How do I fix my tree leaves turning black when I increase their number? I've been working on this tree, following a tutorial on YouTube, and performing every detail in the video.

Everything has been looking alright except for my particle system which I have set up for my leaves which are a png I made with photoshop and taking a picture of tree leaves outside. 

Now in this particle system, if I set the number of emitted particles to higher than 100, all heck breaks loose. If the number is under 100, it looks perfect, but looks like a dying tree as I lose many leaves. That is cool and all, but I also want a live looking tree. Whenever I set this number above 100 like 200 or 500, I get these giant black lumps that seem to disappear when I try to zoom in and inspect them. 

I didn't seem to have this problem before when I used a different leaf png, but I really like this one I made and it is the one I need for the tree. 

I've inspected the png and I can't seem to find anything wrong with it. I even erased the stems thinking maybe they were too numerous and caused the black masses, but to no avail. I even flipped the leaf plane normal thinking maybe it's a simple thing, but still no fix. 

Here is an image that explains the problem. On the left is the tree with a low emission or number of leaves, on the right is the tree with a lot of leaves where the blackness becomes a problem.
Your problem is likely caused by too many transparent objects being stacked in front of each other. Cycles' rays will just try to cross a fixed amount of layers before giving up and rendering black.

You can increase this "fixed amount":

→ In the Render settings for Cycles, under Light Paths, increase the value for the Transparency bounces until the problem goes away.