Propagate a calibration interval without inventing a fossil date

1. Orient: Propagate a calibration interval without inventing a fossil date

Molecular differences can help estimate divergence time only through a model connecting change, rate and time. Under a strict equal-rate clock, two lineages diverging for time t accumulate pairwise expected divergence d=2rt. The factor two represents both lineages, not an arbitrary correction.

2. Explain the evidence and inference model

The original reference divergence0.04 is paired with a stipulated calibration time10±b million years. An older reference time implies a lower per-lineage rate. For an exact target divergence d, target time d/(2r) increases as the rate decreases. Propagate monotonic bounds in the correct direction rather than averaging endpoints and calling them certainty.

A confidently placed fossil ordinarily constrains a minimum lineage age; the lineage may predate its earliest known fossil. A symmetric10±2 interval therefore requires additional justification and is supplied here only as an exercise input. Fossil identity, stratigraphic age and node assignment are distinct evidence requirements.

Rate shifts, multiple substitutions at the same site, unequal lineage rates and uncertainty in the tree can invalidate a simple clock. Percent sequence difference is not always equal to substitutions per site. The displayed interval excludes these effects and has no assigned confidence probability; a narrow conditional interval is not comprehensive historical certainty.

3. Reconstruct a worked example

Reference0.04 and calibration8–12 Myr give rate bounds0.04/(2×12)=0.0016667 to0.04/(2×8)=0.0025 substitutions/site/Myr/lineage. Target0.06 then gives12–18 Myr, nominal15 Myr.

4. Predict and investigate

Predict first: Does an older calibration imply a faster rate or a slower rate for the same reference divergence?

Compare half-width0,2 and4 at target0.06. Reconstruct both rate and time bounds, then explain why a fossil known only to be at least8 Myr old does not justify the symmetric8–12 Myr interval.

Retain the complete matrix, topology, branch lengths or detection assumptions with the first prediction and all conflicting results. These original hypothetical data are not actual specimen observations or measured evolutionary histories.

5. Transfer and defend a changed case

Apply the mechanism to a changed case

Using reference divergence0.04 and calibration8–12 Myr, find the target-time interval for divergence0.08.

Retain your calculation, units and assumptions in the lesson notebook before opening this public practice response.

Compare a worked response

Target divergence is twice the reference, so the strict-clock interval is16–24 Myr. This scaling inherits every calibration and rate assumption; no confidence level or real fossil chronology follows.

6. Reflect and preserve uncertainty

Explain which conclusion is conditional on the model, identify an alternative and propose independent discriminating evidence. Use the General Biology II workspace to preserve a first argument, human critique and revision. Public practice and submitted prose do not establish independent phylogenetic, sampling or practical competence.

Supporting scientific reference, checked 30 October 2026. Original prose, numerical packets and diagrams; no source artwork or exercise is reproduced and no organism handling is requested.