Beside a fallen log
When a leaf decays,
where does it go?
A fallen log is alive with decomposers. Start with a simpler question: how might the mass of one batch of fallen leaves change over time?
Solid and dashed curves show percentages of the same starting mass. They can overlap. The vertical line marks your selected time; values below describe both curves.
Solid green: still in the tracked litter. Hatching: no longer in that pool. The hatching does not specify where matter went.
Two half-lives may lie beyond the 12-unit chart. The preset is disabled in that case.
Time for half the remaining litter mass to leave this pool. A shorter half-life means faster decay. This is a model parameter, not a measured setting for this log.
At your selected time
- Still in the litter
- 50.0 g
- Left the tracked litter
- 50.0 g
- Fraction remaining
- 50.0%
- Reference remaining
- 70.7 g
Loss from a pool is a transfer
Fungi and bacteria help break down dead wood. During decomposition, carbon can be respired as carbon dioxide; other material can enter organisms, dissolved material, or soil. A smaller litter sample does not mean its matter has ceased to exist.
This experiment tracks only how much dry mass remains in an imagined batch of litter. It does not split the lost mass into carbon dioxide, soil, or living things. In particular, lost dry litter mass is not the same measurement as carbon emissions.
Why does the curve flatten?
The model removes the same fraction over equal intervals, rather than the same number of grams. Starting with 100 g, one half-life leaves 50 g; the next leaves 25 g, then 12.5 g. The amount lost per interval shrinks as less remains. With this equation the pool approaches zero without reaching it at a finite time.
The equation is M(t) = M₀ exp(−kt) = M₀ × 2−t/H, where H is half-life and k = ln(2)/H. There are no new inputs. Both the chosen rate and the reference rate stay constant throughout each hypothetical trajectory. Changing a control redraws the whole scenario; it is not a treatment applied midway.
What a real log adds
A real log contains different materials, moisture conditions, and communities of organisms. Its rate can change over time. Fragmentation and leaching can also move material out of a measured sample. This single-pool litter model has no changing weather, inputs, microbial growth, or resistant residue. Its time units are not calibrated years, and its curve is not a countdown for this park’s log.
Sources
- Max Planck Institute for Biogeochemistry: Olson’s model — the first-order pool equation and the no-input exponential case.
- Tláskal and colleagues, 2021 — complementary roles of fungi and bacteria in deadwood decomposition and carbon cycling.
- US Forest Service: deadwood in the carbon cycle — interacting biological and physical drivers.
Original illustration and implementation. Values are hypothetical examples, not fitted field data.