There are two ways this can affect the other aniamls. One, too many rabbits are populating and have no preditor. Two, the rabbits staying balanced and not populating but too many animals in the area. Or for them they sadly die.
And one would affect the other animals in the food web a lot because if all the grass was to be eatin by the millions of over populating rabbits all the grass would disappear causing both the rabbits and other animals to starve.
Two, if they were to stay balanced still again they could invade on land that is too small or already has the amount of animals it is able to handle.
Hope this helped you. :3