According to Portland State University anthropologist Cameron Smith, any 2000 year long Worldship journey would have to carry a minimum of 10,000 people to secure the success of the endeavor. And a starting population of 40,000 would be even better, in case a large percentage of the population died during during the journey.
Gardner-O’Kearny calculated each population’s possible trajectory over 300 years, or 30 generations. Because there are a lot of random variables to consider, he calculated the trajectory of each population 10 times, then averaged the results. (With one exception: The starting population of 40,000 is so large that it takes 18 hours to complete each simulation, so he calculated that trajectory only once.)
Genetic diversity keeps groups healthy, and larger populations tend to have more diversity.
When 10,000 people are housed in one starship, there’s a potential for a giant catastrophe to wipe out almost everyone onboard. But when 10,000 people are spread out over five ships of 2000 apiece, the damage is limited.
The revised Battlestar Galactica television show had survivors in the range of 50,000 and dropping to about 38000. The show was inferior in terms of the ending and plot but they did have the right numbers to maintain long term genetic diversity.