In whichever order events occur — if the new bars or the bike lanes come first — the two have become awkwardly linked. When a low-income community gets bike lanes, I've heard residents worry about what's coming next. When a redeveloped neighborhood gets them, long-time neighbors pose a different question: Why didn't anyone paint bike lanes until the new people moved in?

Cycling itself, as my colleague Perry Stein has written, has become a heated symbol of gentrification. Bike lanes are treated as harbingers of demographic change, or evidence of preferential treatment, or synonymous with well-off white men (all this, despite the fact that Census data shows low-income commuters are the most likely to bike).

This fraught bike-lane tension, though, is based more on perception than data. So a group of researchers at McGill University and the University of Quebec in Montreal tried to quantify the connection between gentrification and cycling infrastructure. Elizabeth Flanagan, Ahmed El-Geneidy and Ugo Lachapelle, in work presented this week at the Transportation Research Board annual meeting, mapped cycling infrastructure in Chicago and Portland alongside demographic change in neighborhoods between 1990 and 2010.

In both cities, they found "a bias towards increased cycling infrastructure in areas of privilege."

Here is Chicago. On this map, the lines represent bike lanes, the green triangles bike parking and the pink dots the 2014 Divvy Stations in the city's bikeshare system. Darker areas are places that underwent the most change in a gentrification index the researchers created that takes into account changes in the white population, education levels, homeownership, median incomes and home values.

And here is Portland (which doesn't yet have a bikeshare system):

In both cities, denser neighborhoods closer to the center of town were more likely to have bike infrastructure. But in Portland, so were census tracts where the share of homeowners and college-educated residents was rising. In Chicago, race was relevant: Neighborhoods with large white populations, or an influx of whites, were more likely to get these bike investments.

The authors are cautious about the chicken-and-egg question behind these patterns: Do cities build this infrastructure where they believe people live who are likely to use it (or lobby for it)? Or does the creation of bike lanes attract certain people? Are bike lanes really a part of the process of neighborhood change, or a sign when it's underway? The researchers sidestep the answer by suggesting that gentrification and cycling infrastructure "mirror" each other in these two cities.

That conclusion at least speaks to why bike lanes — basic infrastructure that could benefit anyone — have become culturally divisive. They are associated with so much more (and more than just the loss of street space): with unequal public resources and privilege and change.