Section: New Results

Analysis of structures resulting from meristem activity

Acquisition and design of plant geometry

Participants : Frédéric Boudon, Christophe Pradal, Christophe Godin, Christian Fournier, Ibrahim Chedaddi, Mathilde Balduzzi, Julien Diener.

Virtual 3D model of plants are required in many areas of plant modeling. They can be used for instance to simulate physical interaction of real plant structures with their environment (ligth, rain, wind, pests, ...), to set up initial conditions of growth models or to assess their output against real data. In the past decade, methods have been developed to digitize plant architectures in 3D [61] , [52] . These methods are based on direct measurements of position and shape of every plant organ in space. Although they provide accurate results, they are particularly time consuming. More rapid and automated methods are now required in order to collect plant architecture data of various types and sizes in a systematic way. In this aim, we explore the use of pictures, laser scanner and video.

• Reconstruction of plant architecture from 3D laser scanner data. (Chakkrit Preuksakarn, Mathilde Balduzzi, Frédéric Boudon, Christophe Godin, Pascal Ferraro [Labri, Bordeaux], Yassin Refahi )

  We investigate the possibility to use 3D laser scanners to automate plant digitizing. We are developing algorithms to reconstruct branching systems without leaves or foliage from scanner data or from scan simulated on plant mock-up obtained using different digitizing method.

  For branching systems, a number of automatic methods were proposed in the literature to reconstruct plausible branching structures from laser scanner data. The question of their assessment and accuracy is however critical for further exploitation in biological applications. For this, we developed an evaluation pipeline to assess reconstruction accuracy. A laser scan database on which experts built reference reconstructions is used as a basis of the evaluation. A graphical editor has been developed to help experts to reconstruct semi automatically reference structures. The evaluation pipeline is given two plant structures and compares their organization. Similar elements are identified based on geometric criteria using an optimization algorithm. The organization of these elements is then compared and their similarity is quantified. Two indices of geometrical and structural similarities are defined, and automatic reconstructions can thus be compared to reference structures to assess their accuracy. The method is successful at capturing the variation of similarities between two structures as different levels of noise are introduced. A first comparative evaluation of the different methods of the literature has been designed and conducted. This work has been published in the special issue of Annals of Botany on FSPMs [16] . A procedure to automatically determine phyllotactic angles from scans of small plants has been added recently to the reconstruction pipeline.

  Figure 2. Comparison of different methods of the litterature to reconstruct plant architecture from laser scanner data. On the left, the original scan and on the rigth, the resulting reconstructions using three different methods. These reconstructions are quantitativelly assessed using our evaluation pipeline presented in [16]

  In the context of the PhD of M. Balduzzi, we also investigated the reconstruction of tree foliage from 3D scans. Such elements are crucial to study the interaction of the plant with its environment. However, laser scans contain outliers in the silhouette of the scans that make the meshing of the pointset extremely difficult. New generation of laser scanners provide intensity of the laser reflected on the surface of scanned objects. This intensity depends on the distance to the object, its optical property and the incidence angle. A first work on this topic showed that after correcting the distance effect, the incidence angle can be deduced from the intensity. From this result, we developed a reconstruction pipeline using the scan intensities and based on Shape-From-Shading. Outliers being along the edge of the surface point cloud, we chose to develop a propagation SFS method initialized with points of the scans with high quality. We proved that surface with constant intensity are necessarily surfaces of constant slope or sand-pile surfaces. Using this result, a propagation method along iso-intensity regions was developed. These surfaces can then be sampled to provide a smooth point set without outliers. This work has been presented by M. Balduzzi for her thesis defense in november.

• Reconstruction from video. (Frédéric Boudon, Jerome Guenard [IRIT, Toulouse], Geraldine Morin [IRIT, Toulouse], Pierre Gurdjos [IRIT, Toulouse], Vincent Charvillat [IRIT, Toulouse])

  Even if mature computer vision techniques allow the reconstruction of challenging 3D objects from images, dedicated methods for generating 3D plant models must be devised due to the high complexity of plant topology. In collaboration with our colleagues from IRIT, Toulouse, we developed an analysis-by-synthesis method which generates 3D models of plants from both images and a priori knowledge of the plant species.

  Our method is based on a skeletonisation algorithm which allows to generate a possible skeleton from a foliage segmentation. Then, a 3D generative model, based on a parametric model of branching systems that takes into account botanical knowledge is built. This method extends previous works by constraining the resulting skeleton to follow hierarchical organization of natural branching structure. 3D models are then generated. 2D projections of the models can be compared with the original image to assess the visual accuracy of the reconstruction. We optimise the parameter values of the generative model based on the 2D projection criterion. Realistic results are obtained on different species of plants, in particular vineyards. This work has been presented at the Mathematical Methods for Curves and Surfaces conference and published in LNCS [42] .

• Reconstruction of virtual fruits from pictures. (Ibrahim Chedaddi, Mik Cieslak, Nadia Bertin [Inra, Avignon], Frédéric Boudon, Christophe Godin, Michel Genard [Inra, Avignon], Christophe Goz-Bac [Université Montpellier 2])

  This research theme is supported by the Agropolis project MecaFruit3D.

  The aim of this work is to provide methods for generating fruit structure that can be integrated with models of fruit function. To this end, we used a modeling pipeline previously developped by Mik Cieslak in the OpenAlea platform. This methods involves two steps: (1) generating a 3D volumetric mesh representation of the entire fruit, and (2) generating a complex network of vasculature that is embedded within this mesh. Previous studies demonstrated the possibility to create species-specific models of fruit structure with relatively low effort [49] . We focus now on validating the vasculature networks by quantitatively comparing them to experimental data from the litterature.

  These physiological data will be combined with a mechanical model of fruit growth, to investigate the effects of fruit structure on quality (see section 6.4.2 ).

• Reconstruction of root structures. (Julien Diener, Fredéric Boudon, Christophe Pradal, Christophe Godin, Philippe Nacry [BPMP, INRA], Christophe Périn [AGAP, CIRAD], Anne Dievart [AGAP, CIRAD], Xavier Draye [UCL, Belgium])

  This research theme is supported by the Agropolis through the Rhizopolis project and by NUMEV.

  Similarly to aerial part of plants, new needs for automatic digitizing of root systems emerge. Most existing methods focus only on semi-automatic approaches. This does not support the high-throughput capabilities of acquisition systems. In the context of the RhizoScan project, we previously designed a prototype of an automatic image analysis pipeline to extract root system architecture of branching systems grown in Petri boxes. This pipeline provides i) a set of model based image segmentation method, ii) the extraction of a graph representation of the root system, and iii) a method to identify the root axes organization. This year, we improved and extended the pipeline in the following way:

  1. We integrated a validation step in the workflow based on the comparison method presented in [16] .

  2. We participated in an international collaboration with the Université Catholique de Louvain (Belgium), the CPIB of the University of Notthingham (UK), the University of Vienna (Austria), the Jülich research center (Germany) and INRA, to develop a standard file format for root architecture. The resulting format (RSML) is described in a publication to appear in Plant Physiology in 2015 (details can be found at rootsystemml.github.io ).

  3. We have initiated a collaboration to integrate visual data mining methods developed by the Zenith team in order to improve the automation of the image analysis pipeline.

  4. In general, the robustness of the pipeline has been improved. In particular, an optimization method has been designed to select the root axes hierarchy that respect specific botanical constraints.

Modeling the plant ontogenic programme

Participants : Christophe Godin, Yann Guédon, Jean-Baptiste Durand, Pierre Fernique, Christophe Pradal, Jean Peyhardi.

This research theme is supported by two PhD programmes.

The remarkable organization of plants at macroscopic scales may be used to infer particular aspects of meristem functioning. The fact that plants are made up of the repetition of many similar components at different scales, and the presence of morphological gradients, e.g. [46] , [54] , [55] , [51] , provides macroscopic evidence for the existence of regularities and identities in processes that drive meristem activity at microscopic scales. Different concepts have been proposed to explain these specific organizations such as "morphogenetic programme" [59] , "age state" [50] or "physiological age" [48] . All these concepts state that meristem fate changes according to position within the plant structure and during its development. Even though these changes in meristem fate are specific to each species and lead to the differentiation of axes, general rules can be highlighted [50] , [48] . Here we develop computational methods to decipher these rules.

• Relating branching structure to the shoot properties (Jean Peyhardi, Yann Guédon, Evelyne Coste [AGAP, AFEF team], Catherine Trottier [I3M], Yves Caraglio [AMAP], Pierre-Eric Lauri [AGAP, AFEF team])

  Shoot branching structures often take the form of a succession of homogeneous branching zones and have been analyzed using segmentation models such as hidden semi-Markov chains. Axillary meristem fates are influenced by local properties of the parent shoot such as for instance its growth rate or local curvature. The objective of this work, which is part of the PhD subject of Jean Peyhardi, is to develop statistical models that generalize hidden semi-Markov chains with the capability to incorporate explanatory variables that vary along the parent shoot (e.g. maximum growth rate of the leaf, surface of the leaf, length of the internode, local curvature of the parent shoot). More precisely, the simple multinomial distributions that represent the axillary productions observed in the different branching zones are replaced by multinomial generalized linear models (GLMs). Since the two classical categories of multinomial GLMs that correspond either to nominal or ordinal categorical response variables were not appropriate, we chose to develop a new family of multinomial GLMs called partitioned conditional GLMs [38] that enable to tackle hierarchically-structured categorical response variables. Typically, we need to distinguish different timing of branching (e.g. immediate shoot, one-year-delayed shoot and latent bud), different categories of offspring shoots (e.g. among one-year-delayed shoots, vegetative short shoot, vegetative long shoot and flowering shoot) and to specialize the explanatory variables for certain categories of offspring shoots (e.g. the growth of the parent shoot influence the immediate offspring shoots but not the one-year-delayed offspring shoots). The resulting integrative models are called semi-Markov switching partitioned conditional GLMs and have been applied to apple and pear tree branching structures.

• Genetic determinisms of the alternation of flowering in apple tree progenies. (Jean-Baptiste Durand, Jean Peyhardi, Baptiste Guitton [AGAP, AFEF team], Yan Holtz [AGAP, AFEF team] Catherine Trottier, Evelyne Costes, Yann Guédon)

  A first study was published to characterize genetic determinisms of the alternation of flowering in apple tree progenies. Data were collected at two scales: at whole tree scale (with annual time step) and a local scale (annual shoot, which corresponds to portions of stem that were grown during the same year). Two replications of each genotype were available.

  Indices were proposed for early detection of alternation during the juvenile phase. They were based on a trend model and a quantification of the deviation amplitudes and dependency, with respect to the trend. This allows to quantify alternation from the yearly numbers of inflorescences at tree scale.

• Identifying and characterizing patterns in tree-structured data (Pierre Fernique, Jean-Baptiste Durand, Yann Guédon).

  In the context of Pierre Fernique's PhD (Montpellier 2 University and CIRAD), two complementary approaches were developed for analyzing patterns in tree-structured data:

  • multitype branching processes relying on local dependency properties for analyzing motifs.

  • multiple change-point models relying on long-term dependencies for segmenting trees in homogeneous zones.

  In multitype branching processes, the plant development is viewed as a demographic process, a parent entity of a given type generating child entities of different types (e.g. vegetative and flowering entities). Formally, the botanical entity properties are summarized as a categorical state variable. The number of child entities in each state is modeled through discrete multivariate distributions. Model selection procedures are necessary to specify parsimonious generation distributions. We developed an approach based on probabilistic graphical models to identify and exploit properties of conditional independence between numbers of children in different states, so as to simplify the specification of their joint distribution. The graph building stage was based on exploring the space of possible chain graph models, which required defining a notion of neighbourhood of these graphs [33] . To relax the strong constraints regarding dependencies induced by parametric distributions, mixture of graphical models were also considered [41] . Multitype branching processes were applied to the analysis of the patchiness pattern (consisting of canopies made of clumps of either vegetative or flowering growth units) in mango trees.

• Simulating fruit tree phenology (A.S. Briand, Frédéric Boudon, Frédéric Normand [CIRAD, HortSys, Réunion Island], Anaëlle Dambreville, Jean-Baptiste Durand, Pierre Fernique, Yann Guédon, Christophe Pradal, Pierre-Eric Lauri [AFEF team, AGAP])

  Mango is a tropical tree characterized by strong asynchronisms within and between trees. To study more precisely the interplay between the plant structural components, we built an integrative model to simulate the plant development based on the L-system formalism and GLM to model the dependencies between events. This model has been started during the internship of A. Jestin last year and has been continued during the visit of F. Boudon at the Hortsys lab in the Réunion island. The model has been extended this year to model growth and phenology of shoots and inflorescences (internship of A.S. Briand). For this, the sizes of the different organs is modelled by statistical laws estimated from measurements that depends on their positions in the architecture. The growth speed of organs is modulated by the temperature. This model will serve as a basis for further ecophysiological study in silico.

• Integrative developmental growth stages of shoots (Anaëlle Dambreville, Yann Guédon, Pierre-Eric Lauri [AFEF team, AGAP], Frédéric Normand [CIRAD, HortSys, Réunion Island])

  Plant growth, i.e. the increase of organ dimensions over time, and development, i.e. the change in plant structure, are often studied as two separate processes. However, there is structural and functional evidence that these two processes are strongly related. Our aim was to investigate the co-ordination between growth and development using mango trees, which have well-defined developmental stages. Developmental stages, determined in an expert way, and organ sizes, determined from objective measurements, were collected during the vegetative growth and flowering phases of two cultivars of mango. For a given cultivar and growth unit type (either vegetative or flowering), a multi-stage model based on absolute growth rate sequences deduced from the measurements was first built, and then growth stages deduced from the model were compared with hand-annotated developmental stages. Strong matches were obtained between both stages, leading to a consistent definition of integrative developmental growth stages. The growth stages highlighted growth asynchronisms between two topologically connected organs, namely the vegetative axis and its leaves. Integrative developmental growth stages emphasize that developmental stages are closely related to organ growth rates and can be interpreted in terms of the possible physiological processes (hydraulics, biomechanics and carbohydrate partitioning) underlying these stages.

• Characterizing the successive flowering phases of strawberry in relation to genetic determinants (Yann Guédon, Béatrice Denoyes [INRA, UMR BFP, Villenave d’Ornon], Justine Perrotte)

  Our aim was to characterize the successive flowering phases of perpetual flowering strawberry genotypes, which is of particular importance for better predicting fruit production. We applied multiple change-point models for the synchronous segmentation of the individuals of a given genotype in successive flowering phases. We identified two groups of genotypes that differ by the intensity of the flowering at the end of the flowering period. Using a genetic approach, we identified a locus controlling the flowering intensity at the end of the flowering period that likely explain these two groups of genotypes.

• Self-nested structure of plants. (Christophe Godin, Romain Azais, Farah Ben Naoum, Jean-Baptiste Durand, Alain Jean-Marie)

  In a previous work [6] , we designed a method to compress tree structures and to quantify their degree of self-nestedness. This method is based on the detection of isomorphic subtrees in a given tree and on the construction of a DAG (Directed Acyclic Graph, equivalent to the original tree, where a given subtree class is represented only once (compression is based on the suppression of structural redundancies in the original tree). In the compressed graph, every node representing a particular subtree in the original tree has exactly the same height as its corresponding node in the original tree.

  The method proposed in [6] thus compresses a tree in width, but not in height. In a new work, we designed an extension of this compression method in which a tree is compressed in both width and height. The method is based on the detection of so-called quasi-isomorphic paths in a tree and on the compression of these paths in height. A paper describing the corresponding algorithms has been submitted recently for publication.

  The degree of self-nestedness is defined in [6] as the edit-distance between the considered tree structure and its nearest embedded self-nested version. Indeed, finding the nearest self-nested tree of a structure without more assumptions is conjectured to be an NP-complete or NP-hard problem. We thus designed a heuristic method based on interacting simulated annealing algorithms to tackle this difficult question. This procedure is also a keystone in a new topological clustering algorithm for trees that we propose. In addition, we obtain new theoretical results on the combinatorics of self-nested structures. The redaction of an article is currently in progress.

Analyzing the influence of the environment on the plant ontogenic programme

Participants : Jean-Baptiste Durand, Christian Fournier, Christophe Godin, Yann Guédon, Christophe Pradal, Jean Peyhardi, Pierre Fernique, Guillaume Garin.

This research theme is supported by three PhD programs.

The ontogenetic programme of a plant is actually sensitive to environmental changes. If, in particular cases, we can make the assumption that the environment is a fixed control variable (see section 6.2.2 ), in general the structure produced by meristem results from a tight interaction between the plant and its environment, throughout its lifetime. Based on observations, we thus aim to trace back to the different components of the growth (ontogenetic development and its modulation by the environment). This is made using two types of approaches. On the one hand, we develop a statistical approach in which stochastic models are augmented with additional time-varying explanatory variables that represent the environment variations. The design of estimation procedures for these models make it possible to separate the plant ontogenetic programme from its modulation by the environment. On the other hand, we build reactive models that make it possible to simulate in a mechanistic way the interaction between the plant development and its environment.

• Influence of environment conditions and horticultural practices on the branching and axillary flowering structures of fruit tree shoots. (Yann Guédon, Evelyne Costes [AFEF Team, AGAP], Ted DeJong [UC Davis], Claudia Negron [UC Davis]).

  In the context of a collaboration with Claudia Negron and Ted DeJong, we studied the influence of water availability [24] and pruning practices on the branching and axillary flowering structures of different categories of almond shoots. Stochastic models (hidden semi-Markov chains) were built for the branching and axillary flowering structures of different categories of almond shoots corresponding to different genetic backgrounds, levels of irrigation and pruning practices.

• Analyzing growth components in trees. (Yann Guédon, Yves Caraglio [AMAP], Olivier Taugourdeau [AMAP])

  We identified robust indicators that summarize the respective importance of ontogeny and environmental constraints (mainly related to light environment) in forest tree development. In this context, tree growth data correspond to the retrospective measurement of annual shoot characteristics (e.g. length, number of branches) along the main stem. We applied segmentation models to identify tree growth phases. These segmentation models, which are hidden semi-Markov chains, were compared with simple hidden Markov chains that correspond to the environment-driven development assumption. This statistical modelling approach was applied to both evergreen (Corsican pine and silver fir) and deciduous (sessile oak and Persian walnut) tree species growing in contrasted conditions ranging from managed forest stands to unmanaged understoreys. Growth phase duration distributions estimated within these segmentation models characterize the respective importance of ontogeny and environmental constraints in tree development at the population scale and have very contrasted characteristics in terms of shape and relative dispersion between ontogeny-driven and environment-driven tree development. These characteristics may change over tree life, reflecting changes in tree competition. Growth phase duration distributions summarize the joint trajectory of tree ontogeny and environment without requiring tree growth follow-up data for their estimation.

• Analyzing fruit tree phenology in various climatic conditions from the shoot to the orchard scale Yann Guédon, Juliano Dutra Schmitz [Universidade Federal de Pelotas, Brazil], Pierre-Eric Lauri [AFEF team, AGAP], Jean-Michel Legave [AFEF team, AGAP], Gustavo Malagui [Universidade Tecnológica Federal do Paraná]

  A first study was conducted at the shoot scale on four apple cultivars characterized by various chilling requirements and grown in two contrasting winter temperature conditions [20] . Our hypothesis was that shoot architecture is strongly affected by winter temperatures determining both the position and budburst of vegetative laterals with a lower effect on their outgrowth. A two-step approach was designed to quantify at the shoot scale i) the branching pattern and ii) two phenological stages of vegetative laterals, budburst and outgrowth. The branching pattern analysis combined various methods: branching sequence alignement and clustering, hidden semi-Markov chain and multiple change point model for segmenting branching sequences into homogeneous zones. A categorical variable, the branching zone, was built to summarize the lateral position along the shoot. It was integrated into the phenological analysis, based on a zero-inflated Poisson model, as a factor together with the cultivar and the winter temperature. We showed in this way that temperature had a main effect on the distribution of vegetative laterals along the shoot. It also strongly affected budburst, which was also affected by the cultivar and the branching zone. The outgrowth of the lateral was not significantly affected by temperature but was significantly affected by the cultivar and the branching zone. Furthermore, the delayed senescence and subsequent leaf persistence during winter, characterizing the apple tree in the mild winter temperature condition, had only a weak effect on the distribution of vegetative laterals and on budburst and lateral outgrowth. The actual shoot architecture and budburst result thus from an ordered sequence of events with a pivotal role of winter temperatures on the dormancy completion of individual lateral buds.

  A second study was conducted at the orchard scale. The time-course variation of dates of flowering stages was established for seventeen chronological sequences corresponding to various apple tree cropping areas in Europe (Belgium, France, Germany, Italy, Switzerland), north Africa (Morocco) and southern Brazil. Our aim was to characterize the relationship between flowering advances in fruit trees and global warming and to compare the northern and the southern hemisphere situations. We applied piecewise constant and linear homoscedastic models to these phenological series. The sudden advance of flowering dates detected at the end of the 1980s in the European locations can be explained by changes in rates for completion of heat requirements, essential to the development of floral primordia within buds. No effect of the global warming could be detected in the Brazilian flowering series and we only found a direct effect of the chilling temperature on the flowering date the same year (the colder the Austral winter, the earlier the flowering date).

• Investigating how architectural development interfer with epidemics and epidemic control (Christian Fournier, Corinne Robert [EGC], Guillaume Garin [ITK], Bruno Andrieu [EGC], Christophe Pradal)

  Sustainable agriculture requires the identification of new, environmentally responsible strategies of crop protection. Modelling of pathosystems can allow a better understanding of the major interactions inside these dynamic systems and may lead to innovative protection strategies. In particular, functional–structural plant models (FSPMs) have been identified as a means to optimize the use of architecture-related traits. A current limitation lies in the inherent complexity of this type of modelling, and thus the purpose of this paper is to provide a framework to both extend and simplify the modelling of pathosystems using FSPMs.

  Different entities and interactions occurring in pathosystems were formalized in a conceptual model [21] . A framework based on these concepts was then implemented within the open-source OpenAlea modelling platform, using the platform's general strategy of modelling plant–environment interactions and extending it to handle plant interactions with pathogens. New developments include a generic data structure for representing lesions and dispersal units, and a series of generic protocols to communicate with objects representing the canopy and its microenvironment in the OpenAlea platform. Another development is the addition of a library of elementary models involved in pathosystem modelling. Several plant and physical models are already available in OpenAlea and can be combined in models of pathosystems using this framework approach.

  Two contrasting pathosystems are implemented using the framework and illustrate its generic utility. Simulations demonstrate the framework's ability to simulate multiscaled interactions within pathosystems, and also show that models are modular components within the framework and can be extended. This is illustrated by testing the impact of canopy architectural traits on fungal dispersal. This study provides a framework for modelling a large number of pathosystems using FSPMs. This structure can accommodate both previously developed models for individual aspects of pathosystems and new ones. Complex models are dissassembled into separate knowledge sources originating from different specialist areas of expertise and these can be shared and reassembled into multidisciplinary models. The framework thus provides a beneficial tool for a potential diverse and dynamic research community.