# Maximizing Tree Utility in a given Region

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.

Put short,

1. Is my inference from the mentioned paper by Xu et al. correct?
2. 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.
• I'm guessing it's going to have something to do with what "better" you're talking. In terms of shade, you don't want them too close ("wasted" overlap). In terms of agriculture, for species with crosspolination or such, you'll want them close (although not too close). Is the goal to encourage animal populations? Is it to increase soil quality and moisture retention? Air cleaning? Forest growth? Wind reduction? Climate change? I would expect it's a very complex topic, so you'll at least likely need to clarify more :) Jul 27 at 21:29
• I agree with @JeopardyTempest its a complex matter. You should also consider in terms of shade that if the bigger trees is occupying the southernmost point in the grid the opposite point will get little Sun. Jul 27 at 21:56
• @JeopardyTempest I sincerely appreciate your kind suggestions. I've elaborated on what exactly I needed endorsement/rejection on and what I was referring to by "better". I hope the changes make it easier for you to help me out. Thanks! Jul 29 at 1:36
• I have no knowledge of the subject at all, but hopefully it will help any of those who do to know what you are looking for :) Jul 29 at 3:02
• Lumber companies plant them in ( many) straight rows . The planting equipment works well that way and subsequent maintenance and care are simpler. Jul 30 at 2:06