Livestock is recognized as one of the major drivers of current and future global change. This is caused on the production side, by the substantial resource requirements (land and water) per unit of output, and the related greenhouse gas emissions, and on the consumption side, by the growing demand due to population and economic growth. Our paper investigates whether productivity gains which enabled to the crop sector to satisfy the increased demand under decreasing real prices, and with little additional land, in the past decades, can be expected in the livestock sector in the future. To answer this question, we implement the recursively dynamic partial equilibrium bottom-up model of the global agriculture and forest sectors (GLOBIOM), expanded by a newly developed livestock module. The livestock module is based on the Sere and Steinfeld livestock production system classification, characterized by detailed input-output coefficients, including manure and greenhouse gas emissions. Our results show that if the production system composition is allowed to freely adapt to economic and resource constraints, the increases in per hectare productivity will allow satisfying the 2030 demand for ruminant products with less land than in 2000, and the livestock product prices will remain stable. This contrasts with the numbers obtained, when the ruminant production system structure is kept constant as in 2000, resulting among others in three times higher carbon prices. The adaptation in the livestock sector is hence a condition for sustainable future development, and it has to be taken into account when designing future policies.