How strongly does diet variation explain variation in isotope values of animal consumers?

Analysis of stable isotopes in consumers is used commonly to study their ecological and/or environmental niche. There is, however, considerable debate regarding how isotopic values relate to diet and how other sources of variation confound this link, which can undermine the utility. From the analysis of a simple, but general, model of isotopic incorporation in consumer organisms, we examine the relationship between isotopic variance among individuals, and diet variability within a consumer population. We show that variance in consumer isotope values is directly proportional to variation in diet (through Simpson indices), to the number of isotopically distinct food sources in the diet, and to the baseline variation within and among the isotope values of the food sources. Additionally, when considering temporal diet variation within a consumer we identify the interplay between diet turnover rates and tissue turnover rates that controls the sensitivity of stable isotopes to detect diet variation. Our work demonstrates that variation in the stable isotope values of consumers reflect variation in their diet. This relationship, however, can be confounded with other factors to the extent that they may mask the signal coming from diet. We show how simple quantitative corrections can recover a direct 1:1 correlation in some situations, and in others we can adjust our interpretation in light of the new understanding arising from our models. Our framework provides guidance for the design and analysis of empirical studies where the goal is to infer niche width from stable isotope data.