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

本项目的主要目标是对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进行解释分析。模拟模型和实验研究令人信服地证明了资源供给率或地形变化等内源性和外源性空间异质性对生态群落多样性共存和维持的重要性。然而，数学家和生态学家仍然缺乏对运作机制的分析性理解，特别是在全空间、随机环境中。研究人员通过使用广泛的模型（从元种群模型到相互作用的粒子系统和点过程）扩展了现有的异质性效应分析；他们发展了矩近似，用平均密度和协方差来表达空间种群动态，以简化分析，同时保留异质和内源异质性。本研究使用矩近似和更标准的技术，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。野外生态学家很早就知道，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——一个地区有哪些物种和多少物种可以共同生活。然而，生态建模者经常对生物多样性的小尺度空间格局找到简单的解释，这些格局是由植物或动物之间的相互作用（如竞争或捕食）引起的，而忽略了环境的可变性。最近，计算机模拟模型在调和这两个阵营方面取得了长足的进展，但是(1)模拟显示了模式的发生，但并不总是解释为什么；(2)即使是功能强大的计算机也有局限性（例如，试图模拟一个大陆上的每一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，将生物之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显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，并将提供对环境变化如何导致生态群落多样性的更一般的理解。

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.