Well it completely depends on number of houses and trees. To know this you'd have to know the number of squares taken up by water and cliffs. There are 20 acres in New Leaf, and thus 5120 total squares not including water, cliffs and buildings.
The maximum amount could be as many empty spaces as there are in town, I believe...not quite sure though. I've seen some people with them almost completely covering the town, so it could be possible ; o ;