Are food web structures well represented in isotopic spaces?

Isotopic analyses are increasingly used to assess the structure of food webs and a series of isotopic functional indices have been proposed in the last decade to characterize this structure. These indices are based on the foundational assumption that proximity in the isotopic space informs on trophic similarity between species. While it has been recognized for long that this simplifying assumption should be used with caution, no formal evaluation of its domain of validity has been performed to date. We here simulate a large number (15 000) of food webs with varying characteristics to assess (i) whether isotopic distance is a good proxy of trophic dissimilarity; (ii) whether isotopic functional indices are good proxies of trophic functional properties; and (iii) how the quality of these two proxies depend on various species and food web properties. We first demonstrate that isotopic distance is moderately correlated with trophic similarity in simulated food webs. We find, however, that two isotopic community metrics investigated (Rao's index of functional divergence and nearest neighbour distance index of functional originality) are good indicators of community trophic structure, especially in food webs with large connectance, and when predators have low levels of diet specialization. We also find that isotopic functional indices are decreasingly reliable as they aim at characterizing more subtle functional patterns (such as standard deviation of nearest neighbour distance, an index of between species variation in originality). Taken together, our results suggest that the reliability of the isotopic mapping of consumers decreases with their number of potential prey species, but increases with their number of realized prey species. Consequently, isotopic reliability decreases in species-rich food webs with low connectance, large vertical diversity and large incidence of omnivory. Our study highlights that researchers should not hope to grasp subtle patterns of food web structure based solely on widely used isotopic indices. They should instead envisage mobilizing such isotopic information in combination with complementary data types.