The animal whose absence would have the greatest negative effect on the ecosystem is the wolf.
Wolves are at the top of the predator hierarchy in this ecosystem, as they not only keep the populations of foxes and deer in check but also indirectly affect the rabbit population by controlling the fox population. The loss of wolves could lead to an overpopulation of foxes, which would then decrease the rabbit population significantly. Additionally, deer populations might also rise unchecked, which could lead to overgrazing and degradation of the ecosystem.
Therefore, the correct answer is: wolf.