Is the infertility caused by Jacob?

Fertile people become infertile on the island because Jacob doesn't want additional players in the game (especially kids, as seen by the Others). Jacob didn't touch Jin in the sideways, therefore Jin is not infertile. This may be messed up by Claire, Aaron, and Walt but it seems like Aaron and Walt were deliberately chosen to come to the island for one reason or another (with Claire and Michael only as catalysts to get them there).

But, Jin was fertile on the island. Maybe this was to get Sun off the island and out of the game since Jin is the candidate (we recently pretty much found out that Widmore is working with Jacob). But Ben (who had to have been working with MIB off-island, even if it was unintentional) was the one to convince Sun to come back to the island, not Locke (who was working with Widmore and therefore Jacob).

This is admittedly far-fetched and incomplete, but food for thought nonetheless.

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