The sustainability of coupled social-ecological systems (SESs) hinges on their long-term ecological dynamics. Land conversion generates extinction and functioning debts, i.e. a time-delayed loss of species and associated ecosystem services. Sustainability theory, however, has not so far considered the long-term consequences of these ecological debts on SESs. We investigate this question using a dynamical model that couples human demography, technological change and biodiversity. Human population growth drives land conversion, which in turn reduces biodiversity-dependent ecosystem services to agricultural production (ecological feedback).Technological change brings about a demographic transition leading to a population equilibrium. When the ecological feedback is delayed in time, some SESs experience population overshoots followed by large reductions in biodiversity, human population size and well-being, which we call environmental crises. Using a sustainability criterion that captures the vulnerability of an SES to such crises, we show that some of the characteristics common to modern SESs (e.g. high production efficiency and labor intensity, concavedown ecological relationships) are detrimental to their long-term sustainability. Maintaining sustainability thus requires strong counteracting forces, such as the demographic transition and land-use management. To this end, we provide integrative sustainability thresholds for land conversion, biodiversity loss and human population size -each threshold being related to the others through the economic, technological, demographic and ecological parameters of the SES. Numerical simulations show that remaining within these sustainable boundaries prevents environmental crises from occurring. By capturing the long-term ecological and socioeconomic drivers of SESs, our theoretical approach proposes a new way to define integrative conservation objectives that ensure the long-term sustainability of our planet.

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Ecological theory is essential to predict the effects of global changes such as habitat loss and fragmentation on biodiversity. Species–area relationships (SAR), metapopulation models (MEP) and species distribution models (SDM) are commonly used tools incorporating different ecological processes to explain biodiversity distribution and dynamics. Yet few studies have compared the outcomes of these disparate models and investigated their complementarity. Here we show that the processes underlying SAR (patch area), MEP (patch isolation) and SDM (environmental conditions) models can be compared with a common statistical framework. Our approach allows for species and community‐level predictions under current and future landscape scenarios, facilitates multi‐model comparison and provides the machinery for integrating multiple mechanisms into one model. We apply this framework to the distribution of eight focal vertebrate species in current and future projected landscapes where 10% of the landscape is lost to land‐use change in southwestern, Quebec, Canada. Based on a model selection approach, we found that a model including patch area was the top ranked model for four of our focal species and models including patch isolation and environmental conditions were the top ranked models for two focal species each. Community‐level predictions of models based on patch area, patch isolation and environmental conditions for both current and future landscapes showed high spatial overlap, however, patch area models always predicted a reduction of species richness per patch whereas both the patch isolation and environmental conditions models predicted an increase or decrease in species richness per patch following habitat loss and fragmentation. Our comparative tool will allow ecologists and conservation practitioners to relate structural uncertainty to key mechanisms underlying each model. Ultimately, this approach is one step in the direction of deriving robust predictions for the change and loss of biodiversity under global change, which is key for informing conservation plans.