You somehow managed to settle in a little, previously uninhibited part of the earth. There you have waited and lived for 20/30 years, patiently waiting for the last zombie to rot away, drawing off the occasional raider attack. You send a scout party to finally check on the outside world, and when (if) they come back, you receive the notice that as far as they saw, the world is deserted, and that yours may be the last group of Homo Sapiens in the world. You then look over your shoulder and start wondering if you, your group of 37 people (including your parents) and your dog will be enough to repopulate the whole country/continent/world.

The ancient taboo of incest came into being for a reason (a reason that apparently many European royal families didn't hear about): Inbreeding.
If close relatives procreate during various generations, it can lead to exposure of recessive genetic traits. This can lead to:

• Reduced fertility both in litter size and sperm viability
• Increased genetic disorders
• Fluctuating facial asymmetry
• Lower birth rate
• Higher infant mortality
• Slower growth rate
• Smaller adult size
• Loss of immune system function
• DECLINE OF POPULATION AND FINALLY EXTINCTION

To avoid this, a minimum effective population (Ne) is required to maintain a population stable. An effective population is "the number of breeding individuals in an idealized population that would show the same amount of dispersion of allele frequencies under random genetic drift or the same amount of inbreeding as the population under consideration"
An effective population for dummies is: "the number of reproductively fit individuals in a population that are most likely not to share close relatives"

Since you may not be able to carry a group of 20,000 people to your safe haven, take note of this:
The "50/500" rule dictates that a Ne of 50 is necessary to prevent an unacceptable rate of inbreeding, while a Ne of 500 is required to maintain overall genetic variability.

To calculate your group's Ne, use this simple equation i found in this page of wikipedia:



Where Nm is male population and Nf is female population (of reproductive age)