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[Distribution changes and refugia of three spruce taxa since the last interglacial.]

Based on the current distribution information and 19 environmental variables data, we used the maximum entropy model to simulate the suitable distribution of Picea likiangensis var. likiangensis, P. purpurea and P. wilsonii in the last interglacial, Last Glacial Maximum, Mid- Holocene and present. The results from such modelling were validated by pollen data. We analyzed the relationship between species distribution dynamics and climate change, and then speculated the cryptic refugia of those species. Both the areas under the receiver operating characteristic curves and the verification results from pollen data indicated high accuracy of the model results. Results showed that isothermality was the most important factor influencing the distribution of P. likiangensis var. likiangensis and mean temperature of the warmest quarter was the most important for the distribution of both P. purpurea and P. wilsonii. Temperature was more important than precipitation in driving species distributions. Three species expanded their distribution ranges in Last Glacial Maximum due to their cold-adapted ecological habitat and the deep canyon topography feature which benefited their migration. There might be refugia of both P. wilsonii and P. purpurea in last interglacial, and they respectively located in Shennongjia Mountain in Hubei and Erlang Mountain and its nearby mountains in Sichuan. Our results, to some extent, made accurate prediction of the suitable distribution of three spruce species in the key periods since last interglacial, and speculated refugia of P. purpurea and P. willsonii. Our findings provided reference for better understanding of the formation mechanism of the present distribution of Picea and prediction of distribution changes in the future and sustainable management and protection of three spruce species.