Death Assemblage to Living Community Offset Corrector
Invert a supplied identifiable nonnegative living-to-death preservation/mixing response and report reconstruction residual; negative physical solutions error rather than clipping, and response is not inferred from one assemblage.
Description
Preservation and mixing can transform a living community into a death assemblage.
Preservation and mixing can transform a living community into a death assemblage. Inverting a supplied response requires an identifiable system.
Invert a supplied identifiable nonnegative living-to-death preservation/mixing response and report reconstruction residual; negative physical solutions error rather than clipping, and response is not inferred from one assemblage.
When to use Death Assemblage to Living Community Offset Corrector
Use this tool to invert a supplied identifiable nonnegative living-to-death preservation/mixing response and report reconstruction residual; negative physical solutions error rather than clipping, and response is not inferred from one assemblage.
Prepare the fossil measurements or occurrence records and the chosen calibration parameters. Retain the stated coordinate, age and measurement conventions.
How to use Death Assemblage to Living Community Offset Corrector 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 observedDeathAssemblageCounts, livingToDeathResponseMatrix using the field table and calculation rules, then run the tool.
- Read inferredLivingCommunityCounts, reconstructedDeathCounts, maximumAbsoluteReconstructionResidual. 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 |
|---|---|---|---|
| observedDeathAssemblageCounts | Observed death assemblage counts | list of number | Required |
| livingToDeathResponseMatrix | Living to death response matrix | list of list of number | Required |
Use a nonnegative square response for 1–16 states and aligned nonnegative observations. Solve by pivoted Gaussian elimination; reject singular or poorly conditioned matrices and negative physical solutions. Reconstruct observations and report maximum absolute residual.1
response matrix × inferred living counts = observed death counts Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| inferredLivingCommunityCounts | Inferred living community counts | list of number |
| reconstructedDeathCounts | Reconstructed death counts | list of number |
| maximumAbsoluteReconstructionResidual | Maximum absolute reconstruction residual | number |
{
"input": {
"observedDeathAssemblageCounts": [
8,
6
],
"livingToDeathResponseMatrix": [
[
1,
0.5
],
[
0,
1
]
]
},
"output": {
"inferredLivingCommunityCounts": [
5,
6
],
"reconstructedDeathCounts": [
8,
6
],
"maximumAbsoluteReconstructionResidual": 0
}
}Limitations and assumptions
The response must be independently supplied; no clipping or response estimation is performed.
Numbers and computed results must be finite; overflow produces an error. Matrices are limited to 128 rows and 128 entries per row; other numeric lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Taphonomic Time Averaging Mixing Model Estimate: Combine supplied age-distribution components by the law of total variance, distinguishing within/between temporal mixing; no inferred depositional duration or deconvolved event dates. For a complementary task, use Sampled-in-Bin Occurance Normalizer: Normalize sampled-in-bin occurrence counts by measured rock exposure and caller recovery probability, not by unequal bin duration alone; no unsampled-bin imputation.
References
Similar or alternative tools
- Taphonomic Time Averaging Mixing Model Estimate
Combine supplied age-distribution components by the law of total variance, distinguishing within/between temporal mixing; no inferred depositional duration or deconvolved event dates.
- Sampled-in-Bin Occurance Normalizer
Normalize sampled-in-bin occurrence counts by measured rock exposure and caller recovery probability, not by unequal bin duration alone; no unsampled-bin imputation.