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

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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.