Simultaneous estimation of diet composition and calibration coefficients with fatty acid signature data

Abstract

Knowledge of animal diets provides essential insights into their life history and ecology, although diet estimation is challenging and remains an active area of research. Quantitative fatty acid signature analysis (QFASA) has become a popular method of estimating diet composition, especially for marine species. A primary assumption of QFASA is that constants called calibration coefficients, which account for the differential metabolism of individual fatty acids, are known. In practice, however, calibration coefficients are not known, but rather have been estimated in feeding trials with captive animals of a limited number of model species. The impossibility of verifying the accuracy of feeding trial derived calibration coefficients to estimate the diets of wild animals is a foundational problem with QFASA that has generated considerable criticism. We present a new model that allows simultaneous estimation of diet composition and calibration coefficients based only on fatty acid signature samples from wild predators and potential prey. Our model performed almost flawlessly in four tests with constructed examples, estimating both diet proportions and calibration coefficients with essentially no error. We also applied the model to data from Chukchi Sea polar bears, obtaining diet estimates that were more diverse than estimates conditioned on feeding trial calibration coefficients. Our model avoids bias in diet estimates caused by conditioning on inaccurate calibration coefficients, invalidates the primary criticism of QFASA, eliminates the need to conduct feeding trials solely for diet estimation, and consequently expands the utility of fatty acid data to investigate aspects of ecology linked to animal diets.

Keywords: QFASA; diet estimation; food web; qfasar; quantitative fatty acid signature analysis.

Figure 1

A polar bear (Ursus maritimus) family feeding on a ringed seal (Phoca hispida). Photograph credit: U.S. Geological Survey, Alaska Science Center. Previously published by Ecology and Evolution 5:1249–1262

Figure 2

An example with six fatty acids (FA) illustrating how calibration coefficients are used to transform signatures between the predator and prey spaces

Figure 3

A ternary plot illustrating a grid of diet proportions regularly spaced throughout the range of all possible diets comprised of up to three prey types, with an increment of 0.1 between proportions. Similar diet grids with the larger mammal and fish prey libraries were used to establish example diets to test the performance of the model

Figure 4

Estimation results for the grid of 210 diets based on the mammal library: (a) the distribution of bias among the estimated diet proportions, and (b) true values of the calibration coefficients used to construct predator signatures based on the mammal library, with estimates obtained in the diet grid and realistic diet analyses

Figure 5

Estimation results for the grid of 210 diets based on the fish library: (a) the distribution of bias among the estimated diet proportions, and (b) true values of the calibration coefficients used to construct predator signatures based on the mammal library, with estimates obtained in the diet grid and realistic diet analyses

Figure 6

True (bars) and estimated (circles) diet proportions for the realistic Chukchi Sea polar bear diet analysis with the mammal library, for (a) adult females, (b) adult males, (c) subadult females, and (d) subadult males

Figure 7

True (bars) and estimated (circles) diet proportions for the realistic gray seal diet analysis with the fish library, for (a) spring‐sampled females, (b) spring‐sampled males, (c) fall‐sampled females, and (d) fall‐sampled males

Figure 8

Unconditional estimates of calibration coefficients for Chukchi Sea polar bears, along with the two sets of values derived from a mink feeding trial. The feeding trial values have been scaled so they sum to the number of fatty acids to allow a meaningful comparison

Figure 9

Mean estimated diet of Chukchi Sea polar bears obtained with unconditional estimation and by conditioning on the marine‐fed mink calibration coefficients for (a) adult females, (b) adult males, (c) subadult females, and (d) subadult males. Error bars represent one standard error of the mean