While there is good evidence linking animal introductions to impacts on native communities via disease emergence, our understanding of how such impacts occur is incomplete. Invasion ecologists have focused on the disease risks to native communities through “spillover” of infectious agents introduced with nonindigenous hosts, while overlooking a potentially more common mechanism of impact, that of “parasite spillback.” We hypothesize that parasite spillback could occur when a nonindigenous species is a competent host for a native parasite, with the presence of the additional host increasing disease impacts in native species. Despite its lack of formalization in all recent reviews of the role of parasites in species introductions, aspects of the invasion process actually favor parasite spillback over spillover. We specifically review the animal‐parasite literature and show that native species (arthropods, parasitoids, protozoa, and helminths) account for 67% of the parasite fauna of nonindigenous animals from a range of taxonomic groups. We show that nonindigenous species can be highly competent hosts for such parasites and provide evidence that infection by native parasites does spillback from nonindigenous species to native host species, with effects at both the host individual and population scale. We conclude by calling for greater recognition of parasite spillback as a potential threat to native species, discuss possible reasons for its neglect by invasion ecologists, and identify future research directions.

Invasion ecology urgently requires predictive methodologies that can forecast the ecological impacts of existing, emerging and potential invasive species. We argue that many ecologically damaging invaders are characterised by their more efficient use of resources. Consequently, comparison of the classical ‘functional response’ (relationship between resource use and availability) between invasive and trophically analogous native species may allow prediction of invader ecological impact. We review the utility of species trait comparisons and the history and context of the use of functional responses in invasion ecology, then present our framework for the use of comparative functional responses. We show that functional response analyses, by describing the resource use of species over a range of resource availabilities, avoids many pitfalls of ‘snapshot’ assessments of resource use. Our framework demonstrates how comparisons of invader and native functional responses, within and between Type II and III functional responses, allow testing of the likely population-level outcomes of invasions for affected species. Furthermore, we describe how recent studies support the predictive capacity of this method; for example, the invasive ‘bloody red shrimp’Hemimysis anomalashows higher Type II functional responses than native mysids and this corroborates, and could have predicted, actual invader impacts in the field. The comparative functional response method can also be used to examine differences in the impact of two or more invaders, two or more populations of the same invader, and the abiotic (e.g. temperature) and biotic (e.g. parasitism) context-dependencies of invader impacts. Our framework may also address the previous lack of rigour in testing major hypotheses in invasion ecology, such as the ‘enemy release’ and ‘biotic resistance’ hypotheses, as our approach explicitly considers demographic consequences for impacted resources, such as native and invasive prey species. We also identify potential challenges in the application of comparative functional responses in invasion ecology. These include incorporation of numerical responses, multiple predator effects and trait-mediated indirect interactions, replacement versus non-replacement study designs and the inclusion of functional responses in risk assessment frameworks. In future, the generation of sufficient case studies for a meta-analysis could test the overall hypothesis that comparative functional responses can indeed predict invasive species impacts.