Collector Curve Species Accumulation Extrapolator
Fit a reciprocal-linearized Michaelis–Menten collector curve and flag prediction extrapolation; distinct from existing one-segment new-species/effort slope, with no guaranteed asymptotic true diversity.
Description
A collector curve relates observed richness to sampling effort.
A collector curve relates observed richness to sampling effort. A saturating Michaelis–Menten model can represent diminishing additions.
Fit a reciprocal-linearized Michaelis–Menten collector curve and flag prediction extrapolation; distinct from existing one-segment new-species/effort slope, with no guaranteed asymptotic true diversity.
When to use Collector Curve Species Accumulation Extrapolator
Use this tool to fit a reciprocal-linearized Michaelis–Menten collector curve and flag prediction extrapolation; distinct from existing one-segment new-species/effort slope, with no guaranteed asymptotic true diversity.
Prepare the fossil measurements or occurrence records and the chosen calibration parameters. Retain the stated coordinate, age and measurement conventions.
How to use Collector Curve Species Accumulation Extrapolator and understand its results
- Prepare the fossil measurements or occurrence records and the chosen calibration parameters. Retain the stated coordinate, age and measurement conventions.
- Enter collectionEfforts, cumulativeObservedRichness, predictionEffort using the field table and calculation rules, then run the tool.
- Read fittedAsymptoticRichness, fittedHalfSaturationEffort, modelPredictedRichness, isPredictionExtrapolated, reciprocalFitRSquared. 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 |
|---|---|---|---|
| collectionEfforts | Collection efforts | list of number | Required |
| cumulativeObservedRichness | Cumulative observed richness | list of number | Required |
| predictionEffort | Prediction effort | number | Required |
Use positive increasing efforts and aligned positive nondecreasing cumulative richness. Regress reciprocal richness against reciprocal effort, require positive intercept and nonnegative half-saturation, and evaluate positive prediction effort. Flag predictions outside the observed range.1
Each sequence checked for increasing order must contain at least two strictly increasing values. The least-squares fit needs at least two aligned observations and a varying independent variable; a constant dependent variable has reported R² of 1.
richness = asymptote × effort/(half-saturation effort + effort) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| fittedAsymptoticRichness | Fitted asymptotic richness | number |
| fittedHalfSaturationEffort | Fitted half saturation effort | number |
| modelPredictedRichness | Model predicted richness | number |
| isPredictionExtrapolated | Is prediction extrapolated | boolean |
| reciprocalFitRSquared | Reciprocal fit r squared | number |
{
"input": {
"collectionEfforts": [
1,
2,
4
],
"cumulativeObservedRichness": [
5,
6.666666666666667,
8
],
"predictionEffort": 8
},
"output": {
"fittedAsymptoticRichness": 10.000000000000002,
"fittedHalfSaturationEffort": 1.0000000000000004,
"modelPredictedRichness": 8.888888888888891,
"isPredictionExtrapolated": true,
"reciprocalFitRSquared": 1
}
}Limitations and assumptions
Reciprocal fitting changes error weighting; asymptotic richness is not guaranteed true diversity.
Numbers and computed results must be finite; overflow 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. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Good's U Sample Coverage: Compute Good’s U=1-f1/N on positive observed abundance counts; coverage estimates sampled individual probability mass, not species completeness or a guarantee that rare taxa were found. For a complementary task, use Shareholder Quorum Subsampling Coverage: Audit caller taxon draw order to a simple observed-frequency share quorum; explicitly not a full randomized shareholder-quorum subsampling algorithm with dominant-taxon and singleton coverage conventions.
References
Similar or alternative tools
- Good's U Sample Coverage
Compute Good’s U=1-f1/N on positive observed abundance counts; coverage estimates sampled individual probability mass, not species completeness or a guarantee that rare taxa were found.
- Shareholder Quorum Subsampling Coverage
Audit caller taxon draw order to a simple observed-frequency share quorum; explicitly not a full randomized shareholder-quorum subsampling algorithm with dominant-taxon and singleton coverage conventions.