Maximum likelihood approach to diet estimation and inference based on fatty acid signatures
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Diet compositions of marine predators are often of interest for marine ecologists in trophic structure studies where non-lethal sampling has created a need for non-invasive diet estimation techniques. Methods using fatty acids have been developed to obtain dietary estimates that have previously been difficult to acquire. Building on the existing method, quantitative fatty acid signature analysis (QFASA), we have constructed a maximum likelihood approach to estimating dietary proportions. This novel approach includes random effects to account for the unobserved prey that were consumed by the predator. Not only does it include variability of the prey and predator FA signatures in the model, but with the use of parametric bootstrapping, we can obtain confidence bounds on these diet estimates as well. These bounds will prove to be accurate for proportions away from the edges of the simplex. It is also able to include covariates in the model. With use of a link function, the diet proportions are assumed to be a function of the covariates. The coefficients of this relationship are then optimized by using the same likelihood function as before, only subbing the link function in place of the diet proportions. This method yields a summary diet for all unique sets of covariates. It also allows for inference on diet estimates between various groups, such as sex, age or environmental factors. Simulations show that not only are the summary estimates accurate, but the inference leads to making the correct decision in all cases run. Finally, these techniques are used to analyze two real life data sets. The first is a captive study of harbour seals, for which true diets are known. This shows us that our method is estimating as accurately as QFASA. The second is a study of grey seals off of Sable Island. For this set, sex and type of population growth on Sable are recorded for each seal, so the covariate method is applied here. In comparison to QFASA, our method appears to yield similar summary estimates, and the test yielded results in agreement with the beliefs of biologists.