SCIENCE · INVESTIGATE AND EXPLAIN

Explain selection without giving evolution a goal

Follow how differential reproduction changes an existing heritable variant.

Learning outcome: Calculate a normalized next-generation frequency and identify conditions that the model excludes.

Starting recap

Allele frequency is the fraction carrying an allele in this haploid model. Relative reproductive contribution compares expected descendants, not strength, need or moral value.

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Try

At 50% A, A contributes 1.5 relative units and a contributes 1. The next A frequency is 0.75/(0.75+0.5)=0.6.

Open the experiment

Predict

Will an advantageous A appear if its initial frequency is zero? What happens when both types contribute equally?

Your prediction and reason

Experiment

Compare initial 50% with relative contributions 1, 1.5 and 0.5. Capture the trajectories. Then test 0% A with contribution 2 and 100% A with contribution 0.

Follow differential reproductive contribution

Worked teaching model · synthetic values · A deterministic haploid model runs for 12 generations. A contributes w and a contributes 1 per individual. No mutation, migration, finite-population sampling or changing environment occurs. Relative contribution is not a probability and may exceed 1.

Initial A frequency: 50 % Relative reproductive contribution of A: 1.5 relative to a = 1

Reset keeps your prediction, captures and practice history.

Frequency through generations

Each point records one generation; connecting lines do not model changes within a generation. A missing next-generation frequency is left undefined rather than drawn as zero.

Inspect the generation trace

Generation	A (%)
0	50.000
1	60.000
2	69.231
3	77.143
4	83.505
5	88.364
6	91.929
7	94.471
8	96.245
9	97.465
10	98.295
11	98.857
12	99.235

Calculated values on the same fixed scale
Row	Quantity	Value (%)
1	A frequency at generation 0	50
2	A frequency at generation 1	60
3	A frequency at generation 2	69.2308
4	A frequency at generation 3	77.1429
5	A frequency at generation 4	83.5052
6	A frequency at generation 5	88.3636
7	A frequency at generation 6	91.9294
8	A frequency at generation 7	94.4708
9	A frequency at generation 8	96.2447
10	A frequency at generation 9	97.4647
11	A frequency at generation 10	98.2954
12	A frequency at generation 11	98.8571
13	A frequency at generation 12	99.2352

A frequency after 12 generations: 99.235%.

p_next = p × w / (p × w + 1 − p). Contributions are normalized into a frequency. A missing allele cannot appear without a source; when all individuals have zero contribution, there is no next generation to normalize.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Normalize contributions, not intentions

At initial A frequency p = 0.5 and relative contribution w = 1.5, A contributes p × w = 0.75 units. The other type contributes (1 − p) × 1 = 0.5. A therefore makes up 0.75/1.25 = 0.6 of the next generation.

The update is p_next = p × w / (p × w + 1 − p). Here p is a fraction from zero to one and w is a relative contribution. A value above one is allowed because w is not a probability.

Natural selection requires heritable variation associated with different reproductive success. It does not describe organisms changing because they “need” a trait. Environmental conditions affect which differences matter. Background: OpenStax, population genetics.

Test boundary cases

Set w = 1. Both types contribute equally, and every generation retains its starting frequency. Set w above one: an existing A generally increases in this deterministic model. Set w below one: it decreases.

If A starts absent, multiplying its contribution cannot create it. Mutation or immigration would be needed to introduce an absent variant, and neither occurs here. If every individual is A and w = 0, total reproductive contribution is zero. There is no next-generation frequency; the model reports it as undefined instead of inventing zero or retaining 100%.

Separate a teaching mechanism from a population claim

The model is haploid and deterministic. It omits dominance, finite sampling, changing environments and interactions among genes. It shows a consequence of assumed reproductive differences; it does not measure those differences.

To explain a real frequency change, collect evidence about inheritance and relative reproductive success, alongside alternative mechanisms such as migration or drift. A rising allele frequency alone is insufficient to identify selection. In your report distinguish the measured change, the proposed mechanism and observations that could challenge it.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Explain why the model describes a population changing over generations, not individuals acquiring a needed allele. Name an observation that would distinguish reproductive differences from chance.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Compare offspring counts with an inheritance model Next: Distinguish drift from a selective advantage

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