A model of mass extinction accounting for the differential evolutionary response of species to a climate change

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 half of all species went 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 as 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 some taxa - in particular, vegetation - to the climate through changing the albedo of the Earth's surface and (ii) species' adaptive evolutionary response to a climate change. We show that whether a species goes extinct or not depends on a subtle interplay between the scale of the climate change and the rate of species' evolutionary response. We also show that species' 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.