These differences emerge due to multiple-species interactions, often referred to (across various contexts) as higher-order interactions, trait-mediated indirect interactions, non-trophic interactions, and non-consumptive predator effects 7, 8, 9, 10. Observed community dynamics thus often differ from simple predictions based on pairwise interactions 6, 7, 8. However, quantifying species interaction strengths (i.e., the effect of one species on the abundance of a second one, such as the effect of a predator on its prey) is challenging because species are embedded in complex communities and interaction strength between two species often depends on direct and indirect interactions with other species in the community. Similar content being viewed by othersÄetermining the factors and mechanisms influencing the distribution and strengths of species interactions is crucial to understand and predict the dynamics and stability of ecological communities 1, 2, 3, 4, 5. We thus strongly recommend using the population-dynamic approach because it is robust, precise, and provides a scalable mechanistic framework to detect and quantify MPEs. Finally, parameters estimated with the direct FR approach lack mechanistic interpretation, which limits the understanding of the mechanisms driving multiple predator interactions and potential extension of this approach to more complex food webs. As a consequence, these two approaches often fail in detecting risk reduction. We found that the predictions of the direct FR and the multiplicative risk models are very similar and underestimate predation rates when prey density is high or prey depletion is substantial. Here we compare the strengths, limitations and predictions of the three approaches using simulated data sets. To rectify these biases, two approaches based on FR modelling have recently been proposed: the direct FR approach and the population-dynamic approach. The multiplicative risk model, traditionally used to detect these emergent multiple predator effects (MPEs), is biased because it assumes linear functional response (FR) and no prey depletion. Non-independent interactions among predators can have important consequences for the structure and dynamics of ecological communities by enhancing or reducing prey mortality rate through, e.g., predator facilitation or interference.
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