Quantifying uncertainty in tree biomass
Ecology & Environment 2026 · material for the class after the Miyawaki field visit and for the class project
Four interactive pages. They take you from a dice roll to a biomass number for a whole plot, with an honest statement of how sure you are. They prepare you for the class project.
Read the pages in this order
Each page builds on the one before it. Do not skip ahead. Open the pages on a laptop or tablet if you can; the charts are small on a phone.
Page 1 · start here
From Dice to a Tree
What "probability 1/6" really means; guessing a hidden die from its rolls; expected value; why an average has less spread than a single roll; all of it applied to 250 hypothetical readings of one tree; then the bootstrap, and Monte Carlo for a tree measured only once.
Page 2 · after page 1
How an Equation Is Born
The tree weight equation read one piece at a time, seen as a picture on log axes, then built from harvested trees. Its two kinds of doubt: a and b are not known exactly, and a real tree is not on the line.
Page 3 · after page 2
Monte Carlo, One Tree
Roll five dice, build a pile of 20,000 possible answers for one tree, read the pile, find out which source of error matters most, and learn how to write the result.
Page 4 · after page 3
From 25 Trees to a Plot
Each tree is ± 40 %, but the total of 25 trees is only ± 12 %. A three-tree example worked by hand shows why, then the 25 trees, then what the per-hectare number means.
How to use each page
- Read the "Words used on this page" box first. It is at the top of every page and explains every word and short form used below it.
- Press Step once or twice and watch what a single step does. Only then press Play at slow speed.
- Press Fast-forward once you understand one step. It does all the draws of that panel at once, from a few hundred on page 1 to 20,000 on pages 3 and 4.
- Change the numbers and play. Type a different tree, switch a die off, make an error bigger or smaller, and watch what happens to the pile. Nothing you do can break a page; Reset brings it back.
- Read the "What to notice" box at the bottom before moving to the next page.
For the project
- Page 2 shows how species, diameter, height and wood density go into the equation.
- Page 3 is the method for one tree: choose the size of each die from your own readings, run the dice, report the median and the 95 % interval, and name the biggest source of error.
- Page 4 is the method for the whole plot: add the trees round by round, keeping shared errors (the equation, the density value of a species) apart from independent errors (your readings, the scatter of each tree).
- Write the result the way page 3, Panel E shows. If you convert to per hectare, add the warning from page 4, Panel D.
The pages run entirely in your browser. Nothing is uploaded. The numbers on them are examples. Replace them with your own field data for the project.