Which sci-fi book features a future earth ruled by women and a carnivorous plant...?

called a snipper snapper? I am trying to trace a book for my dad and he can't remember the title. All I have is a plot overview; a futuristic earth, overgrown with vegetation; women rule the planet, men are a rarity and guarded fervently by any women lucky enough to "own" one; the humans live in the trees as the ground is full of carnivorous plants - the most feared being a crocodile-like plant called a snipper snapper.