Three metrics of species diversity – species richness, the Shannon index and the Simpson index – are still widely used in ecology, despite decades of valid critiques leveled against them. Developing a robust diversity metric has been challenging because, unlike many variables ecologists measure, the diversity of a community often cannot be estimated in an unbiased way based on a random sample from that community. Over the past decade, ecologists have begun to incorporate two important tools for estimating diversity: coverage and Hill diversity. Coverage is a method for equalizing samples that is, on theoretical grounds, preferable to other commonly used methods such as equal‐effort sampling, or rarefying datasets to equal sample size. Hill diversity comprises a spectrum of diversity metrics and is based on three key insights. First, species richness and variants of the Shannon and Simpson indices are all special cases of one general equation. Second, richness, Shannon and Simpson can be expressed on the same scale and in units of species. Third, there is no way to eliminate the effect of relative abundance from estimates of any of these diversity metrics, including species richness. Rather, a researcher must choose the relative sensitivity of the metric towards rare and common species, a concept which we describe as ‘leverage.' In this paper we explain coverage and Hill diversity, provide guidelines for how to use them together to measure species diversity, and demonstrate their use with examples from our own data. We show why researchers will obtain more robust results when they estimate the Hill diversity of equal‐coverage samples, rather than using other methods such as equal‐effort sampling or traditional sample rarefaction.

Background Intraspecific variation in foraging niche can drive food web dynamics and ecosystem processes. In particular, male and female animals can exhibit different, often cascading, impacts on their interaction partners. Despite this, studies of plant-pollinator interaction networks have focused on the partitioning of the floral community between pollinator species, with little attention paid to intraspecific variation in plant preference between male and female bees. We designed a field study to evaluate the strength and prevalence of sexually dimorphic foraging, and particularly resource preferences, in bees. Study design We observed bees visiting flowers in semi-natural meadows in New Jersey, USA. To detect differences in flower use against a shared background of resource (flower) availability, we maximized the number of interactions observed within narrow spatio-temporal windows. To distinguish observed differences in bee use of flower species, which can reflect abundance patterns and sampling effects, from underlying differences in bee preferences, we analyzed our data with both a permutation-based null model and random effects models. Findings We found that the diets of male and female bees of the same species were often dissimilar as the diets of different species of bees. Furthermore, we demonstrate differences in preference between male and female bees. We show that intraspecific differences in preference can be robustly identified among hundreds of unique species-species interactions, without precisely quantifying resource availability, and despite high phenological turnover of both bees and plant bloom. Given the large differences in both flower use and preferences between male and female bees, ecological sex differences should be integrated into studies of bee demography, plant pollination, and coevolutionary relationships between flowers and insects.

14 15 1. Intraspecific variation in foraging niche can drive food web dynamics and 16 ecosystem processes. Field studies and theoretical analysis of plant-pollinator 17 interaction networks typically focus on the partitioning of the floral community 18 between pollinator species, with little attention paid to intraspecific variation 19 among plants or foraging bees. In other systems, male and female animals 20 exhibit different, cascading, impacts on interaction partners. Although the 21 foraging ecology of male bees is little known, we expect foraging preferences to 22 differ between male and female bees, which could strongly impact plant-23 pollinator interaction outcomes. 242. We designed an observational study to evaluate the strength and 25prevalence of sexually dimorphic foraging preferences in bees. 263. We observed bees visiting flowers in semi-natural meadows in New 27Jersey, USA. To detect differences in flower use against a shared background 28resource availability, we maximized the number of interactions observed within 29 narrow spatio-temporal windows. To distinguish observed differences in bee use 30 of flower species, which can reflect abundance patterns and sampling effects, 31 from underlying differences in bee preferences, we analyzed our data with both a 32permutation-based null model and random effects models. 334. We found that the diets of male and female bees of the same species 34were often as dissimilar as the diets of bees of different species. Furthermore, we 35 demonstrate differences in preference between male and female bees, and 36identify plant species that are particularly attractive to each sex. We show that 37intraspecific differences in preference can be robustly identified within 38interactions between hundreds of species, without precisely quantifying resource 39 availability, and despite high phenological turnover. 40 5. Given the large differences in flower use and preference between male 41 and female bees, ecological sex differences should be integrated into studies of 42 bee demography, plant pollination, and coevolutionary relationships between 43 flowers and insects. 44 45

It is important to understand how biodiversity, including that of rare species, affects ecosystem function. Here, we consider this question with regard to pollination. Studies of pollination function have typically focused on pollination of single plant species, or average pollination across plants, and typically find that pollination depends on a few common species. Here, we used data from 11 plant–bee visitation networks in New Jersey, USA, to ask whether the number of functionally important bee species changes as we consider function separately for each plant species in increasingly diverse plant communities. Using rarefaction analysis, we found the number of important bee species increased with the number of plant species. Overall, 2.5 to 7.6 times more bee species were important at the community scale, relative to the average plant species in the same community. This effect did not asymptote in any of our datasets, suggesting that even greater bee biodiversity is needed in real-world systems. Lastly, on average across plant communities, 25% of bee species that were important at the community scale were also numerically rare within their network, making this study one of the strongest empirical demonstrations to date of the functional importance of rare species.