Chapter 14 Population structure and demography

Skills this lab builds. 4DEE: Core Ecological Concepts → Populations. Ecology Practices → Natural history; Fieldwork; Data analysis and interpretation. Cross-Cutting Themes → Space & Time. BioSkills: Process of Science → “Describe sources of error and uncertainty in data”; Modeling & Simulation → Purpose of Models.

A ponderosa pine takes decades to do anything you could measure in a semester. So ecologists who study long-lived organisms almost never watch a population change. Instead they substitute something else for time — and then defend the substitution.

That is the skill this lab teaches. You will visit a population once, and reconstruct its history from what is standing in front of you.

14.1 Choosing a track

This lab runs in three versions. They use different populations and the same analysis. Your instructor will tell you which one you are doing.

Track Where What you measure Weather
A. Campus ponderosa Walking distance from class Trunk diameter of every tree in your plot Works in snow
B. Centennial Forest NAU’s teaching forest, short drive Same, across a management contrast Works in snow
C. Virtual cemetery Indoor, computer lab Age at death from online records Indoor

All three produce the same four-column datasheet, so the analysis script does not care which one you did.

14.2 Background

14.2.1 Substituting structure for time

Imagine two forests. In the first, there are many small trees, fewer medium ones, and a handful of large ones. In the second, there are almost no small trees, and nearly all of the trees are the same middling size.

Neither forest told you its history. But you can read it anyway.

The first forest has a reverse-J size distribution — lots of young individuals constantly replacing the few that die. That is what a population that has been reproducing steadily for a long time looks like.

The second forest has a gap where the small trees should be. Something stopped recruitment. And because all the survivors are a similar size, they probably established at roughly the same time, in a single pulse.

Here is why that matters in Flagstaff. Fire scars at Chimney Spring, just northwest of town, record fires every 4.9 years on average between 1540 and 1876 (Fort Valley Experimental Forest records). Frequent, low-intensity fire killed pine seedlings before they could grow into the canopy, and the forest stayed open. After 1876 — grazing removed the fine fuels that carried fire, and later, fire suppression became policy — the fires stopped. Seedlings that would have burned survived instead.

The result is a size-class distribution with a century of management history written into it, standing on the ground you can walk to from this classroom.

14.2.2 The static life table, and its assumption

If you are willing to assume the population has been growing at a constant rate with constant mortality — a stable stage distribution — then a single snapshot of size classes can be converted into a survivorship curve, as though you had followed one cohort from birth to death.

That assumption is often wrong, and the Flagstaff ponderosa forest is a good example of how wrong it can be. A recruitment pulse after 1876 violates it badly.

This does not make the method useless. It makes the method conditional, and knowing the condition is the difference between a number and a number you trust. Part of your assignment is to say whether your population plausibly meets the assumption, and what it would mean for your conclusions if it does not.

14.2.3 Survivorship curves

Plotting the log of the number of survivors against age gives one of three shapes:

  • Type I — most die old. Mortality is concentrated late.
  • Type II — constant risk of dying at every age. A straight line on a log scale.
  • Type III — most die young. Enormous early mortality, then a few survivors persist.

A pine that produces thousands of seeds and recruits a handful of trees is a textbook Type III. A modern human population is close to Type I. If you run Track C, you will generate one of these from real records.

14.3 Track A — Campus ponderosa

14.3.2 Objectives

To infer the recent history of a tree population from its size structure, and to state the assumptions that inference depends on.

14.3.3 Materials

  1. Diameter tape, or a standard tape measure
  2. Flagging or pin flags to mark your plot corners
  3. A 30 m tape for laying out the plot
  4. Datasheet and clipboard
  5. Optional: a second person’s independent measurement of the same tree

14.3.4 Procedure

  1. Lay out a plot. Working in groups of 3–5, establish a 20 m × 20 m plot in the stand your TA assigns you. Mark all four corners before you measure anything.

  2. Measure every tree. For every ponderosa pine rooted inside the plot, measure the diameter at breast height (DBH) — 1.37 m above the ground on the uphill side. Record each tree as its own row. Do not round to convenient numbers.

  3. Include the small ones. Every tree above 2.5 cm DBH counts. The small trees are the entire story of this lab, and they are the ones people skip because they are tedious. If a stem is below 2.5 cm, record it as a seedling in your notes but not in the datasheet.

  4. Check your measurement error. Have a second person re-measure five trees without looking at your numbers. Record both. You will report the difference.

  5. Optional — age from whorls. Ponderosa pine puts out one whorl of branches per year. On saplings short enough to see the whole stem, count the whorls from the base to the tip to estimate the tree’s age, and measure the distance between successive whorls to recover its growth history. One visit, one tree, a decade of data.

14.3.5 Recording your data

Every track uses the same four columns:

Site,Group,IndividualID,Value,ValueType

For Track A, Value is DBH in centimetres and ValueType is DBH_cm. Use Group for whatever you are comparing — plot number, or open stand versus dense stand.

14.4 Track B — Centennial Forest extension

The Centennial Forest is NAU’s own research, teaching and demonstration forest, and it contains stands under different management histories: thinned, burned, and untreated.

Run the identical protocol in two contrasting stands and use Group to distinguish them. This is space-for-time substitution — you are not watching one stand change, you are comparing stands that have travelled different distances from the same starting point.

Access requires a permit; your instructor arranges this in advance.

14.5 Track C — Virtual cemetery (indoor fallback)

When the weather makes fieldwork impossible, this track builds the same life table from human records instead of trees. It is adapted from Lanza’s TIEE module (see Acknowledgements), which uses gravestone records, online cemetery databases, and census data.

  1. Choose two groups to compare — two time periods, two regions, or two categories your TA approves.
  2. Collect at least 50 individuals per group from an online cemetery database, recording birth year and death year.
  3. Compute age at death for each individual.
  4. Record one row per individual, with Value as age at death in years and ValueType as AgeAtDeath_yr.

Because the analysis is shared, everything you do from here is identical to Track A.

14.6 Analysis

14.6.1 One setting you must get right

Near the top of the script there is a line that reads record_type. Set it to "standing" for Tracks A and B, and "death" for Track C.

This is not a formatting detail. In Track A, every tree you measured is alive — your counts are survivors. In Track C, every record is a death — your counts are deaths. Survivors and deaths do not become a life table by the same arithmetic, and if you set this wrong the script will still run and still draw you a survivorship curve. It will just be wrong in a way that looks entirely reasonable.

Deciding which kind of data you collected is part of the analysis, not a preliminary to it.

14.6.2 Running the script

Open PopulationStructure.R. It will:

  1. Bin your individuals into classes
  2. Plot the distribution so you can see its shape
  3. Build a static life table
  4. Plot survivorship on a log scale so you can identify the type

Look at the distribution before you compute anything. The shape is the result. The life table is how you put numbers on it.

14.7 Assignment

Turn in to your TA:

  1. Your size-class (or age-class) distribution figure, with a one-sentence description of its shape.
  2. Your static life table.
  3. Your survivorship curve, and which type it most resembles.
  4. Your measurement-error check: the mean absolute difference between the two observers, and whether it is large enough to change your conclusions.
  5. The assumption paragraph. State whether your population plausibly has a stable stage distribution. If you think it does not, explain what specifically violates it, and say which of your conclusions survive anyway.

Item 5 is worth as much as items 1–4 combined. Anyone can bin numbers. The skill is knowing what the bins are allowed to tell you.

14.8 Acknowledgements

Track C is adapted from: Lanza, Janet. 2012. Demography from physical cemeteries, “virtual cemeteries,” and census data. Teaching Issues and Experiments in Ecology, Vol. 8, Experiment #1. https://www.esa.org/tiee/vol/v8/experiments/lanza/abstract.html

Fire return interval figures for Chimney Spring are from the Fort Valley Experimental Forest centennial volume, Olberding and Moore (eds.), 2008. https://www.fs.usda.gov/rm/pubs/rmrs_p055/rmrs_p055_038_047.pdf