The roles of adaptation, chance, and history on evolution of the toxic dinoflagellate Alexandrium minutum Halim, under selective conditions simulating global change, have been addressed. Two toxic strains (AL1V and AL2V), previously acclimated for two years at pH 8.0 and 20°C, were transferred to selective conditions: pH 7.5 to simulate acidification and 25°C. Cultures under selective conditions were propagated until growth rate and toxin cell quota achieved an invariant mean value at 720 days (ca. 250 and ca. 180 generations for strains AL1V and AL2V, respectively). Historical contingencies strongly constrained the evolution of growth rate and toxin cell quota, but the forces involved in the evolution were not the same for both traits. Growth rate was 1.5–1.6 times higher than the one measured in ancestral conditions. Genetic adaptation explained two‐thirds of total adaptation while one‐third was a consequence of physiological adaptation. On the other hand, the evolution of toxin cell quota showed a pattern attributable to neutral mutations because the final variances were significantly higher than those measured at the start of the experiment. It has been hypothesized that harmful algal blooms will increase under the future scenario of global change. Although this study might be considered an oversimplification of the reality, it can be hypothesized that toxic blooms will increase but no predictions can be advanced about toxicity.