What is the evolution metaphor about water flowing downhill?

As part of my biology undergrad degree, I took a course on the Origin of Species, where we read Darwin’s book and also several other readings about the origins of evolution.

I recall that during this course we talked about a metaphor to the effect of "Like water flows downhill to fill every available lower spot, species evolve into every available niche," which really helped me understand Darwin’s viewpoint on natural selection. But I cannot find this metaphor anywhere online.

What is the source for this metaphor? I don’t recall it being in the Origin itself, but I could be wrong.