So, I assume that if you put 100 people on a spaceship and sent them to wherever, they’d get very inbred in a few generations. How many people would you need for this to not happen, accounting for the fact that there will eventually be people who are infertile or die before having children?
There are actually two issues:
The most obvious effect of inbreeding is the increase in homozygosity for deleterious mutations, causing more birth defects.
A subtler effect is the loss of genetic diversity reducing a population’s ability to continue to evolve in response to future selection pressures. This would be especially important when migrating to a new environment with new selection pressures the species has never encountered before.