Strange 2D sprites' transparency issue

Hi. I’ve got this rendered forest with transparent sprites (white background added in post production):

Why these black rectangles occur? It’s clearly due to sprites’ edges, but why isn’t everything transparent?
Every plane has the same material (with few varied textures):

Plus following settings are on:
It’s 2.79, cycles render. Can somebody explain it, please?

Cycles is hitting its limit of transparent light paths and further instances result in the black solids.
Increase the transparency depth.

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Thank you.