Cyanobacteria blooms (blue-green algae) have existed on earth for more than 3 billion years, making two essential contributions to the evolution of life: photosynthesis and oxygen production. 

When all other life forms are destroyed through apocalyptic phenomena, the cockroaches will subsist on the blue-green algae that sustains itself on the phosphates that run into rivers and lakes from farming, detergent use and in sewage.

Cyanobacteria use the phosphate to grow, and when they die, the phosphate goes back into the water, ready for the next bloom.