[kqr]

It still seems you're taking the density as a given, as the independent variable, and deriving some image of appropriate infrastructure based on that.

It might be the case that density is not independent at all, and indeed is changed when you change the type of infrastructure.

(Not to mention that bicycle and pedestrian infrastructure is far, far cheaper than that for heavier vehicles.)

[maxerickson]

Do you think if we built bike paths that 3 billion people would move to the US?

[malermeister]

You could have dense cities and high speed rail in between, it doesn't need to be all populated.

[maxerickson]

Right, the overall density is a coarse measure of the resources available for infrastructure (presuming that they will at least correlate with population and distance). If you have higher density, it is very likely there will be relatively more resources to deploy in a given area.

[kqr]

Density works also locally.