Populations respond to changes in environment through plastic and adaptive mechanisms. However, the interactions between genetic adaptation and physiological plasticity to global change conditions are not well understood. We experimentally evolved the marine copepod, Acartia tonsa, for 20 generations to ambient and greenhouse (low pH, high temperature) conditions followed by a three-generation reciprocal transplant to identify the physiological and genetic mechanisms of adaptation to greenhouse conditions and to test the impact of rapid adaptation on plasticity. We measured changes in allele frequency and gene expression in adapted and transplanted lines for each generation of the transplant. Between adapted lines, we found rapid adaptation with changes in allele frequencies and differences in gene expression in genes related to cytoskeleton maintenance, stress response, and energetics. After transplantation, both lines increasingly converged on the adaptive transcriptional profile with each generation. However, the ambient line achieved this through plastic mechanisms, without changes in allele frequencies, while the greenhouse line required selective mortality that resulted in loss of genetic diversity and shift in allele frequencies. These results show that adaptive plasticity can enable short term persistence to conditions (ambient lines in greenhouse conditions), but over moderate time scales (20 generations), this plasticity is replaced by genetic adaptation that results in mortality and loss of genetic diversity when environmental conditions change, even after a return to ambient conditions. This work experimentally reveals the costs of rapid adaptation to global change and highlights the importance of genetic variation for physiological plasticity for population persistence in future environments.