During much of the Late Pleistocene stage, the world's most widespread biome was the so-called "mammoth steppe" - a cold, dry grassland which spanned eastward all the way from Spain to Canada. It was the favoured habitat of many iconic Pleistocene megafauna species.
Roughly 12,000 years ago, the mammoth steppe suddenly disappeared, replaced by tundra and boreal forest. Some put it down to humans killing off the local megafauna which were needed to maintain the grassland, but the prevailing hypothesis is that the climate became warmer, and therefore wetter, allowing shrubs, mosses and trees to move in.
For more information, see https://en.wikipedia.org/wiki/Mammoth_steppe.
In my world I want to have a ~10,000 square kilometre island, situated roughly here:
(Where the thick black dot is. Ignore the red arrow, that was in the original picture for some reason.)
And, more importantly, I'd like this island to contain a remnant of the mammoth steppe, and thus be a refugium for many extinct Beringian creatures. So, assuming that the Climatic Hypothesis is correct, how can I justify the mammoth steppe not being displaced by other biomes here?