I've studied the matter somewhat, but I'm not an expert on the matter - will always be a student. Here's what I figure and I'll try to keep it kind of brief, there is a lot of complexity to manage in the question.
The mature animals breed first and leave first. The herd gathers under the light of the late summer full moon the pheromones circulating in the herd triggers estrus, but a cow is only ready to breed for a relatively few hours, so the bull needs to keep the cows close when that is happening. For the fertile cows it is about three weeks until they come into estrus again, but the next full moon is four weeks which starts to skew the next round of estrus, and even more so by the third and fourth moon. The bulls run out of steam somewhat because they prioritize mating over eating during this time so they drop out of the herd earlier. If you look at the "rut" that way instead of a one time thing, it gives you more strategies to work with.
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