Experiment 1
Keep the contributions fixed. Change A from 20% to 0%. Can a favored variant appear?
Check the prediction
No. With no mutation or immigration, zero stays zero if B reproduces.
Evolution by natural selection
Reproduction changes the composition.
Calculate a frequency update, distinguish frequency from population size, and explain why selection has no foresight.
Start with: Fractions. A heritable variant is passed from parent to offspring; a generation is one round of reproduction.
01 · Commit to a prediction
What do you expect?
No. Begin with 20 A and 80 B. They contribute 40 A and 80 B offspring: A is 40/120 = 1/3. The denominator changes too.
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02 · Change an assumption
Predict. Change. Explain.
Before changing a control, say what should move and why. Start with the experiments below. Reset restores the starting model; it preserves your written responses.
Experiment 2
Reset, then make wA = wB = 1. Explain the flat curve.
Check the prediction
Both contributions multiply their groups equally, so composition stays 20%. A flat frequency does not specify total population size.
0 to 100 · step 1
0 to 3 · step 0.1
0 to 3 · step 0.1
1 to 30 · step 1
Calculated model output. The table gives the same values. Displayed values are rounded; calculations keep full precision.
Read the plotted data as a table
03 · Connect the mechanism
From the picture to the quantities.
Selection is a difference in reproductive contribution associated with inherited variation. It changes a population across generations. Individuals do not acquire a needed variant because the environment rewards it. The denominator is the combined contribution from all variants. Fitness here is reproductive contribution under fixed conditions, not strength or moral value.
p′ = p wA / [p wA + (1−p) wB]
p is the fraction of A, from 0 to 1; the control displays percent. p′ is its next-generation fraction. wA and wB are nonnegative relative contributions, from 0 to 3 here. Time t is an integer number of generations. A zero denominator means no offspring and therefore no next-generation frequency.
Worked example
With 20 A and 80 B parents, wA = 2 and wB = 1 give contributions 40 and 80. Normalize by 120 to obtain p′ = 1/3. In the next generation, use thirds: A contributes 2/3 and B contributes 2/3, so p″ = 1/2. Multiplying both contributions by ten changes neither frequency.
Assumptions and limits
This is a deterministic haploid or clonal model with faithful inheritance, constant contributions and no drift, mutation, migration or frequency dependence. Fractional contributions are expectations. It does not specify absolute abundance, diploid dominance or a real species. If all present variants have zero contribution, reproduction stops and the frequency is undefined.
The annotated sources distinguish established results from this lesson’s original examples.
04 · Follow the structure
Where else does this apply?
Microbial variants
Inherited resistance can change reproductive success in a particular environment.
Boundary: Mutation, costs without treatment, horizontal transfer and finite populations need extra terms.
Replicating digital variants
A copying rule can change the share of inherited program variants.
Boundary: Only a defined copying-and-inheritance process fits. Purposeful human design is not explained by this model.
05 · Retrieve without hints
Close the explanation. Try a new case.
Write an answer before opening its feedback. Later, return directly here without rereading above. Recognition, explanation and transfer are separate outcomes. No page action or answer reveal measures mastery.
Recognition and explanation
Reveal reasoning and rubric
No. You need heritable variation associated with different reproductive contributions and population change across generations.
Self-check: Separate within-life change, inheritance and differential reproduction.
Calculation
Reveal reasoning and rubric
Equal parent counts contribute offspring in a 1:3 ratio, so A becomes 1/4.
Self-check: Normalize by both groups, not by the original population.
Novel transfer
Reveal reasoning and rubric
No. The deterministic model omits genetic drift. Random inheritance and survival can change finite populations. Measurement error or omitted fitness differences are other possibilities; one rise does not establish selection.
Self-check: Identify an omitted process and avoid inferring selection from frequency change alone.
On a later day, try again and record actual evidence in the curriculum. A later unaided explanation and a fresh transfer problem give stronger evidence than immediate familiarity. No reminder is scheduled.
Sources & scope
What supports the lesson?
- OpenStax, Concepts of Biology §11.2. Heritable variation, differential reproduction, mutation and drift.
Original teaching examples. Reference links need a connection; the lesson itself does not. Built 2026-10-11. Learner understanding is not assessed.