Véronique Letort

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.

A model-based analysis of the dynamics of carbon balance at the whole-plant level in Arabidopsis thaliana

Arabidopsis thaliana (L.) Heynh. is used as a model plant in many research projects. However, few models simulate its growth at the whole-plant scale. The present study describes the first model of Arabidopsis growth integrating organogenesis, morphogenesis and carbon-partitioning processes for aerial and subterranean parts of the plant throughout its development. The objective was to analyse competition among sinks as they emerge from patterns of plant structural development. The model was adapted from the GreenLab model and was used to estimate organ sink strengths by optimisation against biomass measurements. Dry biomass production was calculated by a radiation use efficiency-based approach. Organogenesis processes were parameterised based on experimental data. The potential of this model for growth analysis was assessed using the Columbia ecotype, which was grown in standard environmental conditions. Three phases were observed in the overall time course of trophic competition within the plant. In the vegetative phase, no competition was observed. In the reproductive phase, competition increased with a strong increase when lateral inflorescences developed. Roots and internodes and structures bearing siliques were strong sinks and had a similar impact on competition. The application of the GreenLab model to the growth analysis of A. thaliana provides new insights into source-sink relationships as functions of phenology and morphogenesis.

Automated Cell Tracking and Analysis in Phase-Contrast Videos (iTrack4U): Development of Java Software Based on Combined Mean-Shift Processes

Cell migration is a key biological process with a role in both physiological and pathological conditions. Locomotion of cells during embryonic development is essential for their correct positioning in the organism; immune cells have to migrate and circulate in response to injury. Failure of cells to migrate or an inappropriate acquisition of migratory capacities can result in severe defects such as altered pigmentation, skull and limb abnormalities during development, and defective wound repair, immunosuppression or tumor dissemination. The ability to accurately analyze and quantify cell migration is important for our understanding of development, homeostasis and disease. In vitro cell tracking experiments, using primary or established cell cultures, are often used to study migration as cells can quickly and easily be genetically or chemically manipulated. Images of the cells are acquired at regular time intervals over several hours using microscopes equipped with CCD camera. The locations (x,y,t) of each cell on the recorded sequence of frames then need to be tracked. Manual computer-assisted tracking is the traditional method for analyzing the migratory behavior of cells. However, this processing is extremely tedious and time-consuming. Most existing tracking algorithms require experience in programming languages that are unfamiliar to most biologists. We therefore developed an automated cell tracking program, written in Java, which uses a mean-shift algorithm and ImageJ as a library. iTrack4U is a user-friendly software. Compared to manual tracking, it saves considerable amount of time to generate and analyze the variables characterizing cell migration, since they are automatically computed with iTrack4U. Another major interest of iTrack4U is the standardization and the lack of inter-experimenter differences. Finally, iTrack4U is adapted for phase contrast and fluorescent cells.

A stochastic model of tree architecture and biomass partitioning: application to Mongolian Scots pines

BACKGROUND AND AIMS Mongolian Scots pine (Pinus sylvestris var. mongolica) is one of the principal species used for windbreak and sand stabilization in arid and semi-arid areas in northern China. A model-assisted analysis of its canopy architectural development and functions is valuable for better understanding its behaviour and roles in fragile ecosystems. However, due to the intrinsic complexity and variability of trees, the parametric identification of such models is currently a major obstacle to their evaluation and their validation with respect to real data. The aim of this paper was to present the mathematical framework of a stochastic functional-structural model (GL2) and its parameterization for Mongolian Scots pines, taking into account inter-plant variability in terms of topological development and biomass partitioning. METHODS In GL2, plant organogenesis is determined by the realization of random variables representing the behaviour of axillary or apical buds. The associated probabilities are calibrated for Mongolian Scots pines using experimental data including means and variances of the numbers of organs per plant in each order-based class. The functional part of the model relies on the principles of source-sink regulation and is parameterized by direct observations of living trees and the inversion method using measured data for organ mass and dimensions. KEY RESULTS The final calibration accuracy satisfies both organogenetic and morphogenetic processes. Our hypothesis for the number of organs following a binomial distribution is found to be consistent with the real data. Based on the calibrated parameters, stochastic simulations of the growth of Mongolian Scots pines in plantations are generated by the Monte Carlo method, allowing analysis of the inter-individual variability of the number of organs and biomass partitioning. Three-dimensional (3D) architectures of young Mongolian Scots pines were simulated for 4-, 6- and 8-year-old trees. CONCLUSIONS This work provides a new method for characterizing tree structures and biomass allocation that can be used to build a 3D virtual Mongolian Scots pine forest. The work paves the way for bridging the gap between a single-plant model and a stand model.

Exploring individual HPV coinfections is essential to predict HPV-vaccination impact on genotype distribution: A model-based approach

INTRODUCTION As for other vaccines that only target a subset of circulating pathogen types, human papillomavirus (HPV) immunization raises the concern of a potential risk of genotype replacement. Potential interactions between HPV types may affect infection acquisition and clearance. However, the existence and the nature of these interactions are still largely unknown. Here, we assess how such interactions might affect the impact of HPV vaccination on genotype distribution in the long term. METHODS We develop two mathematical models of the transmission of oncogenic HPV infections that include interactions between vaccine and nonvaccine genotypes to examine the influence of different coinfection dynamics (simultaneous vs. sequential clearance of coinfections) on the evolution of nonvaccine prevalences postimmunization. RESULTS After introducing vaccination, the two models give contrasting genotype-replacement outcomes. When hypothesizing that coinfections clear sequentially, genotype replacement depends on whether vaccine and nonvaccine genotypes reduce or favor the acquisition by one or the other. Interestingly, the hypothesis that coinfections clear simultaneously always leads to genotype replacement, even when infections with vaccine types favor the acquisition of infections with nonvaccine types. CONCLUSION Our results suggest that predictions regarding HPV genotype replacement strongly depend on the assumptions describing the dynamics (acquisition and clearance) of coinfections. In particular, HPV genotype replacement could be compatible with synergistic interactions between types affecting infections acquisition, contrary to previous suggestions. Understanding better how concurrent infections with multiple types change the acquisition and time to clearance of type-specific infections is essential to be able to predict the impact of vaccination on genotype distribution. Longitudinal data collection in populations, particularly examining infection and coinfection acquisition and clearance, is needed to better predict HPV-vaccine impact.

A Functional and Structural Mongolian Scots Pine (Pinus sylvestris var. mongolica) Model Integrating Architecture, Biomass and Effects of Precipitation

Mongolian Scots pine (Pinus sylvestris var. mongolica) is one of the principal tree species in the network of Three-North Shelterbelt for windbreak and sand stabilisation in China. The functions of shelterbelts are highly correlated with the architecture and eco-physiological processes of individual tree. Thus, model-assisted analysis of canopy architecture and function dynamic in Mongolian Scots pine is of value for better understanding its role and behaviour within shelterbelt ecosystems in these arid and semiarid regions. We present here a single-tree functional and structural model, derived from the GreenLab model, which is adapted for young Mongolian Scots pines by incorporation of plant biomass production, allocation, allometric rules and soil water dynamics. The model is calibrated and validated based on experimental measurements taken on Mongolian Scots pines in 2007 and 2006 under local meteorological conditions. Measurements include plant biomass, topology and geometry, as well as soil attributes and standard meteorological data. After calibration, the model allows reconstruction of three-dimensional (3D) canopy architecture and biomass dynamics for trees from one- to six-year-old at the same site using meteorological data for the six years from 2001 to 2006. Sensitivity analysis indicates that rainfall variation has more influence on biomass increment than on architecture, and the internode and needle compartments and the aboveground biomass respond linearly to increases in precipitation. Sensitivity analysis also shows that the balance between internode and needle growth varies only slightly within the range of precipitations considered here. The model is expected to be used to investigate the growth of Mongolian Scots pines in other regions with different soils and climates.

Insights into Persistence Mechanisms of a Zoonotic Virus in Bat Colonies Using a Multispecies Metapopulation Model

Rabies is a worldwide zoonosis resulting from Lyssavirus infection. In Europe, Eptesicus serotinus is the most frequently reported bat species infected with Lyssavirus, and thus considered to be the reservoir of European bat Lyssavirus type 1 (EBLV-1). To date, the role of other bat species in EBLV-1 epidemiology and persistence remains unknown. Here, we built an EBLV-1−transmission model based on local observations of a three-cave and four-bat species (Myotis capaccinii, Myotis myotis, Miniopterus schreibersii, Rhinolophus ferrumequinum) system in the Balearic Islands, for which a 1995–2011 serological dataset indicated the continuous presence of EBLV-1. Eptesicus serotinus was never observed in the system during the 16-year follow-up and therefore was not included in the model. We used the model to explore virus persistence mechanisms and to assess the importance of each bat species in the transmission dynamics. We found that EBLV-1 could not be sustained if transmission between M. schreibersii and other bat species was eliminated, suggesting that this species serves as a regional reservoir. Global sensitivity analysis using Sobols method revealed that following the rate of autumn−winter infectious contacts, M. schreibersiis incubation- and immune-period durations, but not the infectious period length, were the most relevant factors driving virus persistence.

Modeling tree crown dynamics with 3D partial differential equations

We characterize a trees spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.

Characterization of the effects of inter-tree competition on source–sink balance in Chinese pine trees with the GreenLab model

We investigate the characteristics of individual tree response to competition on source–sink balance through the functional–structural plant model GreenLab. Four Chinese pine (Pinus tabulaeformis Carr.) trees were destructively sampled and were divided into two groups: high-density group and low-density group. First, the effects of density on organ dimensions and on organ relative mass were analysed based on experimental measurements. These were primary indicators of the plant response to competition. Second, the hidden parameters of the GreenLab model, as well as a tree-specific characteristic surface, were estimated using the data of total tree biomass for needle and wood compartments, for each of the four trees in parallel. The quality of the fitting is finally validated using data of individual organ mass at shoot level for the sampled branches. The Mann–Whitney Student’s t test showed that there were significant differences between the shoot attributes of the two groups for shoot diameter, shoot biomass and needle biomass. No significant difference was found for current year shoot lengths of the two groups. The parametric identification of the model allowed estimating and comparing the amount of biomass that was allocated to primary growth and to secondary growth in the two density conditions. It showed that biomass allocated to secondary growth (ring compartment) was the most strongly affected by density, and that the organ demand satisfaction ratio profiles of each of these trees were a relevant, integrated indicator of the tree state.

Calibration of Topological Development in the Procedure of Parametric Identification: Application of the Stochastic GreenLab Model for Pinus sylvestris var. mongolica

Climate, biophysical conditions and human activities all contribute to the occurrences of ecosystem and environment problems, i.e. water scarcity, desertification, salinization, in arid and semiarid zone of North China. Mongolian Scots pine tree (Pinus sylvestris var. mongolica) is one of the principal species of the windbreak and sand-fixing forest in this area. In this paper, we presented the calibration process of stochastic GreenLab model based on experiment data. Specific plant topology and sink–source parameters were estimated for Mongolian Scots pine trees through optimizing procedure. The fitting results showed that the calibration process were reasonable and acceptable. The model produced a variety of three-dimensional visual representations of Mongolian Scots pine trees with different topological structures simulated by Monte Carlo methods. This model can be used to describe the plant development and growth in a stand level, taking into accounts the variations in plant topology and biomass.