Researchers have pinpointed the approximate date and cause of extinction [psu.edu] of woolly mammoths on St. Paul Island, Alaska [wikipedia.org]:
While the Minoan culture on Crete was just beginning, woolly mammoths were disappearing from St. Paul Island, Alaska, according to an international team of scientists who have dated this extinction to 5,600 years ago.
[...] In this study, three different spores from fungi that grow on large animal dung were extracted from lake cores and used to determine when the mammoths were no longer on the island. Proxies in sediments from cores from a lake near the cave were used to determine the time of the demise of the mammoth population. [...] Sediment DNA from the lake cores showed the presence of mammoth DNA until 5,650 years ago, plus or minus 80 years. After that time, there is no mammoth DNA and so no mammoths on the island. The youngest of the newly dated mammoth remains' dates fall within the mammoth DNA range and the fungal spore dates as well.
[...] The island, which formed between 14,700 and 13,500 years ago rapidly shrank until 9,000 years ago and continued slowly shrinking until 6,000 years ago and now is only 42 square miles in area. [...] The shrinking of the island concentrated the mammoths in a smaller area and diminished available water. Pollen from the lake cores indicate that the area around the lake was denuded of vegetation by the mammoths. Like elephants today, when the water became cloudy and turgid, the mammoths probably dug holes nearby to obtain cleaner water. Both of these things increased erosion in the area and helped fill in the lake, decreasing the available water even more. After the extinction of the mammoths, the cores show that erosion stopped and vegetation returned to the area. In essence, the mammoths contributed to their own demise. The researchers note that this research "highlights freshwater limitation as an overlooked extinction driver and underscores the vulnerability of small island populations to environmental change, even in the absence of human influence."
Timing and causes of mid-Holocene mammoth extinction on St. Paul Island, Alaska [pnas.org] (open, DOI: 10.1073/pnas.1604903113)
Related: Woolly Mammoth Genome Sequenced [soylentnews.org]