My goal is to build an algorithm whose fundamental goal at the most basic level is, given the current tree configuration of a particular region, to output the best coordinates to plant the next tree. Tree configuration refers to the coordinates of all the trees in a particular region.
Let me begin by defining the term tree utility, which includes the overall qualitative measure of properties such as the integrity of the forest, thriving capability of the local ecosystem, reduced competition of resources (for the trees), and so on.
From this paper by Xu et al. (2021), I get the notion that naturally formed forests tend towards a uniform spatial distribution. But I'm not confident regarding my inference, being entirely untrained in this field. I am aware that the paper was based on the forest patterns of a particular species of plants. But the quoted text below from the mentioned paper pursued me to believe that at least my inference - a uniform spatial structure maximizes tree utility - can be generalized to most, if not all species
The study on the structure of natural forests based on uniform angle index distribution shows that the number of trees in a random distribution microenvironment in natural forests is more than 50% and can usually be divided into two types, R1 (dumbbell-shaped random unit) and R2 (torch-shaped random unit) (Figure 1), with a similar proportion (R1:R2 = 1:2), and it has nothing to do with forest distribution zone, tree species, or forest type
Assuming my inference isn't wrong, I devised the following basic framework for the mathematical model I'll use to build my algorithm.
Consider a 4x4 grid and suppose a tree exists at position (1,1), the top left corner. Where should I plant the next tree to maximize the tree utility of the area?
I hypothesize that the more adjacent trees there are to a unit square in the grid, the better it is. Which makes (2,2) the answer to the question I asked above. The mathematical model I will build based on this hypothesis will generalize this process to an arbitrary MxN grid.
The ultimate implication of this hypothesis is that the closer the tree distribution in a given region is to a uniform distribution, the more the tree utility is maximized. I try to illustrate my point a little better through the images below.
- Is my inference from the mentioned paper by Xu et al. correct?
- Is my hypothesis - the closer a forest's spatial distribution is to uniformity, the higher the tree utility - sound? If yes, I'd appreciate references to related literature. If not, please elaborate on the reasons for it to be fallacious.