Data from: Integrating abundance and diet data to improve inferences of food web dynamics

1. Both population abundances and chemical tracers are useful tools for studying consumer-resource interactions. Food web models parameterized with abundances are often used to understand how interactions structure communities and to inform management decisions of complex ecological systems. Unfortunately, collecting abundance data to parameterize these models is often expensive and time-consuming. Another approach is to use chemical tracers to estimate the proportional diets of consumers by relating the tracers in their tissues to those found in their food sources. Although tracer data are often inexpensive to collect relative to abundances, diet proportions provide little information on the per-capita consumption rates of consumers. Here, we show how integrating these data sources can be used to better estimate of consumption rates. 2. Our modeling approach informs traditional multispecies population abundance models using proportional diet data. We used simulations to determine whether integrated food web datasets were more informative than traditional abundance datasets and demonstrated the use of our integrated approach by estimating consumption rates of humpback whales (\textit{Megaptera novaeangliae}) in the western Gulf of Alaska using abundances coupled with stable isotopes as a tracer. 3. Our simulations demonstrated that integrated models improved the ability to resolve alternative hypotheses about the functional response and yielded more precise parameter estimates relative to standard food web models. The integrated data approach was especially informative under low sample sizes or high process variance. Our application of the integrated modeling approach to humpback whale indicated that fish averaged about 25\% of whale diets, though this proportion declined over the course of the study. We also found that traditional abundance model estimates of humpback whale consumption were non-estimable and that the integrated food web model led to estimable consumption rates. 4. Our results show that integrating stable isotopes and abundance datasets provides an exciting way forward for parameterizing multispecies models in data-limited systems. We expect that future developments of these integrated approaches will extend current food web theory by allowing ecologists to study predation dynamics over seasonal time scales and at the individual level