As civilization advances, poetry almost inevitably declines.

Literal

Civilization [subject-が] advance [as-につれて], poetry [topic-は] nearly inevitably declines.

~につれて means 'as X progresses/happens, Y follows' — it tracks a correlated change over time. 殆ど (ほとんど, almost) + 必然的に (inevitably) = 'almost inevitably.' An elegant literary observation.