title: Examining the quantitative estimation of some diets in marine environments via biomarkers
Creators: name: Fitzpatrick, AE
Publisher: name: University of Tasmania
Year: 2022

description: The motivation for this study comes from the special challenges confronting ecologists needing to know what eats what along the chains of food webs in the Antarctic and Subantarctic marine ecosystems. The specific focus is with the top trophic levels. Apex predators there spend most of the time roaming the seas, or the skies above the seas, and minimal time on land or in accessible waters. Exemplar predators referenced throughout are seals – particularly phocids. They can be observed and studied only intermittently in comparatively narrow time slots, making it hard to identify their diets via conventional methods, be it by observation or by messy direct or indirect studies of stomach contents – inherently inaccurate and virtually useless for assessing the relative quantities of the different food types consumed. Consequently there is great interest in biochemical based methods for quantifying a predator’s diet through the processing of biomarkers passed from the eaten to the eater. Initially the study was intended to be about the application of mathematical statistics to this biomarker approach for quantifying diets. But in principle the applied mathematician should be acquainted with the client researcher’s application because this dictates the analyses. At a level to inform the nonspecialist, explanations are given for food webs, habitats and the key organisms and organism groups that should be factors in the production and transmission of biomarkers. A lot of the development of the biomarker approach was carried out against the backdrop of the North Atlantic and adjacent environments. Much of that work informs the discussion here even though the primary interest remains with the Antarctic and Subantarctic regions. Both regions are subject to substantial spatial and temporal variability in the conditions influencing the production and consumption of prey organisms, and hence the biomarkers ultimately transmitted to apex predators. And from currently published information, it is concluded that the only biomarker classes that could be considered for quantitative estimates of dietary compositions are stable isotopes and fatty acids. The basic models for solution with either class are founded on systems of simple mass-balance equations with convex combinations of prey biomarker measurements on one side, and those of the predator on the other. There are a number of applications claiming to estimate diets with stable isotope based models. All use a Bayesian approach, or something equivalent. There is just one application based on fatty acids. It is called Quantitative Fatty Acid Signature Analysis (QFASA). The ‘signature’ is a vector of proportions of individual fatty acids present in a prey item or in a sample of tissue from a consumer. A biomarker in this case is a subset of the vector’s components. The stable isotope matter was examined first. An example problem was generated from published summary data and used as a vehicle to assess two different Bayesian approaches which are at the core of published successor methods for estimating diets from stable isotopes. Commonly the specific problems put forward for the Bayesian analyses are underdetermined and hence unidentifiable. The generated example problem also is underdetermined. The promoters of the methods either ignore the fault or claim that, with the Bayesian approach, inferences about the estimates do not require identifiability; unlike the case with frequentist statistics. The veracity of the claim was subjected to vigorous scrutiny. Adopting a naive perspective, the example problem was analysed with the two basic approaches using MCMC procedures designed for those approaches and written to facilitate diagnostics and tuning and – slightly unusual in the Bayesian context – goodness of fit measurement and model selection. Parallel MLE analyses were also effected. In all, nothing of value for estimations or inferences was able to be uncovered. Other well known solution methods were also trialled on an equally well known underdetermined problem data set. Effectively they work by mapping out the solution space of the mass-balance equations through direct sampling supplemented sometimes with simple linear programmes. Despite claims by their promoters that some inferences can be drawn from this mapping, it is shown to be useless for detecting anything about diets. It is also shown that the mapping is virtually the same as the posterior produced by the Bayesian approach which, by association, is therefore shown also to be useless for that purpose. This does not disprove the possibility that an underdetermined stable isotope analysis method may be merged with a QFASA one to produce useful dietary estimates. But it is found that QFASA has insurmountable problems of its own. Its evaluation starts with explanations of fatty acids as characterising moieties of lipids, followed by further explanations of the processes by which fatty acids are formed and transformed within organisms along metabolic and catabolic pathways – all influencing the relationships between fatty acids in the tissues and those in the diet. The implicit presumption within QFASA is that the processes are passive and deterministic. In reality they are actively controlled within the organism’s systems. It is argued from a system identification perspective that the estimation of the tissue fatty acids as functions of the dietary ones is a practical impossibility. By virtue of necessity and the measurement process (by gas chromatography) the units by which the fatty acid complements are identified, manipulated and compared with each other are vectors of proportions of component fatty acids, called fatty acid profiles or compositions. It is shown that the methods of conventional multivariate statistics can not work with fatty acid profiles. Summaries are presented of the salient bits of the late John Aitchison’s treatments of the statistical analysis of compositional data, which is in complete contrast to the mathematics and mathematical statistics applied to the foundations of QFASA. But it is shown also that the assumptions necessary for Aitchison’s methods do not hold with a probable majority of fatty acid profiles met in the marine environment. Much of our statistical requirements can be effected with basic tests of dissimilarity or distance between two profiles or between two samples of profiles supplemented where possible with post hoc tests. A simple randomisation test for the difference between samples of profiles was created using inter-profile distances. And for the many cases where summary profile sample statistics were available, but the data itself was not, another test for differences between profiles was devised. The application of these tests in parallel where possible with a pre-packaged non-parametric analysis of variance method at least suggested that some of the fatty acid dietary transfer mechanisms were in support of QFASA and some were not. Whatever the case, the overriding fact is that the method can not do the job claimed for it by virtue of inapplicable mathematics, unattainable system identification and the invalidity of some fundamental assumptions because of failures of common sense rather than the concomitant absence of scientific rigour.