Why would they need a "bottleneck population reduction"? If we assume Daryl and Carol are the same ages as the actors who portray them, she's only four years older than he is. At their age, and in real life, that's an all but insignificant gap.
I'm making an assumption about who the erstwhile redneck Daryl might have wanted to date when the population was filled with 20 year olds. Perhaps Daryl was always a bit deeper.