Biology · Meiosis & Patterns of Inheritance

Polygenic traits, penetrance and gene-environment interactions

A measured leaf length usually does not fall into just two Mendelian categories. Several loci can contribute, growing conditions matter, and individuals sharing one focal genotype can differ. The earlier K/L seedling model now helps organise these possibilities.

Begin with the cell-division lesson and Heredity, Variation & Evolution: recognise homologous chromosomes, sister chromatids, a locus and an allele. DNA, Replication & Repair explains how copying makes two sister DNA molecules. Gene Expression helps with the later distinction between transmitting a sequence and expressing a trait. Here, fractions and conditional probabilities are explained alongside the cases. All chromosome-count examples use a specified diploid model; the final lessons introduce extensions rather than requiring advanced genetics beforehand.

Back to the Biology map

By the end, you can

Distinguish transmission, penetrance, expressivity and population variation, and interpret a constructed genotype-by-environment response without claiming a universal trait prediction.

Several loci can contribute to one measurement

Polygenic means that more than one gene influences a trait. Effects need not be equal or additive, and a locus may affect more than one characteristic. Polygenic inheritance, interactions among loci and an environmental influence describe different parts of an explanation.

Our deliberately additive two-locus model starts at 10 units and adds 2 for each uppercase allele copy. aabb has 10 units, Aabb 12, AaBb 14, AABb 16 and AABB 18 in the specified environment. AaBb and AAbb both have two counted copies and thus the same model value, despite different genotypes.

This construction shows how multiple contributions can produce several values rather than two categories. It does not prove a normal distribution, assign the same effect to real alleles, or capture all gene interactions. Continuous measurements can also be influenced by environmental and developmental variation; a smooth distribution alone does not identify its mechanism.

A specified additive model gives five possible copy totals

A specified two-locus additive toy response at one environment, with equal per-copy effects and no dominance or epistasis. Selected genotypes illustrate the five copy totals; they are not all genotypes or predicted population frequencies. Connecting line, if used, illustrates the assigned discrete rule rather than interpolating measured genotypes or showing continuous population data.

Read the diagram in words

aabb, Aabb, AaBb, AABb and AABB have zero through four counted uppercase copies and model values 10, 12, 14, 16 and 18. AAbb also has two copies and therefore value 14 in this model.

Assigned trait value
Genotype	Uppercase allele copies across the two loci	Assigned trait value (Model units)
aabb	0	10
Aabb	1	12
AaBb	2	14
AABb	3	16
AABB	4	18

AAbb also has two counted copies
Description	Uppercase allele copies across the two loci	Assigned trait value (Model units)
AAbb also has two counted copies	2	14

Uppercase allele copies across the two loci: 0–4

Assigned trait value (Model units): 0–20

Value = 10 + 2 × counted copies
One specified environment
Selected genotypes, not genotype frequencies

Ask whether the trait appears, then how it appears

Penetrance is the proportion carrying a specified genotype or variant who show the defined phenotype under a stated scoring scope. If our invented cohort contains 20 carriers assessed at the same stage and 15 show the trait, its descriptive penetrance is 15/20 = 75%. Five carriers lacking the trait do not prove that their allele disappeared.

Expressivity describes differences in the phenotype's form or degree among those in whom it is expressed. In the illustration, trait-present individuals can have arbitrary scores 1, 2 or 4. Those scores describe degree within the scoring system, rather than the probability of transmitting the allele.

Age, genetic background, environment and measurement criteria can affect which cases are counted. A 75% figure therefore needs a defined population and observation scope. It is not a universal forecast for a new individual, and it is not an allele frequency. The 1/2 transmission probability in a specified heterozygous cross and penetrance after transmission answer separate questions.

Presence and degree are separate measurements

An invented cohort already carrying the same focal genotype, assessed at the same defined age and conditions. Scores are arbitrary severity categories among trait-present individuals. This is a descriptive illustration, not a population estimate, allele-transmission rate or forecast. Equal symbols count individuals rather than DNA copies. Do not place absent individuals on the expressivity scale as though absence had been assigned a severity score.

Read the diagram in words

Fifteen of twenty carriers show the defined trait, so the cohort's descriptive penetrance is 75%. The separate expressivity scale shows possible scores 1, 2 and 4 among trait-present individuals; no score frequencies are supplied.

Specified genotype V
Individual	Specified phenotype
1	●
2	●
3	●
4	●
5	●
6	●
7	●
8	●
9	●
10	●
11	●
12	●
13	●
14	●
15	●
16	○
17	○
18	○
19	○
20	○

15 + 5 = 20

15 / 20 = 75% trait present

Example expressivity categories among trait-present individuals
Description	Expressivity category
Arbitrary score	1
Arbitrary score	2
Arbitrary score	4

All 20 already carry the focal genotype
15 / 20 = 75% trait present
Scores describe degree, not transmission
Same specified scoring stage and conditions

●: Trait present
○: Trait absent

Compare responses across conditions

Return to the constructed K/L leaf model at one developmental stage. In Environment 1, K averages 6 mm and L 8 mm. In Environment 2, K averages 14 mm and L 10 mm. K's environmental contrast is 8 mm, whereas L's is 2 mm. The model illustrates genotype-by-environment interaction because the response depends on genotype.

The ranking reverses too: L is larger in the first environment and K in the second. Interaction does not always require a rank reversal; unequal response differences can occur while the ordering stays the same. Nor does a response mean K's DNA has changed into L's.

The lines connect the two specified conditions to aid comparison. They do not establish a response at every unshown environment or provide real experimental evidence. A research comparison would need adequate replication, measurement and design to separate relevant causes and estimate uncertainty.

The earlier K/L responses depend on environment

The same constructed K/L response model introduced in Heredity, Variation & Evolution. No replicate distribution, significance test or fitted variance components are supplied. The reused values preserve continuity and do not add evidence to the earlier constructed example.

Read the diagram in words

K has values 6 and 14 mm, a contrast of 8 mm. L has 8 and 10 mm, a contrast of 2 mm. The contrast of contrasts is 6 mm, and the ranking reverses between the two conditions.

Mean leaf length at the specified stage
Specified environment	Genotype K (mm)	Genotype L (mm)
Environment 1	6	8
Environment 2	14	10

Unequal responses illustrate interaction
Genotype	Environment 1 → Environment 2 (mm)
K	+8 mm
L	+2 mm

Mean leaf length at the specified stage (mm): 0–16

Unequal responses illustrate interaction
L is larger in Environment 1; K in Environment 2
Contrast of contrasts: 6 mm
Connections compare categories, not unshown environments

Keep variation among people or plants separate from one individual

Heritability is a statistical property of trait variation in a defined population and environment, under the chosen model and method. It is not the fraction of an individual's trait made by genes. An estimate of 0.7 therefore does not divide one person's measured height into 70% genetic material and 30% environment.

A shared family phenotype can arise through inherited variants and shared conditions. A high heritability estimate does not show that a trait cannot change if conditions change, and it does not identify the causal loci. Strong environmental effects can coexist with substantial genetic differences among individuals in the current setting.

To develop a useful prediction, specify the trait, developmental stage, genetic information and environment, then test it against new relevant observations. A genotype-to-trait model trained in one set of conditions may need further checking in another. The inheritance route remains essential, but it is only part of a complete explanation.

Worked example

Three percentages with different denominators

In an Aa × AA one-locus transmission model, 1/2 of offspring are expected to inherit a. In our separate carrier cohort, 15 of 20 show the specified trait, giving 75% descriptive penetrance. A heritability example of 0.7 concerns variation in a defined population, rather than either of those denominators. These numbers must not be exchanged just because all can be written as percentages.

For the K/L response comparison, compute within each genotype first: K changes by 14 − 6 = 8 mm and L by 10 − 8 = 2 mm. Their contrast of contrasts is 8 − 2 = 6 mm. The supplied model has no replicate data, so this is a descriptive calculation, not a statistical test or a percentage of the trait attributed to one gene.

Check your understanding

Our carrier cohort has 15 trait-present and five trait-absent individuals. Does 75% describe allele transmission?
Show reasoning
No. It describes the fraction already carrying the focal genotype who meet the phenotype criterion at the stated stage. Transmission concerns which offspring receive an allele.
K and L differ by 2 mm in Environment 1 but by 4 mm in the opposite direction in Environment 2. What relationship does that show in the model?
Show reasoning
Their responses to environment differ and their ordering reverses, illustrating genotype-by-environment interaction. The values do not establish a real experiment, statistical significance or DNA change.
Does heritability 0.7 mean an individual's trait is 70% genetic and therefore fixed?
Show reasoning
No. It describes variation in a particular population and environmental setting under a statistical analysis. It does not partition one individual or establish how changeable the trait is.

What to carry forward

Use the appropriate denominator and context for transmission, expression and population variation.

References

Resources supporting this lesson’s explanations and examples.

Talking Glossary — Chromosome sets, maps and polygenic traits (Live glossary)National Human Genome Research InstituteScientific glossaryTalking Glossary — Chromosome sets, maps and polygenic traits (Live glossary)Genetic map Polygenic traitgenome.gov
Help Me Understand Genetics — Inheritance and expression (Live guide)National Library of Medicine · MedlinePlus GeneticsScientific education guideHelp Me Understand Genetics — Inheritance and expression (Live guide)Reduced penetrance and variable expressivity Genomic imprinting and uniparental disomy Heritabilitymedlineplus.gov
Quantitative Genetics for Plant Breeding — G × E (Chapter 10)William Beavis, Kendall Lamkey, Katherine Espinosa, Anthony Assibi Mahama and Walter Suza · Iowa State UniversityOpen university textbook chapteriastate.pressbooks.pubRead source

Individual	Specified phenotype
1	●
2	●
3	●
4	●
5	●
6	●
7	●
8	●
9	●
10	●
11	●
12	●
13	●
14	●
15	●
16	○
17	○
18	○
19	○
20	○

Individual	Specified phenotype
1	●
2	●
3	●
4	●
5	●
6	●
7	●
8	●
9	●
10	●
11	●
12	●
13	●
14	●
15	●
16	○
17	○
18	○
19	○
20	○

Individual	Specified phenotype
1	●
2	●
3	●
4	●
5	●
6	●
7	●
8	●
9	●
10	●
11	●
12	●
13	●
14	●
15	●
16	○
17	○
18	○
19	○
20	○