Combine calibrated fossil ranges without ignoring conflicting evidence

1. Define the time interpretation

Fossil succession can correlate strata because organisms appeared, changed and disappeared through time. Numerical ages for ranges require independent calibration. An observed fossil range is not automatically a globally synchronous biological boundary: sampling, environment, preservation and reworking affect what is found.

2. Connect observations, mechanism and assumptions

This fictional library gives taxon A 90–100 Ma, B 84–96 Ma and C 80–91 Ma. Assuming correct identification and no reworking, co-occurrence requires an age in the intersection of their ranges. A and C overlap only 90–91 Ma, while A and B overlap 90–96 Ma.

An independent coeval ash layer is dated 92±b Ma using a hard interval. Intersect that interval with the fossil constraint. If their younger bound exceeds their older bound, there is no joint admissible age. Do not turn that empty set into a negative duration or average incompatible endpoints.

An older fossil eroded into a younger deposit can violate the unreworked assumption without invalidating evolution or radioactive decay. A mineral age in an inherited grain can similarly precede deposition. The appropriate response is a source/context audit and an explicit competing explanation, not automatic rejection of whichever observation is less convenient.

3. Reconstruct the worked packet

For A+C the fossil interval is 90–91 Ma. Ash 92±1 gives 91–93 Ma, leaving the boundary age 91 Ma as a single admissible point. Ash 92±0 instead conflicts with the fossil interval.

4. Predict and investigate

Predict first: What should happen when two independently supplied age constraints do not overlap?

Compare all three taxon pairs at the same ash uncertainty, then tighten the ash interval. Retain empty intersections explicitly. Propose reworking, incorrect identification and non-coeval ash as distinguishable hypotheses rather than interchangeable excuses.

5. Test a changed case

Apply the evidence to a changed case

For B+C and ash 92±2 Ma, what is the shared interval? What does an exact boundary mean?

Retain the chronology, calculations and assumptions before opening public feedback.

Compare a worked response

B+C overlap 84–91 Ma, intersecting ash 90–94 Ma in 90–91 Ma. An interval shrinking to a point would be exact only under the supplied hard bounds and assumptions, not zero real-world uncertainty.

6. Retain a defensible observation notebook

Preserve the original prediction, complete observations/relationships, calculations, uncertainty convention and rejected alternative. All sections and isotope packets here are invented instructional cases, not actual mapped outcrops or measured isotope analyses. Public practice is not independent reasoning review or supervised field competence.

Method and mechanism reference, checked 30 October 2026. Original prose, diagrams, numerical packets and exercises.