I can't give a number but one of the key factors to consider would be the rate of loss of sex alleles at the CSD locus.
An individual queen carries two in her genotype but others in the sperm in her spermatheca, apparently up to 19.

If there were only a small number of colonies on the island the genetic diversity at the CSD locus would reduce very quickly as a queen only carries two alleles in her genotype meaning she can only produce drones carrying one or other of these two alleles.

I was at a lecture a couple of years ago where it was pointed out that a closed population which falls to only 6 of the 19 sex alleles present in the population is at the point of no return. Diploid drones are a huge drain on colony resources and there is a strong inverse correlation between the amount of diploid drone brood, ie gaps in the brood, and colony winter survival.

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