Compare sequence-read hypotheses without calling a genotype by fraction alone

1. Frame the molecular question

A sequence read is a measurement with orientation, alignment and error assumptions, not a direct declaration of an organism’s genotype. At a candidate position, alternate-supporting reads can reflect a genuine variant, sequencing error, mapping to a similar region, contamination or a mixed sample. The surrounding evidence and quality controls matter as much as the observed fraction.

2. Explain mechanisms and assumptions

The original packet contains twenty reads and compares two explicit hypotheses: reference-only with alternate error probability e, and a balanced heterozygous model with alternate probability one-half. Under independent equal-quality reads, their binomial coefficient is the same and cancels in the likelihood ratio. We report log10 of that ratio to avoid mistaking extremely large numbers for certainty.

A likelihood ratio measures how the specified data compare under these two models. It is not a posterior probability: priors and other hypotheses are missing. In particular, an all-alternate packet can favor the balanced model over reference-only while being better explained by a homozygous-alternate model that was not included. Comparing only two choices does not make either complete.

Correlated errors, strand imbalance, alignment bias and duplicate molecules can invalidate the independent-read calculation. Independent confirmation and careful sample provenance address different failure modes. Sequence data can also raise privacy and consent issues; do not infer personal identity, diagnosis or function from the fictional count. No biological sample collection or sequencing procedure is requested.

3. Work a quantitative example

For ten alternate and ten reference reads with e=0.01, log10 likelihood ratio is 20log10(0.5)−10log10(0.01)−10log10(0.99)≈14.023. This strongly favors the balanced model over that reference-error model, but it is not a 100% genotype probability and excludes several alternatives.

4. Predict and investigate

Predict first: Can a large likelihood ratio between two hypotheses prove that no third explanation is possible?

Compare alternate counts zero, ten and twenty at two assigned error probabilities. State the compared hypotheses each time. Explain why all-alternate support calls for another model rather than declaring a balanced genotype solely because it beats reference-only.

Retain the first prediction, settings and complete evidence ledger in the lesson notebook. All sequences and numerical packets are original bounded teaching examples, not real genes, observed samples or performed experiments.

5. Apply the reasoning to a changed case

Apply the mechanism to a changed case

With four independent reads, two alternate and two reference, compare balanced p=0.5 against reference-only error p=0.1. Find the likelihood ratio after canceling the common binomial coefficient.

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

Compare a worked response

The ratio is 0.5⁴/(0.1²×0.9²)=0.0625/0.0081≈7.716. This is relative support between those two specified models, not a posterior probability or a functional conclusion.

6. Reflect and retain evidence

Which independent observation would separate the molecular mechanism from an assay, sample or model artifact? State orientation, units, controls, biological replication and omitted alternatives. Public practice and written plans do not certify independently demonstrated reasoning or actual supervised laboratory participation.

Sources and course continuation

Scientific supporting reference, checked 30 October 2026. Original prose, packets and diagrams; no source exercise or figure reproduced. Continue through General Biology I for mixed evidence and retained project review. No genetic engineering, biological culture or clinical procedure is requested.