Interesting. I have never quite thought about the example of trees but it's possible something like that is going on. If someone would know, it would be Geoffrey West from the Santa Fe Institute and indeed he delivers: http://www.pnas.org/content/106/17/7040.full

According to their theory: "(...) the average distance between the trunks of individuals (trees) of the same size scales linearly with radius (of the tree)"