Competition & Biodiversity in Heterogeneous Landscapes: Model Simplification through Moment Equations

帕卡拉9807755 本项目的主要目标是从理论上解释空间环境异质性对生态系统群落动态和生物多样性的影响，模拟模型和实验研究已经有力地证明了内生和外生空间异质性（如资源供给率或地形的变化）对生态群落共存和维持多样性的重要性。 然而，数学家和生态学家仍然缺乏对运行机制的分析理解，特别是在完全空间的随机环境中。 研究人员通过使用广泛的模型（从集合种群模型到相互作用的粒子系统和点过程）扩展了对异质性影响的现有分析;他们开发了矩近似，以平均密度和协方差表示空间种群动态，以简化分析，同时保留外源和内源异质性。 本研究采用矩近似法和更标准的技术，分析了环境异质性、内源异质性及其相互作用对植物和海洋潮间带群落生态模型中种群动态和竞争结果的影响。 野外生态学家早就知道，土壤或温度等环境因素的小尺度变化会影响生态群落的结构和多样性--即一个地区内有哪些物种和多少物种可以生活在一起。然而，生态学建模者往往对由植物或动物之间的相互作用引起的小尺度生物多样性空间格局找到简单的解释。最近，计算机模拟模型在重新协调这两个阵营方面取得了很大进展，但是（1）模拟表明模式会发生，但并不总是能解释原因;（2）即使是强大的计算机也有其局限性（例如，试图模拟一个大陆上的每棵树来预测全球气候变化的影响可能是鲁莽的）。 本研究建立了简单的数学模型，将生物体间相互作用引起的空间变异性与环境引起的空间变异性结合起来，探讨这两种变异性如何影响群落的结构和多样性。 这些简单模型的结果最终将展示如何建立更复杂和更现实的模型，以预测生物多样性和生态系统生产力的模式，并将提供一个更普遍的理解，即环境的可变性如何导致生态群落的多样性。

Pacala9807755 The primary goal of this project is to interpretanalytically the effects of spatial environmental heterogeneityon the community dynamics and biodiversity of ecological systems.Simulation models and experimental studies have convincinglydemonstrated the importance of endogenous and exogenous spatialheterogeneity, such as variation in resource supply rate ortopography, to the coexistence and the maintenance of diversityin ecological communities. However, both mathematicians andecologists still lack analytic understanding of the mechanismsoperating, particularly in fully spatial, stochasticenvironments. The investigators extend existing analyses of theeffects of heterogeneity by using a wide range of models (frommetapopulation models to interacting particle systems and pointprocesses); they develop moment approximations, which expressspatial population dynamics in terms of mean densities andcovariances, to simplify the analysis while preserving bothexogenous and endogenous heterogeneity. The study uses momentapproximations, and more standard techniques, to analyze theeffects of environmental heterogeneity, endogenous heterogeneity,and their interaction on population dynamics and competitiveoutcomes in ecological models of plant and marine intertidalcommunities. Field ecologists have long known that small-scalevariability in environmental factors such as soils or temperaturecan affect the structure and diversity of ecological communities--- which and how many species can live together in a region.Ecological modellers, however, have often found simpleexplanations for small-scale spatial patterns of biodiversity,caused by interactions between plants or animals (such ascompetition or predation), that ignore environmental variability.Computer simulation models have recently gone a long way towardreconciling these two camps, but (1) simulations show thatpatterns occur, but do not always explain why; and (2) evenpowerful computers have limits (it could be foolhardy, forexample, to attempt to simulate every tree on a continent inorder to predict the effects of global climate change). Thisstudy develops simple mathematical models that combine spatialvariability caused by interactions between organisms with spatialvariability caused by the environment to explore how these twokinds of variability affect the structure and diversity ofcommunities. The results from these simple models will eventuallyshow how to build more complex and realistic models that canpredict patterns of biodiversity and ecosystem productivity, andwill provide a much more general understanding of how variabilityin the environment leads to diversity in ecological communities.