Natural selection, inheritance and genetic drift: sources & model

Meet two real peppered-moth forms. Follow survivors, trace inherited copies into offspring, and replay a population under different conditions. Compare the teaching model with what researchers actually measured.

What supports the explanation?

What this model assumes

1. One authored diploid, two-allele population model; no intermediate insularia forms, migration, overlapping generations or multiple loci.
2. Adult wing-form classification stays fixed in this model. Individual developmental and plastic changes are separate biological mechanisms.
3. Survival probabilities, fixed offspring count and pool assignment are teaching rules, not fitted field ecology or universal lifetime fitness.
4. Photographs show real individuals, not measured CC/Cc/cc genotypes, sexes, sizes or calibrated camouflage values.
5. Recorded seeded runs are reproducible calculations, not field observations; finite outcomes can differ from ideal expected values.
6. Real source studies measured different subjects and timescales. Human screen-search performance is not a bird-predation measurement.
7. The paper activity uses different die-based probabilities from the app and cannot establish a statistical effect from one short run.
8. Selection concerns contribution in context: Inherited differences can affect expected contribution to future generations through survival and reproduction. “Fitness” in this context does not mean strongest, smartest or morally best. A trait’s contribution depends on conditions. A form favored by one survival rule need not be favored by another, and a chance result is not a universal ranking.
9. One locus, two tracked copies: This diploid teaching model uses C and c at one locus: CC and Cc are carbonaria-like; cc is typica-like. The carbonaria allele is dominant for this adult classification. Dominance does not give a C copy a greater transmission probability from a Cc parent: either tracked copy is chosen with probability 1/2. The intermediate insularia forms found in nature are omitted.
10. What the computer samples: Each adult receives a stored survival draw. Surviving parents are sampled uniformly, with replacement, from separate female and male pools; one copy is sampled from each selected parent. New individuals receive alternating pool labels, an authored fixed-sex-ratio rule rather than a model of sex determination. If either pool has no survivors, this run stops under its mating rule. The computer must not invent parents to keep it going.
11. Transparent teaching probabilities: Pale-favored survival uses 0.60 for dark-form adults and 0.90 for pale-form adults. Equal probabilities use 0.80 for both. Dark-favored reverses the first contrast. These are event probabilities chosen to make the mechanism visible; they are neither source estimates nor lifetime reproductive fitness. Changing an animation speed or revisiting an event must not resample its recorded outcome.
12. An ideal reference is not the next finite result: For an ideal randomly mating population with C frequency p, let wD and wP denote the chosen dark and pale event-survival probabilities. Starting genotype proportions are p², 2p(1−p), (1−p)². The mean survival is W = wD[p² + 2p(1−p)] + wP(1−p)², and the ideal survivor-copy frequency is p′ = wD p / W. At p = 1/2 and wD = 0.6, wP = 0.9, this gives W = 0.675 and p′ = 4/9. The ideal next dark-form fraction is 56/81. These calculations do not force a finite run to hit those values.
13. Use the actual surviving pools: Let pF and pM be C-copy fractions in the two surviving parent pools. Under this model’s independent sampling, P(CC) = pF pM; P(Cc) = pF(1−pM) + (1−pF)pM; P(cc) = (1−pF)(1−pM). Expected offspring C frequency is (pF + pM)/2. Its conditional variance is [pF(1−pF) + pM(1−pM)]/(4N). The familiar p(1−p)/(2N) form requires equal pool frequencies. This concerns a distribution of possible runs, not a promise about every small-versus-large comparison.
14. Variation can arise and then disappear: Mutation changes DNA sequence; inherited changes can introduce variants. Mutation and selection are different mechanisms. A variant does not appear because a population anticipates what would help. Mutation processes may nevertheless be biased or environmentally influenced. With no mutation or migration in our closed model, an absent allele cannot reappear merely through selection or ordinary copying. This is a model boundary, not a claim that all real populations stay fixed forever.
15. How could we test when a variant arose?: Luria and Delbrück compared patterns of virus-resistant bacteria among independently grown cultures. Their 1943 results supported inherited changes arising independently of the selecting virus in that case. This separates the origin of a variant from its later detection under selection. It is not a moth mutation-rate measurement or a claim that environments never affect mutation processes. No culture experiment is proposed here.
16. A useful chance calculation: Suppose all 40 adults survive, exactly one of the 20 female parents is Cc, and all other parents are cc. An offspring has probability 1/40 of receiving C through its female parent and zero through its male parent. The chance that none of 40 offspring receives C is (39/40)⁴⁰, about 0.3632. This is conditional on these specific pools and sampling rules. It is not a universal probability that a new variant disappears.
17. Individual plasticity is a different question: Eacock and colleagues documented background-related color change in peppered-moth caterpillars, including responses when their eyes were obscured. Their study distinguishes larval plasticity from genetically determined adult wing-pattern forms. Thus “these modeled adults keep their category” must not become “individual organisms can never change appearance.”
18. The live-moth study: include the denominator: Cook and colleagues reported Majerus’s 4,864 released moths across six years. Moths absent four hours after sunrise were presumed eaten; approximately 26% of disappearing individuals were directly observed being eaten by birds. In 2006, 28/34 carbonaria remained, compared with 629/774 typica. This one raw yearly comparison points the other way from the overall evidence. The source’s combined analysis accounts for different overall predation among years; our model does not convert its short-term estimate into lifetime fitness.
19. Artificial targets: what “censored” means: Walton and Stevens placed 250 targets resembling each form, with printed wings and edible bodies, and checked them at 6, 24 and 48 hours. The original workbook codes bird-predation events as 1, despite naming the column “Censored”; 0 includes final survivors and other outcomes. A non-avian or otherwise excluded outcome leaves the risk set without becoming an observed bird-predation event. It does not establish survival beyond that time.
20. Reconstructing a survival curve: The product-limit estimate multiplies (1 − dᵢ/nᵢ) over observed event times, where nᵢ is the number still at risk and dᵢ the bird-predation events. Events are processed before censoring at the same recorded time. The data give 48-hour estimates about 0.6446 for typica-like and 0.4343 for carbonaria-like targets: a difference of about 21.03 percentage points. This is not simply final survivors divided by 250. We do not repeat the paper’s internally inconsistent reported test-statistic/p-value combination or label this as a new complete statistical analysis.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Real peppered-moth photographs by Ben Sale, CC BY 2.0: flickr.com/photos/33398884@N03/4777708667 and /5857613284. License: creativecommons.org/licenses/by/2.0/. Uncropped, resized source photographs in an authored teaching-population composition. The photographed individuals’ genotypes were not measured; the population and inheritance records are authored calculations, not field observations.