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Mass extinction is a phenomenon in the history of life on Earth when a considerable number of species go extinct over a relatively short period of time. The magnitude of extinction varies between the events, the most well known are the ``Big Five'' when more than one half of all species got extinct. There were many extinctions with a smaller magnitude too. It is widely believed that the common trigger leading to a mass extinction is a climate change such a global warming or global cooling. There are, however, many open questions with regard to the effect and potential importance of specific factors and processes. In this paper, we develop a novel mathematical model that takes into account two factors largely overlooked in the mass extinctions literature, namely, (i) the active feedback of phytoplankton to the climate through changing the albedo of the ocean surface and (ii) the species's adaptive evolutionary response to a climate change. We show that whether species goes extinct or not depends on a subtle interplay between the scale of the climate change and the rate of the evolutionary response. We also show that species's response to a fast climate change can exhibit long transient dynamics (false extinction) when the species population density remain at a low value for a long time before recovering to its safe steady state value. Finally, we show that the distribution of extinction frequencies predicted by our model is generally consistent with the fossil record., Comment: 26 pages, 19 figures