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

生态学家努力了解的自然界的模式通常是许多相互作用的过程的结果。为什么美国有大约1100种鸟类，而不是110种或11,000种？要回答这样一个问题，仅列出所有因素是不够的；我们需要知道哪些因素更重要，哪些因素更不重要。例如，生态学家会问，就像厨师知道食谱中哪些成分是必不可少的一样，在被人类活动改变的生态系统中，哪些“成分”对保护生物多样性至关重要，哪些则不那么关键。该项目的目标首先是为生态学家提供更好的工具，基于一种名为“方差函数分析”(FANOVA)的通用统计方法，识别在创建观察到的模式中最重要的因素。其次，新工具将被用来扩展生态学理论，解释相互竞争的物种如何共存，确定哪些生命速率(例如，不同年龄的存活率)对种群丰度的波动贡献最大，以及确定哪些生命速率，在哪些年龄或生命阶段，对种群内无法用可观察到的特征解释的巨大生命结果差异(如后代总数)贡献最大。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，教其他人使用新工具。FANOVA是一种用于非线性投入产出关系的通用方差分解方法，将输出方差分解为来自每一输入变量的直接贡献、来自所有阶数(成对、三元组等)相互作用的贡献以及无法解释的残差变异。许多生态学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行的，推理必须来自与经验数据相适应的动态模型。本项目将探索FANOVA如何在这些情况下发挥常规ANOVA在简单实验设计中所起的作用，使用与经验数据相适应的模型回答有关不同过程的相对重要性的问题。FANOVA并不是即插即用的：一般的配方通常在计算上很难处理，在高维情况下也很难解释。每个新的应用程序都需要克服这些挑战。具体目标包括：(1)开发准确和完整版本的生命表响应实验分析，并使用对数百个已发表模型的荟萃分析将FANOVA与当前方法进行比较；(2)扩展最近发展的基于FANOVA的量化共存机制的方法，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，确定种群内生殖成功的随机变异的大小如何与生活史和功能特征相关；(4)开发通用的系统工具，以确定在生命周期中何时何地运气(生存和繁殖力等结果的随机差异)对一生的结果最重要；(5)开发统计理论，以确定应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NSF的法定使命，并通过使用基金会的智力优势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.