Collaborative Research: A general approach to partitioning contributions from multiple drivers affecting individuals, populations, and communities

生态学家努力理解的自然界模式通常是许多相互作用过程的结果。为什么美国有大约1100种鸟类，而不是110种或1.1万种？要回答这样的问题，列出所有的影响因素是不够的；我们需要知道哪些更重要，哪些不重要。就像厨师知道食谱中哪些成分是必不可少的一样，生态学家会问，例如，在一个被人类活动改变的生态系统中，哪些“成分”对于保护生物多样性是至关重要的，哪些是不那么重要的。这个项目的目标是，首先，为生态学家提供更好的工具，以识别在创造观察模式中最重要的因素，基于一种称为“方差功能分析”（fANOVA）的通用统计方法。其次，新工具将用于扩展解释竞争物种如何共存的生态理论，确定哪些生命率（例如，不同年龄的存活率）对种群丰度的波动贡献最大，并确定哪些生命率，在哪个年龄或生命阶段，对种群内寿命结果（如后代总数）的巨大变化贡献最大，而这些变化无法用可观察的特征来解释。研究人员还将开发新的计算方法和统计理论，以扩大fANOVA在生态学中的适用性，并举办研讨会，教其他人使用这些新工具。fANOVA是一种非线性输入输出关系的通用方差分解方法，它将输出方差分解为各输入变量的直接贡献、各阶相互作用（成对、三元组等）的贡献以及未解释的残差。许多生态问题涉及在大空间和时间尺度上运行的过程，因此实验操作是不可可行的，推断必须来自与经验数据相适应的动态模型。本项目将探讨fANOVA如何在这些情况下发挥作用，传统方差分析在简单的实验设计中发挥作用，使用适合经验数据的模型回答有关不同过程的相对重要性的问题。fANOVA不是“即插即用”：在高维情况下，一般的方法通常在计算上难以处理，难以解释。每个新应用程序都需要克服这些挑战。具体目标包括：(1)建立一个准确完整的生命表反应实验分析版本，并对数百个已发表的模型进行荟萃分析，将fANOVA与现有方法进行对比；(2)扩展最近发展的基于fanova的共存机制量化方法，以包括具有明确空间结构和聚集物种分布的系统；(3)通过对已发表模型的荟萃分析，确定种群内终生生殖成功随机变异的大小与生活史和功能性状的关系；(4)开发通用的系统工具，以确定生命周期中运气（生存和繁殖力等结果的随机差异）何时何地对终生结果最重要；(5)发展统计理论，以确定如何构建模型以对运气进行最佳估计和推断。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The patterns in nature that ecologists strive to understand are usually the result of many interacting processes. Why are there about 1100 bird species in the US, rather than 110 or 11,000? To answer a question like that, it is not enough to list all the contributing factors; we need to know which ones are more and less important. Like a cook who knows which ingredients are essential for a recipe, ecologists ask, for example, what 'ingredients' are crucial for preserving biodiversity in an ecosystem altered by human activities, and which are less critical. The goal of this project are first, to give ecologists better tools for identifying the factors most important in creating observed patterns, based on a general statistical method called "Functional Analysis of Variance" (fANOVA). Second, the new tools will be used to extend ecological theories explaining how competing species can coexist, to identify which vital rates (e.g., survival rates at different ages) contribute most to fluctuations in population abundance, and to identify which vital rates, at which ages or life-stages, contribute most to the large within-population variation in lifetime outcomes (such total number of offspring) that cannot be explained by observable traits. The researchers will also develop new computing methods and statistical theory to broaden the applicability of fANOVA in ecology and conduct workshops to teach others to use the new tools. fANOVA is a general variance decomposition method for nonlinear input-output relationships, decomposing output variance into direct contributions from variation in each input, contributions from interactions of all orders (pairwise, triplets, etc.), and unexplained residual variation. Many ecological questions involve processes operating over large spatial and temporal scales, so experimental manipulations are infeasible and inference must come from dynamic models fitted to empirical data. This project will explore how fANOVA can play the role in these situations that conventional ANOVA does in simple experimental designs, answering questions about the relative importance of different processes using models fitted to empirical data. fANOVA is not 'plug and play': the general recipe is often computationally intractable and hard to interpret in high-dimensional situations. Each new application needs to overcome these challenges. Specific objectives include: (1) Develop an exact and complete version of Life Table Response Experiment analysis, and using a meta-analysis of hundreds of published models to contrast fANOVA with current approaches; (2) Extend recently developed fANOVA-based methods of quantifying coexistence mechanisms to include systems with explicit spatial structure and clumped species distributions; (3) Determine how the magnitude of within- population random variation in lifetime reproductive success is related to life history and functional traits through a meta-analysis of published models; (4) Develop general systematic tools to determine when or where in the life cycle luck (random differences in outcomes such as survival and fecundity) matters the most for lifetime outcomes; (5) Develop statistical theory to determine how models should be constructed for optimal estimation and inference about luck.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.