> So does the algae itself consume oxygen (aerobic respiration?), or produce oxygen (photosynthesis?) in order to survive? Sorry, I study inorganic geochemistry but don't know much of anything about biology or botany. > >

The Algae both consumes and produces oxygen - at first it's necessarily producing more than it consumes, in order to get the carbon it needs to grow in size, but when it's as big as it's going to get those numbers start balancing out.

Add in the fact that dead algae decaying take oxygen solely from the water, while living algae photosynthesising put their oxygen both into the water below and the air above, and you get a net decrease in oxygen over time (barring gas transfer, which as mentioned is blocked by the matting effect)

Another part of the problem is that the algae only produces oxygen in the daytime, and consumes it constantly, so at night the oxygen level in the water drops - and if something can't survive at night-time oxygen levels then it dies, and starts decaying, further lowering the oxygen levels.