Towards understanding interactions in a complex world: Design and analysis of multi‐species functional response experiments

The functional response describes feeding rates of consumers as a function of resource density. While models for feeding on a single resource species are well studied and supported by a large body of empirical research, consumers feeding on multiple resource species are ubiquitous in nature. However, laboratory experiments designed for parameterizing multi‐species functional responses (MSFR) are extremely rare, mainly due to logistical challenges and the non‐trivial nature of their statistical analysis. Here, we describe how these models can be fitted to empirical data in a Bayesian framework. Specifically, we address the problem of prey depletion during experiments, which can be accounted for through dynamical modelling. In a comprehensive simulation study, we test the effects of experimental design, sample size and noise level on the identifiability of four distinct MSFR models. Additionally, we demonstrate the method's versatility by applying it to a list of empirical datasets. We identify experimental designs for feeding trials that produce the most accurate parameter estimates in two‐ and three‐prey scenarios. Although noise introduces systematic bias in parameter estimates, model selection performs surprisingly well for the four MSFRs, almost always identifying the correct model even for small datasets. This flexible framework allows the simultaneous analysis of feeding experiments from both single‐ and multi‐prey scenarios, either with or without prey depletion. This will help to elucidate mechanisms such as prey selectivity, prey switching and their implications for food web stability and biodiversity. Our approach equips researchers with the appropriate statistical tools to improve the understanding of feeding interactions in complex ecosystems.