Modeling spatial competition for light in plant populations with the porous medium equation

Beyer, Robert; Etard, Octave; Cournède, Paul-Henry; Laurent-Gengoux, Pascal

doi:10.1007/s00285-014-0763-1

Cited by 7 publications

(4 citation statements)

References 25 publications

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“…In RS2, leaf proportion and SLA were 5 and 20% greater at 15 m than 3 m, suggesting the impact of increased shading duration at 3‐m distance. In this limited environment, forage plants might experience increased SLA, instead of leaf weight, to improve light capture (Peri et al, 2006; Beyer et al, 2015).…”

Section: Discussionmentioning

confidence: 99%

Shading Effects on Marandu Palisadegrass in a Silvopastoral System: Plant Morphological and Physiological Responses

et al. 2019

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The understanding of plant morphological and physiological responses to shading can contribute to developing sustainable silvopastoral systems (SPS). Our objective was to evaluate the shading effect on herbage accumulation (HA), plant‐part composition, physiology, and canopy structural characteristics of Marandu palisadegrass {Urochloa brizantha (Hochst. ex A. Rich.) R.D. Webster [syn. Brachiaria brizantha (Hochst. ex A. Rich.) Stapf]} under intermittent defoliation in a SPS with Eucalyptus urograndis (hybrid of Eucalyptus grandis W. Hill ex Maiden and Eucalyptus urophylla S.T. Blake) in Sinop, Mato Grosso, Brazil. The experimental design was a randomized complete block arranged under a strip‐split‐plot, where the plots were allocated to four distances from the Eucalyptus grove (3, 6, 10, and 15‐m) in the SPS, on both faces (north and south), with four replications. The evaluations were done during two summer rainy seasons (RS1 and RS2) and one dry season (DS). The herbage accumulation (HA) in RS1 (4290 kg DM ha–1) was 51% greater than in RS2. The greatest canopy height, light interception, and leaf area index (LAI) values were measured during RS1 (25 cm, 91%, and 3.5 cm2 cm–2, respectively). Leaf photosynthesis rate was less at the 3‐m distance (12.5 μmol CO2 m–2 s–1) than at other distances (17.3 μmol CO2 m–2 s–1). We conclude that Marandu palisadegrass has the ability to physiologically adapt to shaded environments, although the dynamics along the whole tree growing cycle needs to be considered so that grass productivity can be sustained in the long‐term. Core Ideas Longer shading impacted canopy structure and forage accumulation at 3‐m distance. Physiological responses shows reduced light effects on the forage growth pattern. Morphologic composition and sward characteristics were only affected at 3‐m distance. Leaf photosynthesis rate was lesser close to the grove. Silvopastoral systems is an option for livestock production in the Brazilian Amazon.

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Section: Discussionmentioning

confidence: 99%

Shading Effects on Marandu Palisadegrass in a Silvopastoral System: Plant Morphological and Physiological Responses

et al. 2019

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“…x There exist more realistic and complex models to represent competition for light in plants population. Beyer et al [2015] describes tree crowns development by a transport equation on foliage density. In this model, light ressource is allocated to the different individuals proportionally to their foliage volume.…”

Section: Example Of Schneider Modelmentioning

confidence: 99%

Mean field approximation of a heterogeneous population of plants in competition

Della Noce,

Mathieu,

Cournède

2019

Preprint

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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.

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“…The gradient ∇ x L points locally in the direction of the greatest rate of increase of intercepted light. In addition, similar to Beyer et al (2014) we define the flux to correspond to the existing leaf density in x , so that finally we have…”

Section: Model Frameworkmentioning

confidence: 99%

“…In the context of macroscopic individual plant modeling, so far notably in the form of diffusion equations, it has proven applicable for root growth and proliferation (see Page and Gerwitz, 1974 for the original approach, Reddy and Pachepsky, 2001 for a review of later developments and Dupuy et al, 2010 for a current advance). A 2D diffusion approach for the foliage of crops with the objective to model competition in different field densities, without considering the vertical dimension, was presented by Beyer et al (2014). Partial differential equations can generate, even from only a few terms, complex self-adapting dynamics, which is indeed present in biological systems.…”

Section: Introductionmentioning

confidence: 99%

Modeling tree crown dynamics with 3D partial differential equations

2014

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We characterize a tree's 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.

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Modeling spatial competition for light in plant populations with the porous medium equation

Cited by 7 publications

References 25 publications

Shading Effects on Marandu Palisadegrass in a Silvopastoral System: Plant Morphological and Physiological Responses

Shading Effects on Marandu Palisadegrass in a Silvopastoral System: Plant Morphological and Physiological Responses

Mean field approximation of a heterogeneous population of plants in competition

Modeling tree crown dynamics with 3D partial differential equations

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