This is how Genetics works (in real life).
Let's say Goku/Vegeta is Saiyan SS, and Chichi/Bulma is Human HH.
See those SH's? That's Gohan, Goten, Trunks and Bra. In this scenario, there's a 100% Chance that the child will have Dominant Saiyan genes.
In this Scenario, SH is Gohan, and HH is Videl. In this instance, the SH inside the Grid is Pan, and all the other SH's and HH's are hypothetical. This shows that there will be a 50% Chance of a child with the Dominant Saiyan genes, the other 50% chance is full human.
Now, assuming there's no funny business involved within the either family :ermm: most of the remaining descendants will turn out either SH or HH.
Now, if Goku's Great(x10) SH grandson were to have kids with Vegeta's Great (x10) SH Grand daughter, there's a 50% chance that the child will turn out SH, 25% chance of it turning out HH, and 25% chance of turning out SS.
EDIT: Forgot this part.
Now, assuming two such SS Descendants appear and have kids, there's a 100% Chance that any child they would have turns out to be a full Saiyan! Even an SS with an SH has at 50% chance of churning out a SS, so it's all good.
Therefore, presuming real life genetics were to have some sort of affect on DBZ logic, it wouldn't be too big of a stretch for Saiyans to repopulate.
Now that I've wasted all your time, get on with your lives, you losers!
PS: I'm an even bigger loser for doing this!