New statistical tools for quantitative fatty acid signature analysis and the development of an accompanying R package

对捕食者食量进行可靠估计的统计模型对于生物学家研究海洋生态系统中的捕食者/猎物关系至关重要。定量脂肪酸特征分析(QFASA)是一种相对较新的食物估计方法，其中每种猎物在食物中的估计比例是通过使用统计方法匹配捕食者和猎物中的脂肪酸来确定的。虽然QFASA的验证研究表明，与以前的海豹、海鸟和海狮等捕食性动物的食物估计方法相比，该方法具有一些明显的优势，但它们也揭示了该技术的局限性，以及QFASA需要进化以克服现在更容易理解的一些问题。在这项拟议的工作中，我们将研究用于改进QFASA的新的统计技术。从统计学的角度来看，处理QFASA数据是具有挑战性的，因为脂肪酸特征和饮食估计都是成分，而且往往包含零，因此不能使用标准的多变量分析程序和通常的对数比方法来管理成分数据。此外，被采样的捕食者的数量往往比感兴趣的变量的数量少得多。*还需要新的方法来处理与从黑貂岛附近自由放养的灰海豹及其猎物收集的大量脂肪酸数据相关的一些实际问题。最终，我们希望使用QFASA来更好地了解资源利用的个体和时间变化，以及种群密度和猎物可获得性等因素的变化如何影响个体内部和个体之间的变化。*目前，科学家还没有广泛使用QFASA工具。这项提议的一个重要目标，也是将直接使加拿大这一领域的研究人员受益的一个目标是创建一个QFASA R包，其中现有的方法和这里提出的方法被整合起来，便于生物学家使用。*建议的工作可以概括为1)新的成分数据分析统计方法的发展，以改进QFASA饮食估计程序，2)由真实的QFASA数据驱动的新的统计工具，以及3)QFASA R包，其中包括1)和2)中开发的工具的汇编以及以前开发的QFASA方法。**

Statistical models that yield reliable estimates of predators' diets are critical to biologists studying predator/prey relationships in marine ecosystems. Quantitative fatty acid signature analysis (or QFASA) is a relatively recent diet estimation method in which the estimated proportion of each species of prey in the diet is determined by matching fatty acids in the predator and prey using statistical methods. While QFASA validation studies have demonstrated that the method offers some clear advantages over previous diet estimation methods for predators such as seals, seabirds and sea lions, they have also revealed limitations with the technique and a need for QFASA to evolve to overcome some of the issues that are now more understood. In this proposed work, we will investigate novel statistical techniques for the revamping of QFASA. Dealing with QFASA data is challenging from a statistical point of view because both the fatty acid signatures and diet estimates are compositional and often contain zeros, precluding the use of standard multivariate analysis procedures and the usual log ratio methods for managing compositional data. Furthermore the number of sampled predators is often much less than the number of variables of interest.******New methods are also needed to handle some of the practical problems of interest associated with the large amount of fatty acid data collected from free-ranging grey seals and their prey near Sable Island. Ultimately, we want to use QFASA to gain a better understanding of individual and temporal variation in resource utilization and how changes in factors such as population density and prey availability may influence variation both within and among individuals. ******Currently QFASA tools are not widely available to scientists. A significant goal of this proposal, and one that will directly benefit Canadian researchers in this field, is the creation of a QFASA R package where existing methods and those proposed here are consolidated and made easily accessible to biologists. ******The proposed work may be summarized as the development of 1) new compositional data analysis statistical methodology to improve the QFASA diet estimation procedure, 2) new statistical tools driven by real-life QFASA data, and 3) a QFASA R package which consists of a compilation of the tools developed in 1) and 2) along with previously developed QFASA methods.**