Separate a community from its observation process

Define the community evidence

Different cells or molecules need not contribute equally to an observed community dataset. Recovery, lysis susceptibility, amplification, marker-copy differences and classification can create class-specific representation. A read fraction is therefore not automatically a cell fraction. This lesson interprets already supplied recovery factors and gives no extraction or amplification procedure.

Connect mechanism and boundary

The original true record contains A30 and B70 units. Independently supplied recovery probabilities rA and rB produce expected observed counts 30rA and 70rB. The observed A fraction is 30rA/(30rA+70rB). Because these are expectations, fractional units are allowed; actual counts would also have sampling variation not included in this deterministic comparison.

If the recovery factors are genuinely known for this record, dividing each observed count by its factor reconstructs the original counts. If the factors are unknown, many true compositions could produce the same observations. Calling the inverse correction calibrated without independent evidence would simply substitute an assumption for a measurement.

Even validated average factors may vary with sample matrix or class state. A useful community audit retains original counts, the source of each correction and uncertainty or missingness rather than reporting a precise corrected composition without its assumptions. No actual species, clinical finding or treatment performance follows from these class labels.

Reconstruct the original record

At rA=0.25, rB=0.75, expected observed counts are 7.5 and 52.5, so A appears as 0.125 rather than its true 0.3. Dividing by the supplied factors returns 30 and 70; this works only because those factors are stipulated independently.

Predict and investigate

Predict first: Can a minority class appear even rarer solely because its recovery differs?

Compare equal and unequal recovery while keeping the underlying community fixed. Reconstruct each denominator, then state what would be unknowable if the factors were not independently supplied.

Defend a changed case

Apply the mechanism to a changed boundary

Use rA=0.75, rB=0.25. Find observed A fraction and corrected A fraction.

Retain the first response, units, uncertainty and any prior feedback exposure in the notebook before comparing this public explanation.

Compare a worked response

Observed counts 22.5 and 17.5 sum 40, giving A fraction 0.5625. Correcting by the declared factors returns 30/100=0.3. The reversal is observational, not an actual population change.

Retain bounded evidence

Preserve the original record, first reasoning, units, sources and feedback exposure in the Microbiology evidence workspace. All numerical records are original fictional evidence, not measured field or treatment performance. No culture, process setup, biological handling or safety certification is requested.

Primary mechanism context, checked 31 October 2026. Original teaching and numerical examples; no source operating procedures reproduced.