Dr Love Dalen of the Swedish Museum of Natural History said that the woolly mammoths were a fairly dynamic species that went through local extinctions, expansions and migrations.
Dalen and other researchers analysed DNA samples from 300 specimens from woolly mammoths.
The scientists were able to determine how many mammoths were present at any given time from the samples as well as tracing their migration patterns.
They found that mammoths nearly went extinct 120,000 years ago when the world warmed up for a while.
They also found that the decline that led to extinction started 20,000 years ago when the Ice Age was at its height, rather than 14,000 years ago when the world started warming again as previously believed.
They scientists speculate that it became so cold that the grass that they fed on became scarce and the decline was spurred on as the Ice Age ended, possibly as the grassland on which they thrived was replaced by forests in the south and tundra in the north.
The results have been published in the Proceedings of the Royal Society B.