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

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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.