Segregation transmits variants; dominance describes a phenotype relationship, not an allele’s fate.
By the end: Use a one-locus inheritance model and recognize where it stops describing real traits.
Copies separate during reproduction
A diploid genotype records the two alleles at a locus. AA and aa are homozygous; Aa is heterozygous. Gametes are reproductive cells carrying one chromosome set in this model. Meiosis is a division process in the reproductive life cycle that separates chromosome copies. The two alleles segregate, and each gamete ultimately receives one copy at this locus. In the simple Mendelian model, an Aa parent supplies A to half its gametes and a to half. Fertilization joins one gamete from each parent.
A Punnett square combines possible gametes and their probabilities. It predicts probabilities for offspring under the model, not a guaranteed set of four children. For Aa crossed with Aa, the genotype probabilities are one quarter AA, one half Aa, and one quarter aa. Successive births are separate draws under the stated assumptions.
Derive offspring probabilities from gametes
At an autosomal locus, a diploid parent has two chromosome copies with corresponding positions. In an Aa parent, one carries A and the other a. Before meiotic divisions, chromosomes copy their DNA. The divisions then distribute chromosome material into cells with one chromosome set. The simplified result at this locus is gametes carrying A or a, each with probability one half. The parent does not blend the alleles into an intermediate sequence. Its offspring receives a discrete copy at this position from each contributing gamete.
Fertilization combines a gamete from each parent, so an Aa by Aa cross has two choices on each side. For the path in which both supply A, multiply one half by one half to get one quarter AA. The path A from the first and a from the second also has probability one quarter. Reversing those parental origins gives another one quarter. Both latter paths make the genotype Aa, so add them to get one half. The remaining path gives aa with probability one quarter.
Multiplication here assumes the allele in one parent's contributing gamete is independent of the allele in the other parent's gamete. Addition combines alternative paths that cannot occur simultaneously for the same offspring. These are different operations with different reasons. A parent either contributes A or contributes a at this locus. An Aa offspring can result by either parental order, but not both orders at once. Keeping the gamete origins visible explains the factor of two in the heterozygote probability without memorizing the final ratio.
Two parental orders produce the same heterozygote
Constructed Aa × Aa cross. Each column is one possible gamete-origin path, not one promised offspring. Each gamete choice has probability one half, and independent union gives each path weight one quarter. Positions and connector lengths are schematic.
The resulting one-to-two-to-one ratio describes probabilities, not a four-offspring schedule. With four independent offspring, the expected number of aa offspring is four times one quarter, which equals one. Yet the chance that none is aa is three quarters multiplied by itself four times, or 81 divided by 256, about 31.64%. The chance that all four are aa is one quarter to the fourth power, or one divided by 256, about 0.39%. Outcomes far from the expected count remain possible under an ordinary cross.
A useful check is to recover the expected allele frequency among offspring. Imagine one hundred offspring represented by the model's expected counts of 25 AA, 50 Aa, and 25 aa. AA contributes fifty A copies and Aa another fifty, making one hundred among two hundred locus copies. The expected A frequency is therefore one half. Actual families need not match those counts. Their finite sample of transmissions can change realized frequencies even when each heterozygous parent has an equal probability of transmitting either allele.
The model assumes ordinary Mendelian transmission, the stated parental genotypes, and no genotype-dependent loss between fertilization and the stage counted. If aa offspring are less likely to survive in a particular environment, adult genotype proportions can differ from the probabilities at fertilization. A departure does not automatically imply the gametes segregated incorrectly. It could arise later in the life cycle. Separate the probability of forming a genotype from its probability of appearing in a later sample, and specify which stage a reported ratio describes.
An expected count is not a family quota
Question for four independent Aa × Aa offspring
Calculation
Result
Expected number of aa offspring
4 × 1/4
1
Probability of no aa offspring
(3/4)⁴ = 81/256
31.640625%
Probability all four are aa
(1/4)⁴ = 1/256
0.390625%
Expected A copy frequency per offspring
1/4 + (1/2)/2
50%
Model probabilities, not empirical family data. Independence and unchanged parental genotypes are assumed. The first row is a count expectation; the next two are event probabilities.
Dominance is not strength or prevalence
If Aa and AA share the same phenotype for a defined trait, A is dominant over a for that phenotype. The alleles still segregate separately; a does not disappear inside Aa. Dominance does not imply that A is common, beneficial, or increasing by selection.
Some heterozygotes have an intermediate phenotype, and others express distinguishable effects of both alleles. Many traits depend on many loci and environmental conditions. A variant can have several effects, and its effect can depend on genetic background. Avoid treating a single-letter diagram as a complete model of height, intelligence, disease, or behavior.
Specify which phenotype dominance describes
Dominance compares phenotypes of genotypes for a specified characteristic under specified conditions. If AA and Aa have the same measured color while aa differs, A is completely dominant over a for that color in this model. The term says nothing about which DNA copy is more likely to enter a gamete. An Aa parent still transmits a with probability one half under Mendelian segregation. A recessive allele remains a physical sequence in the heterozygote even when the chosen phenotype does not reveal its presence.
A possible molecular explanation uses a hypothetical pigment pathway. Suppose A permits production of a working enzyme and a produces none of that enzyme. If one working copy supplies enough activity to reach the same measured color as two working copies, Aa and AA can look alike. That is a threshold relationship between enzyme activity and color, not destruction of a. Other molecular relationships produce other dominance patterns. This constructed explanation illustrates how a phenotype can conceal a genotype difference without claiming that every dominant allele works through an enzyme threshold.
Change the measurement and the relationship can change. Suppose expected enzyme amounts are zero units in aa, fifty in Aa, and one hundred in AA, while visible color reaches its maximum at forty units. Color shows complete dominance of A, but enzyme amount is intermediate in Aa. If the threshold instead lies above fifty, Aa need not share the AA color. Dominance belongs to the defined phenotype and conditions, not to an allele in every possible measurement. The table separates molecular amount from the resulting categorical observation.
The same genotype can be intermediate for one measurement
Genotype
Constructed enzyme amount
Color if maximum begins at 40 units
aa
0 units
No pigment
Aa
50 units
Maximum measured color
AA
100 units
Maximum measured color
Hypothetical molecular-to-phenotype mapping, not measured biology. A is completely dominant for this categorical color, while Aa has intermediate enzyme amount. The units and threshold are constructed, not a universal mechanism of dominance.
For Aa by Aa, complete dominance gives a three-quarter probability of the A-associated phenotype, because AA and Aa probabilities add. But the A copy frequency remains one half, and the fraction carrying a is three quarters. Only one quarter express the recessive phenotype. The same offspring model therefore gives 75%, 50%, and 25% for different questions. Before using a ratio, write whether you mean organisms with a phenotype, organisms carrying an allele, or copies of that allele among all copies at the locus.
Dominance also does not determine fitness. Imagine that the A-associated color makes organisms conspicuous in one environment but reduces detection in another. Expected reproductive contribution could differ between environments without any change in segregation or in which phenotype is dominant. Measuring color establishes neither contribution. To predict selection in a diploid population, we need expected contributions for AA, Aa, and aa under the relevant conditions. A color that is dominant can decline, and a recessive color can increase, if their reproductive consequences support those changes.
Now compare incomplete dominance, where the heterozygote is intermediate for the measured trait, with distinguishable effects of both alleles, often called codominance. Neither changes the one-quarter, one-half, one-quarter genotype probabilities of the same Aa cross under our transmission assumptions. For guided practice, keep the genotype probabilities fixed and relabel the phenotype column under each relationship. Three distinguishable phenotypes can follow one-to-two-to-one probabilities even though complete dominance had reduced the visible categories to three quarters and one quarter.
Keep transmission fixed while changing the phenotype model
Relationship for the measured trait
AA, probability 25%
Aa, probability 50%
aa, probability 25%
Complete dominance
A-associated appearance
Same appearance as AA
Different appearance
Incomplete dominance
One extreme
Intermediate appearance
Other extreme
Codominance
Only A-associated effect
Both distinguishable effects
Only a-associated effect
Schematic phenotype relationships for the same ideal Aa × Aa cross. Genotype probabilities do not change. The table makes no claim about fitness, allele prevalence, or the inheritance of a complex real trait.
Work through the mechanism
Combine gametes at one locus
AA: 25%. Aa: 50%. aa: 25%.
Duplicate letters represent identical allele types on different parental copies. The four equally weighted paths are possibilities, not four promised offspring. No selection, mutation, transmission distortion, or sex linkage. Presets replace both parental genotypes immediately.
Cross
AA
Aa
aa
Aa × Aa
25%
50%
25%
Aa × aa
0%
50%
50%
AA × aa
0%
100%
0%
Assume ordinary Mendelian segregation, equally viable offspring, and one autosomal locus.
Compare the three available crosses
The inheritance lab lets you choose three pairs of parental genotypes. It immediately changes gamete paths and genotype proportions, without generating a random family or following survival. Start with the two-heterozygote preset and identify both Aa paths before reading the totals. Each cell has weight one quarter because it pairs two parental-copy choices of weight one half. The repeated letters in a homozygous parent will matter in the next presets. They are separate possible copy origins even when they have identical allele labels.
Choose Aa by aa and predict the result before reading the display. The first parent supplies A or a equally. The second supplies a regardless of which parental copy enters its gamete. Two of the four displayed paths give Aa and two give aa, so each genotype has probability one half. AA is impossible because the second parent cannot contribute A. Among one hundred expected offspring, fifty Aa contribute fifty A copies while fifty aa contribute none. Expected A frequency is fifty divided by two hundred, or 25%.
The carrier fraction for A in that same cross is instead 50%, since fifty of the expected one hundred organisms carry it. If A is completely dominant for the trait, the A-associated phenotype also has probability 50%. The a carrier fraction is 100%, because every offspring receives a from the aa parent. An allele can occur in every offspring while occupying only three quarters of their gene copies. Universal carriage is not fixation, which would require every copy at the locus to be a.
Count copies in the two possible Aa × aa outcomes
Constructed, equally weighted offspring possibilities, not two guaranteed births. Every possible offspring carries a, but a is not fixed: one quarter of expected locus copies are A. The paired circles represent locus copies; geometry is schematic.
Now choose AA by aa. Every first-parent gamete supplies A, and every second-parent gamete supplies a. All four paths therefore give Aa. Every offspring is expected to be heterozygous, but A frequency is still one half because each offspring has one A among two copies. Both allele carrier fractions are 100%. A uniform visible phenotype can thus coexist with two alleles in every individual. Uniform appearance is not evidence that a population lacks genetic variation, and uniform genotype at one locus does not describe the rest of its genome.
The three presets also show why a family cross is not a whole-population mating model. A family conditions on two known parents. A population contains different genotypes and mating patterns, and parents may contribute different numbers of offspring. To combine family results, weight each cross by its share of offspring rather than treating every mating type as equally common. For a constructed mixture, let half the offspring come from Aa by aa and half from AA by aa. The combined genotype probabilities are zero AA, three quarters Aa, and one quarter aa.
Check that mixture by counting expected copies. Out of one hundred offspring, seventy-five Aa carry seventy-five A copies among two hundred total copies, giving 37.5%. Alternatively average the two cross-specific copy frequencies, one quarter and one half, using equal offspring weights. Their mean is three eighths, also 37.5%. The 75% A carrier fraction answers a different question. This mixture is a paper calculation, not another lab control. Agreement between methods checks the arithmetic and identifies the weights a population prediction requires.
Weight crosses by their share of offspring
Cross supplying offspring
Offspring weight
AA
Aa
aa
A copy frequency
Aa × aa
1/2
0%
50%
50%
25%
AA × aa
1/2
0%
100%
0%
50%
Combined offspring
1
0%
75%
25%
37.5%
Constructed paper mixture, not an extra lab mode. The combined A carrier fraction is 75%, but seventy-five A copies among two hundred expected locus copies give 37.5% A frequency.
Recombination changes combinations
Chromosomes carry many loci. Recombination during meiosis can exchange DNA between homologous chromosomes and create new combinations of existing alleles. Nearby loci often remain associated more frequently than independent assortment predicts. A one-locus Punnett square has no information about that linkage.
Sexual reproduction reshuffles variation but does not usually create new alleles by the act of segregation itself. Mutation supplies sequence changes; recombination can separate a useful allele from a harmful neighbor or combine variants. Real inheritance also includes sex-linked, organellar, and other exceptions outside the autosomal model used here.
Track chromosome combinations without inventing alleles
A one-locus square deliberately ignores other positions on the same chromosome. To add a second locus, use A and a at the first position and B and b at the second. A parent can be AaBb while carrying A with B on one homologous chromosome and a with b on the other. Write that arrangement as AB paired with ab. Another AaBb parent can instead carry Ab paired with aB. Single-locus genotypes match, but chromosome combinations differ, so gamete combinations need not match.
Assume the AB and ab arrangement and begin with a limiting model in which no recombination occurs between these loci. Half the gametes receive AB and half ab. There are no Ab or aB gametes in this model, even though each locus separately transmits its two alleles equally. Now allow a constructed recombination fraction of 20%. This means 20% of gametes carry combinations unlike those original chromosome pairs. With reciprocal classes equally frequent, Ab and aB each occupy 10%, while AB and ab each occupy 40%.
Check each locus separately after this reshuffling. A appears in AB and Ab gametes, so its frequency is 40% plus 10%, or 50%. B appears in AB and aB, again totaling 50%. Recombination changed associations between loci without changing either allele frequency in this constructed gamete pool. It did not create a new A, a, B, or b sequence. The diagram schematically shows segment exchanges. The 20% fraction is an assumed gamete proportion, not a physical distance or a claim about a particular organism.
A segment exchange changes two-locus combinations
Schematic exchange of existing chromosome segments; distances are not genetic-map units. This drawing compares combinations, not every chromatid or meiotic stage. The accompanying 20% recombinant-gamete example is constructed, not inferred from this geometry.
Contrast that linked case with independent assortment. If the alleles at the two loci assort independently in this parent, each combination has probability one half multiplied by one half, or one quarter. An AB gamete is then no more likely than Ab. Nearby loci often retain parental associations more often than this, so multiplying single-locus probabilities without checking linkage can give a wrong two-locus prediction. Conversely, linkage does not invalidate the one-half transmission probability at each locus in the model. It changes the joint combinations, not necessarily their separate totals.
Mutation answers a different question. A sequence change can create a variant that was not present in the copied sequence before. Ordinary segregation distributes existing copies, and the recombination example exchanges existing variants between chromosome combinations. What happens afterward depends on reproduction, environment, and chance. A new combination might have higher expected contribution under one condition and lower contribution under another. Its current usefulness does not establish that past recombination occurred to produce that benefit. A history of inheritance and an explanation of selective spread require separate evidence.
Finally, audit where the simple autosomal model stops. Organellar inheritance and sex-linked inheritance can transmit copies by different routes, and many traits depend on several interacting loci and environmental inputs. Even a correct genotype prediction at one locus need not predict the whole phenotype. Use a one-locus square when the question concerns that locus and its stated transmission assumptions. Use the chromosome comparison when associations matter. Neither drawing estimates a person's traits, health, or reproductive outcomes; both isolate inheritance mechanisms so their predictions and limitations can be checked.
Joint gamete frequencies can change while each allele stays at one half
Gamete or marginal allele
No recombination between loci
20% recombinant gametes
Independent assortment
AB
50%
40%
25%
ab
50%
40%
25%
Ab
0%
10%
25%
aB
0%
10%
25%
A at locus 1
50%
50%
50%
B at locus 2
50%
50%
50%
Constructed models for a parent with AB paired with ab, assuming equal reciprocal classes. The first four rows partition gamete types. The last two are marginal allele frequencies, not additional gamete classes; do not add all six rows together.
Exercises
A recessive variant can persist
For Aa × Aa with complete dominance of A, what fraction of offspring carry a and what fraction express the recessive phenotype?
Hint
Count Aa as a carrier even though it does not express the recessive phenotype.
Worked answer
Genotypes
Probability
Aa or aa: carry a
75%
aa: recessive phenotype
25%
Genotype transmission does not erase a hidden recessive allele.
Aa and aa together make 75% carriers of a. Only aa expresses the recessive phenotype, with probability 25%. These are probabilities for each offspring, not a promise about a family of four.
Dominant but declining
An allele is dominant for a color trait. Does that imply it will spread if its carriers leave fewer surviving offspring in the current environment?
Hint
Dominance and reproductive success describe different relationships.
Worked answer
Concept
What it specifies
Dominance
Heterozygote phenotype
Fitness
Reproductive contribution
Frequency
Share of gene copies
Do not infer the last two from dominance alone.
No. Dominance says how the heterozygote appears, not how many gene copies it contributes. Selection can reduce a dominant allele when the associated phenotype lowers reproductive success. To predict the amount, we need genotype-specific fitness, starting frequencies, and assumptions about other mechanisms.
Sources and further reading
The explanations and exercises are complete without these optional links. The references cover inheritance, population mechanisms, and evidence for ancestry. Source annotations distinguish textbook explanations, secondary history, and a primary paper whose bibliographic identity alone was checked. The examples are constructed teaching models, not empirical estimates or professional decision advice.