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This meta-analysis shed light on the quantitative adaptive responses of feeding behaviour of Cattle (C) and Small Ruminants (SR), facing variations of sward characteristics, notably of sward height (SH, 18. 7 ± 13.9 cm) and herbage bulk density (HBD, 1.73 ± 1.30 kg DM / m3). All responses expressed a plateau stressing an adaptive limit with extreme values of SH and HBD. The minimum plateau of BR (46.9 ± 14.6 min-1) is around 40 min-1, while IR values (different for C and SR, respectively 69.1 ± 38.1 vs. 99.9 ± 45.7 g/min/kg BW) ranged between a minimum and maximum plateau around 50 and 100 g/min/kg BW. Two other pasture management factors affect IR, namely forage allowance (10.16 ± 6.0, DM % BW) and daily proportion of time spent grazing (0.30 ± 0.08). The results obtained confirm the specifically key role of BM (1.80 ± 127 mg DM/kg BW) on IR. The regressions are IR=145 (1-exp (-b BM), b being equal respectively for C and SR and C to 0.44 vs. 0.54. This literature review has also revealed fundamental differences in behaviour between C and SR although no study to date has attempted to compare them simultaneously. SR have to chew more (2.7 ± 1.2 vs. 1.6 ± 0.5 JM/bite) to ingest the same amount of DM per bite than C, expressed in relation to BW, which allow them to ingest slightly quickly.ImplicationsThis article, following the previous one of Boval and Sauvant (2019), proposes a quantitative appraisal of the ingestive behaviour of grazing ruminants, based on studies published over 40 years, as well as well robust average values and relationships, considering inter- and intra-study effects and animal species specificities. This knowledge should contribute to a better overall understanding of the behavioural adaptation of ruminants at pasture, to the identification of key threshold values and appropriate parameters of interest to be considered, and to improve the efficiency and sensitivity of automatic devices, which are booming in the context of precision livestock farming at pasture.

Empirical and phenomenological based models are used to represent biological and physiological processes. Phenomenological models are derived from the knowledge of the mechanisms that underlie the behaviour of the system under study, while empirical models are derived from analysis of data to quantify relationships between variables of interest. For studying biological systems, the phenomenological modeling approach offers the great advantage of having a structure with variables and parameters with physical meaning that enhance the interpretability of the model and its further used for decision making. The interpretability property of models, however, remains a vague concept. In this study, we tackled the interpretability property for parameters of phenomenological-based models. To our knowledge, this property has not been deeply discussed, perhaps by the implicit assumption that interpretability is inherent to the phenomenological-based models. We propose a conceptual framework to address the parameter interpretability and its implications for parameter identifiability. We use as battle horse a simple but relevant model representing the enzymatic degradation ofβ–casein by aLactococcus lactisbacterium.

Methanogenic archaea occupy a functionally important niche in the gut microbial ecosystem of mammals. Our purpose was to quantitatively characterize the dynamics of methanogenesis by integrating microbiology, thermodynamics and mathematical modelling. For that,in vitrogrowth experiments were performed with pure cultures of key methanogens from the human and ruminant gut, namelyMethanobrevibacter smithii, Methanobrevibacter ruminantiumandMethanobacterium formicium. Microcalorimetric experiments were performed to quantify the methanogenesis heat flux. We constructed an energetic-based mathematical model of methanogenesis. Our model captured efficiently the dynamics of methanogenesis with concordance correlation coefficients of 0.94 for CO2, 0.99 for H2and 0.97 for CH4. Together, experimental data and model enabled us to quantify metabolism kinetics and energetic patterns that were specific and distinct for each species despite their use of analogous methane-producing pathways. Then, we testedin silicothe interactions between these methanogens under anin vivosimulation scenario using a theoretical modelling exercise.In silicosimulations suggest that the classical competitive exclusion principle is inapplicable to gut ecosystems and that kinetic information alone cannot explain gut ecological aspects such as microbial coexistence. We suggest that ecological models of gut ecosystems require the integration of microbial kinetics with nonlinear behaviours related to spatial and temporal variations taking place in mammalian guts. Our work provides novel information on the thermodynamics and dynamics of methanogens. This understanding will be useful to construct new gut models with enhanced prediction capabilities and could have practical applications for promoting gut health in mammals and mitigating ruminant methane emissions.