The question that comes up every so often among editors has come up again: what do you do in a case such as Fish breed for one stage of their life cycles – or is it Fish breed for one stage of their life cycle?
If that one leaves you feeling uncertain, you’re in great company. Everyone who works with the English language has wondered about that one for ages. Even the style guides are mushy on it. So don’t feel as though somehow there’s a clue space that you’re not in on this one. It’s one of those things that the English language is not suitably designed to handle (another one is Either you or I [are/am] going).
Generally, I think, the leaning is towards using the singular where reasonable. In case like Fish breed for one stage of their life cycle, there is additional justification for this because one could assert that all the fish have the same life cycle in the abstract.
But what do you do with something like They each held a cake in their hands? After all, each person might have the cake in both hands. They each held a cake in their hand is clearer but might sound ugly. Each one held a cake in his hand is a problem if there are males and females, and Each one held a cake in his/her hand is ugly. Best to do something like Each of them held a cake in one hand if you can, or, better, There was a cake in the hand of each of them.
But isn’t it annoying that we should feel the need to shift flow and emphasis just to deal with a syntactic inadequacy of our language!