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Bannink, A., van Lingen, H. J., Ellis, J. L., France, J., & Dijkstra, J. (2016). The contribution of mathematical modeling to understanding dynamic aspects of rumen metabolism. Frontiers in Microbiology, 7, 1820.
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.
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Baranowski, P., Krzyszczak, J., Slawinski, C., Hoffmann, H., Kozyra, J., Nieróbca, A., et al. (2015). Multifractal analysis of meteorological time series to assess climate impacts. Clim. Res., 65, 39–52.
Abstract: Agro-meteorological quantities are often in the form of time series, and knowledge about their temporal scaling properties is fundamental for transferring locally measured fluctuations to larger scales and vice versa. However, the scaling analysis of these quantities is complicated due to the presence of localized trends and nonstationarities. The objective of this study was to characterise scaling properties (i.e. statistical self-similarity) of the chosen agro-meteorological quantities through multifractal detrended fluctuation analysis (MFDFA). For this purpose, MFDFA was performedwith 11 322 measured time series (31 yr) of daily air temperature, wind velocity, relative air humidity, global radiation and precipitation from stations located in Finland, Germany, Poland and Spain. The empirical singularity spectra indicated their multifractal structure. The richness of the studied multifractals was evaluated by the width of their spectrum, indicating considerable differences in dynamics and development. In log-log plots of the cumulative distributions of all meteorological parameters the linear functions prevailed for high values of the response, indicating that these distributions were consistent with power-law asymptotic behaviour. Additionally, we investigated the type of multifractality that underlies the q-dependence of the generalized Hurst exponent by analysing the corresponding shuffled and surrogate time series. For most of the studied meteorological parameters, the multifractality is due to different long-range correlations for small and large fluctuations. Only for precipitation does the multifractality result mainly from broad probability function. This feature may be especially valuable for assessing the effect of change in climate dynamics.
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Bojar, W., Knopik, L., Żarski, J., & Kuśmierek-Tomaszewska, R. (2016). Integrated assessment of crop productivity based on the food supply forecasting. Agricultural Economics – Czech, 61(11), 502–510.
Abstract: Climate change scenarios suggest that long periods without rainfall will occur in the future often causing instability of the agricultural products market. The aim of our research was to build a model describing the amount of precipitation and droughts for forecasting crop yields in the future. In this study, we analysed a non-standard mixture of gamma and one point distributions as the model of rainfall. On the basis of the rainfall data, one can estimate parameters of the distribution. Parameter estimators were constructed using a method of maximum likelihood. The obtained rainfall data allow confirming the hypothesis of the adequacy of the proposed rainfall models. Long series of droughts allow one to determine the probabilities of adverse phenomena in agriculture. Based on the model, yields of barley in the years 2030 and 2050 were forecasted which can be used for the assessment of other crops productivity. The results obtained with this approach can be used to predict decreases in agricultural production caused by prospective rainfall shortages. This will enable decision makers to shape effective agricultural policies in order to learn how to balance the food supplies and demands through an appropriate management of stored raw food materials and import/export policies.
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De Swaef, T., Bellocchi, G., Aper, J., Lootens, P., & Roldan-Ruiz, I. (2019). Use of identifiability analysis in designing phenotyping experiments for modelling forage production and quality. J. Experim. Bot., 70(9), 2587–2604.
Abstract: Agricultural systems models are complex and tend to be over-parameterized with respect to observational datasets. Practical identifiability analysis based on local sensitivity analysis has proved effective in investigating identifiable parameter sets in environmental models, but has not been applied to agricultural systems models. Here, we demonstrate that identifiability analysis improves experimental design to ensure independent parameter estimation for yield and quality outputs of a complex grassland model. The Pasture Simulation model (PaSim) was used to demonstrate the effectiveness of practical identifiability analysis in designing experiments and measurement protocols within phe-notyping experiments with perennial ryegrass. Virtual experiments were designed combining three factors: frequency of measurements, duration of the experiment. and location of trials. Our results demonstrate that (i) PaSim provides sufficient detail in terms of simulating biomass yield and quality of perennial ryegrass for use in breeding, (ii) typical breeding trials are insufficient to parameterize all influential parameters, (iii) the frequency of measurements is more important than the number of growing seasons to improve the identifiability of PaSim parameters, and (iv) identifiability analysis provides a sound approach for optimizing the design of multi-location trials. Practical identifiability analysis can play an important role in ensuring proper exploitation of phenotypic data and cost-effective multi-location experimental designs. Considering the growing importance of simulation models, this study supports the design of experiments and measurement protocols in the phenotyping networks that have recently been organized.
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