Not the short story you're looking for, but The Hellstrom Chronicle is a 1971 pseudoscience mocumentary in the same vein: the struggle for survival between humans and insects. The conclusion is that insects will "win" due to their adaptability and ability to reproduce rapidly and humans' inability to organize due to excessive individualism.

The film is an odd duck: it's satirical and knowingly pseudoscience yet it won both the 1972 Academy Award and BAFTA Award for Best Documentary Feature.

https://en.wikipedia.org/wiki/The_Hellstrom_Chronicle