竞争植物非齐性总体的平均场近似
Mean field approximation of a heterogeneous population of plants in competition
摘要：
田间植物间竞争的过程仍然知之甚少。然而，它们解释了一个领域的异质性的很大一部分，并可能有长期的后果，特别是在混合林分。建模可以帮助更好地理解这些现象，但需要模拟不同个体之间的相互作用。在大群体的情况下，从实验数据评估非齐性总体模型的参数在计算上是棘手的。本文研究了具有随机初始条件和个体参数的大型动力系统的平均场近似，系统的相互作用由个体间的成对势表示.在这种近似下，每个个体都与一个无限拥挤的群体相互作用，这个群体由一个概率测度来概括，即平均场极限分布，它本身就是一个非线性双曲型偏微分方程的弱解。特别地，混沌传播现象意味着当种群规模趋于无穷大时，个体是渐近独立的。这一结果提供了一个可能的简化推理问题的观点。模拟的平均场分布，包括在一个半拉格朗日计划的插值步骤，使用高斯过程回归，示出了一个非齐性总体模型，代表植物在竞争光。
英文摘要：
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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