In art class it was revered to as values. Basically the closer an item is the more details you will see. so a branch that is just behind the focal point of the picture (the bad ass guy in your pic) will have a lot more visible details (i.e. Bark, missing bark, moss growing on the tree etc.) but a branch further back (like the back part of the tree) may just be a silhouette. Other things may also play into backgrounds like weather (fog, rain), or even the time of day, and light sources beyond the view of the picture. This might be over thinking it all. But if your going for hyper realistic drawings, sometimes its good to think about the objects outside the view of the in the picture, but how they will affect what you are drawing.

As far as my previous comment, the coloring of the branches will be affected by distance. I don't mean to alter the color in a way that is unnatural. Just that another way to show distance to tint each layer with a darker tone. Hopefully this is all useful to you.