Tuesday, December 4, 2012

Do Cities Densify or Disperse as They Grow?

In a recent post, Chris Bradford has built on some of the findings I made on weighted density last month to show how housing affordability has relatively little relation to density.  In the graph below, I have a look at a related subject: the relation of total population to density, to determine whether cities tend to grow denser as they grow larger.  I use urbanized, rather than weighted density, since the purpose here is to determine the relative change in extent of the built-up area at various population levels, and plot it against MSAs ranked in order of population (not population itself). A trendline with period 20 is overlaid on the scatter plot.

As predicted by the correlation data from an earlier post, urbanized density is here shown to be significantly related to total population, yet the scatterplot teases out some intriguing nuances in the data.  For instance, urbanized density shows little change for MSAs up to a population of around 200,000 (around point 150 on the X axis).  A modest upward trend is visible for cities between 200,000 and 700,000, after which the line slopes sharply upward. How to explain these trends?

An economic model using a simplistic urban land value gradient (illustrated as the New Urbanist transect) would find the results entirely predictable: as a city grows in extent, the time value of a central location becomes increasingly large relative to the price value of a peripheral location, such that we'd expect to see a slowing in the rate of growth of the urbanized area over time as either 1) new residents locate in existing, centrally-located neighbourhoods, 2) new greenfield developments are built at higher densities or both.

Using averages of urbanized area density for each population level, it is possible to visualize this process in action.  At left, I show the travel time in minutes from fringe to center (assuming for simplicity's sake a perfectly circular and monocentric city with no topographical impediments, and using the mean US commuting speed of 32 mph) holding density constant at 2,000 people per square mile, which represents the average density for MSAs of below 400,000 inhabitants.* At right are the same figures using the densities that are actually observed for each of the population ranges.

For smaller cities, even significant increases in population do not cause travel distance to the center to increase to unpleasant levels (bearing in mind that the typical person wants to devote no more than one hour per day to commuting), so densities do not increase – in fact, for cities less than 150,000, growth appears to track with a slight decrease.  Significant increases in urbanized density kick in only when travel distance from fringe to center approaches 20 minutes, and rapidly increase thereafter in an apparent attempt to keep maximum one-way travel time close to 30 minutes.  Were larger cities comparable in density to smaller ones, one-way travel times from the urban edge could approach one hour for cities of around 5,000,000.

At this point, I might expect Wendell Cox to interject with his contrary finding that "the general tendency is for cities to become more dispersed (less dense) as they grow."  Cox's conclusion was drawn from a statistical study of urbanized area density for cities from each of the 1950 to 2010 censuses, in which he found that most have indeed become less dense over time even as their populations increased dramatically during this 60-year period.  How can this be reconciled with the figures above?

In a nutshell, because the 1950-2010 time period covers a transportation, zoning and family planning revolution that completely altered commuting patterns and household composition.  In 1950, the interstate highway system did not yet exist, and relatively little new housing had been built following the emergence of zoning in the late 1920s due to the Depression and the lean war years.  The combined effects of these two developments – speedy access to city hinterlands combined with rules that prevented intensification of and discouraged investment in existing neighborhoods – no doubt contributed to a massive decentralization that overrode the natural tendency for urbanized density to increase with growth.  Additionally, household size contracted as the birth rate declined, which would tend to cause a steady decline in population density even where the concentration of housing units remained constant.

In fact, examining the fastest growing cities during the period 1980-2010, after the completion of the bulk of the interstate highway system, there is clear evidence of a swing back toward higher urban densities, particularly in those places that had little pre-automobile urbanism to de-densify either through abandonment or gentrification. Las Vegas, for instance, which had a population of 25 at the dawn of the auto era, is almost twice as dense as it was in the 1980 census. In Phoenix, lot sizes for new single family detached homes declined steadily after peaking in the late 1970s, leading to an odd situation in which neighborhoods on the urban fringe are often denser than much more centrally located ones. Notable exceptions include Southeastern boomtowns like Atlanta and Charlotte which, however, saw their density declines slow or cease after 1980.**

These numbers help provide a partial explanation for the data in an earlier post, Commutes, Tradeoffs and the Limits of Urban Growth, where I noticed that mean commuting times did not increase in step with population growth, and provides further reassuring evidence that even automobile-based urban expansion (i.e. suburbanization) contains a natural braking mechanism that will eventually slow the rate at which new land is consumed for development.

*Of course the average travel distance to the center will be less for the MSA as a whole, and most new residents will not be commuting to the center at all, typically reducing their commuting times.  The model is a deliberate oversimplification intended to illustrate basic trends.

**Interestingly, both Atlanta and Charlotte pursued major mass transit projects around this time period (MARTA's heavy rail system and the LYNX light rail, respectively) while much denser Las Vegas did not.  One could speculate that car commutes in Las Vegas were much shorter due to its density-driven compact urban area, leading to less political pressure for alternative forms of transportation to serve suburban commuters (despite being considerably larger than Charlotte population-wise, Las Vegas currently occupies only 56% of its land area).  Perhaps coincidentally, Atlanta and Charlotte, of very similar densities, approved tax increases to fund rail service at around the same respective point in their population development Atlanta at 1.8 million, and Charlotte at 1.5 million.


  1. Atlanta and Charlotte have rather irregular road networks, while Las Vegas has a regular grid of arterials, and a better freeway network relative to its size. Perhaps Las Vegas' more efficient car travel led to lower demand for transit?

    1. Well, Las Vegas actually has far fewer lane miles than Atlanta on a per capita basis – in fact, only one third the amount:


      My guess is that is also due to Las Vegas' density. Denser cities appear to generally have fewer miles/capita, which I guess is partly due to geography and partially due to denser cities having less need for high speed transportation, controlling for population size, since their commuters simply don’t have as far to go.

    2. My guess is that part of that is due to Vegas having a more efficient transportation network (in addition to the size disparity): grid networks appear significantly better at handling more traffic per lane-mile. Vegas' arterial network is a second-level grid imposed over top of the local street (non)network, whereas Atlanta is built out of an antebellum environment where the second-level networks consist of repurposed turnpikes (etc.) which help funnel traffic onto the same few paths, magnifying demand for more lane-miles on them.

      I would also bet that Phoenix, Albuquerque, and the Texas cities also follow Vegas' pattern.

    3. That's a good point, Steve. A gridded road network based on auto transport should produce a highly decentralized, all-points-to-all-points system, and that is exactly what we see in Vegas and Phoenix (but slightly less so in Houston, with its monocentric freeway system) with their extremely low concentration of jobs in the "downtown."

  2. Definitely in Canada, densities have gone up since 1950 for new greenfield single family development, at least in Calgary, Vancouver and Toronto (maybe not Montreal). The arrival of the automobile into the mass market in the 50s means suddenly a huge increase of undeveloped land within reasonable commuting distance of downtown. Now, there is virtually none within reasonable commuting distance of downtown, only within reasonable distance of suburban job centres in the case of Toronto.

    The least dense neighbourhoods of Toronto were almost all built from around 1950-1965, including areas around the Don Valley in North York, Central Etobicoke and Southern Mississauga and South Oakville. The 60s and 70s saw a rental tower boom that increased densities, I think mostly in the 50s-60s suburban areas of Toronto and Mississauga. 50s-60s areas without the towers have densities often under 5000ppsm at the census tract level, compared to new development that's typically 8,000-20,000 ppsm.

    Same with Calgary, outside downtown, density does not decrease as you go further out, in fact, I would say it decreases, although this is difficult to measure. However, if you look at a density map of the city (using Geosearch 2011), you'll see the NW suburbs are noticeably denser than the single family neighbourhoods surrounding Calgary's core.

    If you look at Vancouver's new developments (like around Langley), there's tons of townhouses and small lot 2 storey single family homes, while earlier developments have larger lot bungalows.

    In all 3 cities, there is a lot of tear down action in these 50s-60s neighbourhoods to build either much larger homes that take advantage of the large lots, or to subdivide the properties, with bungalows being replaced by pairs of 2 storey narrower lot homes.

    All this is reflected by significant increases in weighted density at the urban area level (more than 500ppsm increases from 2006 to 2011). There is also of course other forms of intensificaton, like highrises and brownfield redevelopment occuring in all 3 cities.

    You might notice I didn't mention Montreal. It would probably would have followed a similar pattern as the other 3 cities, if it weren't for the fact that the 1945-1970 development was unusually dense, especially in non-English areas.

    Here are some areas built in that period that are typical of the time
    Late 40s to early 50s: http://goo.gl/maps/8PJI9
    From around 1950: http://goo.gl/maps/Q3ljX
    From around 1960: http://goo.gl/maps/mZSXV
    Late 1960s: http://goo.gl/maps/oDKYS

    The 1945-1955 development of Montreal might actually be denser than pre-1945. 1955-1970 development was less dense, but still denser than today. Again, this does not include the Anglo suburbs of 1945-1970, especially those of 1955-1970 (West Island) which were much less dense, even less dense than what is being built today in Montreal's suburbs.

    I think another reason for denser development with growth is that bigger cities are usually more congested, so not only is the distance to the core greater but the travel time is greater still.

    1. Thanks, Nicolas -- I really ought to have included Canadian cities on this list as well. I just wasn't sure what source to use for urbanized density. The Geosearch site is a lot of fun to explore, though.

      The differences between Francophone and Anglophone urbanism that you allude to are intriguing -- are these reflective of cultural differences, do you think, or were there different planning regimes in French-speaking parts of Canada that encouraged different forms of urbanization?

    2. Quebec's GDP per capita was 22-30% lower than Ontario's from 1945 to 1970. English (non-Irish) Quebecers were still quite a bit wealthier during that period, so if you exclude them, the difference would be even greater, although I don't know how much greater. I'm not sure if that's enough to account for the difference between the two cities though.

      The Anglophone suburbs of Montreal are just as low density as the low density parts of suburban Toronto though, so it's hard to say if it was related to planning, unless it was done at the suburb level.

      Quebec City has a bit of the Montreal style post-war urbanism, but not nearly on the same scale. I'm not sure if that would be because Quebec City is smaller, or maybe more white collar, or some other reason.

      Montreal development was significantly denser than in Toronto before WWII as well. Montreal had mostly rows of attached triplexes and duplexes in its streetcar suburbs, while in Toronto, there were a lot of detached and semi detached homes, and maybe a few rowhouses, but relatively few apartments. Pre-streetcar, Montreal seems to have been a city of dense 3-5 storey apartment buildings and some rowhouses, although virtually nothing remains of neighbourhoods that were built from 1800-1870 (only the Old Port, which was built up earlier- though has buildings from that time). In Toronto, it was mostly rowhouses as far as I know, often with front setbacks (not the case in Montreal).

      One of the things that surprised me looking into Montreal was how aside from the Old Port, the city is not that old. In 1870, its population smaller than several American cities outside the East Coast that it has since outgrown. St Louis seems to have been significantly larger, Cincinnati was larger too, and even Buffalo was probably about the same size (officially, it was a bit larger). 1870 is around the time streetcars came into play, so I would expect that areas built up before that time would have to be dense enough to walk to all your daily needs.

    3. I would never have guessed about the economic disparity -- that's very interesting to learn. The quantity of attached small apartments in Montreal really is quite amazing, now that I look at the city a bit more closely. In similarity of extent and urban form only Brooklyn can rival it, I would say. It's clear why Montreal was such a good candidate for a subway system compared to other Canadian cities.

      That particular style of apartment building is so distinctive, too, yet it seems to stop abruptly, with no examples I can see in Ottawa or any further west. That reminds me a bit of the Philadelphia rowhouse, which also has a narrowly-constrained geographical range due to obscure historical forces (but not economic ones, as far as I can tell).

    4. The economic disparity played a major role in the tensions between French and English Canadians that almost led to Quebec voting to separate. Basically, when the English conquered New France, they were the ones who established the major companies (starting with fur traders). For a long time, the big companies were owned by Canadians of English and Scottish background, and English was the language of business in Quebec, which made it difficult for French speaking Quebecois to move up the social ladder.

      Anyways, much of Ottawa's older housing is similar to Southern Ontario's, which makes sense since they are culturally similar and were mostly built for American, British and Irish immigrants and not Quebecois.

      However, there is a bit of housing in Ottawa that's similar to Montreal's, though often not attached, which likely has to do with Ottawa's smaller size (especially historically). The housing in small towns in Quebec is similar.

      Ottawa: http://goo.gl/maps/tRQBK
      Small Quebec town: http://goo.gl/maps/YYz9l

      Basically, I think the architecture (flat roofs and balconies) has to do with cultural factors, while the housing type (dense and apartments) might be due to economic forces.

      I'm not sure though, it could be partly cultural too. How would the historical incomes of say, New Orleans, compare to DC? I suspect New Orleans was poorer, yet the housing there is mostly shotgun bungalows compared to rowhouses in DC. And unlike most other Southern cities, New Orleans is quite old, so that can't be the reason for lower density housing types.

      I suspect Philadelphia could rival Montreal in terms of extend of its rowhouse density (which is about as dense as Montreal's attached apartments) if it weren't for urban renewal and decay.

    5. New Orleans is an interesting example, being likewise a Francophone city that came under the rule of an Anglophone power, but with Spanish urbanist and architectural heritage (the city burned down and was rebuilt during Spanish rule in the late 1700s – there is apparently almost nothing left of the French colonial architecture). It's my impression that the city was wealthier than DC during the first half of the 19th century (it was much larger), and perhaps not significantly less wealthy through at least the 1920s.

      As far as I can tell what happened is really something of a cultural break following US control of the city. The Spanish had constructed a traditional city of attached single-family and multi-family dwellings (the French Quarter) that was more reminiscent of a European city than almost any to the north. Immediately beside this, the English-speaking population (the French Quarter remained Francophone) built a typically "American" downtown of office high-rises and broad streets. This contrast can still easily be seen in aerial images:


      My guess is that this "American-style urbanization" carried over into residential development as well, and what eventually resulted was a style of home typical of the deep South – the shotgun house, but adapted for higher densities (though exceptionally narrow widths and minimal side setbacks). We could speculate that if the French or Spanish had retained control, the result might possibly have been something closer to Montreal, with more attached or apartment housing. But that's only a guess. It may have been that American influence would have won out eventually anyways, just due to proximity and immigration patterns, but it's impossible to say. With its very large size in the pre-industrial era and strong French influence through the 19th c., though, it still is perplexing to me why there is so little attached housing.

      DC, by contrast, fell between the rowhouse influence of the mid-Atlantic and the townhouse influence of the urbanized old South (Richmond and Charleston, not to mention Alexandria and Georgetown). I would say that these regional stylistic/cultural influences overwhelmed any economic trend toward SFD homes.

      As to why the mid-Atlantic gravitated toward attached housing, and the South and New England generally did not, there's no single explanation that's compelling to me, either economic or cultural. Salem, MA, was one of the largest cities in the United States in the 1790s-1820s, yet it has no rowhouses. Neither does Providence, not many anyways. Yet Baltimore and Philadelphia do, even though Philly was explicitly founded on typically "Anglo" anti-density, pseudo-suburbanist planning principles (Penn's idealization of the large-lot SFD home).

      That suggests that economic forces outweigh cultural influences, but then again, Philadelphia had a strong German cultural influence in its formative years, and interior PA cities like Lancaster and York, although a fraction of the size of Philly and surrounded by vast amounts of flat land, were initially built almost entirely of rowhouses, suggesting that culture/regional style can outweigh economics. There are no easy answers here, it seems!

  3. Not on topic - but: have you seen this article that addresses the "who" aspect of urban development?


  4. This is gonna sound really anal, for which I do apologise - but could you label your graph's axes? :) I can only assure you that I wouldn't care if I didn't find the work fascinating!

    1. Not anal in the least, and I'm glad you enjoyed the post. The y-axis shows persons per square mile (within a city's urbanized area, as defined by the Census bureau), while the x-axis is simply a ranking of American metropolitan statistical areas by population (e.g. point 1 is the lowest pop. metro, while #350 is New York), and has no real independent significance. All population statistics were drawn from Census data via Fact Finder: http://factfinder2.census.gov/faces/nav/jsf/pages/index.xhtml