Should fatty acid signature proportions sum to 1 for diet estimation?

Abstract

Knowledge of predator diets, including how diets might change through time or differ among predators, provides essential insights into their ecology. Diet estimation therefore remains an active area of research within quantitative ecology. Quantitative fatty acid signature analysis (QFASA) is an increasingly common method of diet estimation. QFASA is based on a data library of prey signatures, which are vectors of proportions summarizing the fatty acid composition of lipids, and diet is estimated as the mixture of prey signatures that most closely approximates a predator's signature. Diets are typically estimated using proportions from a subset of all fatty acids that are known to be solely or largely influenced by diet. Given the subset of fatty acids selected, the current practice is to scale their proportions to sum to 1.0. However, scaling signature proportions has the potential to distort the structural relationships within a prey library and between predators and prey. To investigate that possibility, we compared the practice of scaling proportions with two alternatives and found that the traditional scaling can meaningfully bias diet estimators under some conditions. Two aspects of the prey types that contributed to a predator's diet influenced the magnitude of the bias: the degree to which the sums of unscaled proportions differed among prey types and the identifiability of prey types within the prey library. We caution investigators against the routine scaling of signature proportions in QFASA.

qfasar: quantitative fatty acid signature analysis with R

“…), or chi‐square (Stewart, Iverson & Field ) distances, whose performance properties differ and may influence their suitability for individual investigations (Bromaghin et al . , ; Bromaghin, Budge & Thiemann ). Variances are estimated by bootstrapping the prey library and re‐estimating each predator's diet (Beck et al .…”

“…prep_sig() performs two tasks: replace proportions that are missing or equal to zero with a small positive value, and potentially rescale proportions. Proportions can be scaled to sum to 1, left unscaled, or left unscaled and augmented with an additional proportion so that all sum to 1 (Bromaghin, Budge & Thiemann ).…”

“…Although a detailed description does not appear to have been published, the simulations involve dividing prey‐type data into two subsets and using cross validation. Bromaghin, Budge & Thiemann () used a conceptually similar leave‐one‐prey‐out approach. Each prey animal in turn is temporarily removed from the library and its signature is modelled identically to diet estimation without calibration coefficients.…”

“…Assuming a predator's true diet equals its estimated diet, the expected value of the distance is essentially fixed if model assumptions are met and variation in the distance is due to random selection of individual prey (Bromaghin ). When simulating predator signatures, variation is maximized when bootstrap sample sizes of prey signatures are minimized (Bromaghin, Budge & Thiemann ). The function gof() therefore uses bootstrap samples of size 1 from each prey type to simulate a maximum‐variance null distribution for each predator's minimized distance measure, returning the proportion of simulated signatures whose minimized distance measure exceeds the value observed during diet estimation, with small values indicating predators whose signatures may be poorly approximated.…”

“…qfasar is, in part, a compilation of methods associated with recent research of the performance properties of QFASA (Bromaghin ; Bromaghin et al . , ; Bromaghin, Budge & Thiemann ). In addition, qfasar includes procedures that have not been published, with the intent that it be useful for both diet estimation and as a research‐support tool.…”