arXiv subjects

Paul-Henry Cournède

Publications and source records attributed to Paul-Henry Cournède.

25 records · Page 2Linked to original sources

arXiv2019

Mean field approximation of a heterogeneous population of plants in competition

The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to better understand these phenomena but requires simulating the interactions between different individuals. In the case of large populations, assessing the parameters of a heterogeneous population model from experimental data is intractable computationally. This paper investigates the mean-field approximation of large dynamical systems with random initial conditions and individual parameters, and with interaction being represented by pairwise potentials between individuals. Under this approximation, each individual is in interaction with an infinitely-crowded population, summarized by a probability measure, the mean-field limit distribution, being itself the weak solution of a non-linear hyperbolic partial differential equation. In particular, the phenomenon of chaos propagation implies that the individuals are independent asymptotically when the size of the population tends towards infinity. This result provides perspectives for a possible simplification of the inference problem. The simulation of the mean-field distribution, consisting in a semi-Lagrangian scheme with an interpolation step using Gaussian process regression, is illustrated for a heterogeneous population model representing plants in competition for light.

math.AP↗

arXiv2017

Likelihood ratio test for variance components in nonlinear mixed effects models

Mixed effects models are widely used to describe heterogeneity in a population. A crucial issue when adjusting such a model to data consists in identifying fixed and random effects. From a statistical point of view, it remains to test the nullity of the variances of a given subset of random effects. Some authors have proposed to use the likelihood ratio test and have established its asymptotic distribution in some particular cases. Nevertheless, to the best of our knowledge, no general variance components testing procedure has been fully investigated yet. In this paper, we study the likelihood ratio test properties to test that the variances of a general subset of the random effects are equal to zero in both linear and nonlinear mixed effects model, extending the existing results. We prove that the asymptotic distribution of the test is a chi-bar-square distribution, that is to say a mixture of chi-square distributions, and we identify the corresponding weights. We highlight in particular that the limiting distribution depends on the presence of correlations between the random effects but not on the linear or nonlinear structure of the mixed effects model. We illustrate the finite sample size properties of the test procedure through simulation studies and apply the test procedure to two real datasets of dental growth and of coucal growth.

stat.ME↗

arXiv2017

A critical analysis of resampling strategies for the regularized particle filter

We analyze the performance of different resampling strategies for the regularized particle filter regarding parameter estimation. We show in particular, building on analytical insight obtained in the linear Gaussian case, that resampling systematically can prevent the filtered density from converging towards the true posterior distribution. We discuss several means to overcome this limitation, including kernel bandwidth modulation, and provide evidence that the resulting particle filter clearly outperforms traditional bootstrap particle filters. Our results are supported by numerical simulations on a linear textbook example, the logistic map and a non-linear plant growth model.

stat.CO↗

arXiv2010

Parametric identification of a functional-structural tree growth model and application to beech trees (Fagus sylvatica)

Functional-structural models provide detailed representations of tree growth and their application to forestry seems full of prospects. However, owing to the complexity of tree architecture, parametric identification of such models remains a critical issue. We present the GreenLab approach for modelling tree growth. It simulates tree growth plasticity in response to changes of their internal level of trophic competition, especially topological development and cambial growth. The model includes a simplified representation of tree architecture, based on a species-specific description of branching patterns. We study whether those simplifications allow enough flexibility to reproduce with the same set of parameters the growth of two observed understorey beech trees (Fagus sylvatica L.) of different ages in different environmental conditions. The parametric identification of the model is global, i.e. all parameters are estimated simultaneously, potentially providing a better description of interactions between sub-processes. As a result, the source-sink dynamics throughout tree development is retrieved. Simulated and measured trees were compared for their trunk profiles (fresh masses and dimensions of every growth units, ring diameters at different heights) and compartment masses of their order 2 branches. Possible improvements of this method by including topological criteria are discussed.

math.DS↗

arXiv2010

Quantitative Genetics and Functional-Structural Plant Growth Models: Simulation of Quantitative Trait Loci Detection for Model Parameters and Application to Potential Yield Optimization

Background and Aims: Prediction of phenotypic traits from new genotypes under untested environmental conditions is crucial to build simulations of breeding strategies to improve target traits. Although the plant response to environmental stresses is characterized by both architectural and functional plasticity, recent attempts to integrate biological knowledge into genetics models have mainly concerned specific physiological processes or crop models without architecture, and thus may prove limited when studying genotype x environment interactions. Consequently, this paper presents a simulation study introducing genetics into a functional-structural growth model, which gives access to more fundamental traits for quantitative trait loci (QTL) detection and thus to promising tools for yield optimization. Methods: The GreenLab model was selected as a reasonable choice to link growth model parameters to QTL. Virtual genes and virtual chromosomes were defined to build a simple genetic model that drove the settings of the species-specific parameters of the model. The QTL Cartographer software was used to study QTL detection of simulated plant traits. A genetic algorithm was implemented to define the ideotype for yield maximization based on the model parameters and the associated allelic combination. Key Results and Conclusions: By keeping the environmental factors constant and using a virtual population with a large number of individuals generated by a Mendelian genetic model, results for an ideal case could be simulated. Virtual QTL detection was compared in the case of phenotypic traits - such as cob weight - and when traits were model parameters, and was found to be more accurate in the latter case. The practical interest of this approach is illustrated by calculating the parameters (and the corresponding genotype) associated with yield optimization of a GreenLab maize model. The paper discusses the potentials of GreenLab to represent environment x genotype interactions, in particular through its main state variable, the ratio of biomass supply over demand.

math.ST↗

arXiv2009

A morphogenetic crop model for sugar-beet (Beta vulgaris L.)

This paper is the instructions for the proceeding of the International Symposium on Crop. Sugar beet crop models have rarely taken into account the morphogenetic process generating plant architecture despite the fact that plant architectural plasticity plays a key role during growth, especially under stress conditions. The objective of this paper is to develop this approach by applying the GreenLab model of plant growth to sugar beet and to study the potential advantages for applicative purposes. Experiments were conducted with husbandry practices in 2006. The study of sugar beet development, mostly phytomer appearance, organ expansion and leaf senescence, allowed us to define a morphogenetic model of sugar beet growth based on GreenLab. It simulates organogenesis, biomass production and biomass partitioning. The functional parameters controlling source-sink relationships during plant growth were estimated from organ and compartment dry masses, measured at seven different times, for samples of plants. The fitting results are good, which shows that the introduced framework is adapted to analyse source-sink dynamics and shoot-root allocation throughout the season. However, this approach still needs to be fully validated, particularly among seasons.

q-bio.TO↗

arXiv2007

The Influence of Photosynthesis on the Number of Metamers per Growth Unit in GreenLab Model

GreenLab Model is a functional-structural plant growth model that combines both organogenesis (at each cycle, new organs are created with respect to genetic rules) and photosynthesis (organs are filled with the biomass produced by the leaves photosynthesis). Our new developments of the model concern the retroaction of photosynthesis on organogenesis. We present here the first step towards the total representation of this retroaction, where the influence of available biomass on the number of metamers in new growth units us modelled. The theory is introduced and applied to a Corner model tree. Different interesting behaviours are pointed out.

q-bio.TO↗