermuscular fat, internal (visceral) fat, carcass lean and non-fat visceral components. In Scotland, all lambs were CT-scanned, at the start and end of the feed intake trial, to predict total carcass fat and muscle weights based on pre-existing prediction equations calibrated for crossbred lambs (Bünger et al., 2011) as well as the rumen volume (including reticulum) (Lambe et al., 2022).

Two criteria of feed efficiency were derived from these measured traits: Feed Conversion Ratio (FCR) and Residual Feed Intake (RFI). FCR was calculated as the ratio between DMI and ADG, in Ireland, France and Scotland. RFI was estimated as the residual from a multiple linear regression of FI over production and maintenance requirements. In Ireland, New Zealand, France and Scotland, metabolic BW and ADG are included to account for maintenance and production requirements, respectively. In France, Scotland and Uruguay, ultrasound body composition (MD and/or REA and BFT) was also included in the regression to account for production. In Scotland, CT-measured body composition (total carcass fat and muscle weights) were included in the regression models for FCR and RFI.

### 2.1.2. GHG

In New Zealand, Ireland, Norway and Uruguay GHG emissions (CO₂ and CH₄) and O₂ consumption were all recorded with Portable Accumulation Chambers (O' Connor et al., 2021; Robinson et al., 2014). Methane (ppm), O₂ (%) and CO₂ (%) measurements were obtained over a 50-min measurement period at three specific time points (0, 25 and 50 min) using the RKI Eagle 2 monitor (Weatherall Equipment and Instruments Ltd, UK). Ambient temperature and atmospheric pressure were also recorded in one-minute intervals and used to convert gases emissions or consumption in grams per day at standard temperature and pressure conditions. In Uruguay, animals were measured twice in the last weeks of the feed intake test. In Norway, animals were measured daily during two weeks under each diet (same weeks as the recording of FI), so each animal had 20 gas measurements. In New Zealand, animals were measured twice during the feed intake test period, during weeks three and five. In Ireland, 180 of the growing animals were measured once for gaseous emissions within one week of the feed intake trial. As other animals were on separate feed intake trials the final number of records with feed intake and gaseous emissions was 419.

Methane and CO₂ emissions were considered as absolute emissions (g/day). Methane yield and methane intensity were calculated as the ratio of absolute methane over dry matter intake (g/kg MS) or over BW (g/ kg BW), respectively.

The description of the measured traits, as well as the fixed effects used in models are presented in Table 2. Briefly, the main fixed effects affecting feed efficiency and/or gas emissions were: the year, pen, litter size, suckling method (maternal or artificial), diet, age and sex.

### 2.2. Proxies tested

Different traits were considered as putative proxies for feed intake, feed efficiency or methane emissions depending on the study as shown in Table 2. Most of the proxies were the traits recorded during the feed intake trial, such as BW or body composition. In Scotland, New Zealand and Norway, the number of feeding events per day were also retrieved from the data and tested as a possible proxy.

In France, blood and rumen fluid samples were collected at the end of the intake trial. In New Zealand, tissue samples were collected from the animals near their birth and rumen fluid samples were collected at the time of the PAC measurements during the trial. DNA was extracted from the blood and tissue samples, and genotyping was performed using the
<table><caption>**Table 2**
List of recorded traits and proxies tested according to each study.</caption><thead><tr><th></th><th>France</th><th>Scotland</th><th>Uruguay</th><th>Ireland</th><th>New Zealand</th><th>Norway</th></tr></thead><tbody><tr><td>Feed intake</td><td>Average daily DMI</td><td>Average daily DMI</td><td>Average DEI</td><td>Average daily DMI</td><td>Average daily DMI</td><td>Average daily DMI</td></tr><tr><td>Bodyweight</td><td>Metabolic BW at the end of the feed intake trial</td><td>BW pre-trial, post-trial and mid test metabolic BW</td><td>BW at each visit to the drinker</td><td>BW pre-trial</td><td>BW twice weekly during trial</td><td>Daily BW during trial</td></tr><tr><td>GHG emissions</td><td></td><td></td><td>Absolute CH<sub>4</sub>, absolute CO<sub>2</sub></td><td>Absolute CH<sub>4</sub>, CH<sub>4</sub> yield, CH<sub>4</sub> intensity</td><td>Absolute CH<sub>4</sub>, CH<sub>4</sub> yield, CH<sub>4</sub> intensity, absolute CO<sub>2</sub></td><td>Absolute CH<sub>4</sub>, CH<sub>4</sub> yield, CH<sub>4</sub> intensity, absolute CO<sub>2</sub></td></tr><tr><td>Feeding behaviour</td><td></td><td>Average daily number of feeding events</td><td></td><td></td><td>Average daily number of feeding events</td><td>Average daily number of feeding events</td></tr><tr><td>Body composition (ultrasound)</td><td>Ultrasound measurements of fat and muscle depth at the end of the 6-week feed intake trial.</td><td>Ultrasound measurements of fat and muscle depth at the start and end of the 6-week feed intake trial.</td><td>Ultrasound measurements of fat depth and muscle area at the end of the 6-week feed intake trial.</td><td>Ultrasound measurements of fat and muscle depth at the start of the feed intake trial at pasture.</td><td>Predicted weight of carcass muscle and internal, subcutaneous and intermuscular fat depots at the start of the feed intake trial.</td><td></td></tr><tr><td>Body composition (CT scan)</td><td></td><td>Predicted total carcass fat and muscle weights at the start and end of the 6-week feed intake trial</td><td></td><td></td><td></td><td></td></tr><tr><td>Rumen volume (CT scan)</td><td></td><td>Total volume of rumen + reticulum measured from spiral CT scans</td><td></td><td></td><td></td><td></td></tr><tr><td>Body condition scores</td><td></td><td></td><td></td><td>Body condition scores were taken at the start of the feed intake trial on mature animals.</td><td></td><td></td></tr><tr><td>Ruminal microbiota</td><td>16S ARN sequencing (V4-V5 region)<br>(nb ASV<sup>1</sup>=582)</td><td></td><td></td><td></td><td>Restriction enzyme-reduced representation sequencing</td><td></td></tr><tr><td>Genetic markers</td><td>Illumina 50 K SNP chip (29,830 SNP after cleaning)</td><td></td><td></td><td></td><td>Genotyped on nested Illumina 5-600k Ovine SNP chips imputed to 600k Illumina Ovine HD SNP chip genotypes</td><td></td></tr><tr><td>Fixed effects</td><td>Year, pen, suckling method, litter size</td><td>Year, sex</td><td>Year, feed efficiency test, pen, sex</td><td>For growing animals: birth and rearing type<br>For ewes: parity, production stage, litter reared (or carried)<br>Both contemporary group of date by treatment</td><td>Birth/rearing rank and contemporary group</td><td>Silage quality, breed, date, period</td></tr></tbody></table>

<footnote n="1">¹: ASV=Amplicon Sequence Variant; BW = Bodyweight; DEI = Daily Energy Intake; DMI = Dry Matter Intake; GHG = Greenhouse Gas.</footnote>
<table><caption>**Table 3**

. Prediction models for feed intake, feed efficiency and methane emissions, and strategies of validation per country.</caption><thead><tr><th>Country</th><th>Predicted trait</th><th>Prediction strategy</th><th>Statistical method</th><th>Effects included in the models<sup>1</sup></th></tr></thead><tbody><tr><td>France</td><td>FI, RFI, FCR</td><td>Cross-validation</td><td>sPLS regression</td><td><ul><li>fixed eff., BW</li><li>Genotypes</li><li>Ruminal microbiota (ASV)</li><li>fixed eff., BW, ruminal microbiota (ASV)</li><li>BW, ADG, body comp. (US)</li><li>BW, ADG, body comp. (CT)</li><li>Fixed eff., BW, ADG, body comp. (US)</li><li>Fixed eff., BW, ADG, Body comp. (CT)</li><li>BW, rumen volume</li><li>BW, average daily nb of FE</li><li>Fixed eff., BW, average daily nb of FE</li><li>BW, ADG, CH<sub>4</sub>, CO<sub>2</sub></li></ul></td></tr><tr><td>Scotland</td><td>FI, FCR</td><td>Independent validation</td><td>Multiple ordinary linear regression</td><td><ul><li>fixed eff., FI24, FI48, FI72, random eff.<sup>*</sup></li><li>fixed eff., FI24, FI48, FI72, FI24<sup>2</sup>, FI48<sup>2</sup>, FI72<sup>2</sup>, random eff.<sup>*</sup></li><li>fixed eff., FI24, FI24<sup>2</sup>, random eff.<sup>*</sup></li><li>fixed eff., ADG, random eff.<sup>*</sup></li><li>fixed eff., BW, random eff.<sup>*</sup></li><li>fixed eff., BW, BW<sup>2</sup>, random eff.<sup>*</sup></li><li>fixed eff., ADG, BW, random eff.<sup>*</sup></li><li>fixed eff., BW, FI24, random eff.<sup>*</sup></li><li>fixed eff.</li><li>fixed eff., BW, ADG</li><li>fixed eff., BW, body comp. (US)</li><li>fixed eff., BW, body comp. (CT)</li><li>fixed eff., average daily nb of FE</li><li>fixed eff., CH<sub>4</sub>, CO<sub>2</sub></li><li>fixed eff.</li><li>fixed eff., BW, ADG</li><li>fixed eff., BW, body comp. (US)</li><li>fixed eff., BW, body comp. (CT)</li><li>fixed eff., feeding behaviour</li><li>fixed eff., feed intake</li><li>fixed eff., genomic</li><li>fixed eff., metagenome</li><li>fixed eff., BW, ADG, body comp. (US)</li><li>fixed eff., BW, ADG, US, CH<sub>4</sub></li><li>fixed eff., BW, BCS</li><li>fixed eff., BW, ADG, body comp. (US)</li><li>fixed eff., BW, ADG, body comp. (US), FI</li></ul></td></tr><tr><td>Uruguay</td><td>FI</td><td>Independent validation</td><td>Linear Model<br/>Non-linear model<br/>Random forest<br/>k-nearest neighbour</td><td><ul><li>fixed eff., random effects<sup>*</sup></li><li>fixed eff., FI24, FI72, random eff.<sup>*</sup></li><li>fixed eff., FI24, FI48, FI72, FI24<sup>2</sup>, FI48<sup>2</sup>, FI72<sup>2</sup>, random eff.<sup>*</sup></li><li>fixed eff., FI24, FI24<sup>2</sup>, random eff.<sup>*</sup></li><li>fixed eff., ADG, random eff.<sup>*</sup></li><li>fixed eff., BW, random eff.<sup>*</sup></li><li>fixed eff., BW, BW<sup>2</sup>, random eff.<sup>*</sup></li><li>fixed eff., ADG, BW, random eff.<sup>*</sup></li><li>fixed eff., BW, FI24, random eff.<sup>*</sup></li><li>fixed eff.</li><li>fixed eff., BW, ADG</li><li>fixed eff., BW, body comp. (US)</li><li>fixed eff., BW, body comp. (CT)</li><li>fixed eff., average daily nb of FE</li><li>fixed eff., CH<sub>4</sub>, CO<sub>2</sub></li><li>fixed eff.</li><li>fixed eff., BW, ADG</li><li>fixed eff., BW, body comp. (US)</li><li>fixed eff., BW, body comp. (CT)</li><li>fixed eff., feeding behaviour</li><li>fixed eff., feed intake</li><li>fixed eff., genomic</li><li>fixed eff., metagenome</li><li>fixed eff., BW, ADG, body comp. (US)</li><li>fixed eff., BW, ADG, US, CH<sub>4</sub></li><li>fixed eff., BW, BCS</li><li>fixed eff., BW, ADG, body comp. (US)</li><li>fixed eff., BW, ADG, body comp. (US), FI</li></ul></td></tr><tr><td>New Zealand</td><td>FI, RFI</td><td>None</td><td>Linear regression</td><td><ul><li>fixed eff., BW, ADG</li><li>fixed eff., BW, body comp. (US)</li><li>fixed eff., BW, body comp. (CT)</li><li>fixed eff., average daily nb of FE</li><li>fixed eff., CH<sub>4</sub>, CO<sub>2</sub></li><li>fixed eff.</li><li>fixed eff., BW, ADG</li><li>fixed eff., BW, body comp. (US)</li><li>fixed eff., BW, body comp. (CT)</li><li>fixed eff., feeding behaviour</li><li>fixed eff., feed intake</li><li>fixed eff., genomic</li><li>fixed eff., metagenome</li><li>fixed eff., BW, ADG, body comp. (US)</li><li>fixed eff., BW, ADG, US, CH<sub>4</sub></li><li>fixed eff., BW, BCS</li><li>fixed eff., BW, ADG, body comp. (US)</li><li>fixed eff., BW, ADG, body comp. (US), FI</li></ul></td></tr><tr><td>Ireland</td><td>FI, RFI, FCR in nulliparous</td><td>Cross-validation</td><td>Linear regression</td><td><ul><li>fixed eff., BW, ADG</li><li>fixed eff., BW, body comp. (US)</li><li>fixed eff., BW, body comp. (CT)</li><li>fixed eff., average daily nb of FE</li><li>fixed eff., CH<sub>4</sub>, CO<sub>2</sub></li><li>fixed eff.</li><li>fixed eff., BW, ADG</li><li>fixed eff., BW, body comp. (US)</li><li>fixed eff., BW, body comp. (CT)</li><li>fixed eff., feeding behaviour</li><li>fixed eff., feed intake</li><li>fixed eff., genomic</li><li>fixed eff., metagenome</li><li>fixed eff., BW, ADG, body comp. (US)</li><li>fixed eff., BW, ADG, US, CH<sub>4</sub></li><li>fixed eff., BW, BCS</li><li>fixed eff., BW, ADG, body comp. (US)</li><li>fixed eff., BW, ADG, body comp. (US), FI</li></ul></td></tr><tr><td>Norway</td><td>FI</td><td>None</td><td>Linear regression</td><td><ul><li>fixed eff., BW</li><li>fixed eff., average daily nb of FE</li><li>fixed eff., BW, average daily nb of FE</li><li>fixed eff., CH<sub>4</sub></li><li>fixed eff., CO<sub>2</sub></li><li>fixed eff., BW</li><li>fixed eff., feed intake</li><li>fixed eff., feed intake, BW</li><li>fixed eff., average daily nb of FE</li></ul></td></tr><tr><td>Absolute CH<sub>4</sub>, CH<sub>4</sub> yield, CH<sub>4</sub> intensity</td><td>Absolute CH<sub>4</sub>, CH<sub>4</sub> yield</td><td>None</td><td>Linear regression</td><td><ul><li>fixed eff., BW</li><li>fixed eff., feed intake</li><li>fixed eff., feed intake, BW</li><li>fixed eff., average daily nb of FE</li></ul></td></tr></tbody></table>

Illumina 50 K SNP chip. Ruminal microbiota from rumen fluid was assessed through metabarcoding or metagenomics in France (Le Graverand et al. 2023) and New Zealand (Hess et al., 2023), respectively. For metabarcoding, details are provided in Le Graverand et al. (2023). In New Zealand, metagenome profiles were generated using restriction enzyme-reduced representation sequencing (RE-RRS) (Hess et al., 2020).

## 2.3. Prediction models and accuracies

Prediction models for feed intake, feed efficiency and methane emissions were developed and assessed separately by each country to identify, independently, the best proxies depending on the available

data of each national protocol (Table 3).

A model may overfit if it captures random noise during training, instead of biological signals. When a model overfits, it will not generalize well: the overfitted model will poorly predict phenotypes from new data unseen during training. Thus, it is important to distinguish the training and the validation accuracies. Training accuracies are computed with data used during training. Thus, training accuracy is the maximum expected accuracy but it is unrealistically high when models overfit. Validation accuracies are computed with a new dataset unseen during training (phenotypic values and proxies). Validation accuracies are not inflated when models overfit. Validation sets came either from k-fold cross-validation (20% of the data were isolated from the database as validation set for New-Zealand and France, while 12% for Ireland) or

<footnote n="1">¹ Abbreviations of effects fitted in the models: ADG=Average Daily Gain; ASV=Amplicon Sequence Variant; Body comp.=body composition; BW=Body weight; CT=Computed Tomography; Fixed eff. = fixed effects; FE = feeding events; FI = feed Intake; FI24, FI48 and FI72=feed intake during 24 h, 48 h or 72 h respectively prior to PACs measurements; GHG = Greenhouse Gases; Random eff.=Random effects; US=Ultra Sound.</footnote>

<footnote>* : random effects include animal and PACs unit effects.</footnote>
independent populations (different breed in Uruguay or a second year of recording in Scotland).

In Norway, a series of linear models were tested using the GLM Procedure in SAS (SAS Inst. Inc., Cary, NC, USA; SAS Institute, 2011) to predict feed intake (daily dry matter intake), absolute CH₄ emission, CH₄ yield and CH₄ intensity. Terms tested in the model included fixed effects (time of feed, silage quality, breed, period), BW and the average number of feeding events per day as covariates. Feed intake was included as a covariate in prediction models of methane emissions, and gaseous emissions (absolute methane and absolute carbon dioxide) were included as covariates in prediction models of feed intake.

In Ireland, generalised linear models were fitted for CH₄ emissions and FI related traits with the GLM Procedure in SAS. For FI, RFI and FCR, analyses were performed separately for nulliparous (lamb and hogget) and ewes (pregnant, lactating or dry ewes). Potential proxies considered across both the nulliparous and ewe dataset and across all traits included animal breed composition, BW of the animal at FI recording and contemporary group (date of FI measurement by treatment group). When the nulliparous animals were under investigation, additional proxies were tested: ADG from birth to the point of FI measurement and ultrasound muscle and fat depth (recorded at approximately 150 days of age) and birth and rearing type of the lamb were added as fixed effects. Additional proxies were considered with ewes: parity (1, 2, 3, 4, ≥5), litter size reared (or carried in the case of pregnant ewes) and production stage (pregnant, lactating or dry). Cross-validations were performed for each trait separately, whereby data on the dependent variable under investigation was masked on approximately one eighth of animals and this process were repeated 100 times per trait.

In New Zealand, a series of linear models were tested using the GLM Procedure in SAS. Firstly, for each dependent variable a base model was fitted consisting of age of dam, birth/rearing rank and contemporary group fitted as fixed effects with birthday deviation fitted as covariate. A second model included the previous variables, plus BW and bodyweight gain. Subsequent models included the previous variables and either: i) body composition assessed through ultrasound scanning (BFT), ii) body composition assessed through computed tomography scanning (subcutaneous fat, intermuscular fat, internal fat, carcass lean and non-fat visceral components), iii) feeding behaviour traits (average daily number of feeding events), iv) greenhouse gas traits (considered for prediction of FI and RFI) including absolute methane, absolute carbon dioxide and absolute total gas emitted (methane + carbon dioxide) and v) feed intake (considered for the prediction of greenhouse gas traits).

In New Zealand, genomic and metagenomic predictions were also investigated. Genomic prediction was based on high-density imputed genotypes as described by Hess et al., 2023) (Table 2). Metagenome profiles were generated, from rumen samples collected whilst the animals were in the feed intake facility. The proportion of phenotypic variance adjusted for fixed effects by either breeding value (G), metagenome value (M) or the sum of both (G + M) and the correlation between the true and predicted value when using cross-fold validation are reported for these methods.

In Uruguay, the training dataset included 680 Australian Merino lambs of six feed efficiency trials. Validation accuracy was evaluated with independent datasets (not used during model training) in Australian Merino (n = 113), Corriedale (n = 186), and Dohne Merino (n = 279). Prediction models considered for feed intake were the linear regression (equation of a straight line), nonlinear regression (supervised learns generalized additive models), k-nearest neighbours' regression (uses the k-nearest neighbours' algorithm for regression) and random forest regression (tree-based algorithms for regression). The mlr R package was used for these analyses (Bischl et al., 2016). For the prediction of absolute methane emissions (g/day), nine repeated-measure mixed models were evaluated with the objective of identifying the most suitable one for Australian Merino lambs (n = 1741). The fixed effects included in the models were contemporary group defined by year*feed efficiency test* pen, date and daytime of the methane

emission measurement. Age of the lamb, average daily gain (ADG) during the feed efficiency test and metabolic body weight (MW) were included as covariates in the model, and animal and PAC units were included as random effects. Then, models differed on the additional covariates included: feed intake (and squared feed intake) as average metabolizable energy intake (kcal/day) recorded 24 hours (FI24 and FI24²), 48 hours (FI48 and FI48²), or 72 hours (FI72 and FI72²) before the methane emission measurement by PACs.

In France, the methodology to select the best model and to estimate the accuracy has been described in (Le Graverand et al., 2023). Briefly, sparse partial least squares regressions (sPLSR) were applied, using the mixOmics R package (version 6.18.1) (Rohart et al., 2017) in order to predict FI, RFI and FCR. For sPLS, two hyperparameters had to be tuned: the number of components and the number of variables per component. The tuning was limited to 1 to 20 components. No restriction was set on the tuning of the number of variables per component. The best models were selected through 5-fold cross-validations (on average 220 lambs in training sets and 60 in the validation set) repeated 50 times, based on the RMSE (Square root of the mean of squared errors) criteria. First, three groups of variables were used independently for sPLSR: fixed effects with BW, genotypes and ruminal microbiota. In a second step, ruminal microbiota was considered along with fixed effects and BW in order to estimate the added value of ruminal microbiota for the prediction of traits.

In Scotland, various multiple ordinary linear regression models were fitted in Genstat (19th edition; VSN International Ltd., 2018) to predict feed intake (average daily dry matter intake), RFI and FCR. Terms tested in the models included fixed effects (sex and year), mid-test metabolic bodyweight (calculated as (bodyweight predicted at 3 weeks after the start of the feed intake trial)⁰.⁷⁵) body composition assessed through ultrasound or CT scan, feeding behaviour and rumen volume. The data from lambs phenotyped in 2021 (n = 120 lambs) were used as the training data set to develop prediction equations, which were validated on the data from lambs phenotyped in 2022 (n = 119 lambs).

For all predictions, the R² of models (proportion of phenotypic variance explained by the model) and/or the RMSE are reported for the training and validation sets, except for CH₄ emissions in the Uruguayan dataset where models were compared using the Akaike Information Criterion (AIC). For mixed models tested in the dataset from New Zealand, correlations between true and predicted values were provided rather than R², and these correlations were not divided by the square root of heritability (for models including genomics) in order to compare the prediction accuracies of both mixed models tested.

## 3. Results

### 3.1. Feed intake and feed efficiency

Depending on the datasets, different methodologies were applied. In Norway, models were trained and evaluated on a single training dataset, whereas validation strategies in a separate data set were systematically set up for Ireland, France and Scotland. Uruguay and New Zealand used both methodologies, with or without a cross or independent validation (Table 3). As training metrics are always equivalent or higher than validation prediction metrics, results were reported in two tables: first, training accuracies (R²<sub>train</sub> or AIC<sub>train</sub>) represent the models' goodness of fit for in each dataset (Table 4) and second, the validation accuracies (R²<sub>valid</sub>, r<sub>valid</sub> or AIC<sub>valid</sub>) denote the models' predictive performance datasets (Table 5).

With most models, training accuracies were higher for FI than RFI and FCR. Only in France, training accuracies were larger for RFI when microbiota data were used. In Scotland, training accuracies were higher for FCR than FI when models did not account for the feeding behaviour (Table 4).

Irrespective of the country and the model, the best training accuracies for feed intake were obtained when models included BW and/or
<table><caption>**Table 4**

Model training accuracies for feed intake, residual feed intake and feed conversion ratio.</caption><thead><tr><th rowspan="2">Country</th><th rowspan="2">N<sup>2</sup></th><th rowspan="2">Methodology</th><th rowspan="2">Proxies in model<sup>2**</sup></th><th colspan="2">Feed intake (g/d or kcal/d)</th><th colspan="2">Residual feed intake (g/d)</th><th colspan="2">Feed conversion ratio</th></tr><tr><th>R<sup>2</sup><sub>train</sub></th><th>RMSE<sub>train</sub></th><th>R<sup>2</sup><sub>train</sub></th><th>RMSE<sub>train</sub></th><th>R<sup>2</sup><sub>train</sub></th><th>RMSE<sub>train</sub></th></tr></thead><tbody><tr><td rowspan="2">France</td><td rowspan="2">220<sup>1</sup></td><td rowspan="2">sPLSR</td><td>fixed eff., BW</td><td>0.75</td><td>129.09</td><td>0.24</td><td>125.37</td><td>0.35</td><td>0.90</td></tr><tr><td>Genetics (SNPs)</td><td>0.67</td><td>149.40</td><td>0.59</td><td>91.89</td><td>0.66</td><td>0.65</td></tr><tr><td rowspan="10">Scotland</td><td rowspan="10">120</td><td rowspan="10">Multiple ordinary linear regression</td><td>ruminal microbiota (ASVs)</td><td>0.34</td><td>211.01</td><td>0.84</td><td>57.18</td><td>0.29</td><td>0.94</td></tr><tr><td>BW, ADG, body comp. (US)</td><td>0.33</td><td>298</td><td>-</td><td>-</td><td>0.62</td><td>1.59</td></tr><tr><td>BW, ADG, body comp. (CT)</td><td>0.36</td><td>292</td><td>-</td><td>-</td><td>0.65</td><td>1.52</td></tr><tr><td>fixed eff., BW, ADG, body comp. (US)</td><td>0.33</td><td>298</td><td>-</td><td>-</td><td>0.62</td><td>1.59</td></tr><tr><td>fixed eff., BW, ADG, body comp. (CT)</td><td>0.36</td><td>290</td><td>-</td><td>-</td><td>0.65</td><td>1.52</td></tr><tr><td>BW, rumen volume</td><td>0.33</td><td>298</td><td>0.09</td><td>220</td><td>0.53</td><td>1.76</td></tr><tr><td>BW, average daily nb of FE</td><td>0.80</td><td>164</td><td>0.72</td><td>123</td><td>0.71</td><td>1.38</td></tr><tr><td>fixed eff., BW, average daily nb of FE</td><td>0.80</td><td>164</td><td>0.72</td><td>123</td><td>0.72</td><td>1.37</td></tr><tr><td rowspan="4">Uruguay</td><td rowspan="4">680</td><td>linear model</td><td>BW, ADG, CH<sub>4</sub>, CO<sub>2</sub></td><td>0.74</td><td>0.346<sup>1</sup></td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>non-linear model</td><td>BW, ADG, CH<sub>4</sub>, CO<sub>2</sub></td><td>0.77</td><td>0.327<sup>1</sup></td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>random forest</td><td>BW, ADG, CH<sub>4</sub>, CO<sub>2</sub></td><td>0.77</td><td>0.328<sup>1</sup></td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>k-nearest neighbor</td><td>BW, ADG, CH<sub>4</sub>, CO<sub>2</sub></td><td>0.78</td><td>0.324<sup>1</sup></td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="10">New Zealand</td><td rowspan="10">800<sup>3§</sup></td><td rowspan="10">linear regression</td><td>fixed eff.</td><td>0.65</td><td>337</td><td>0.02</td><td>1.31</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, ADG</td><td>0.89</td><td>187</td><td>0.02</td><td>1.32</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, body comp. (US)</td><td>0.90</td><td>180</td><td>0.08</td><td>1.28</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, body comp. (CT)</td><td>0.92</td><td>178</td><td>0.15</td><td>0.94</td><td>-</td><td>-</td></tr><tr><td>fixed eff., average daily nb of FE</td><td>0.90</td><td>171</td><td>0.18</td><td>1.2</td><td>-</td><td>-</td></tr><tr><td>fixed eff., CH<sub>4</sub>, CO<sub>2</sub></td><td>0.90</td><td>182</td><td>0.06</td><td>1.29</td><td>-</td><td>-</td></tr><tr><td>fixed eff., genomic</td><td>-</td><td>-</td><td>0.39</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., metagenome</td><td>-</td><td>-</td><td>0.77</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="2">Ireland</td><td rowspan="2">362</td><td rowspan="2">linear regression</td><td>fixed eff., BW, ADG, body comp. (US)</td><td>0.75</td><td>253</td><td>0.06</td><td>252</td><td>0.65</td><td>1.74</td></tr><tr><td>fixed eff., BW, ADG, US, CH<sub>4</sub></td><td>0.83</td><td>234</td><td>0.11</td><td>234</td><td>0.66</td><td>1.71</td></tr><tr><td rowspan="8">Norway</td><td rowspan="8">1120</td><td rowspan="8">linear regression</td><td>fixed eff., BW, BCS</td><td>0.60</td><td>454</td><td>0.14</td><td>455</td><td>-</td><td>-</td></tr><tr><td>fixed eff.</td><td>0.80</td><td>217</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW</td><td>0.91</td><td>145</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., average daily nb of FE</td><td>0.81</td><td>215</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, average daily nb of FE</td><td>0.91</td><td>217</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., CH<sub>4</sub></td><td>0.95</td><td>109</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., CO<sub>2</sub></td><td>0.89</td><td>165</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

Metrics computed on training sets: R<sup>2</sup><sub>train</sub>=coefficient of determination; RMSE<sub>train</sub>=root mean square error.

2* N refers to the number of animals on which the adjustment metric was calculated.

2** Abbreviations of effects fitted in the models: ADG=Average Daily Gain; Body comp.=body composition; BW=Body weight; CT=Computed Tomography; Fixed eff. = fixed effects; FE=Feeding events; FI24, FI48 and FI72=feed intake during 24 h, 48 h or 72 h, respectively prior to PACs measurements; GHG = Greenhouse Gases; ASV=Amplicon Sequence Variant; US=Ultra Sound.

2§ Average number of animals over the 50 repetitions of five-fold cross validations.

2§§ Average number of animals over cross validations (each cohort being a different fold).

† RMSE expressed in kcal/day

Proxies with no significant effects (p-value>0.05) in the prediction model are in italics.

fixed effects. In France, the model based on sheep genotypes reached the second highest training accuracy for FI (R<sup>2</sup><sub>train</sub>=0.67), after the model based on fixed effects and BW (R<sup>2</sup><sub>train</sub>=0.75). In Scotland, the average number of meals along with BW and fixed effects explained well feed intake (R<sup>2</sup><sub>train</sub>=0.80). In Norway and Ireland, the highest training metrics were obtained for FI when methane emissions were included in the model. In New Zealand, all training R<sup>2</sup> for FI were above 0.89, except for the model relying only on fixed effects (R<sup>2</sup><sub>train</sub>=0.65). Regardless of the prediction methodology applied, training accuracies for FI in the Uruguayan dataset were very close, ranging from 0.74 to 0.78.

For RFI, the highest training accuracy in France was obtained with ruminal microbiota (R<sup>2</sup><sub>train</sub>=0.84). In Scotland, feeding behaviour along with BW explained well RFI (R<sup>2</sup><sub>train</sub>=0.72, with or without fixed effects in the model). According to training accuracies, best FCR proxies in Ireland were: fixed effects, the BW, body weight gain along with body composition or methane emissions (R<sup>2</sup><sub>train</sub>=0.65 and 0.66, respectively), the BW and feeding behaviour in Scotland (R<sup>2</sup><sub>train</sub>=0.71 and 0.72, with or without fixed effects in the model) and SNPs in France (R<sup>2</sup><sub>train</sub>=0.66).

For the validation sets, the highest prediction accuracies for FI were obtained with regressions including BW and feeding behaviour (R<sup>2</sup><sub>valid</sub>=0.78) in Scotland (Table 5). Then, the best predictions were obtained for FI with fixed effects and BW in France (R<sup>2</sup><sub>valid</sub>=0.71). In Uruguay, FI predictions reached intermediate accuracies (R<sup>2</sup><sub>valid</sub> from 0.20 to 0.37). The implementation of different statistical models did not change the range of accuracies for the Uruguayan data.

For RFI, the best validation accuracies were obtained with models relying on BW and feeding behaviour in Scotland (R<sup>2</sup><sub>valid</sub>=0.65), on sheep genotypes in France (R<sup>2</sup><sub>valid</sub>=0.22) and metagenome in New Zealand (r<sub>valid</sub>=0.47). For FCR, the best predictions were obtained when models relied on BW, ADG and body composition assessed by ultrasound (R<sup>2</sup><sub>valid</sub>=0.58) in Scotland. In France, the best predictions were obtained with fixed effects and BW or with sheep genotypes (R<sup>2</sup><sub>valid</sub>=0.25).

## 3.2. Methane emissions

Methane emissions were predicted with datasets from Norway, Ireland, New Zealand and Uruguay. Depending on the datasets, different methodologies were applied. In Norway and Uruguay predictions were trained and evaluated on a single dataset, whereas cross-validation strategies were set up for New Zealand and Ireland (Table 3). So, training metrics are reported for Norway, Ireland, New Zealand and Uruguay (Table 6), and prediction metrics on the validation set is reported for New Zealand and Ireland (Table 7).

In Norway and New Zealand, training accuracies were higher for absolute methane than methane yield and methane intensity (for Norway, only). In Ireland, adjustment of methane yield and absolute methane were similar (R<sup>2</sup><sub>train</sub> from 0.83 to 0.89).

In Norway, whatever the trait, the best training accuracies were obtained with feed intake and BW included in the models. In New Zealand, the highest training accuracies were obtained with models
<table><caption>**Table 5**

Model validation accuracies for feed intake, residual feed intake and feed conversion ratio.</caption><thead><tr><th rowspan="2">Country</th><th rowspan="2">N**</th><th rowspan="2">Methodology</th><th rowspan="2">Proxies in model<sup>a</sup></th><th colspan="2">Feed intake (g/d)</th><th colspan="3">Residual feed intake (g/d)</th><th colspan="2">Feed conversion ratio</th></tr><tr><th>R<sup>2</sup><sub>valid</sub></th><th>RMSE<sub>valid</sub></th><th>r<sub>valid</sub></th><th>R<sup>2</sup><sub>valid</sub></th><th>RMSE<sub>valid</sub></th><th>R<sup>2</sup><sub>valid</sub></th><th>RMSE<sub>valid</sub></th></tr></thead><tbody><tr><td rowspan="3">France</td><td rowspan="3">57<sup>b</sup></td><td rowspan="3">sPLSR+ cross-validation</td><td>fixed eff. + BW</td><td>0.71</td><td>144.34</td><td>-</td><td>0.14</td><td>137.38</td><td>0.25</td><td>1.03</td></tr><tr><td>Genetics (SNPs)</td><td>0.35</td><td>218.42</td><td>-</td><td>0.22</td><td>133.56</td><td>0.25</td><td>1.08</td></tr><tr><td>ruminal microbiota (ASV)</td><td>0.27</td><td>230.76</td><td>-</td><td>0.08</td><td>153.39</td><td>0.18</td><td>1.10</td></tr><tr><td rowspan="10">Scotland</td><td rowspan="10">119</td><td rowspan="10">Multiple ordinary linear regression<br/>+ independent validation</td><td>fixed eff. + BW + ruminal<br/>microbiota (ASV)</td><td>0.62</td><td>162.19</td><td>-</td><td>0.08</td><td>144.85</td><td>0.19</td><td>1.06</td></tr><tr><td>BW + ADG + body comp.<br/>(US)</td><td>0.17</td><td>390</td><td>-</td><td>-</td><td>-</td><td>0.58</td><td>1.85</td></tr><tr><td>BW + ADG + body comp.<br/>(CT)</td><td>0.20</td><td>386</td><td>-</td><td>-</td><td>-</td><td>0.54</td><td>1.94</td></tr><tr><td>fixed eff. + BW + ADG +<br/>body comp. (US)</td><td>0.17</td><td>390</td><td>-</td><td>-</td><td>-</td><td>0.58</td><td>1.85</td></tr><tr><td>fixed eff. + BW + ADG +<br/>body comp. (CT)</td><td>0.12</td><td>401</td><td>-</td><td>-</td><td>-</td><td>0.54</td><td>1.94</td></tr><tr><td>BW + rumen volume</td><td>0.17</td><td>390</td><td>-</td><td>0.01</td><td>293</td><td>0.01</td><td>2.84</td></tr><tr><td>BW + average daily nb of FE</td><td>0.78</td><td>200</td><td>-</td><td>0.65</td><td>182</td><td>0.15</td><td>2.63</td></tr><tr><td>fixed eff. + BW + average<br/>daily nb of FE</td><td>0.78</td><td>200</td><td>-</td><td>0.65</td><td>182</td><td>0.15</td><td>2.63</td></tr><tr><td rowspan="5">Uruguay<sup>1</sup></td><td rowspan="5">113 to<br/>277</td><td>linear model</td><td>BW + ADG + CH<sub>4</sub> + CO<sub>2</sub></td><td>0.25 to<br/>0.37</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>+ independent validation</td><td>BW + ADG + CH<sub>4</sub> + CO<sub>2</sub></td><td>0.21 to<br/>0.35</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>non-linear model</td><td>BW + ADG + CH<sub>4</sub> + CO<sub>2</sub></td><td>0.23 to<br/>0.27</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>+ independent validation</td><td>BW + ADG + CH<sub>4</sub> + CO<sub>2</sub></td><td>0.20 to<br/>0.31</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>random forest</td><td>BW + ADG + CH<sub>4</sub> + CO<sub>2</sub></td><td>0.20 to<br/>0.31</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="2">New Zealand</td><td rowspan="2">200<sup>b</sup></td><td>Mixed models</td><td>fixed eff. + genomic</td><td>-</td><td>-</td><td>0.29</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>+ cross-validation</td><td>fixed eff. + metagenome</td><td>-</td><td>-</td><td>0.47</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="2">Ireland</td><td rowspan="2">45<sup>#</sup></td><td rowspan="2">Linear regression + cross-validation</td><td>fixed eff. + BW + ADG + US</td><td>0.57</td><td>357.58</td><td>0.02</td><td>252.12</td><td>0.30</td><td>2.37</td></tr><tr><td>fixed eff. + BW + ADG + US<br/>+ GHG emissions</td><td>0.12</td><td>508.78</td><td>0.03</td><td>400.73</td><td>-</td><td>-</td></tr></tbody></table>

Metrics computed on validation sets: r<sub>valid</sub>=Pearson correlation; R<sup>2</sup><sub>valid</sub>=coefficient of determination; RMSE<sub>valid</sub>=root mean square error.

* Fixed Eff.=Fixed effects; BW=body weight; ADG = Average Daily Gain; US=body composition from ultrasound; CT= body composition from computed tomography; BCS = body condition score; GHG = greenhouse gases; FE=Feeding events.

** N refers to the number of animals on which the prediction accuracy was calculated.

# Number of animals over 100 repetitions of cross-validation.

§ Average number of animals over the 50 repetitions of five-fold cross validations.

¶¶ Average number of animals over cross validations (each cohort being a different fold).

¹ range of accuracies for each model obtained with 3 different independent populations (113 Australian Merino or 186 Corriedale or 277 Dohne Merino).

relying on BW and body composition for absolute methane (R<sup>2</sup><sub>train</sub>=0.39) and methane yield (R<sup>2</sup><sub>train</sub>=0.13). The training accuracy was slightly lower when the model relied on FI to explain absolute CH<sub>4</sub> (R<sup>2</sup><sub>train</sub>=0.33).

In Uruguay, the best model for absolute methane emissions (AIC<sub>train</sub>=9199) included fixed and random effects, BW and feed intake recorded over the last 24 hours only (Table 6).

The best validation accuracies for the predictions of methane emissions (absolute methane or methane yield) were obtained in the Irish dataset with feed intake included, for both absolute methane and methane yield. In the dataset from New Zealand, the best predictions were obtained with metagenome among the proxies rather than sheep genome, for both studied methane traits (Table 7).

## 4. Discussion

The mitigation of methane emissions and the improvement of feed efficiency are two key objectives internationally to not only tackle the consequences of climate change and variability but also help in addressing the challenges of sustainable livestock production. International collaborations enable results that originate from different datasets to be truly independent validations of methods and protocols to monitor complex phenotypes associated with environmental impact which is of interest to other countries (Conington et al., 2022).

Here, we have collated prediction results from six countries where feed efficiency and GHG emissions were being studied to consider their

inclusion into planned national breeding programmes (Farrell et al. 2022; Johnson et al. 2022; Marie-Etancelin et al. 2019; Navajas et al. 2022; Tortereau et al. 2020). Here, country-specific protocols are applied to record feed intake and then estimate feed efficiency (Table 1). These protocols were carried out on animals from different breeds, and at different ages (from post-weaning to adult ewes). The biology underlying feed intake, feed efficiency and GHG emissions varies with age and physiological status, as highlighted by low to moderate phenotypic correlations between ages for feed intake and feed efficiency (Muir et al., 2020) and for methane emissions (O'Connor et al., 2024). It is thus likely that relevant proxies for these traits differ between protocols. Therefore, pooling data of all the six countries together would probably not identify the best proxies for each situation.

GHG emissions were recorded across 4 countries with a common device: Portable Accumulation Chambers with gas emissions measured using the same gas analyser (Goopy et al., 2011). In small ruminants, PACs are becoming the main device to record GHG emissions for breeding purposes: although PACs were able to recover only a part of the methane release (70% on average), measurements with PACs were highly correlated (r = 0.99) with CH<sub>4</sub> masses recovered by mass flow controllers (Levrault et al., 2023). Nevertheless GHG emissions from sheep can also be obtained using the GreenFeed equipment that was designed specifically for this species (Rozier et al. 2021; Tortereau et al. 2023).

The identification of proxies for feed intake and/or feed efficiency and for GHG emissions is attractive, as it will benefit breeding
<table><caption>**Table 6**

Model training accuracies for methane emissions.</caption><thead><tr><th rowspan="2">Country</th><th rowspan="2">N*</th><th rowspan="2">methodology</th><th rowspan="2">Proxies in model**</th><th colspan="3">Absolute CH<sub>4</sub> (g/d)</th><th colspan="3">CH<sub>4</sub> yield</th><th colspan="3">CH<sub>4</sub> intensity</th></tr><tr><th>R<sup>2</sup><sub>train</sub></th><th>RMSE<sub>train</sub></th><th>AIC<sub>train</sub></th><th>R<sup>2</sup><sub>train</sub></th><th>RMSE<sub>train</sub></th><th>R<sup>2</sup><sub>train</sub></th><th>RMSE<sub>train</sub></th></tr></thead><tbody><tr><td rowspan="10">Uruguay</td><td rowspan="10">1741</td><td rowspan="10">linear regression</td><td>fixed eff., random eff.</td><td>-</td><td>-</td><td>9560</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., FI24,FI48, FI72, random eff.</td><td>-</td><td>-</td><td>9305</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., FI24,FI48, FI72, FI24<sup>2</sup>,FI48<sup>2</sup>, FI72<sup>2</sup>, random eff.</td><td>-</td><td>-</td><td>9274</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., FI24, FI24<sup>2</sup>, random eff.</td><td>-</td><td>-</td><td>9264</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., ADG, random eff.</td><td>-</td><td>-</td><td>9489</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, random eff.</td><td>-</td><td>-</td><td>9329</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, BW<sup>2</sup>, random eff.</td><td>-</td><td>-</td><td>9334</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., ADG, BW, random eff.</td><td>-</td><td>-</td><td>9312</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, FI24, random eff.</td><td>-</td><td>-</td><td>9199</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="10">New Zealand</td><td rowspan="10">800<sup>†</sup></td><td rowspan="10">linear regression</td><td>fixed eff.</td><td>0.09</td><td>2.77</td><td>-</td><td>0.06</td><td>0.006</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, ADG</td><td>0.34</td><td>2.36</td><td>-</td><td>0.06</td><td>0.006</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, body composition (US)</td><td>0.34</td><td>2.37</td><td>-</td><td>0.08</td><td>0.006</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, body composition (CT)</td><td>0.39</td><td>2.46</td><td>-</td><td>0.13</td><td>0.006</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., average daily nb of FE</td><td>0.36</td><td>2.33</td><td>-</td><td>0.09</td><td>0.006</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., FI</td><td>0.33</td><td>2.37</td><td>-</td><td>0.09</td><td>0.006</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Mixed models</td><td>0.35</td><td>-</td><td>-</td><td>0.35</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., genomic</td><td>0.86</td><td>-</td><td>-</td><td>0.60</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fix eff., metagenome</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="3">Ireland</td><td rowspan="3">180</td><td rowspan="3">linear regression</td><td>fixed eff., BW, ADG, body composition (US)</td><td>0.86</td><td>3.13</td><td>-</td><td>0.83</td><td>0.004</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff., BW, ADG, US, feed intake</td><td>0.89</td><td>2.79</td><td>-</td><td>0.84</td><td>0.004</td><td>-</td><td>-</td><td>-</td></tr><tr><td>fixed eff.</td><td>0.75</td><td>5.10</td><td>-</td><td>0.01</td><td>0.002</td><td>0.30</td><td>0.05</td><td>0.05</td></tr><tr><td rowspan="4">Norway</td><td rowspan="4">40</td><td rowspan="4">linear regression</td><td>fixed eff., BW</td><td>0.88</td><td>3.62</td><td>-</td><td>0.02</td><td>0.002</td><td>0.33</td><td>0.05</td><td>0.05</td></tr><tr><td>fixed eff., feed intake</td><td>0.94</td><td>2.56</td><td>-</td><td>0.01</td><td>0.001</td><td>0.57</td><td>0.04</td><td>0.04</td></tr><tr><td>fixed eff., feed intake, BW</td><td>0.94</td><td>2.55</td><td>-</td><td>0.05</td><td>0.002</td><td>0.69</td><td>0.03</td><td>0.03</td></tr><tr><td>fixed eff., average daily nb of FE</td><td>0.76</td><td>5.11</td><td>-</td><td>0.02</td><td>0.002</td><td>0.32</td><td>0.04</td><td>0.04</td></tr></tbody></table>

Metrics computed on training sets: R<sup>2</sup><sub>train</sub>=coefficient of determination; RMSE<sub>train</sub>=root mean square error; AIC<sub>train</sub>=Akaike information criterion.

* N refers to the number of animals on which the adjustment metric was calculated.

** Fixed Eff.=Fixed effects; BW=body weight; ADG = Average Daily Gain; GHG = Greenhouse Gas emissions; US=body composition from ultrasound; CT= body composition from computed tomography; FE= feeding events; FI24, FI48 and FI72=feed intake during 24 h, 48 h or 72 h respectively prior to PACs measurements; random eff. = random effects.

§ Average number of animals over cross validations (each cohort being a different fold).

<table><caption>**Table 7**

Model validation accuracies for methane emissions.</caption><thead><tr><th rowspan="2">Country</th><th rowspan="2">N*</th><th rowspan="2">methodology</th><th rowspan="2">Proxies in model**</th><th colspan="3">Absolute CH<sub>4</sub></th><th colspan="3">CH<sub>4</sub> yield</th><th colspan="3">CH<sub>4</sub> intensity</th></tr><tr><th>r<sub>valid</sub></th><th>R<sup>2</sup><sub>valid</sub></th><th>RMSE<sub>valid</sub></th><th>r<sub>valid</sub></th><th>R<sup>2</sup><sub>valid</sub></th><th>RMSE<sub>valid</sub></th><th>R<sup>2</sup><sub>valid</sub></th><th>RMSE<sub>valid</sub></th></tr></thead><tbody><tr><td rowspan="2">New Zealand</td><td rowspan="2">200<sup>†</sup></td><td>Mixed models</td><td>fixed eff., genomic</td><td>0.13</td><td>-</td><td>-</td><td>0.10</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>+ cross-validation</td><td>fixed eff., metagenome</td><td>0.32</td><td>-</td><td>-</td><td>0.30</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="2">Ireland</td><td rowspan="2">45<sup>#</sup></td><td>Linear regression</td><td>fixed eff., BW, ADG, US</td><td>-</td><td>0.31</td><td>4.65</td><td>-</td><td>0.04</td><td>0.0039</td><td>-</td><td>-</td></tr><tr><td>+ cross-validation</td><td>fixed eff., BW, ADG, US, FI</td><td>-</td><td>0.34</td><td>4.61</td><td>-</td><td>0.21</td><td>0.0037</td><td>-</td><td>-</td></tr></tbody></table>

Metrics computed on validation sets: r<sub>valid</sub>=Pearson correlation; R<sup>2</sup><sub>valid</sub>=coefficient of determination; RMSE<sub>valid</sub>=root mean square error.

* N refers to the number of animals on which the prediction accuracy was calculated.

** Fixed Eff.=Fixed effects, BW=body weight; ADG = Average Daily Gain; US=body composition from ultrasound; FI=Feed intake.

# Number of animals over 100 repetitions of cross-validation.

§ Average number of animals over cross validations (each cohort being a different fold).

companies or breeders' associations that cannot afford high-cost equipment such as automatic feeders or PACs although industry-wide initiatives may go some way to addressing the high costs. Here, we tested, for each dataset, a variety of phenotypes as putative proxies of feed intake, feed efficiency and methane emissions.

The comparison of training and validation accuracies in datasets from France, New Zealand and Uruguay confirms the well-known problem of overfitting. A striking example is observed with ruminal microbiota in the French dataset, with 16sRNA proxies. The accuracy for RFI drops from 0.84 in the training set to 0.08 in the validation set. Here, overfitting might be even more important because ruminal microbiota data are noisy and high-dimensional (Table 2) (Domingos, 2012). The different types of variables (quantitative vs. qualitative) could also explain part of the observed overfitting. As the same bias could be observed with other proxies, we have to keep in mind that training accuracies can largely exceed validation accuracies. Only validation accuracies can help assess whether proxies will generalize well, when it comes to predict new animal phenotypes.

Ruminal microbiota proxies had low validation prediction accuracies. For example, in New Zealand, methane emissions were predicted with a moderate accuracy of r<sub>valid</sub>=0.32 (Table 7), while feed intake (Table 5) was predicted in France with validation accuracy R<sup>2</sup><sub>valid</sub>=0.27. As the ruminal microbiota might be difficult to sample routinely (as it requires oral tubing of the animals), and assessing ruminal microbiota through 16 s RNA sequencing or through RE-RRS still remains expensive, it is difficult to see how this proxy would be worth using routinely.

The predictive ability of feeding behaviour was tested in Scotland, Norway and New Zealand. When it was considered as an explanatory variable (through the number of feeding events), training accuracies were improved for feed intake and RFI. In Scotland, training accuracies reached 0.72 for RFI and 0.80 for FI. In Norway and New Zealand, training accuracies respectively reached 0.91 and 0.90 for FI (Table 4). Validation accuracies remained high when FI was predicted from the feeding behaviour and BW (R<sup>2</sup><sub>valid</sub>=0.78 in Scotland). Positive or negligible genetic correlations have been estimated between RFI and the number of feeding events per day in the Romane breed (r<sub>g</sub>=+0.51) or in
different maternal breeds from New Zealand ($r_g = +0.13$), respectively (Johnson et al. 2022; Marie-Etancelin et al. 2019). The average number of feeding events is also negatively correlated with methane emissions (Johnson et al. 2022). Negative correlations between the number of feeding events per day and CH₄ emissions, and positive correlations between the number of feeding events per day and RFI have been confirmed in another dataset (Sepulveda et al., 2022). Including feeding behaviour as a proxy of feed intake, RFI and CH₄ emissions looks promising. In the studies presented here, feeding behaviour was retrieved from automatic feeders. Cheaper technologies, for instance allowing the recording of visits to the feeder without feed intake, have to be developed and implemented in order to reasonably consider feeding behaviour as a potential proxy (Johnson et al. 2023). In these six datasets, water intake was not recorded, but this trait has been proposed as a good proxy of DMI in beef cattle (Blake et al., 2023) and it has been reported in sheep that animals more efficient in water use tend to present a improved feed efficiency (Barros de Freitas et al. 2021). Future studies in sheep should evaluate the opportunity of recording water intake as a proxy of DMI.

Moderate validation accuracies ($R^2_{valid}$ from 0.20 to 0.37) were reached when FI was predicted from GHG emissions, in the Uruguayan dataset. Previous research indicated that information from PACs together with body weight can be used to accurately predict feed intake (Macleay and Scanlan, 2021; Robinson et al., 2016). This would indicate that PACs would allow to measure GHG emissions and estimate feed intake, although only moderate prediction accuracies were obtained in the gathered studies. PACs could thus have an interesting cost benefit ratio for breeding purposes if GHG emissions and feed intake can be derived from its use.

Validation accuracies were higher for feed intake than for feed efficiency traits, particularly for RFI (Table 5). Therefore, predicting feed intake would be more reliable than predicting feed efficiency itself. The highest prediction accuracies of feed intake and FCR were obtained with BW and/or growth among the proxies. However, both traits are “subtracted” from the feed intake to calculate RFI, which could explain the low “predictability” of RFI. Other proxies must be identified in order to enable the computation of RFI from predicted feed intake. Late integration of proxies from different biological layers, scarcely improved prediction accuracies for RFI (Le Graverand 2023). A strategy to circumvent the difficulty to predict RFI would be to directly include feed intake along with production traits in a multi-trait selection, rather than using the predicted RFI index in selection (Kennedy et al. 1993).

Finally, it will be necessary to test different strategies for integrating the most relevant predictors (Picard et al., 2021) depending on when and how integration is organized, prediction quality can be modified.

## 5. Conclusion

The use of proxies to enable most sheep breeding organizations to include new traits such as feed intake, feed efficiency and GHG emissions in their breeding programs is necessary. Here, with results from six countries, obtained on different breeds, but with similar protocols and devices, we highlighted that the recording of body weights and fixed effects should help in predicting at least feed intake. Feeding behaviour has also been highlighted as a promising proxy to consider. Nevertheless, feed intake is much easier to predict than efficiency when computed as RFI. Ruminal traits, although biologically linked to the digestive process in ruminants were not identified as good phenotypic proxies for the traits studied here.

## Funding

Countries received funding from their own national funding organisation, under the umbrella of the Joint 2018 call of the three ERA-NETs (SusAn (grant number 696231), FACCE ERA-GAS (grant number 696356), and ICTAGRI 2 (grant number 618123):

Ireland: Dept. of Agriculture, Food and Marine Competitive Research Funding Programme, ERA-GAS (2019EN202; GrassToGas).

Scotland: UK Department for Environment, Food and Rural Affairs (Defra).

Norway: Research Council of Norway (grant number 309158).

France: French funding agency (ANR) (GrassToGas project – ERA-GAS no 39413).

Uruguay: Instituto Nacional de Investigación Agropecuaria (INIA).

New Zealand: Funded by Beef and Lamb New Zealand Genetics and the New Zealand Government through the Ministry of Primary Industries to support the objectives of the Global Research Alliance on Agricultural Greenhouse Gases.

## CRediT authorship contribution statement

Q. Le Graverand: Writing – review & editing, Validation, Investigation, Formal analysis, Data curation. N. Lambe: Writing – review & editing, Validation, Resources, Investigation, Formal analysis, Data curation. F. McGovern: Writing – review & editing, Validation, Supervision, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation. E.A. Navajas: Writing – review & editing, Visualization, Resources, Investigation, Funding acquisition, Project administration. P. Johnson: Writing – review & editing, Visualization, Resources, Project administration, Investigation, Funding acquisition, Formal analysis. N. McHugh: Writing – review & editing, Methodology, Formal analysis, Data curation. I. De Barbieri: Writing – review & editing, Methodology, Investigation, Conceptualization. G. Ciappesoni: Methodology, Formal analysis, Data curation, Conceptualization. S. Rowe: Writing – review & editing, Visualization, Resources, Project administration, Investigation, Funding acquisition, Formal analysis. B.A. Åby: Writing – review & editing, Project administration, Funding acquisition, Formal analysis. J. Conington: Writing – review & editing, Project administration, Funding acquisition, Conceptualization. C. Marie-Etancelin: Writing – review & editing, Validation, Resources, Investigation, Funding acquisition, Conceptualization. F. Tortereau: Writing – review & editing, Writing – original draft, Validation, Resources, Investigation, Funding acquisition, Conceptualization.

## Declaration of competing interest

Authors have no competing interest to declare.

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