Compositional Data Methodology in the Context of Quantitative Fatty Acid Signature Analysis

在海洋生态系统中，估计捕食者的饮食尤其具有挑战性，因为捕食通常不能直接观察到。在此背景下，利用非参数统计技术，定量脂肪酸特征分析（QFASA）被设计为估计捕食者饮食的间接方法，并已成功地应用于各种海鸟、海洋哺乳动物和鱼类。最近，我的课题组开发了最大统一脂肪酸特征分析（MUFASA），与QFASA一样，它也利用了捕食者和猎物脂肪酸之间的关系，但在最大似然估计（MLE）框架下。虽然这些饮食估计方法具有非侵入性的优点，但它们依赖于几个难以在实践中验证的假设，但这些假设可能会对结果产生重大影响。此外，脂肪酸特征和饮食估计都代表了组成数据，通常被定义为多元数据，其成分被限制为一个常数。这些限制，以及数据的其他特征，例如相对大量的组件和数据包含零的倾向，都给统计带来了挑战。在与研究海洋哺乳动物种群的生物学家的合作中，我的研究项目的长期目标是解决目前FASA方法固有的局限性，并通过适用于成分数据的新颖统计方法提供更准确的饮食估计。这项研究也将同时推进成分数据分析领域的技术，可以扩展到各种应用。本研究的一个短期目标是为成分数据开发新的变量选择技术。我的研究的这一方面是由一个重要的，但很大程度上是突出的问题，即如何选择最佳子集的猎物类型和/或脂肪酸包括在模型。另一个目标是将鲁棒性纳入FASA方法，以处理与模型假设的偏差。新开发的可能性结构将在实现这些目标方面发挥关键作用。作为一种新方法，MUFASA尚未得到广泛的研究和改进，例如扩展到更灵活的参数密度，也将考虑。这项研究将有助于我们了解FASA技术用于海洋捕食者饮食估计的优点和局限性，解决与这些方法相关的一些计算挑战，并有可能产生更准确的饮食估计。新的方法将通过现有的R软件包QFASA和composition提供给相关用户。我提议的研究将为统计学和生物学之间的跨学科合作提供机会，并为5名本科生和4名研究生提供由现实数据和应用驱动的培训。

In the marine ecosystem, estimating predator diets can be especially challenging since feeding cannot typically be directly observed. In this context, and using nonparametric statistical techniques, quantitative fatty acid signature analysis (QFASA) was devised as an indirect method of estimating predator diets and has since successfully been applied to a variety of seabird species, marine mammals and fish. Recently, my research group developed maximum unified fatty acid signature analysis (MUFASA) which, like QFASA, also utilizes the relationship between predator and prey fatty acids but in the maximum likelihood estimation (MLE) framework. While these diet estimation methods have the advantage of being non-invasive, they rely on several assumptions that are difficult to verify in practice, but which can significantly impact results. Additionally, both the fatty acid signatures and diet estimates represent compositional data, commonly defined as multivariate data with components restricted to sum to a constant. These constraints, as well as other features of the data, such as the relatively large number of components and the propensity of the data to involve zeros, impose statistical challenges. In collaboration with biologists studying marine mammal populations, the long-term objective of my research program is to address current limitations inherent in FASA methods and provide improvements for more accurate diet estimation through novel statistical methodology appropriate for compositional data. This research will also simultaneously advance the area of compositional data analysis with techniques that can be extended to a variety of applications. One short-term objective of this research is the development of new variable selection techniques for compositional data. This aspect of my research is motivated by the important, but largely outstanding problem of how to choose the best subset of prey types and/or fatty acids to include in the models. Another goal is the incorporation of robustness into FASA methods to handle deviations from model assumptions. The newly developed likelihood structure will play a pivotal role in addressing these objectives. Being a new procedure, MUFASA has not yet been extensively studied and improvements, such as extensions to more flexible parametric densities, will also be considered. This research will contribute to our understanding of the advantages and limitations of FASA techniques for marine predator diet estimation, address some of the computational challenges associated with these methods, and potentially yield more accurate estimates of diet. The new methodology will be made accessible to relevant users through the existing R packages QFASA and Compositional. My proposed research will provide opportunities for interdisciplinary collaborations between statistics and biology, as well as training driven by real-life data and applications for 5 undergraduate and 4 graduate students.