Self Thinning Slope
Fit log mean-stem dry mass versus log stem density to observed self-thinning samples; unlike Reineke DBH stand density, no fixed -3/2 slope or maximum-density relationship is imposed.
Description
Self-thinning observations relate mean stem mass to density in logarithmic coordinates.
Self-thinning observations relate mean stem mass to density in logarithmic coordinates. Fitting the observed relationship does not impose a universal −3/2 slope.1
Fit log mean-stem dry mass versus log stem density to observed self-thinning samples; unlike Reineke DBH stand density, no fixed -3/2 slope or maximum-density relationship is imposed.
When to use Self Thinning Slope
Use this tool to fit log mean-stem dry mass versus log stem density to observed self-thinning samples; unlike Reineke DBH stand density, no fixed -3/2 slope or maximum-density relationship is imposed.
Gather the tree inventory, plot measurements or model parameters. Check diameter, area, time and moisture conventions; keep paired observations aligned.
How to use Self Thinning Slope and understand its results
- Gather the tree inventory, plot measurements or model parameters. Check diameter, area, time and moisture conventions; keep paired observations aligned.
- Enter stemDensitiesPerHa, meanStemDryMassKg using the field table and calculation rules, then run the tool.
- Read logMassLogDensitySlope, logFitRSquared. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| stemDensitiesPerHa | Stem densities per ha | list of number | Required |
| meanStemDryMassKg | Mean stem dry mass kg | list of number | Required |
Pair positive density and mean dry mass observations, with at least two samples and varying log density. Fit ordinary least squares and return slope and R² in log coordinates.
The least-squares fit needs at least two aligned observations and a varying independent variable; a constant dependent variable has reported R² of 1.
log mean stem dry mass=intercept+slope × log stems/ha Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| logMassLogDensitySlope | Log mass log density slope | number |
| logFitRSquared | Log fit r squared | number |
{
"input": {
"stemDensitiesPerHa": [
100,
200,
400
],
"meanStemDryMassKg": [
8,
4,
2
]
},
"output": {
"logMassLogDensitySlope": -1.0000000000000004,
"logFitRSquared": 1
}
}Limitations and assumptions
The fit does not establish a maximum-density envelope or causal thinning law.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Thinning Q-Factor Diameter Step: Normalize caller descending geometric q targets over equally spaced diameter classes, conserving supplied total density; these are continuous planning targets, not actual integer trees or an ecological prescription. For a complementary task, use Weibull Diameter Distribution: Predict Weibull diameter-class count inventory under supplied shape/scale, retaining below/above surveyed class tails; not random sampling or inferred stand-table coefficients.
References
-
Self Thinning Slope — tool.io
Similar or alternative tools
- Thinning Q-Factor Diameter Step
Normalize caller descending geometric q targets over equally spaced diameter classes, conserving supplied total density; these are continuous planning targets, not actual integer trees or an ecological prescription.
- Weibull Diameter Distribution
Predict Weibull diameter-class count inventory under supplied shape/scale, retaining below/above surveyed class tails; not random sampling or inferred stand-table coefficients.