Olson's Single-Exponential Litter Decay

Jerry Olson's 1963 paper gave decomposition ecology its working equation: litter loses a constant proportion of whatever remains in each equal interval, so mass remaining falls exponentially as $X = X_0 e^{-kt}$. One fitted constant describes a whole litter type. It is still, sixty years on, the most-used relation in the field.

It is also, once again, the same equation as everything else. Radioactive decay is this with $\lambda$ for $k$. Chlorine vanishing down a water main is this exactly. A capacitor discharging through a resistor is this with $1/RC$ for $k$. Light dying away through a canopy or through a coloured solution is this with depth instead of time. Whenever a quantity loses a fixed fraction of itself per unit of the independent variable, this is the solution, and $1/k$ is always the characteristic scale. The familiar rules of thumb transfer intact: the half-life is $\ln 2 / k$, about three time constants take you to 95 %, five take you to 99 %.

The range of $k$ is the most important fact about it, and it spans two orders of magnitude. Boreal spruce needles and montane conifer litter sit at 0.02 to 0.2 per year — half-lives of three to thirty years — which is why the forest floor at high latitudes is thick and holds most of the ecosystem's carbon. Temperate deciduous leaf litter runs 0.2 to 0.6. Lowland tropical rainforest litter runs 1 to 4 per year, so a leaf that falls in January is largely gone by December and there is barely a forest floor to speak of. Borrowing a $k$ across climates is the fastest way to be wrong by a factor of fifty. Within a climate, litter quality does the rest: the lignin-to-nitrogen ratio predicts $k$ better than any other single measurement, which is why nitrogen-rich alder leaves disappear and lignin-rich oak leaves linger in the same wood in the same year.

Now the honest limitation, which is structural rather than a matter of precision. Litter is not one substance. It is at least two pools: a labile fraction of sugars, starches and soluble phenolics that leaches and respires away in weeks, and a recalcitrant fraction of lignin and lignin-bound nitrogen that takes decades. A single exponential fits the first year beautifully, because the first year is dominated by the easy pool leaving. It fits the tail badly. Extended, it insists the litter eventually disappears entirely, whereas real mass loss stalls at an asymptote somewhere around 10 to 30 % of the original. Fit a single $k$ through the early data and extrapolate to year five and the model will confidently tell you the litter is gone while you are standing on it. Double-exponential and asymptotic models exist for exactly this reason, and that stubborn residue is not a rounding error — it is where stable soil organic matter comes from.

Three field cautions when fitting. Ash-correct the masses, because litter picks up mineral soil and an uncorrected final weight understates the loss. Mesh size decides which decomposers get in — a fine mesh excludes soil fauna and can halve the apparent rate. And litterbags sometimes gain weight: fungal hyphae import carbon, fine roots grow in, soil works its way through. That is a sampling artefact, and no $k$ fits it.