Edmonton data lessonHow fast does an Edmonton bur oak grow? A line, a curve and a warning
The City of Edmonton keeps an inventory of the boulevard and open space trees it owns, with a planting date and a trunk diameter for each. Students turn one species into a growth model, fit a straight line and an exponential curve, and discover that the curve that fits best is the one that fails first. The averages, fits and projections below are ours.
The dataset is called Trees, published by the City of Edmonton, which describes it as a map of boulevard and open space trees owned and maintained by the City, adding that not all City-owned trees are captured on this map. When we queried it on 23 October 2026 it held 482,603 trees. Rather than download every record, we asked the City’s data service for the average diameter at breast height of bur oaks, grouped by planting year.
Half the inventory shares one planting date
Before any modelling, a check: 258,504 trees, or 53.6 percent of the file, carry the planting date 1 June 1990, against 15,767 for the next most common year, 2014. Among bur oaks, 1,992 trees share that date. A single day cannot account for half a city’s trees, so we treat the date as a stand-in for “unknown” and leave 1990 out. The file does not say what the date means; that reading is ours.
Bur oaks in the City of Edmonton Trees inventory: our grouped averages by planting year (selected years), with age taken as 2026 minus the planting year. Queried 23 October 2026| Planted in | Age (years) | Mean diameter (cm) | Trees |
|---|
| 2004 | 22 | 16.0 | 169 |
| 2008 | 18 | 12.4 | 369 |
| 2012 | 14 | 9.2 | 449 |
| 2016 | 10 | 8.0 | 1,047 |
| 2020 | 6 | 6.0 | 975 |
| 2024 | 2 | 5.6 | 1,325 |
| 2025 | 1 | 5.6 | 1,289 |
We kept planting years 2004 to 2025 with at least 50 oaks each: 22 points covering 15,848 trees. A least-squares line gives d = 0.5325t + 3.337, about half a centimetre of trunk a year, with r = 0.950 and R squared 0.903. Fitting a straight line to the logarithm of the diameter gives the exponential model d = 4.697(1.0567)t, growth of about 5.67 percent a year, and its R squared is higher, 0.959. Both models come from this short program:import json, math, statistics
with open("by_year_OakBur.json", encoding="utf-8") as f:
years = [(int(r["yr"]), float(r["d"]), int(r["n"])) for r in json.load(f)]
keep = [(2026 - y, d) for y, d, n in years if 2004 <= y <= 2025 and n >= 50]
age = [a for a, _ in keep]
size = [d for _, d in keep]
line = statistics.linear_regression(age, size)
curve = statistics.linear_regression(age, [math.log(d) for d in size])
print("linear: d =", round(line.slope, 4), "t +", round(line.intercept, 3))
print("exponential: d =", round(math.exp(curve.intercept), 3),
"x", round(math.exp(curve.slope), 4), "^ t")
Our two models of bur oak trunk diameter, compared inside and far outside the 1 to 22 year range of the data| Age (years) | Linear model (cm) | Exponential model (cm) |
|---|
| 10 | 8.7 | 8.2 |
| 20 | 14.0 | 14.2 |
| 50 | 30.0 | 74.0 |
| 100 | 56.6 | 1,167 |
Inside the data
From 1 to 22 years the two models stay within about a centimetre of each other, and the curve follows the young trees slightly better, which is why its R squared is higher. On the evidence of the fit alone, a student would choose the exponential.
Outside the data
At 100 years the exponential predicts a trunk more than eleven metres across. A model that grows by the same percentage every year cannot describe a living tree for long, however well it fits the first two decades. The linear model’s 56.6 cm is at least believable.
What age really means
We took age as 2026 minus the planting year, but the file does not say when each diameter was measured. If a tree was last measured years ago, its true age at measurement is smaller. Saying so is part of the answer, not an excuse.
Contains information licensed under the Open Government Licence - City of Edmonton. The inventory is published by the City of Edmonton from its own records and used under the Open Government Licence - Edmonton, which allows commercial use (licence, dataset page). The City of Edmonton does not endorse this page or our classes.
