Climate change is negatively impacting ecosystems and their contributions to human well-being, known as ecosystem services. Previous research has mainly focused on the direct effects of climate change on species and ecosystem services, leaving a gap in understanding the indirect impacts resulting from changes in species interactions within complex ecosystems. This knowledge gap is significant because the loss of a species in a food web can lead to additional species losses or "co-extinctions," particularly when the species most impacted by climate change are also the species that play critical roles in food web persistence or provide ecosystem services. Here, we present a framework to investigate the relationships among species vulnerability to climate change, their roles within the food web, their contributions to ecosystem services, and the overall persistence of these systems and services in the face of climate-induced species losses. To do this, we assess the robustness of food webs and their associated ecosystem services to climate-driven species extinctions in eight empirical rocky intertidal food webs. Across food webs, we find that highly connected species are not the most vulnerable to climate change. However, we find species that directly provide ecosystem services are more vulnerable to climate change and more connected than species that do not directly provide services, which results in ecosystem service provision collapsing before food webs. Overall, we find that food webs are more robust to climate change than the ecosystem services they provide and show that combining species roles in food webs and services with their vulnerability to climate change offer predictions about the impacts of co-extinctions for future food web and ecosystem service persistence. However, these conclusions are limited by data availability and quality, underscoring the need for more comprehensive data collection on linking species roles in interaction networks and their vulnerabilities to climate change.
