Stochastic modelling of tree annual shoot dynamics

Abstract

Context Modelling annual shoot development processes is a key step towards functional-structural modelling of trees. Various patterns of meristem activity can be distinguished in tree shoots, with active periods of phytomer production followed by rest periods. This approach has seldom been integrated in functional-structural tree models. & Aims This paper presents theoretical research work on modelling and computation of the dynamics of tree annual shoots using stochastic processes with various development patterns: continuous or rhythmic, monocyclic or polycyclic, "seasonal" or "a-seasonal", with preformation or neoformation produced from meristem functioning. & Methods The renewal theory is used to compute stochastic aspects of phytomer production, resulting from meristem extension or rest periods and meristem mortality. & Results Continuous development can be modelled with a Bernoulli process, while rhythmic development is modelled by alternation between extension and rest periods, the duration of each period following specific distributions. & Conclusion The application of such stochastic modelling is the estimation of organ production during tree development as a component of the demand in functional- architectural tree models, used for computing biomass production and partitioning. (Résumé d'auteur

Quantifying the Variability of Internode Allometry within and between Trees for Pinus tabulaeformis Carr. Using a Multilevel Nonlinear Mixed-Effect Model

“…A constant allometry rule between the length and biomass of internodes in the GreenLab model (where branches belonging to the same order are identical) has been validated for crops and tree species in the literature [32,44]; however, random processes for growth, death, and branch pattern have also been applied to characterize stochastic structure and functioning in different versions of the GreenLab functional-structural model [66,67], especially stochastic modeling of annual tree shoot dynamics in the recent GL5 version [68]. In this study, single-level, nested two-level and nested three-level nonlinear mixed-effect models were developed for the internode allometry of first-, second-, and third-order branches of Chinese Pine, respectively.…”

“…Tree-or branch-specific allometric models should be developed instead of averaged models to obtain unbiased and accurate internode length predictions. Such models will be useful in determining internode shape and generating stochastic structure as simulated using stochastic models [35,68,70], which will affect light interception, photosynthesis, and tree architecture in functional-structural modeling. Information about the allometric relationships of trees can be used in models to constrain the form and structure of trees to ensure that they conform to natural systems.…”

Tree Growth Modelling Constrained by Growth Equations

“…Greenlab was presented as a mathematical model for plant growth based on AMAP that simulates interactions between plant structure and function [YKRD04, KCDR*08]. A new theory was proposed in [dRKHA12] to compute stochastic aspects of production, resulting from meristem extension, or rest periods and mortality. A stochastic model was developed in [KHCR12] to simulate multiple plant phenotypes with visual output.…”

Tree Topology Estimation

“…Neuron growth modeling has focused on statistical techniques, such as Bayesian networks [24], [28]. Leafy tree models have used flow diffusion and fractals [3], [34], while lightning modeling has focused on the ambient electric field [15], [29]. We develop a generative probabilistic model that captures a wide class of trees with a modicum of parameters, and lends itself well to stochastic search.…”

“…Fortunately, good theoretical and empirical models have been developed in several domains to describe the expected morphology or growth pattern of a particular type of tree. Well-studied trees include blood vessels [31], [33], plant roots [2], [20], neurons [24], [28], leafy trees [3], [34], and lightning [15], [29]. …”