On a world made up of many small islands, each island cannot support a very large population. Although sometimes individuals from one island make it across the ocean to another, this is usually a rare event. I read once that a genetically diverse population of about 5000 humans would be required to ensure that a population can be sustained without inbreeding, and much less than that means that the genetic diversity is not high enough. 

Presume on this island world all land-dwelling species have evolved to have three sexes, such that young share the genetic material of three individuals, not just two. Would sustainable, genetically robust populations require more or fewer individuals in such a set up?

**Update:** It has been pointed out that perhaps the 5000 number is wrong. I'm not sure of the exact number, and will look into it later. Point is: there is probably a threshold of genetic diversity below which inbreeding is a problem. I'd like to know if that threshold is higher or lower with a third parent.