Introduction

  Knowing the local and regional rates of population change is essential for constructing useful community plans.  Accurate projections are important for virtually all aspects of General Plans.  Water, power, safety, health, schools, open space and more are linked to population size.  Without accurate projections it is impossible to anticipate community needs.

  Misinformation about growth can have a significant impact on local planning.  It can be used to justify additional taxes, development projects, and a variety of public services.  Information on population was used by the Dewey-Humboldt Town Manager, Roger Swenson to calculate growth rates.¹  Swenson's results do not appear to be accurate.  In this short article I discuss the calculation of growth rates using US Census Bureau information, and I use Swenson's own base figures to calculate a more accurate rate for Dewey-Humboldt.


Calculating the growth rate

  The basic population growth rate formula for any given year is simply the difference between births per 1,000 and deaths per 1000 divided by 10.

                  % Growth Rate = (BR-DR) / 10

This basic rate is adjusted using migration data to account for residents entering and exiting, and is then constrained by establishing a limit called the carrying capacity.  A full explanation is provided in the book by Wilson and Bossert.²  Calculating growth rates is comparatively simple for human populations in US towns and cities because of the quality of the year-to-year population estimates and regular counts produced by the US Census Bureau.³

  According to the Census Bureau, the population of D-H grew from 3,440 in mid-2000 to 3,613 in mid-2005.  In January, 2006, Swenson used an estimate of the number of residential buildings in D-H multiplied by 2.28 persons per household to estimate the D-H population.  His figure of 3,784 is higher than the Census Bureau figure.  The difference is probably due to differences in estimation method, and to population growth during the additional half year between the time of the Census Bureau's estimate and the time of the Town's estimate.  Moreover, Swenson's figure is probably too high, because it uses number of buildings, but offers no confirmation that all the buildings were occupied.

  If we use the Census Bureau's figures for D-H we find that for the five-year period from mid-2000 to mid-2005, the growth rate was 1.01%.  If we use the higher ending value estimated by Swenson we find that the growth rate was 1.81%.

  Swenson chose to use growth rates much higher than the rates calculated using either Census Bureau or Swenson's own population estimates.  Swenson used 5% as a "Mild" rate, 8% as a "Significant" rate, and 12% as an "Extreme" rate.  Moreover, Swenson used compound calculation.  This is a common approach, but I believe that it is more accurate for Dewey-Humboldt to use a constant rate of increase rather than a compound rate.  I also believe that we should use the rate calculated using the Census Bureau's population estimates as the mild rate and rate calculated using Swenson's population estimate as the Extreme rate.

  Swenson obtained estimates of the number of acres, parcels, and buildings for each of the zoning categories in use in Dewey-Humboldt.  Using the total number of possible building sites Swenson calculated the maximum number of residents that could live in Dewey-Humboldt under the assumption that there would be 2.28 persons per household on each building site.  Swenson then used his growth rates to calculate the number of years to completely fill all available Dewey-Humboldt building sites, the "build-out" period.


Swenson's inflated growth rate and "build-out" estimate

  Using Swenson's "Mild" rate of 5% and a compound calculation of growth, Swenson calculated that all residential properties would "build out" in 29 years reaching a total population of 15,291.  The number of new people would start low, and would end high.  For the 29-year period the average number of new people per year would be 396.8.  Under Swenson's "Extreme" scenario build-out would occur in 12 years, and the average number of new people per year would be 958.9.

  Since growth during the 5-year period from 2000 to 2005 was at most 69 people per year, it seems irrational to say that during the next 29 years there will be 396.8 new people every year, and absurd to say that there could be 958.9 new people every year.

  Swenson concluded that his projections "will be useful in trying to identify how to cope with a quadrupling of population over the next two decades.  Given the "wave" of baby boomers that are [sic] anticipated during the next decade or two, the Extreme growth scenario may be the more likely of the three presented."

  Using exaggerated growth rates Swenson creates a sense of urgency, even emergency when thinking about planning for an exploding population.  Since his beginning population estimate was probably too high, and since his growth rates were three or four times higher than what is actually occurring, it is very important to seek more accurate estimates of our projected growth.


Accurate estimation of D-H future population and years to build-out

  Calculating population growth requires that the birth, death, and migration rates be included.  In some cases these rates are compounded as the number of new people due to births and immigration every year increases along with the population.  "The more you have the more you get."  In other cases the rates are not compounded because birth rates are low and the number of people gained each year is balanced by the number of people dying or moving away.  Growth may be occurring, but the rate is steady rather than accelerating.

  Additions from births are relative few in Dewey-Humboldt, because a large proportion of our population is above child-bearing age.  Moreover, as build-out is approached, emigration, which is already very high for our young people, will increase as children leave Dewey-Humboldt to seek education, employment, and desirable home sites.  If we assume that emigration and deaths are balancing births, the average number of new people being added to the Dewey-Humboldt population by immigration each year is very likely to remain constant or decline over time.

  With constant growth it is pretty easy to calculate the number of years to reach "build-out."  In my analysis I did this using the Census Bureau population figures and then again using Swenson's population figures.  I am calling the Census Bureau results the Mild growth rate and Swenson results the Extreme rate.  Assuming that we do not drastically change our zoning laws to permit more homes than current zoning will allow, the time required to reach build out will probably be somewhere in between my mild and extreme rates.  If we change our zoning laws to permit all lots to be split smaller and smaller to allow more and more homes the rate of growth will be greater.  If we switch to a high-density standard our final build-out population could exceed 100,000, and growth would be extremely fast.

  Mild rate: Using the Census Bureau figures we see that the Dewey-Humboldt population during the period from mid-2000 to mid-2005 grew from 3,440 to 3,613.  Dividing the difference of 173 by 5 we can see that an average of 35 people were added each year.  Assuming that this number will remain constant, the time it will take to reach the "build-out" population of 15,291 will be 339 years [(15,291-3,440)/35].

  Extreme rate:  Using Swenson's population estimate the average number of people added each year was 69.  [((3,784-3,440) =344)/5].  Again assuming that the rate will remain constant, the time to reach build-out will be 167 years [(15,291-3,784)/69].


Comparing Dewey-Humboldt Growth to other Arizona Towns and Cities

  How do the Dewey-Humboldt rates compare to other Arizona cities and towns?  Using the Census Bureau estimates for 89 Arizona incorporated places I found that the average growth rate from mid-2000 to mid-2005 was 2.37%.  Rates varied from 57% for Queen Creek, a town of 5,434, to -2.55% for Clifton, a town of 2,265.

  Towns and cities with growth rates around 5% included Chino Valley, Carefree, Kingman, Peoria, Oro Valley, Show Low, and Casa Grande.  Prescott Valley grew at a rate of 8.1%; Prescott grew at a rate of 3.78%.  Towns like Dewey-Humboldt that grew at a 1% to 2% rate included Tucson, Paradise Valley, Camp Verde, Flagstaff, Williams, Clarkdale, and Sedona.  Jerome grew from 329 to 340, a rate of .85%, and Cottonwood grew at a rate of 3.74%.  Large high-density subdivisions such as Quailwood in Prescott Valley are probably necessary to achieve the higher growth rates.


Number of new houses built each year.

  Some of the misinformation that is being passed around by former Town officials concerns the growth of Dewey-Humboldt as indicated by the number of new homes.  From 2000 to 2005 Swenson estimated that the population increased by about 350.  If we use the value of 2.28 persons per household, the number of new houses for the five-year period was 154, or 31 each year.  We know that a housing boom occurred in 2004-2005.  During that period the number of building permits was perhaps 100 per year.  The number of permits issued declined sharply in 2006.  Though quite a few new houses will be completed in 2006, it is obvious that the former Mayor's repeated claim of 500 new houses per year was totally wrong.


Conclusion:  The value of accurate "build-out" projections

  The slow growth that is occurring in Dewey-Humboldt is a fact.  There was a small boom in 2004-2005, but most Realtors would have to admit that in mid 2006 it appears to be ending.  With current zoning limits our Town and our neighboring communities should not expect problems due to rapid growth.  We will not have an explosive need for services.  We will add kids to the schools very slowly.  Our need for emergency services will grow very slowly.  Our requirements for all amenities will grow slowly.  There will be time for all the service providers to keep up.

  Knowing the time it will take to approach build out we can visualize our town at specific points in the future.  The American Planning Association and Certified Planners everywhere are recommending that urban areas let their planning time scales be 100 to 200 years.  Since we can see what our population will be in 100 to 200 years we have a great opportunity to make plans now for the Dewey-Humboldt that future generations will experience.  Now is the time to leave a legacy of good planning for which our first town government can be remembered and revered.


The Next Step

  A chart of D-H growth projected through 2101 is attached.  To avoid underestimating growth, I prepared the chart using the extreme growth rate and Swenson's higher population estimate for 2005.  The projections in this chart can be checked each year using Census Bureau estimates, and they can be verified and adjusted in 2010, and at every subsequent Census.

  Fairly accurate counts of births, deaths, immigrants and emigrants could be acquired with a few days work.  The Town Council could employ a professional demographer from outside our area, say from NAU or ASU, to make more precise projections.

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1.  Swenson, Roger.  January, 2006.  Town of Dewey-Humboldt Land Use and Land Development Analysis.  Staff Report.

2.  Wilson, Edward O., and William H. Bossert.  1971.  A Primer of Population Biology.  Sinaur Associates, Stamford, Connecticut.  192 pp.

3.  Population Division, U.S. Census Bureau.  June 21, 2006.  Table 4.  Annual Estimates of the Population for Incorporated Places in Arizona.  April 1, 2000 to July 1, 2005.




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