Abstract: Livestock directly contribute to greenhouse gas (GHG) emissions mainly through methane (CH4) and nitrous oxide (N2O) emissions. For cost and practicality reasons, quantification of GHG has been through development of various types of mathematical models. This chapter addresses the utility and limitations of mathematical models used to estimate enteric CH4 emissions from livestock production. Models used in GHG quantification can be broadly classified into either empirical or mechanistic models. Empirical models might be easier to use because they require fewer input variables compared with mechanistic models. However, their applicability in assessing mitigation options such as dietary manipulation may be limited. The major driving variables identified for both types of models include feed intake, lipid and nonstructural carbohydrate content of the feed, and animal variables. Knowledge gaps identified in empirical modeling were that some of the assumptions might not be valid because of geographical location, health status of animals, genetic differences, or production type. In mechanistic modeling, errors related to estimating feed intake, stoichiometry of volatile fatty acid (VFA) production, and acidity of rumen contents are limitations that need further investigation. Model prediction uncertainty was also investigated, and, depending on the intensity and source of the prediction uncertainty, the mathematical model may inaccurately predict the observed values with more or less variability. In conclusion, although there are quantification tools available, global collaboration is required to come to a consensus on quantification protocols. This can be achieved through developing various types of models specific to region, animal, and production type using large global datasets developed through international collaboration.

Abstract: Ruminant production systems are important producers of food, support rural communities and culture, and help to maintain a range of ecosystem services including the sequestering of carbon in grassland soils. However, these systems also contribute significantly to climate change through greenhouse gas (GHG) emissions, while intensi- fication of production has driven biodiversity and nutrient loss, and soil degradation. Modeling can offer insights into the complexity underlying the relationships between climate change, management and policy choices, food production, and the maintenance of ecosystem services. This paper 1) provides an overview of how ruminant systems modeling supports the efforts of stakeholders and policymakers to predict, mitigate and adapt to climate change and 2) provides ideas for enhancing modeling to fulfil this role. Many grassland models can predict plant growth, yield and GHG emissions from mono-specific swards, but modeling multi-species swards, grassland quality and the impact of management changes requires further development. Current livestock models provide a good basis for predicting animal production; linking these with models of animal health and disease is a prior- ity. Farm-scale modeling provides tools for policymakers to predict the emissions of GHG and other pollutants from livestock farms, and to support the management decisions of farmers from environmental and economic standpoints. Other models focus on how policy and associated management changes affect a range of economic and environmental variables at regional, national and European scales. Models at larger scales generally utilise more empirical approaches than those applied at animal, field and farm-scales and include assumptions which may not be valid under climate change conditions. It is therefore important to continue to develop more realistic representations of processes in regional and global models, using the understanding gained from finer-scale modeling. An iterative process of model development, in which lessons learnt from mechanistic models are ap- plied to develop ‘smart’ empirical modeling, may overcome the trade-off between complexity and usability. De- veloping the modeling capacity to tackle the complex challenges related to climate change, is reliant on closer links between modelers and experimental researchers, and also requires knowledge-sharing and increasing technical compatibility across modeling disciplines. Stakeholder engagement throughout the process of model development and application is vital for the creation of relevant models, and important in reducing problems re- lated to the interpretation of modeling outcomes. Enabling modeling to meet the demands of policymakers and other stakeholders under climate change will require collaboration within adequately-resourced, long-term inter-disciplinary research networks

Abstract: All mechanistic rumen models cover the main drivers of variation in rumen function, which are feed intake, the differences between feedstuffs and feeds in their intrinsic rumen degradation characteristics, and fractional outflow rate of fluid and particulate matter. Dynamic modeling approaches are best suited to the prediction of more nuanced responses in rumen metabolism, and represent the dynamics of the interactions between substrates and micro-organisms and inter-microbial interactions. The concepts of dynamics are discussed for the case of rumen starch digestion as influenced by starch intake rate and frequency of feed intake, and for the case of fermentation of fiber in the large intestine. Adding representations of new functional classes of micro-organisms (i.e., with new characteristics from the perspective of whole rumen function) in rumen models only delivers new insights if complemented by the dynamics of their interactions with other functional classes. Rumen fermentation conditions have to be represented due to their profound impact on the dynamics of substrate degradation and microbial metabolism. Although the importance of rumen pH is generally acknowledged, more emphasis is needed on predicting its variation as well as variation in the processes that underlie rumen fluid dynamics. The rumen wall has an important role in adapting to rapid changes in the rumen environment, clearing of volatile fatty acids (VFA), and maintaining rumen pH within limits. Dynamics of rumen wall epithelia and their role in VFA absorption needs to be better represented in models that aim to predict rumen responses across nutritional or physiological states. For a detailed prediction of rumen N balance there is merit in a dynamic modeling approach compared to the static approaches adopted in current protein evaluation systems. Improvement is needed on previous attempts to predict rumen VFA profiles, and this should be pursued by introducing factors that relate more to microbial metabolism. For rumen model construction, data on rumen microbiomes are preferably coupled with knowledge consolidated in rumen models instead of relying on correlations with rather general aspects of treatment or animal. This helps to prevent the disregard of basic principles and underlying mechanisms of whole rumen function.