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

Jari Syväranta,Timo J Marjomäki,Sari Oksanen,Roger I Jones,Anssi Lensu,Wayne M Getz

doi:10.1371/journal.pone.0056094

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.

Highlights

Population niche is an important concept in ecology for understanding species interactions and the structuring of communities
The natural variation associated with our perch and roach d13C and d15N values resulted in a wide percentile range in the bootstrapped The convex hull area (TA) niche areas, and the likelihood of obtaining very different inferred niche area estimates with a given sample size was alarmingly high (Fig. 4)
Our simple evaluation with an unusually large natural data set clearly illustrated how strongly sample size affected the estimates of observed population isotopic niche width, when estimated as a convex hull area (TA) in a d13C–d15N biplot

Summary

Introduction

Population niche is an important concept in ecology for understanding species interactions and the structuring of communities. Hutchinson [1] considered niche an ‘n-dimensional hypervolume’ defined by all the resources exploited by a population. In practise such a volume is impossible to quantify; potentially more tractable is the feeding niche (or trophic niche), which refers to the dietary diversity of an animal [2]. Traditional measures of trophic niche width from gut contents analysis have required laborious examinations of the diets of many individuals in a population, and preferably over an extended time period to take account of temporal fluctuations in diet. More economical and integrative measures of animal diets can potentially be obtained by stable isotope analysis (SIA). SIA offers an appealing method to characterise niche widths of animals

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