An Empirical Evaluation of the Utility of Convex Hull and Standard Ellipse Areas for Assessing Population Niche Widths from Stable Isotope Data

Abstract

Stable isotope analyses are increasingly employed to characterise population niche widths. The convex hull area (TA) in a δ¹³C–δ¹⁵N biplot has been used as a measure of isotopic niche width, but concerns exist over its dependence on sample size and associated difficulties in among-population comparisons. Recently a more robust method was proposed for estimating and comparing isotopic niche widths using standard ellipse areas (SEA), but this approach has yet to be tested with empirical stable isotope data. The two methods measure different kind of isotopic niche areas, but both are now widely used to characterise isotopic niche widths of populations. We used simulated data and an extensive empirical dataset from two fish populations to test the influence of sample size on the observed isotopic niche widths (TA and SEA). We resampled the original datasets to generate 5000 new samples for different numbers of observations from 5 to 80 to examine the statistical distributions of niche area estimates for increasing sample size. Our results illustrate how increasing sample size increased the observed TA; even sample sizes much higher than n = 30 did not improve the precision for the TA method. SEA was less sensitive to sample size, but the natural variation in our empirical fish δ¹³C and δ¹⁵N data still resulted in considerable uncertainty around the mean estimates of niche width, reducing the precision particularly with sample sizes n<30. These results confirm that the TA method is less appropriate for estimating population isotopic niche areas using small samples, especially when considerable population level isotope variation is expected. The results also indicate a need for caution when using SEA as a measure of trophic niche widths for consumers, particularly with low sample sizes and when the distribution and range for population isotope values are not known.