Hi all
I think the only way to get at this question is to really think outside the box. For example, perhaps we are asking the wrong question. Maybe the question should be: how long will the queen refrain from laying eggs. It seems obvious that the cue for shutting down is very strong, cessation of forage and/or onset of cold weather. However, she may simply restart after a given period (diapause?). What if the queen's very survival depends on egg laying?

SEE:
Rueppell, O., Königseder, F., Heinze, J., & Schrempf, A. (2015). 
Intrinsic survival advantage of social insect queens depends on reproductive activation. 
Journal of evolutionary biology, 28(12), 2349-2354.

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