For a species to be able to respond to environmental change, it must either succeed in following its optimal environmental conditions or in persisting under suboptimal conditions, but we know very little about what controls these capacities. We parameterized species distribution models (SDMs) for 135 plant species from the Algerian steppes. We interpreted low false‐positive rates as reflecting a high capacity to follow optimal environmental conditions and high false‐negative rates as a high capacity to persist under suboptimal environmental conditions. We also measured functional traits in the field and built a unique plant trait database for the North‐African steppe. For both perennial and annual species, we explored how these two capacities can be explained by species traits and whether relevant trait values reflect species strategies or biases in SDMs. We found low false‐positive rates in species with small seeds, flowers attracting specialist pollinators, and specialized distributions (among annuals and perennials), low root:shoot ratios, wide root‐systems, and large leaves (perennials only) (R² = .52–58). We found high false‐negative rates in species with marginal environmental distribution (among annuals and perennials), small seeds, relatively deep roots, and specialized distributions (annuals) or large leaves, wide root‐systems, and monocarpic life cycle (perennials) (R² = .38 for annuals and 0.65 for perennials). Overall, relevant traits are rarely indicative of the possible biases of SDMs, but rather reflect the species' reproductive strategy, dispersal ability, stress tolerance, and pollination strategies. Our results suggest that wide undirected dispersal in annual species and efficient resource acquisition in perennial species favor both capacities, whereas short life spans in perennial species favor persistence in suboptimal environmental conditions and flowers attracting specialist pollinators in perennial and annual species favor following optimal environmental conditions. Species that neither follow nor persist will be at risk under future environmental change.