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Ooops, sorry Tilly I missed your question. Basically it's as several people have now responded, the red squirrel is far better at escaping from the Pine Martens which prey on squirrels. Pine Marten populations are increasing so this would appear to be in the Red's interests.
The report is based on statistics (where Pine Martens increase, Greys decline, Reds don't) and the "predation" explanation is only a theory at present, more research is needed to determine if this is the right explanation.
The point was made that Reds have co-existed with PMs for eons and their ability to escape has evolved accordingly, whereas imported Greys have never encounted such predation and have therefore not evolved to counter it.