Cope's Rule Size Trend Slope
Fit signed log body-size trend on an explicit increasing forward-time axis and report multiplicative change; sampling, taxonomic replacement and phylogeny can confound any Cope-rule interpretation.
Description
A body-size trend can be fitted multiplicatively by using log size.
A body-size trend can be fitted multiplicatively by using log size. Time direction determines the sign's interpretation.
Fit signed log body-size trend on an explicit increasing forward-time axis and report multiplicative change; sampling, taxonomic replacement and phylogeny can confound any Cope-rule interpretation.
When to use Cope's Rule Size Trend Slope
Use this tool to fit signed log body-size trend on an explicit increasing forward-time axis and report multiplicative change; sampling, taxonomic replacement and phylogeny can confound any Cope-rule interpretation.
Prepare the fossil measurements or occurrence records and the chosen calibration parameters. Retain the stated coordinate, age and measurement conventions.
How to use Cope's Rule Size Trend Slope 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 timesMyrForward, measuredBodySizes using the field table and calculation rules, then run the tool.
- Read logSizeChangePerMyr, multiplicativeSizeChangePerMyr, fitRSquared. 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 |
|---|---|---|---|
| timesMyrForward | Times myr forward | list of number | Required |
| measuredBodySizes | Measured body sizes | list of number | Required |
Use an increasing forward-time axis and aligned positive sizes. Regress natural-log size, returning signed slope, per-Myr multiplier and R².1
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.
multiplicative change/Myr = exp(log-size regression slope) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| logSizeChangePerMyr | Log size change per myr | number |
| multiplicativeSizeChangePerMyr | Multiplicative size change per myr | number |
| fitRSquared | Fit r squared | number |
{
"input": {
"timesMyrForward": [
0,
1,
2
],
"measuredBodySizes": [
1,
2.718281828459045,
7.38905609893065
]
},
"output": {
"logSizeChangePerMyr": 1,
"multiplicativeSizeChangePerMyr": 2.718281828459045,
"fitRSquared": 1
}
}Limitations and assumptions
Sampling, taxonomic replacement and phylogeny can confound a Cope-rule interpretation.
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.
Alternative or Complementary methods
Use Body Size Frequency Log-Normal Fit Check: Summarize empirical population moments in log body-size space with a caller skewness screen; not a formal distribution goodness-of-fit test or proof of lognormality. For a complementary task, use Net Diversification Rate: Calculate signed event/exposure net diversification with independent origination/extinction counting error; unlike log endpoint richness growth, this requires explicit event and lineage-time inventories.
References
-
Cope's Rule Size Trend Slope — tool.io
Similar or alternative tools
- Body Size Frequency Log-Normal Fit Check
Summarize empirical population moments in log body-size space with a caller skewness screen; not a formal distribution goodness-of-fit test or proof of lognormality.
- Net Diversification Rate
Calculate signed event/exposure net diversification with independent origination/extinction counting error; unlike log endpoint richness growth, this requires explicit event and lineage-time inventories.