Thanks for the explanation. I was thinking in terms of three surviving couples being the only source for all subsequent humanity. Setting aside the redneck jokes, it seems to me that such a situation would result in a genetic nightmare. And as you pointed out, the problem would be even worse for a single pair of animals. Would such lines even be viable?
That would be a severe bottleneck more than likely resulting in extinction. In small populations, the members suffer what is termed the 'founder effect' where recessive genes fix in the population (heterozygous alleles become homozygous alleles) due to drift and can become the only allele in the genome (monomorphism) leading to what has been termed a mutational meltdown. If many deleterious genes fix in the population the chance of extinction increases.(Check Muller's ratchet)
There would likely be problems. Particularly as 3 of the 6 founders were brothers. Some loci in the human genome have more than 200 alleles if memory serves. It is particularly hilarious that the same crowd who assert "all mutations are harmful" can reconcile such genetic diversity with a tiny starting population a few-thousand years ago. Of course the Noah story has many, many problems far more serious than this. Have a chat with a zoo-keeper sometime for example, to consider the problems of 8 people maintaining a global ecology for a year with no recourse to outside services.