Improving our understanding of species’ ranges under rapid climate change requires application of our knowledge of the tolerance and adaptive capacity of populations to changing environmental conditions. ΔTraitSDM are statistical correlational models that attempt to achieve this by explaining species distribution ranges based on phenotypic plasticity and local adaptation of fitness-related traits measured across large geographical gradients. They open a new perspective allowing analysis of intra-specific variation in single and multiple traits, with the rationale that trait (co-)variation and consequently fitness can significantly change across geographical gradients and new climates. Overall, ΔTraitSDM predictions give a less alarming message than previous models of species distribution under new climates, indicating that phenotypic plasticity should considerably help some plant populations to persist under climate change. I will explain the methodological improvements and conceptual challenges of ΔTraitSDM and give some examples based on common-garden data on forest trees.