Abstract: The current talk is concerned with population dynamics under climate change. The evolution of species is modeled by a reaction-diffusion equation in a spatiotemporally heterogeneous environment described by a climate envelope that shifts with a time-dependent speed function. For a general almost periodic speed function, we establish the persistence criterion in terms of the sign of the approximate top Lyapunov exponent and, in the case of persistence, prove the existence of a unique forced wave solution that dominates the population profile of species in the long run. By means of matched asymptotic expansions and numerical simulations, it is observed that fluctuations in the shifting speed or location have negative impacts on the persistence of species, and moreover, the larger the fluctuation is, the more adverse the effect is on the species. In addition, we assert that large fluctuations can always drive a species to extinction. Our numerical results also show that a persistent species under climate change is invulnerable to mild fluctuations, and becomes vulnerable when fluctuations are so large that the species is endangered.