Agricultural intensification, driven by high pesticide and fertilizer use, is a major strategy for feeding the world but can lead to 'intensification traps'—declines in production caused by biodiversity loss at high input levels. A new framework evaluates the risk and magnitude of these traps by simulating biodiversity feedback on crop yields. Intensification traps emerge in most landscape types, but less so in major cereal systems. Small reductions in maximum production (5–10%) can lead to substantial biodiversity gains, creating small-loss large-gain trade-offs. However, context-dependent sensitivity analyses show uncertainty in identifying optimal management. The study recommends case-specific safety margins to prevent double losses in biodiversity and food security. Rising global food demand challenges agricultural production to meet future needs while ensuring food security. Past increases in food production relied on cropland expansion and conventional intensification, which reduced local biodiversity and ecosystem functions, negatively affecting yields. At high management intensities, biodiversity loss can cause negative feedback on yields, leading to hump-shaped production responses. This results in 'lose-lose' situations rather than trade-offs between production and biodiversity. The study identifies five key relationships driving biodiversity and yield in agricultural landscapes. These relationships vary in effect size and shape, defining biodiversity–production relationships. The study found that 73% of artificial landscapes experience intensification traps, with risk and production loss strongly influenced by biodiversity's effect on yields. Three archetypal landscapes showed contrasting responses to intensification, with some systems less sensitive to biodiversity loss. The study highlights the importance of biodiversity in agricultural systems, showing that small reductions in production can lead to large biodiversity gains. This suggests opportunities to increase biodiversity in agricultural landscapes. The study also emphasizes the need for precautionary principles to avoid lose-lose scenarios and to integrate biodiversity into management practices. The study's framework allows evaluating the mechanisms driving intensification traps, which are a significant challenge for global food production and security. However, agricultural systems are complex, requiring simplifications for general assessments. The study recommends case-specific safety margins to prevent intensification traps and promote sustainable management. The findings suggest that small reductions in agricultural production can lead to disproportionately larger biodiversity gains, offering opportunities to reconcile conflicting land-use targets.Agricultural intensification, driven by high pesticide and fertilizer use, is a major strategy for feeding the world but can lead to 'intensification traps'—declines in production caused by biodiversity loss at high input levels. A new framework evaluates the risk and magnitude of these traps by simulating biodiversity feedback on crop yields. Intensification traps emerge in most landscape types, but less so in major cereal systems. Small reductions in maximum production (5–10%) can lead to substantial biodiversity gains, creating small-loss large-gain trade-offs. However, context-dependent sensitivity analyses show uncertainty in identifying optimal management. The study recommends case-specific safety margins to prevent double losses in biodiversity and food security. Rising global food demand challenges agricultural production to meet future needs while ensuring food security. Past increases in food production relied on cropland expansion and conventional intensification, which reduced local biodiversity and ecosystem functions, negatively affecting yields. At high management intensities, biodiversity loss can cause negative feedback on yields, leading to hump-shaped production responses. This results in 'lose-lose' situations rather than trade-offs between production and biodiversity. The study identifies five key relationships driving biodiversity and yield in agricultural landscapes. These relationships vary in effect size and shape, defining biodiversity–production relationships. The study found that 73% of artificial landscapes experience intensification traps, with risk and production loss strongly influenced by biodiversity's effect on yields. Three archetypal landscapes showed contrasting responses to intensification, with some systems less sensitive to biodiversity loss. The study highlights the importance of biodiversity in agricultural systems, showing that small reductions in production can lead to large biodiversity gains. This suggests opportunities to increase biodiversity in agricultural landscapes. The study also emphasizes the need for precautionary principles to avoid lose-lose scenarios and to integrate biodiversity into management practices. The study's framework allows evaluating the mechanisms driving intensification traps, which are a significant challenge for global food production and security. However, agricultural systems are complex, requiring simplifications for general assessments. The study recommends case-specific safety margins to prevent intensification traps and promote sustainable management. The findings suggest that small reductions in agricultural production can lead to disproportionately larger biodiversity gains, offering opportunities to reconcile conflicting land-use targets.