
==== Front
J Anim Sci
J Anim Sci
jansci
Journal of Animal Science
0021-8812
1525-3163
Oxford University Press US

39123286
10.1093/jas/skae219
skae219
Animal Models
AcademicSubjects/SCI00960
Approaches for predicting dairy cattle methane emissions: from traditional methods to machine learning
https://orcid.org/0000-0002-1738-0578
Ross Stephen School of Computing, Ulster University, Belfast BT15 1ED, UK
Sustainable Livestock Systems Branch, Agri Food and Biosciences Institute, Hillsborough BT26 6DR, UK

https://orcid.org/0000-0001-8358-9065
Wang Haiying School of Computing, Ulster University, Belfast BT15 1ED, UK

https://orcid.org/0000-0001-7648-8709
Zheng Huiru School of Computing, Ulster University, Belfast BT15 1ED, UK

https://orcid.org/0000-0002-1994-5202
Yan Tianhai Sustainable Livestock Systems Branch, Agri Food and Biosciences Institute, Hillsborough BT26 6DR, UK

https://orcid.org/0000-0002-5401-0541
Shirali Masoud Sustainable Livestock Systems Branch, Agri Food and Biosciences Institute, Hillsborough BT26 6DR, UK

Corresponding author: h.zheng@ulster.ac.uk
2024
10 8 2024
10 8 2024
102 skae21927 3 2024
07 8 2024
02 9 2024
© The Author(s) 2024. Published by Oxford University Press on behalf of the American Society of Animal Science.
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs licence (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial reproduction and distribution of the work, in any medium, provided the original work is not altered or transformed in any way, and that the work is properly cited. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com.

Abstract

Measuring dairy cattle methane (CH4) emissions using traditional recording technologies is complicated and expensive. Prediction models, which estimate CH4 emissions based on proxy information, provide an accessible alternative. This review covers the different modeling approaches taken in the prediction of dairy cattle CH4 emissions and highlights their individual strengths and limitations. Following the guidelines set out by the Preferred Reporting Items for Systematic Review and Meta-Analyses (PRISMA); Scopus, EBSCO, Web of Science, PubMed and PubAg were each queried for papers with titles that contained search terms related to a population of “Bovine,” exposure of “Statistical Analysis or Machine Learning,” and outcome of “Methane Emissions”. The search was executed in December 2022 with no publication date range set. Eligible papers were those that investigated the prediction of CH4 emissions in dairy cattle via statistical or machine learning (ML) methods and were available in English. 299 papers were returned from the initial search, 55 of which, were eligible for inclusion in the discussion. Data from the 55 papers was synthesized by the CH4 emission prediction approach explored, including mechanistic modeling, empirical modeling, and machine learning. Mechanistic models were found to be highly accurate, yet they require difficult-to-obtain input data, which, if imprecise, can produce misleading results. Empirical models remain more versatile by comparison, yet suffer greatly when applied outside of their original developmental range. The prediction of CH4 emissions on commercial dairy farms can utilize any approach, however, the traits they use must be procurable in a commercial farm setting. Milk fatty acids (MFA) appear to be the most popular commercially accessible trait under investigation, however, MFA-based models have produced ambivalent results and should be consolidated before robust accuracies can be achieved. ML models provide a novel methodology for the prediction of dairy cattle CH4 emissions through a diverse range of advanced algorithms, and can facilitate the combination of heterogenous data types via hybridization or stacking techniques. In addition to this, they also offer the ability to improve dataset complexity through imputation strategies. These opportunities allow ML models to address the limitations faced by traditional prediction approaches, as well as enhance prediction on commercial farms.

This systematic review outlines the strengths and limitations of traditional dairy cattle methane emission prediction approaches, as well as highlights the promising potential of machine learning in methane emission prediction. Special consideration is also given to the prediction of dairy cattle methane emissions on commercial farms.

dairy cattle
estimation
machine learning
methane
modeling
prediction
==== Body
pmcIntroduction

Agriculture is the single largest source of anthropogenic methane (CH4) emissions worldwide, responsible for 40% of man-made CH4 emissions (CCAC, 2021). The overwhelming majority of CH4 emissions from the agricultural sector, some 80%, are generated through enteric fermentation (EF) from ruminant livestock (CCAC, 2021), and of all the ruminant livestock which produce CH4 through EF, cattle production, and dairy cattle in particular, are responsible for more emissions than all other ruminant livestock types combined, responsible for 77% of this majority (Gerber et al., 2013).

The accumulation of national CH4 emission inventories, assessment of potential CH4 mitigation strategies, and identification of low CH4 emitting dairy cattle for selective breeding, all of which help track and reduce agricultural CH4 emissions, require farms to be able to efficiently capture the CH4 emissions produced by dairy cattle upon them (Congio et al., 2022; Shadpour et al., 2022).

A variety of dairy cattle CH4 emission recording technologies exist, including Respiration Chambers, Sulfur Hexafluoride (SF6) Tracers, and GreenFeed Systems (Kass et al., 2022; Liu et al., 2022). Respiration Chambers require a dairy cow to be confined to a chamber for several days. They remain the gold standard for recording CH4 emissions, yet their extensive infrastructure, high cost, and low throughput limit their applicability to research institutes only. SF6 Tracers, which are attached directly to the animal, are less invasive than confinement to Respiration Chambers, however, the equipment and analysis still require considerable investment. In addition to this, their precision can also vary, as animals in close proximity can compound the emissions recorded by each tracer. GreenFeed Systems, portable measurement units the animal can visit voluntarily, are able to achieve higher throughput compared to Respiration Chambers, yet herds need to be trained to interact with the equipment, and their cost still remains a barrier to commercial deployment (Garnsworthy et al., 2019). Therefore, it remains difficult to find a recording technology able to achieve the level of precision desired, at the scale of application necessary, which is both accessible and affordable. Nonetheless, the development of inexpensive and scalable CH4 emission recording technologies is still ongoing, and novel solutions such as Portable Laser Detectors are helping to close this gap.

Yet analogous to direct measurement, the accurate prediction of dairy cattle CH4 emissions using mathematical equations based on proxy information, provides perhaps the most accessible solution, and has therefore seen extensive research (Mills et al., 2003; Bougouin et al., 2019; Kass et al., 2022). The exceptional range of proxy information available has resulted in a vast array of dairy cattle CH4 emission prediction models being developed, from simple statistical models limited to proxies strictly obtainable in commercial farm settings, such as milk fatty acids (MFA; Van Gastelen and Dijkstra, 2016), to complex mathematical models which simulate the multi-stage EF process within dairy cattle, including the rumen environment and microbial synthesis (Kebreab et al., 2006).

Whilst many studies have compared the performance of individual dairy cattle CH4 emission prediction models, a review of the underlying approach each model follows remains to be seen. Here we focus on the implications of the approach taken, rather than the performance of the specific model developed. The limitations of each CH4 emission prediction model belong primarily to the underlying approach, rather than the individual models themselves. A common example can be seen across the performances of statistical CH4 emission prediction models; a model that has been trained on a proxy range similar to that found within the test data will usually outperform another model trained on the same proxies but at a different scale. This does not necessarily mean that one model is objectively “poorer” than the other, rather, the statistical modeling approach dictates that for optimal performance, the model must be applied to data following a similar range to its development. If tested on new data now reflective of the scale in the alternative model, the performance of the previous models would be reversed, therefore making model performance not uniquely the problem of the individual model, but primarily, of the underlying approach taken. Thus, illuminating the strengths and limitations of each modeling approach would provide an overview of the advantages and limitations that each model can expect to experience given the approach taken, allowing reservations to be made before development and deployment.

This study aimed to review the different modeling approaches taken in the prediction of dairy cattle CH4 emissions and highlight their ensuing strengths and limitations. This would provide an overview of the prediction model hierarchy currently in place, as well as the specific boundaries of their performance, and the optimal conditions for their implementation. After illuminating the personality of each modeling approach, the conditions that warrant their application can be further cultivated, and the barriers that limit their efficacy can be overcome, allowing for the accumulation of national CH4 emission inventories, assessment of potential CH4 mitigation strategies, and identification of low CH4 emitting dairy cattle for selective breeding, to become more accessible, accurate, and efficient.

Materials and Methods

Review Protocol

This systematic review was completed adhering to the guidelines set out by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) (PRISMA, 2023). A copy of the checklist and flow diagram that were followed can be found within the Supplementary Data.

Eligibility Criteria

Eligibility criteria were carefully discussed and agreed upon by the authors, which would be checked against the papers returned by the search strategy from the appropriate information sources, in order to determine their inclusion within the discussion.

Due to the vast array of countries, breeds, strategies, technologies, and proxy traits explored in the prediction of dairy cattle CH4 emissions, a specific set of prediction conditions were not outlined, only, that dairy cattle were involved and CH4 emissions were predicted. Acceptable prediction conditions could include dairy cattle under an experimental dietary treatment, a specific management system, or at a certain lactation stage, and all continents, breeds, prediction methodologies, and recording technologies were permitted. Proxies of interest could include dietary composition parameters such as dry matter intake (DMI) and forage proportion, production parameters such as milk yield, metabolism parameters such as gross energy intake (GEI), and physical confirmation parameters such as live weight.

This would ensure that the vast range of CH4 emission prediction approaches investigated in the literature, along with as many of the potential strengths or limitations they experienced, would be represented within the results. This would allow the insights generated to be applied in any situation, regardless of circumstance. To extract the information necessary for the subsequent review, additional eligibility was outlined, including that the full text of the paper be available in English.

Search Strategy

Due to the magnitude of papers in the area explored by this systematic review, a population, exposure, outcome (PEO) framework was used to help break down the research goal into focused, searchable, components (UNC Libraries, 2022). The population was defined as “Bovine,” based on an exposure to “Statistical Analysis or Machine Learning,” with an outcome focused on “Methane Emissions”. This would ensure that only papers which satisfied each component of the research goal would be returned for analysis. Each pillar of the PEO framework was then further broken down into a list of related keywords, to ensure all concomitant literature would be encapsulated during search. The search strategy was executed in December 2022 with no publication year limit set, upon the following information sources: Scopus, EBSCO, Web of Science, PubMed, and PubAg. A copy of the search strategy, including a full list of the search terms used, can be found within the Supplementary Data.

Selection Process

After execution of the search strategy within the information sources outlined above, 299 papers were returned for consideration within this study. This collection was then distilled through a 4 stage, incremental screening process, made up of a duplicate review, title review, abstract review, and full-text review, where the bespoke eligibility criteria previously defined, would need to be satisfied before a paper could progress to the next stage. Only those papers that would make it past the final screening stage of the full-text review, would then be eligible for inclusion within the discussion.

Synthesis of Results

Due to the diversity of countries, breeds, diets, technologies, and proxy traits involved in each eligible paper, a meta-analysis was deemed unsuitable, as the heterogeneity of the datasets prevented direct comparisons. Despite this, to ensure that the design of each eligible paper was of the same standard, a quality assessment checklist was completed for each paper, provided by the Critical Appraisal Skills Programme (CASP, 2022), a template of which, is available in the Supplementary Data.

A thematic analysis was considered a more appropriate approach, as this could compensate for the differences between the eligible papers, whilst still addressing the research goal of the study. To facilitate this, a data extraction spreadsheet was created which recorded the key characteristics of each paper. This covered the production system, cattle breed, sample size, measurement technology, dietary composition, predictive model, and assessment metrics. A single author completed the quality assessment and data extraction process for each eligible paper, the results of which, were then reviewed and confirmed by the remaining authors, where any conflicts were thoroughly discussed and then corrected for. Once the quality assessment and data extraction process had been approved, a thematic analysis was conducted, demarcating the dairy cattle CH4 emission prediction approaches each eligible paper employed, which their findings could be summarized and codified in relation to.

Results

Study Selection

During the duplicate review, there were found to be 179 duplicate papers which were thus removed. A further 32 papers were removed during the title review stage, with the majority of papers focusing on the prediction of feeding efficiency through residual feed intake, rather than CH4 emissions specifically, and therefore not satisfying the defined eligibility criteria. Heritability estimates, genetic correlations, and microbiome compositions in relation to CH4 emissions, rather than the prediction of CH4 emissions themselves, were other priorities that led to paper exclusion during the title review. Those papers that passed the title review screening stage were then inspected in more detail during the abstract review stage, with another 25 papers being removed, which upon closer inspection, were revealed to be more focused on the accuracy of a CH4 emission recording technology, rather than a CH4 emission prediction model. Alternatively, some studies did not have access to recording technology and developed their prediction models based on simulated data. Without actual measurements to compare their developed prediction model results to, these papers were also excluded. Prediction models which considered the emissions of the entire farm, rather than CH4 emissions from dairy cattle specifically, including emissions from other animals and sources, as well as additional GHGs, were also excluded. After the final and most extensive screening stage, the full-text review, 55 papers remained eligible for inclusion within the discussion, a loss in papers here being due to a lack of obtainability. After the completion of the screening process by the first author, the results would then be carefully reviewed by the remaining authors, who would challenge and confirm the allocation of each paper. A detailed overview of the study selection process can be seen in Figure 1.

Figure 1. A diagram of the search protocol and screening process results. SA = statistical analysis, ML = machine learning.

A diagram of the search protocol and screeing process results, outlining the number of papers removed at each stage as well as highlighting the eligbility criteria they violated.

Study Characteristics

After the selection process, 55 papers were deemed eligible for inclusion in the discussion. While each paper shared a similar goal in the prediction of dairy cattle CH4 emissions, they addressed this goal from a variety of perspectives. The overwhelming majority of studies primarily investigated dairy cattle CH4 emission prediction from an environmental perspective. This perspective covered the effect of dietary strategies on enteric CH4 emissions (n = 8) as well as the applicability of models in different regional systems (n = 4). Accommodating both of these methods, some hybrid studies developed new CH4 emission prediction models and compared their performance against extant CH4 emission prediction models on both a more dietary diverse and globally representative heterogeneous dataset (n = 9).

With dairy cattle CH4 emission prediction primarily grounded in statistical analysis, an alternative approach through the application of machine learning (ML) also saw emerging interest and was compared to traditional statistical methods in a number of studies (n = 3).

An exciting revelation in the prediction of dairy cattle CH4 emissions, the ancestry between MFA and ruminal fermentation, was keenly investigated in a number of studies, exploring performance alongside additional traits as well as across differing diets (n = 10). In particular, the prediction of CH4 emissions using MFAs which were acquired using Mid Infrared Spectroscopy (MIRS), a technology that could be readily implemented within commercial farming systems, was given specific attention (n = 6). The performance of this MIRS methodology was also compared against more complex MFA recording technologies in a number of studies, including Gas Chromatography, with their resulting prediction models and accuracies both compared (n = 2).

Dairy cattle CH4 emission prediction was also investigated from a biological perspective. The biochemistry of the rumen environment was simulated using a selection of mathematical submodels, representing key dynamics in the fermentation process such as feed characteristics, rumen degradation, and microbial production, which once combined, could be used to predict enteric CH4 emissions (n = 7). These mathematical models were also used to predict the diurnal variation in enteric CH4 emissions, represented as CH4 emission rate, based on varying fermentation patterns (n = 2).

The genetic correlation between specific traits and different CH4 emission phenotypes, as well as the influence of host genetics or rumen metagenome upon enteric CH4 production, were the handful of methods used by studies which investigated CH4 emission prediction from the genetic perspective (n = 3).

Being a global issue, the included studies represented a range of countries, covering a diverse array of climates and production systems. The majority of studies included data from Europe (n = 34), and others from North America (n = 12), Oceania (n = 9), Asia (n = 4), and South America (n = 2). This range in geographical locations, and as a result, production systems, understandably brought with it a large range of breeds. The majority of studies developed models based on Holstein Friesian (n = 42), and others on Brown Swiss (n = 7), Jersey (n = 7), and Norwegian Red (n = 4). These cattle all varied in terms of age, parity, and lactation stage.

Of the included papers, publication years ranged from 1992 to 2022 (Holter and Young, 1992; Negussie et al., 2022). Yet as some of the papers compared the performances of previously published models, the publication year range when considering extant prediction models compared within studies, began in 1965 (Mills et al., 2003).

A copy of the complete data extraction spreadsheet which was used to record the study characteristics can be found within the Supplementary Data.

Discussion

Summary of Evidence

The key dairy cattle CH4 emission prediction approaches explored across the 55 papers returned included mechanistic modeling, empirical modeling, and ML, with special consideration given to their implementation on commercial dairy farms.

Mechanistic models offer an advantage over empirical models through their accuracy and adaptability, which stem from their mathematical representation of ruminal subsystems. However, obtaining the required data for these models is challenging, significantly limiting their accessibility.

Conversely, empirical models offer a more accessible alternative as they are based on observable and tangible empirical observations. While accuracy may be compromised, this can be compensated for by incorporating additional features into the model. Yet avoiding over-parameterization remains crucial.

ML, an entirely novel approach in the prediction of dairy cattle CH4 emissions, has demonstrated its ability to outperform traditional prediction approaches via the utilization of innovative algorithms and imputation techniques. However, they have also introduced novel challenges to the issue, such as overfitting. Although the prediction of dairy cattle CH4 emissions via ML remains scarce, this approach should be keenly explored in future research, as it could potentially revolutionize the field.

A core theme seen throughout the discussion is the agonizing trade-off between affordability and accessibility. Generally, a more nuanced model will have a better predictive potential, however, this comes at the expense of its applicability, requiring rich data for its implementation.

The deployment of CH4 emission prediction models on commercial dairy farms has received deservingly intense research, and the avenue of MIRS-determined MFAs presents an exciting opportunity for addressment. However, to establish this approach as a widely adopted practice in commercial settings, more robust results are necessary. The formation of international consortia is anticipated to expedite this process and facilitate its widespread implementation. As the research progresses, these models could become an integral part of national and global efforts to monitor and mitigate the impact of livestock on climate change (McParland et al., 2024). A reference list of each modeling approach is outlined in Figure 2.

Figure 2. Eligible papers categorized by dairy cattle methane emission prediction approach.

A table containg the citations of the eligble papers categorised into columns based on the dairy cattle methane emission prediction approach they employed.

Mechanistic Modeling

In order to develop a mechanistic model, it is essential to have a theoretical framework that outlines the mechanism being represented. Once the causal relationships within a mechanism have been illuminated, a mechanistic model can then be developed to simulate the given phenomenon, through simplified mathematical emulations of its underlying behaviors via hierarchical submodels. Based on theory and represented through a mathematical formula, a mechanistic model can then act as a daemon for the chosen system and validate hypotheses upon it (Baker et al. 2018). Given the relentless patterning of the dairy cattle EF process (Mills et al., 2003), the theory required for the application of a mechanistic model in the prediction of CH4 emissions is well established.

For truly accurate predictions of CH4 emissions produced by dairy cattle, one needs to consider not only the nutrient composition of the diet, but also, the substrate of the feed ingested which is actually fermented (Storlien et al., 2014). The mechanistic approach thus has an inherent advantage, as its comprehensive submodel architecture allows for a detailed representation of all the underlying processes involved, to be captured (Kass et al., 2022).

Not only does the submodel architecture of the mechanistic approach secure high predictive accuracy, but it also maintains applicability across a diverse range of scenarios. Mathematically emulating the theory of the EF process it represents, a mechanistic model can be fed any diet, and its submodel components will simulate the corresponding changes in fermentation pattern caused by different dietary treatments accordingly. This flexibility allows the model to remain relevant and effective even under highly specific dietary conditions (Benchaar et al., 1998; Kebreab et al., 2006; Ramin and Huhtanen, 2015).

Whilst the intricacy of mechanistic models does provide a rich foundation for accurate prediction, this comes at the cost of their accessibility and sometimes, even contributes to their own detriment. A mechanistic model is simply a product of the submodels it employs, therefore, the risk of error in the final prediction is compounded by the level of detail the mechanistic model attempts to dive, as each additional submodel brings with it its own potential for error. However, the modularity of the mechanistic approach allows for its individual submodels to mature at their own pace, and updates to existing parameters, or the addition of entirely novel submodels, can help reduce this risk over time, as understanding of the underlying mechanism improves (Benchaar et al., 1998; Gregorini et al., 2013; Brask et al., 2015).

The accuracy of the mechanistic model results is predetermined not only by the fermentation theory represented by its submodels, but also by the accuracy of its input data. As diet digestibility is largely influenced by neutral detergent fiber concentration in the diet, the accurate representation of its input data in the relevant submodels is therefore vital, as any inaccuracies can permeate throughout the model and lead to biased estimates of organic matter fermentation, which is the basis for CH4 production (Huhtanen et al., 2015; Ramin and Huhtanen, 2015). So, whilst the mechanistic representation of the fermentation process through its submodel architecture does provide a foundation for extremely accurate enteric CH4 emission prediction, it does, however, leave exposed the vulnerability of ghosts in the machine, introduced through spurious input data (Kebreab et al., 2006; Storlien et al., 2014; Kass et al., 2022). An overview of the strengths and limitations of the mechanistic approach is provided in Figure 3.

Figure 3. An overview of the strengths and limitations of each dairy cattle methane emission prediction approach. CH4 = methane, DMI = dry matter intake, MFA = milk fatty acids, MIRS = mid infrared spectroscopy, ECMY = energy corrected milk yield, BW = body weight, GC = gas chromatography, ML = machine learning.

A table outlining the strengths and limitations of each dairy cattle methane emission prediction approach highlighted in the discussion.

Empirical Modeling

In contrast with the mechanistic approach, empirical models have no such prejudice of the underlying mechanism, instead, they are based purely on direct observation, opting for a data-driven approach over the theory-driven approach of the mechanistic. This omission of acquaintance between an empirical model and the system it is modeling, however, introduces a shift in the modeling dynamic. Empirical models primarily describe the probabilistic relationships between its constituent features, rather than simulate their reactive functionality, keeping the model aloft in statistical inference rather than grounded in mathematical causality, so much so, that they are commonly referred to as ‘statistical models’ (Cytivia, 2023). Due to this omission of any mathematical description of the theoretical operationality of the systems they are modeling, empirical models are a much more versatile alternative compared to their more demanding mechanistic counterparts (Kebreab et al., 2006; Bell et al., 2016; Dong et al., 2022).

This versatility provides the empirical model with a high degree of structural freedom, able to experiment with the full breadth of explanatory features available during development, improving the potential accuracy attainable (Kebreab et al., 2006; Santiago-Juarez et al., 2016; Bougouin et al., 2019).

However, despite the potential improvement afforded through the inclusion of additional explanatory features, that is not to say that the simple process of increasing the number of features within a model is a guaranteed route to enhanced performance. Over-parameterization of empirical models may actually lead to performances inferior to simpler models (Wilkerson et al., 1995; Mohammed et al., 2011). For an additional model feature to be effective, it needs to explain an independent source of CH4 emission variation or help improve the depth of variation explained by other model features and thus, should not be added irresponsibly (Santiago-Juarez et al., 2016; Bougouin et al., 2019). Of course, while the inclusion of additional model features may improve the predictive ability of the model, this comes at the expense of the empirical model’s accessibility, weakening one of its core attractions as an alternative substitute to mechanistic models. Therefore, to remain both an accessible alternative, as well as a viable one, a balance must be struck between the availability of features and the complexity of the model.

While the versatility of empirical models allows them to be developed in response to any experimental or geographical conditions, this same versatility also confines their deployment to the same range in which they were originally developed, a key limitation of the empirical approach.

In a study comparing the CH4 emission prediction performance of empirical models tested upon datasets from North America, Europe, and Oceania, it was found that GEI-based models performed better in Europe and Oceania, whereas nutrient-based models performed better in North America (Appuhamy et al., 2016). The propensity toward GEI-based models for datasets from Europe and Oceania was believed to be due to the diverse range of diets fed in these regions (NDF = 38-43% of DMI), which GEI is irrespective off. Whereas nutrient-based models depend on specific nutrient compositions for optimal performance, which explained their superior performance in the more amenable North America datasets, reflective of the dietary ranges these nutrient-based empirical models were originally developed on (NDF = 33% of DMI) (Appuhamy et al., 2016). Hence, these GEI-based models, more conversant with the vast range of diets fed in dairy cattle production systems globally, performed best when all North America, Europe, and Oceania datasets were combined, whilst the top performing North America model, nutrient-based, did not breach the top 10, its specific dietary range during development mirrored within the North America dataset, now diluted by the combined dataset encompassing a more diverse range of diets outside of its original developmental range (Appuhamy et al., 2016).

Further admonition of the application of empirical models outside of their original developmental range can be drawn from the varying CH4 conversion factors (Ym, = CH4 energy output over GEI) reported for different regions. The estimated Ym for Canada was 5.53%, for South Africa 7.9 - 9%, and in tropical regions, a Ym of 11.4% was reported (Dong et al., 2022). These discrepancies highlight the influence of environmental factors behind CH4 production and strongly advocate for the grounding of prediction models within the settings they were originally developed in.

While a mechanistic model is based on a theoretical representation of the EF process, an empirical model derives its theory purely from the relationships between the features in the dataset it is trained. This allows a mechanistic model to move freely between datasets, as the theory can react dynamically to the data supplied, whereas empirical models, only familiar with the relationships in the data they were originally trained upon, struggle to adapt to those they are not, and thus, are best suited to their original developmental range.

DMI is the amount of feed ingested by the animal on a moisture-free basis (USDA., 2024). As DMI increases, the gross energy of the animal which is lost as enteric CH4 emissions actually begins to decline (Holter and Young, 1992; Mills et al., 2003; Kebreab et al., 2006). This is due to an increase in the passage rate of rumen digesta, causing excess energy to be diverted toward microbial synthesis (Ramin and Huhtanen, 2013, 2015; Huhtanen et al., 2015). Therefore, empirical models would benefit if they applied a nonlinear approach to the prediction of dairy cattle CH4 emissions, as they would then be able to capture this diminishing returns relationship between CH4 emissions and feed intake. This has been seen in a number of studies where nonlinear variations of empirical models have outperformed the traditional linear structure they utilize for CH4 emission prediction (Mills et al., 2003; Kebreab et al., 2006; Appuhamy et al., 2016).

In one study, a set of simple linear empirical models were compared against nonlinear variations of themselves. The nonlinear versions utilized the same explanatory features yet followed the form of a Mitscherlich equation, an equation that can model a diminishing returns relationship between 2 features. When all models were tested on a combined dataset made up of American and Northern Irish data, all nonlinear versions outperformed their linear counterparts in terms of Root Mean Square Prediction Error (RMSPE), with the nutrient-based nonlinear model in particular, scoring a RMSPE 10% less than its linear variant (Mills et al., 2003). Another study attempted to capture this diminishing returns relationship between CH4 emissions and feeding level, this time through the addition of a modest quadratic element to the empirical equation, which tapered the linear relationship at the max end. The original linear variant achieved an RMSPE of 27.2% whilst the quadratic variant achieved an RMSPE of 25.4%, again stressing the potential improvement an empirical model can expect if converting to a nonlinear structure (Ramin and Huhtanen, 2013).

This transition to a nonlinear structure helps to address the most damaging drawback of the empirical approach; the overprediction that occurs when applied outside their original developmental range. A nonlinear structure can resist the influence of the more extreme values found in a differing dietary range (Mills et al., 2003; Huhtanen et al., 2015; Dong et al., 2022). This not only stresses the potential benefits of empirical models converting to a nonlinear structure, but it also highlights the adaptability of the empirical approach itself. An overview of the strengths and limitations of the empirical approach is provided in Figure 3.

Additional Areas of Explanation for Mechanistic and Empirical Modeling Approaches

The mathematical description of the biological framework under representation, whether directly via empirical models or through submodeling of its interconnected subsystems via mechanistic models, each brings with them its own unique set of challenges, that coincidentally, are addressed by the benefits of the alternative approach. Yet there are phenomena that concern the underlying biological framework that are commonly left unaddressed by both approaches, which, if included, could greatly improve the accuracy of their predictions, now made more representative of the system they are trying to emulate. Therefore, the adoption of biologically sensible constraints within the model can enhance predictive performance and reduce misapplication (Mills et al., 2003).

One such biological constraint that could improve predictive potential is lactation stage. After calving, dairy cow CH4 emissions continue to rise until approximately 100 d in milk (DIM), this emission rate remains relatively constant until 200 DIM, after which, should start to gradually decline before the cow enters their dry period (Vanlierde et al., 2016, 2021). If the influence of lactation stage upon CH4 production could be included within prediction models, the prediction error relative to each stage could potentially be reduced.

Another biological constraint that affects CH4 production in dairy cattle is parity. Primiparous dairy cattle have lower milk production potential, lower feed requirement, and consequently, lower CH4 emissions, compared to multiparous dairy cattle (Bell et al., 2016; Vanlierde et al., 2016). Alongside this, seasonality also appears to affect CH4 production in dairy cattle, with hotter months increasing the chance of heat stress which results in reduced intake and thus, lower emissions (Vanlierde et al., 2016). The subtle influence that each of these biological constraints has on CH4 production could hold impressive potential for the improvement of dairy cattle CH4 prediction model accuracy, which the accessibility of empirical models and flexibility of mechanistic models both allow.

CH4 emissions remain inconsistent between dairy cattle housed under identical conditions and fed the same diet. The variation in emissions amongst a herd is largely due to the feed efficiency of each animal. Feed efficiency is influenced by, heritability, genetic merit, and dietary composition (Agnew and Yan., 2000; Jiang et al., 2024). Highly feed efficient dairy cattle emit less CH4 per kg milk produced due to enhanced energy utilization and in some cases, reduced methanogenic diversity (Khiaosa-ard and Zebeli., 2014). The incorporation of this biological constraint could greatly assist in CH4 emission prediction by refining estimations based on the efficiency of the cow.

Whether incorporated directly as additional parameters within empirical models, or as entirely new submodels within the mechanistic approach, these biological constraints could be integrated by adding weight to the model predictions based on lactation stage, compounding internal parameter coefficients based on parity, or generating unique intercepts based on feed efficiency, represented through genetic similarity.

Machine Learning Modeling

An emerging alternative in the prediction of dairy cattle CH4 emissions is ML models. ML models opt for the same data-driven approach as empirical models, yet unlike empirical models, which rely on statistical inference, they are specifically designed for accurate predictions. Via an exotic algorithmic menu, in combination with hybridization and stacking techniques (Baker et al., 2018; Brownlee., 2021; Ross et al., 2023) ML models provide the necessary flexibility required to facilitate cross-talk and identify relationships between the diverse range of proxy traits available for the prediction of dairy cattle CH4 emissions today (Negussie et al., 2017). This flexibility allows ML models to overcome the limitations of current prediction approaches, by providing an opportunity to combine the versatility of the data-driven empirical approach, with the accuracy of the theory-based mechanistic. Although still in its early stages and requiring further exploration, ML models show promise in improving the accuracy of dairy cattle CH4 emission prediction.

Preliminary investigations have demonstrated the potential of ML models as an alternative vehicle for the direct prediction of dairy cattle CH4 emissions compared to traditional empirical approaches. One study that compared the ability of a ML random forest (RF) model against an empirical multiple linear regression (MLR) model in the prediction of dairy cattle CH4 emissions, demonstrated the superiority of ML, with the RF model able to consistently outperform the MLR model across the multitude of datasets tested (Negussie et al., 2022). The advantage of ML was noticed particularly in the smaller datasets tested, where the RF model was able to attain a Pearson correlation coefficient (r) of 32% in a 3k dataset, while the MLR model was limited to an r of 12%. Interestingly, when the MLR model was trained on a much greater dataset, with 41k records, it still could not manage to beat the predictive performance of the RF model trained on the original 3k dataset, achieving an r of 19%, the RF upon this set achieving 71% (Negussie et al., 2022). The flexibility of the underlying ensemble algorithm that the RF employs is perhaps the reason why this ML model is able to outperform its empirical MLR counterpart. Utilizing random subsets of predictor variables on bootstrapped samples of the data allows the RF to get a much more intimate understanding of the heterogeneous structures within the dataset, of which it takes an average, allowing for more accurate predictions compared to the stricter MLR approach.

ML models are not just restricted to regression predictions either; they can also be utilized for classification problems. This facilitates another interesting approach toward CH4 emission prediction, the classification of dairy cattle into low or high CH4 emitters. Rather than predict individual CH4 emissions directly, ML models can also allow for the assignment of individual animals into emission categories, which can provide a foundation for further mitigation strategies. In one study, a ML Bayesian network (BN) model was developed for the classification of animals into CH4 emission categories of varying intensities (Zheng et al., 2016). The acyclic structure of the BN enables the model to identify and quantify dependencies between predictors, allowing the model to capture complex relationships within the data (Zheng et al., 2016). Using the predictors, energy corrected milk yield (ECMY), forage and breed, the BN model was able to classify dairy cattle into the correct CH4 emission category with 66% accuracy. However, the BN failed to differentiate dairy cattle based on the low CH4 emission category. This was believed to be due to the diminutive number of records in the dataset which were within the low CH4 emission category for training, making up less than 5% of the dataset (Zheng et al., 2016). This makes possessing equal proportions of the emission categories an essential requirement before deployment of ML classification models.

The imputation of complex traits is another boon that ML introduces to the prediction of CH4 emissions. Dataset size can be compounded with the introduction of imputed values, providing a much greater foundation for predictive accuracy to flourish.

In a study comparing model performance based on datasets of increasing intricacy facilitated through ML imputation, each model tested saw consistent improvements as the datasets they were trained on grew (Negussie et al., 2022). One such trait that was imputed was DMI, imputed through the use of the ML algorithm, k-nearest neighbors (kNN), upon its accompanying features. kNN is a nonparametric, lazy learning algorithm that selects a defined total of the closest surrounding data points around a given value using a distance measurement. Once gathered, the algorithm can then use these data points in a democratic vote for classification of the given value to the most popular category of its neighbors or an average of their values for a regression prediction of a missing result (Analytics Vidhya, 2018; G2, 2023). This allowed the dataset to grow from 3k records with no missing data, to a 21k dataset containing imputed DMI values. Data being the lifeblood of prediction models, this increase in dataset size allowed the underlying algorithms of the models tested to become better acquainted with the biological system it was emulating, allowing them to flex their prowess should their potential be fulfilled. At 3k, the r of the models tested ranged from 28 – 52%, at 21k, r jumped up to 75 – 84% (Negussie et al., 2022). Of course, the accuracy of these complex trait imputations is essential in avoiding misleading results and should be validated before uptake (Appuhamy et al., 2016; Negussie et al., 2022).

While the potential of ML in the prediction of dairy cattle CH4 emissions is certainly exciting, that is not to say that they do not also bring with them their own set of challenges. Another study that tested the ability of a ML neural network (NN) model against an empirical partial least squares (PLS) model in the prediction of dairy cattle CH4 emissions produced some contrasting results. Taking advantage of the NN’s hidden layer activation functions which can accommodate nonlinear relationships, the study hypothesized that a NN could better capture the complex relationships of the variables within their dataset, which were subject to causality, nonlinearity, or both (Shadpour et al., 2022). As a result, the nonlinear variant of the NN was able to outperform the PLS model in the majority of predictor sets tested in the study, yet, when a MIRS predictor was added to the test set, the PLS model overtook the nonlinear NN model in terms of predictive performance (Shadpour et al., 2022). The nonlinear NN model outperformed the PLS model using the same predictor set based on the training data, yet failed to generalize to the test data as reliably as the PLS model (Shadpour et al., 2022). This trend led the authors to believe that the reason for the stall in performance of the nonlinear NN model when using the MIRS predictor set was due to overfitting of the model upon the training set, evidenced by its superior performance in the earlier predictor sets as well as training data of the later predictor sets (Shadpour et al., 2022).

Despite being an extremely advanced ML algorithm, deep learning models such as NNs are susceptible to overfitting, especially when the number of neurons in the hidden layer exceeds the number of features supplied to the model (Shadpour et al., 2022), impeding predictive performance on new data. Therefore, to avoid such drawbacks, NN models require extensive tweaking before finding the most favorable parameters that can effectively model the data. Just because a model implements ML, this is no guarantee that the model itself will be able to enjoy the benefits of the underlying algorithm. It must be specifically tailored to the context in which it is being applied. Dutifully, one must respect the underlying nuances of the algorithm, in order to get the most out of its potential, when applying it to a predictive problem.

Whilst mechanistic models hold the crown in terms of prediction accuracy, they leave a lot to be desired in terms of accessibility. Empirical models, on the other hand, provide a much higher degree of versatility, yet at the expense of their applicability. The novel application of modern ML models in the prediction of dairy cattle CH4 emissions, however, through exotic algorithms and combinatorial techniques, could perhaps help bridge this gap, providing a staggering opportunity, for the first time ever, to marry the accuracy of mechanistic models, with the versatility of empirical models, truly revolutionizing the prediction of dairy cattle CH4 emissions. An overview of the strengths and limitations of the ML approach is outlined in Figure 3.

The Optimal Conditions for each Prediction Approach

If one should have access to the necessary input data required for the execution of a mechanistic submodel family, including feed characteristics and rumen composition, as well as digestion, fermentation, and microbial synthesis parameters (Benchaar et al., 1998; Storlien et al., 2014; Huhtanen et al., 2015), then one should certainly employ a mechanistic approach. This demanding yet intricate submodel architecture allows the mechanistic model to eclipse the CH4 production process, and as a result, secures high accuracy whilst remaining adaptable, 2 critical desires of any effective dairy cattle CH4 emission prediction model. Two popular mechanistic models by the names of Karoline and Molly were able to achieve a Concordance Correlation Coefficient (CCC) of 0.95 and 0.92 respectively, when predicting the CH4 emissions of dairy cattle across 55 studies, originally measured using respiration chambers (Kass et al., 2022). The predictions of these mechanistic models were almost identical to the current gold standard for directly recording CH4 emissions, demonstrating just how powerful these models can be should their input data be available. It is therefore not surprising to see mechanistic models consistently outperforming empirical models, particularly when applied to datasets containing a wide range of diets (Benchaar et al., 1998; Kebreab et al., 2006; Ramin and Huhtanen, 2015). When predicting dairy cattle CH4 emissions in a dataset containing over 32 different diets, a modified mechanistic model was able to achieve a RMSPE of 15.40%, which was less than half the RMSPE achieved by a traditional empirical model, far outside its original developmental range, at 33.72% (Benchaar et al., 1998). Yet, this is all based on having access to an exhaustive list of complex input data, severely limiting the likelihood of a mechanistic model ever finding its way on to the commercial farm, instead confined to more fortunate research institutes.

If data availability is more modest, then empirical models present the optimal solution. Whilst one requires extensive data for the implementation of a mechanistic model, an empirical model can be developed based on a single explanatory feature. In one study, a univariate empirical model based on DMI alone was able to explain 42% of the variation in dairy cattle CH4 emissions, a respectable coefficient of determination (r2) for a single explanatory feature (Brask et al., 2015). This versatility is a true merit of the empirical approach. However, one must not confuse versatility with applicability, and as a result, empirical models remain best suited to datasets containing similar ranges as those during their original development. Yet this restriction is not necessarily a disadvantage. One such empirical model that remains globally applicable is the Intergovernmental Panel on Climate Change (IPCC) Tier 2 model, which afforded this pardon via the use of an adjustable Ym based on geography, animal type, production level, and feed efficiency (Dong et al., 2022). When compared against locally developed models in the prediction of dairy cattle CH4 emissions in a combined Chinese dataset, the IPCC Tier 2 2006 model attained an RMSPE of 36.4% whereas the best performing locally developed model was able to achieve a RMSPE less than half this amount, at 17.7% (Dong et al., 2022). Due to its preference for familiar data, one would recommend simply developing a bespoke empirical model based on the data available, rather than looking to apply an appropriate empirical model already published in the literature, and with how versatile and accessible the empirical approach remains, this would not be an arduous process. The inclusivity of the empirical approach allows their models to be developed based on complex experimental data as well as simple commercial data and therefore find themselves deployable in both settings, however, the accuracy attainable will be limited by the intricacy of the data available.

It is perhaps too early to tell the optimal conditions for the application of a ML dairy cattle CH4 emission prediction model, however, one would stress the need to discover what they are, and therefore, anywhere an empirical model can be applied, comparison with a variety of ML algorithms would be of significant value. In preliminary studies, rudimentary ML models have been seen to match the ability of more complex empirical structures, including a RF achieving a similar RMPSE as that of a linear mixed effects model, achieving 13.94% and 14.42% respectively (Ross et al., 2023). With the ever-growing scale and variety of proxy data available for the prediction of dairy cattle CH4 emissions, the non-linear nature of the complex algorithms ML models introduces to the challenge, provides an exciting opportunity to find patterns in the noise which may escape empirical models. Therefore, on smaller, uniform datasets, the empirical approach would be recommended, yet on larger, heterogeneous datasets, one would expect greater accuracy through ML. In addition to this, datasets on which empirical models are to be developed could be even further enhanced by imputation of complex traits via ML.

Predicting CH4 Emissions on the Commercial Farm

Of course, whilst most models are developed in experimental research centers utilizing rich data, the ultimate aim for any dairy cattle CH4 emission prediction model is deployment on the commercial farm. This descent, from the high peaks of research centers to the low valleys of commercial farms, is followed, however, by an equal decline in data opulence. Therefore, special coverage here, is given to models which predict dairy cattle CH4 emissions solely based on proxy traits which are procurable in a commercial farm setting, including production traits such as milk yield and composition, functional traits such as fertility, lactation stage, and calving, and physical confirmation traits such as body condition score and live weight (Shahinfar et al., 2012). The vehicle in which these predictions are made is not exclusive, accepting of any CH4 emission prediction approach, as long as the constituent passengers of each vehicle remain commercially available.

Perhaps the most popular animal performance trait being modeled today, in relation to dairy cattle CH4 emissions; are MFAs. Fermentation of carbohydrates in the rumen results in the production of acetate, butyrate, and propionate (Negussie et al., 2017). Whilst the H2 produced during the synthesis of these metabolites controls enteric CH4 emissions, the metabolites themselves go on to be used extensively in the de novo synthesis of short to medium-chain MFAs within the mammary gland (Rico et al., 2016; Negussie et al., 2017). Therefore, the presence of these metabolite-associated FAs in the milk, essentially denotes the digestive signature of the fermentation process and can be traced back to the CH4 emissions produced in the rumen (Rico et al., 2016; Negussie et al., 2017).

What makes this revelation particularly exciting is the accessibility of the MIRS recording technology. MIRS is a routine procedure already implemented within commercial farming systems worldwide, commonly used to assess the fat, protein, and lactose contents of milk samples from the farm, which can be used to assist in farm management and breeding decisions (Dehareng et al., 2012; Van Gastelen and Dijkstra, 2016; Vanlierde et al., 2016). Therefore, the data required to implement commercially deployable CH4 emission prediction models is already available and accumulating on many commercial farms, with the uptake in those that are not, being both realistic and affordable (Dehareng et al., 2012; Vanlierde et al., 2016; Engelke et al., 2018).

In addition to this, MIRS can also be used to directly measure CH4 emission concentration in the breath of dairy cattle through eructation sampling during milking (Garnsworthy et al., 2012; Lassen et al., 2012; Bell et al., 2014), yet unfortunately, this methodology was not covered within the eligible papers available.

The savvy interpretation of the MFA / enteric CH4 emission relationship, coupled with the accessibility and practicality of the MIRS recording technique, provides an incredible opportunity for CH4 mitigation in a commercial farm setting. This realization has revitalized dairy cattle CH4 emission prediction, with a wealth of studies investigating the development of a variety of MFA-based, commercially applicable, prediction models (Williams et al., 2014; Bougouin et al., 2019; Engelke et al., 2019).

Yet the vast array of MFA-based CH4 emission prediction models have been cross-validated in a number of studies and was found to be inappropriate when applied outside of their original developmental range (Williams et al., 2014; Denninger et al., 2020; Vanlierde et al., 2021) with overprediction ranging between 16 – 91% (Mohammed et al., 2011). A reason for this could be that most MFA-based CH4 emission prediction models seem to have been developed based on experiments offering a specific dietary treatment (Rico et al., 2016). While strong correlations between individual MFAs and enteric CH4 emissions have been found within isolated diets, in datasets comprised of multiple diets, these relationships become much more obscure (Williams et al., 2014; Rico et al., 2016; Van Gastelen and Dijkstra, 2016). Thus MFA-based prediction models, particularly those taking the empirical approach, will fail to find the relationships they depend on in more diverse diets, and as a result, produce weak estimations. This limits the deployment of MFA-based prediction models to datasets of a similar developmental range, which due to the dietary diversity found throughout typical commercial dairy farms across the globe, may be quite limited.

The high accuracies achieved by MFA-based CH4 emission prediction models have instead been attributed to the narrow sample sizes in which they were originally developed on, made up of cows within the same lactation stage and fed the same diet (Van Gastelen et al., 2018b). In order to be robust and applicable across a variety of diets, all future MFA-based CH4 prediction models should be developed upon a more varied dataset in terms of diet composition, animal genetics, management system, and lactation stage (Dehareng et al., 2012; Engelke et al., 2018; Van Gastelen et al., 2018b). One must remain careful, however, as increasing dataset variability, through diet and system diversity, may introduce covariance structures which can lead to spurious results if not properly accounted for during development of the model (Shetty et al., 2017).

Whilst providing an accessible doorway for the prediction of dairy cattle CH4 emissions on commercial farms, models based on MIRS-determined MFAs alone have proved limited in their ability to predict the CH4 emissions of individual dairy cattle (Denninger et al., 2019, 2020; Liu et al., 2022). One way in which this limitation can be overcome is through the addition of alternative animal performance traits such as body weight, milk yield, and lactation stage (Van Gastelen and Dijkstra, 2016; Castro-Montoya et al., 2017; Denninger et al., 2019). This is because the introduction of additional traits can help to explain another dimension behind dairy cattle enteric CH4 emissions which MFAs alone simply cannot account for (Bougouin et al., 2019).

It is commonly understood that increasing the complexity of dairy cattle CH4 emission prediction models leads to higher predictive accuracy, yet whilst complex by design, increasingly intricate CH4 emission prediction models need not become complex by composition. The advent of proxy features opens up such a diverse range of opportunities to capture enteric CH4 emission variation, that the shortcomings of one proxy can be easily made up for by the inclusion of another (Negussie et al., 2022). So, whilst the model itself may become more complex through the introduction of additional explanatory variables, be it only through the inclusion of additional proxy traits obtainable on the commercial farm, then the model can remain commercially sound, maintaining its accessibility, yet also enjoying the benefit of enhanced predictive accuracy (Jiao et al., 2014; Van Gastelen et al., 2018a; Engelke et al., 2019).

This new approach introduced by the commercial devotion begs one to carefully consider the CH4 emission phenotype which is used to assess the prediction accuracy of any MFA-based prediction model. The relationship between enteric CH4 emissions and MFAs can differ based on the CH4 emission phenotype expressed against (Van Gastelen and Dijkstra, 2016). CH4 production (g/d), CH4 yield (g/kg of DMI), and CH4 intensity (g/kg of ECMY) represent a different dimension of enteric CH4 production and as a result, each sees the significance of MFAs for their prediction in a different light (Van Gastelen and Dijkstra, 2016). In one study, when expressed as CH4 yield, MFAs were able to explain 64% of CH4 emission variation, yet when expressed as CH4 production, could only explain 42% (Castro-Montoya et al., 2017). Further demonstrating the variation in MFA significance, each model developed for the prediction of each CH4 phenotype contained different MFAs, highlighting the effect that the phenotype alone has on their significance (Castro-Montoya et al., 2017). Due to its basis within ECMY, MIRS-determined MFA-based models perform better when predicting CH4 intensity compared to CH4 production, demonstrated in one study, through a r2 of 79% and 73%, respectively. (Dehareng et al., 2012).

The narrow yet deep research into, MFA-based, CH4 emission prediction models, has produced an interesting array of adversative results. Of the breadth of MFA-based prediction models developed, no 2 have contained an identical set of MFAs in their equations (Okpara, 2019). Due to the diverse range of MFAs used in the development of each prediction model, it may come as no surprise that the predictive accuracy of each model has also been equally diverse, with r2 of developed models ranging from 13 - 95% (Okpara, 2019; Wang and Bovenhuis, 2019). Therefore, research must continue in order to consolidate this worthwhile endeavor and produce a MIRS determined, MFA-based CH4 emission prediction model which can remain consistent across the variety of conditions found throughout commercial farming systems globally.

Commercial deployment depends on proxy usage rather than prediction approach, and one might notice the limitations of the MFA-based CH4 emission prediction models reviewed here, are not necessarily solely the fault of their MFA predictors, but rather, the empirical approach commonly used to model them. The diversity of commercial farming systems will greatly provoke the empirical limitation of confinement to their original developmental range. A ML approach on the other hand, with its enhanced ability to discover and incorporate relationships found within deep, heterogeneous datasets, may provide a better foundation for the development of more robust MIRS-determined MFA-based prediction models, which can take advantage of the unavoidable diversity of commercial farms to be tested upon. An overview of the opportunities and challenges faced by dairy cattle CH4 emission prediction on commercial dairy farms is provided in Figure 3.

Limitations

The prediction of dairy cattle CH4 emissions is an endeavor that has been ongoing for decades, with some of the earliest prediction models dating back to 1965 (Blaxter and Clapperton, 1965). To accommodate this, there was no limit set for the publication year in the search strategy. The direct comparison between such a historic model and a more recent model using cutting-edge technology such as ML may seem unfair, yet the purpose of this study was to compare the breadth of approaches taken in the prediction of dairy cattle CH4 emissions, making those models made in the previous century, just as relevant and insightful as prediction models made this decade. This also explains why the diversity between studies in terms of conditions, breed, sample sizes, measuring equipment, phenotype, and traits can also be overlooked, as the focus of this review was on the approaches taken, their advantages and disadvantages, and not the direct comparison of specific models.

Four papers that were returned by the search strategy were unfortunately rejected due to unobtainability through the authors’ institutions. Of the databases searched, 2 references were returned with which a matching paper could not be found online (Lovett et al., 2023; Plöchl et al., 2002). Whilst originally unobtainable, the authors graciously received a copy of (Dijkstra et al., 2011) upon request. Whilst a very interesting experiment, as it was simulated, it unfortunately did not meet the eligibility criteria of this review. It did, however, use a mechanistic model to make predictions based on the simulations and as mechanistic models were covered extensively throughout the rest of the included papers, the authors felt that this approach was still well represented without inclusion. The paper (Morante et al., 2016) included an English abstract, however, the remainder of the paper was in Spanish which was unfortunately beyond the eligibility of this review. The English abstract highlighted the use of the IPCC Tier 2 model, which had been involved in a number of the remaining papers, as well as the consideration of lactation stage and parity, which again had also been covered in the remaining papers included within the discussion, therefore it was believed that the content had been touched on in other papers and omission was appropriate.

Despite the elusive papers, the remaining 55 offered a good coverage of the plethora of dairy cattle CH4 prediction models developed in the literature. As a result of this, the modeling paradigms into which the review was distilled were comprehensive enough so that should any omitted model employ the respective approaches outlined, they will likely still see very similar advantages and disadvantages.

Conclusion

Mechanistic models, emulating the intricate rumen environment which produces the CH4 emissions it predicts, are incredibly accurate yet equally demanding. Their necessary input data is especially difficult to obtain, and should it be imprecise, can produce misinformative results. Empirical models, versatile to the data on hand, enjoy respectable CH4 emission prediction accuracies, yet suffer greatly when applied outside of their original developmental range. The prediction of dairy cattle CH4 emissions on commercial farms introduces the noble constraint of utilizing only commercially available proxy traits. However, current commercially deployable CH4 emission prediction models have produced ambivalent results and need to be consolidated before robust predictions of CH4 emissions on commercial dairy farms can be achieved. What may help solidify the prediction of dairy cattle CH4 emissions on commercial farms, as well as address the limitations faced by traditional prediction approaches; are ML models. In providing a platform for data refinement through imputation, enabling the accommodation of diverse data types through hybridization or stacking, and achieving high predictive accuracy via novel algorithms, ML models may hold within them the key to unlocking the full potential of dairy cattle CH4 emission prediction; as long as the additional risks for these rewards can be handled effectively.

Supplementary Material

skae219_suppl_Supplementary_Data

Acknowledgments

This study is a collaboration between Ulster University and the Agri-Food and Biosciences Institute (AFBI) and is funded by the Department of Agriculture, Environment and Rural Affairs (DAERA) through a Postgraduate Studentship.

Abbreviations

BN Bayesian network

CH4 methane

CCC concordance correlation coefficient

DIM days in milk

DMI dry matter intake

ECMY energy corrected milk yield

EF enteric fermentation

GEI gross energy intake

IPCC intergovernmental panel on climate change

kNN k-nearest neighbors

MFA milk fatty acids

MIRS milk mid infrared spectroscopy

MLR multiple linear regression

NDF neutral detergent fiber

NN neural network

PEO population, exposure, outcome

PLS partial least squares

PRISMA preferred reporting standards for systematic reviews and meta-analyses

r Pearson correlation coefficient

r 2 coefficient of determination

RF random forest

SF6 sulfur hexaflouride

Ym methane conversion factor

Conflict of Interest Statement

The authors declare no real or perceived conflicts of interest.
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