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I am skipping the other portions of the summary and conclusions section for brevity. As you can see the lowering in reproductive rates is related to a hormonal response to the increase in density of the population. This explains why rabbits bred in captivity and kept in separate cages have an unchecked birth rate while rabbits in the wild exhibit a lowering in the birth rate as population density increases. None of the articles state that this is an anticipatory lowering in birth rate. Rather it is a response (lowering birth rate) to a change (increase in population density).
The hormonal changes that are observed to cause the lowering in birth rate, seem to be triggered by the increase in aggressive behavior that occurs in these species as population density increases. This causal link is not directly well supported in the articles but is referenced from other research.
That the authors don't use the word "anticipate" has no bearing. Does the regulation kick in before starvation density is reached or after?

Some of these studies take place under controlled conditions where one food & water are assumed to be supplied. Do you suggest they're rigging the results by starving animals?

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