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Anthropogenic climate change threatens production of essential natural resources, including food, fiber, and fresh water, and provisioning of ecosystem services such as carbon sequestration, increasing the risk of societal collapse. The Human and Nature Dynamics (HANDY) model simulates the effect of resource overexploitation on societal collapse but lacks representation of feedbacks between climate change and resource regeneration in ecological systems. We extend the HANDY model by integrating models of climate change and ecological function to examine the risk of societal collapse. We conducted a sensitivity analysis of our expanded model by systematically varying key parameters to examine the range of plausible socio-ecological conditions and evaluate model uncertainty. We find that lowered greenhouse gas emissions and resilient ecosystems can delay societal collapse by up to approximately 500 years, but that any scenario with greater than net-zero greenhouse gas emissions ultimately leads to societal collapse driven by climate-induced loss of ecosystem function. Reductions in greenhouse gas emissions are the most effective intervention to delay or prevent societal collapse, followed by the conservation and management of resilient ecological systems to sequester atmospheric carbon.