Review: Reducing enteric methane emissions improves energy metabolism in livestock: is the tenet right?

The production of enteric methane in the gastrointestinal tract of livestock is considered as an energy loss in the equations for estimating energy metabolism in feeding systems. Therefore, the spared energy resulting from specific inhibition of methane emissions should be re-equilibrated with other factors of the equation. And, it is commonly assumed that net energy from feeds increases, thus benefitting production functions, particularly in ruminants due to the important production of methane in the rumen. Notwithstanding, we confirm in this work that inhibition of emissions in ruminants does not transpose into consistent improvements in production. Theoretical calculations of energy flows using experimental data show that the expected improvement in net energy for production is small and difficult to detect under the prevailing, moderate inhibition of methane production (≈25%) obtained using feed additives inhibiting methanogenesis. Importantly, the calculation of energy partitioning using canonical models might not be adequate when methanogenesis is inhibited. There is a lack of information on various parameters that play a role in energy partitioning and that may be affected under provoked abatement of methane. The formula used to calculate heat production based on respiratory exchanges should be validated when methanogenesis is inhibited. Also, a better understanding is needed of the effects of inhibition on fermentation products, fermentation heat, and microbial biomass. Inhibition induces the accumulation of H2, the main substrate used to produce methane, that has no energetic value for the host, and it is not extensively used by the majority of rumen microbes. Currently, the fate of this excess of H2 and its consequences on the microbiota and the host are not well known. All this additional information will provide a better account of energy transactions in ruminants when enteric methanogenesis is inhibited. Based on the available information, it is concluded that the claim that enteric methane inhibition will translate into more feed-efficient animals is not warranted.

Review: Towards the next-generation models of the rumen microbiome for enhancing predictive power and guiding sustainable production strategies.

The rumen ecosystem harbours a galaxy of microbes working in syntrophy to carry out a metabolic cascade of hydrolytic and fermentative reactions. This fermentation process allows ruminants to harvest nutrients from a wide range of feedstuff otherwise inaccessible to the host. The interconnection between the ruminant and its rumen microbiota shapes key animal phenotypes such as feed efficiency and methane emissions and suggests the potential of reducing methane emissions and enhancing feed conversion into animal products by manipulating the rumen microbiota. Whilst significant technological progress in omics techniques has increased our knowledge of the rumen microbiota and its genome (microbiome), translating omics knowledge into effective microbial manipulation strategies remains a great challenge. This challenge can be addressed by modelling approaches integrating causality principles and thus going beyond current correlation-based approaches applied to analyse rumen microbial genomic data. However, existing rumen models are not yet adapted to capitalise on microbial genomic information. This gap between the rumen microbiota available omics data and the way microbial metabolism is represented in the existing rumen models needs to be filled to enhance rumen understanding and produce better predictive models with capabilities for guiding nutritional strategies. To fill this gap, the integration of computational biology tools and mathematical modelling frameworks is needed to translate the information of the metabolic potential of the rumen microbes (inferred from their genomes) into a mathematical object. In this paper, we aim to discuss the potential use of two modelling approaches for the integration of microbial genomic information into dynamic models. The first modelling approach explores the theory of state observers to integrate microbial time series data into rumen fermentation models. The second approach is based on the genome-scale network reconstructions of rumen microbes. For a given microorganism, the network reconstruction produces a stoichiometry matrix of the metabolism. This matrix is the core of the so-called genome-scale metabolic models which can be exploited by a plethora of methods comprised within the constraint-based reconstruction and analysis approaches. We will discuss how these methods can be used to produce the next-generation models of the rumen microbiome.

Animal board invited review: Quantification of resilience in farm animals.

Resilience, when defined as the capacity of an animal to respond to short-term environmental challenges and to return to the prechallenge status, is a dynamic and complex trait. Resilient animals can reinforce the capacity of the herd to cope with often fluctuating and unpredictable environmental conditions. The ability of modern technologies to simultaneously record multiple performance measures of individual animals over time is a huge step forward to evaluate the resilience of farm animals. However, resilience is not directly measurable and requires mathematical models with biologically meaningful parameters to obtain quantitative resilience indicators. Furthermore, interpretive models may also be needed to determine the periods of perturbation as perceived by the animal. These applications do not require explicit knowledge of the origin of the perturbations and are developed based on real-time information obtained in the data during and outside the perturbation period. The main objective of this paper was to review and illustrate with examples, different modelling approaches applied to this new generation of data (i.e., with high-frequency recording) to detect and quantify animal responses to perturbations. Case studies were developed to illustrate alternative approaches to real-time and post-treatment of data. In addition, perspectives on the use of hybrid models for better understanding and predicting animal resilience are presented. Quantification of resilience at the individual level makes possible the inclusion of this trait into future breeding programmes. This would allow improvement of the capacity of animals to adapt to a changing environment, and therefore potentially reduce the impact of disease and other environmental stressors on animal welfare. Moreover, such quantification allows the farmer to tailor the management strategy to help individual animals to cope with the perturbation, hence reducing the use of pharmaceuticals, and decreasing the level of pain of the animal.

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

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

Towards the quantitative characterisation of piglets' robustness to weaning: a modelling approach.

Weaning is a critical transition phase in swine production in which piglets must cope with different stressors that may affect their health. During this period, the prophylactic use of antibiotics is still frequent to limit piglet morbidity, which raises both economic and public health concerns such as the appearance of antimicrobial-resistant microbes. With the interest of developing tools for assisting health and management decisions around weaning, it is key to provide robustness indexes that inform on the animals' capacity to endure the challenges associated with weaning. This work aimed at developing a modelling approach for facilitating the quantification of piglet resilience to weaning. A total of 325 Large White pigs weaned at 28 days of age were monitored and further housed and fed conventionally during the post-weaning period without antibiotic administration. Body weight and diarrhoea scores were recorded before and after weaning, and blood was sampled at weaning and 1 week later for collecting haematological data. A dynamic model was constructed based on the Gompertz-Makeham law to describe live weight trajectories during the first 75 days after weaning, following the rationale that the animal response is partitioned in two time windows (a perturbation and a recovery window). Model calibration was performed for each animal. Our results show that the transition time between the two time windows, as well as the weight trajectories are characteristic for each individual. The model captured the weight dynamics of animals at different degrees of perturbation, with an average coefficient of determination of 0.99, and a concordance correlation coefficient of 0.99. The utility of the model is that it provides biologically meaningful parameters that inform on the amplitude and length of perturbation, and the rate of animal recovery. Our rationale is that the dynamics of weight inform on the capability of the animal to cope with the weaning disturbance. Indeed, there were significant correlations between model parameters and individual diarrhoea scores and haematological traits. Overall, the parameters of our model can be useful for constructing weaning robustness indexes by using exclusively the growth curves. We foresee that this modelling approach will provide a step forward in the quantitative characterisation of robustness.

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.