Biokinetic process model diagnosis with shape-constrained spline functions

Model-structure identification is important for the optimization and design of biokinetic processes. Standard Monod and Tessier functions are often used by default to describe bacterial growth with respect to a substrate, leading to significant optimization errors in case of inappropriate representation. This paper introduces shape-constrained spline (SCS) functions, which share the qualitative behavior of a number of conventional growth-rate functions expressing substrate affinity effects. A simulated case study demonstrates the capabilities in terms of model identification of SCS functions, which offer a high parametric flexibility and could replace incomplete libraries of functions by a single biokinetic model structure. Moreover, the diagnostic ability of the spline functions is illustrated for the case of Haldane kinetics, which exhibits a distinctively different shape. The major benefit of these spline functions lies in their model discrimination capabilities by indicating in a quick and conclusive way the presence of other effects than substrate affinity

Visualization and Curve-Parameter Estimation Strategies for Efficient Exploration of Phenotype Microarray Kinetics

The Phenotype MicroArray (OmniLog® PM) system is able to simultaneously capture a large number of phenotypes by recording an organism's respiration over time on distinct substrates. This technique targets the object of natural selection itself, the phenotype, whereas previously addressed '-omics' techniques merely study components that finally contribute to it. The recording of respiration over time, however, adds a longitudinal dimension to the data. To optimally exploit this information, it must be extracted from the shapes of the recorded curves and displayed in analogy to conventional growth curves.The free software environment R was explored for both visualizing and fitting of PM respiration curves. Approaches using either a model fit (and commonly applied growth models) or a smoothing spline were evaluated. Their reliability in inferring curve parameters and confidence intervals was compared to the native OmniLog® PM analysis software. We consider the post-processing of the estimated parameters, the optimal classification of curve shapes and the detection of significant differences between them, as well as practically relevant questions such as detecting the impact of cultivation times and the minimum required number of experimental repeats.We provide a comprehensive framework for data visualization and parameter estimation according to user choices. A flexible graphical representation strategy for displaying the results is proposed, including 95% confidence intervals for the estimated parameters. The spline approach is less prone to irregular curve shapes than fitting any of the considered models or using the native PM software for calculating both point estimates and confidence intervals. These can serve as a starting point for the automated post-processing of PM data, providing much more information than the strict dichotomization into positive and negative reactions. Our results form the basis for a freely available R package for the analysis of PM data

Robust forecasting of mortality and fertility rates: a functional data approach

We propose a new method for forecasting age-specific mortality and fertility rates observed over time. Our approach allows for smooth functions of age, is robust for outlying years due to wars and epidemics, and provides a modelling framework that is easily adapted to allow for constraints and other information. We combine ideas from functional data analysis, nonparametric smoothing and robust statistics to form a methodology that is widely applicable to any functional time series data, and age-specific mortality and fertility in particular. We show that our model is a generalization of the Lee-Carter model commonly used in mortality and fertility forecasting. The methodology is applied to French mortality data and Australian fertility data, and we show that the forecasts obtained are superior to those from the Lee-Carter method and several of its variants.Fertility Forecasting, Functional Data, Mortality Forecasting, Nonparametric Smoothing, Principal Components, Robustness.

Increasing influence of heat stress on French maize yields from the 1960s to the 2030s

Improved crop yield forecasts could enable more effective adaptation to climate variability and change. Here, we explore how to combine historical observations of crop yields and weather with climate model simulations to produce crop yield projections for decision relevant timescales. Firstly, the effects on historical crop yields of improved technology, precipitation and daily maximum temperatures are modelled empirically, accounting for a nonlinear technology trend and interactions between temperature and precipitation, and applied specifically for a case study of maize in France. The relative importance of precipitation variability for maize yields in France has decreased significantly since the 1960s, likely due to increased irrigation. In addition, heat stress is found to be as important for yield as precipitation since around 2000. A significant reduction in maize yield is found for each day with a maximum temperature above 32 °C, in broad agreement with previous estimates. The recent increase in such hot days has likely contributed to the observed yield stagnation. Furthermore, a general method for producing near-term crop yield projections, based on climate model simulations, is developed and utilized. We use projections of future daily maximum temperatures to assess the likely change in yields due to variations in climate. Importantly, we calibrate the climate model projections using observed data to ensure both reliable temperature mean and daily variability characteristics, and demonstrate that these methods work using retrospective predictions. We conclude that, to offset the projected increased daily maximum temperatures over France, improved technology will need to increase base level yields by 12% to be confident about maintaining current levels of yield for the period 2016–2035; the current rate of yield technology increase is not sufficient to meet this target