Modeling of radial variations in wood properties and comparison of juvenile and mature wood of four common conifers in Mongolia

Pinus sylvestris L., Pinus sibirica Du Tour, Picea obovata Ledeb., and Larix sibirica Ledeb. are important forest tree species in Mongolia. The radial variations of wood anatomical characteristics, physical and mechanical properties were evaluated by linear or nonlinear mixed-effects models for effective wood utilization of those of conifers. Many of these wood properties either increased or decreased from the pith to the bark and then became nearly constant based on the selected models. The properties of mature wood were estimated by nonlinear mixed-effects models, suggesting that P. sylvestris and L. sibirica are suitable as structural lumber, P. sibirica can be used for furniture and other interior products, and P. obovata is suitable for structural lumber as well as for furniture or interior products.

Practical identifiability in the frame of nonlinear mixed effects models: the example of the in vitro erythropoiesis

Background Nonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity. In order to assess their practical identifiability and estimate confidence intervals for their parameters, most mixed effects modelling programs use the Fisher Information Matrix. However, in complex nonlinear models, this approach can mask practical unidentifiabilities. Results Herein we rather propose a multistart approach, and use it to simplify our model by reducing the number of its parameters, in order to make it identifiable. Our model describes several cell populations involved in the in vitro differentiation of chicken erythroid progenitors grown in the same environment. Inter-individual variability observed in cell population counts is explained by variations of the differentiation and proliferation rates between replicates of the experiment. Alternatively, we test a model with varying initial condition. Conclusions We conclude by relating experimental variability to precise and identifiable variations between the replicates of the experiment of some model parameters.

Taking Kinetic Evaluations of Degradation Data to the Next Level with Nonlinear Mixed-Effects Models

When data on the degradation of a chemical substance have been collected in a number of environmental media (e.g., in different soils), two strategies can be followed for data evaluation. Currently, each individual dataset is evaluated separately, and representative degradation parameters are obtained by calculating averages of the kinetic parameters. However, such averages often take on unrealistic values if certain degradation parameters are ill-defined in some of the datasets. Moreover, the most appropriate degradation model is selected for each individual dataset, which is time consuming and then requires workarounds for averaging parameters from different models. Therefore, a simultaneous evaluation of all available data is desirable. If the environmental media are viewed as random samples from a population, an advanced strategy based on assumptions about the statistical distribution of the kinetic parameters across the population can be used. Here, we show the advantages of such simultaneous evaluations based on nonlinear mixed-effects models that incorporate such assumptions in the evaluation process. The advantages of this approach are demonstrated using synthetically generated data with known statistical properties and using publicly available experimental degradation data on two pesticidal active substances.

Practical Identifiability in the Frame of Nonlinear Mixed Effects Models: the Example of the in vitro Erythropoiesis

Nonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity. In order to assess their practical identifiability and estimate confidence intervals for their parameters, most mixed effects modelling programs use the Fisher Information Matrix. However, in complex nonlinear models, this approach can mask practical unidentifiabilities. Herein we rather propose a multistart approach, and use it to simplify our model by reducing the number of its parameters, in order to make it identifiable. Our model describes several cell populations involved in the in vitro differentiation of chicken erythroid progenitors grown in the same environment. Inter-individual variability observed in cell population counts is explained by variations of the differentiation and proliferation rates between replicates of the experiment. Alternatively, we test a model with varying initial condition. We conclude by relating experimental variability to precise and identifiable variations between the replicates of the experiment of some model parameters.