Synergies and trade-offs for reaching global biodiversity and climate commitments.

The Kunming-Montreal Global Biodiversity Framework strives to expand high-quality protected areas globally, yet faces economic constraints, climate change and human pressures. This requires integrating biological and socio-economic complexity while ensuring equity. We explore multi-target '30 by 30' and '50 by 50' (the 'Half Earth') protected area expansion strategies that combine species diversity with carbon storage, quantifying their effectiveness (the represented proportion of global species richness and carbon stocks), connectivity and cost-efficiency. Under near-current and future climates, single-criterion strategies - based on five taxonomic groups (plants, amphibians, birds, mammals, and reptiles) or carbon alone - achieve effectiveness of 42.3 ± 4.10% and 68.8 ± 8.39% for both targets, whereas multi-goal strategies reach 44.1 ± 0.42% and 67.0 ± 0.89%. Multi-goal strategies reduce connectivity by 2.35% but slightly improve cost-efficiency (2.06% lower cost) and individual-metric effectiveness (mean rise 0.76%). Moving from single- to multi-target strategies increases conserved-area coverage in high-latitude, higher-income countries (by 3.14% and 5.59%), with a corresponding decline in low-income countries (7.31% and 12.6%); single-goal strategies targeting threatened species allocate more coverage to the Global South. By rebalancing North-South responsibilities and easing burdens on low-income nations needing financial support or compensation mechanisms, these findings improve conservation affordability and provide equity insights for implementing Global Biodiversity Framework and Paris Agreement.