08 Genetics and Inheritance

Core Concepts: Genes, Alleles, and Traits

Genetics is the study of heredity and variation. Heredity explains how biological information passes from parents to offspring, while variation explains why individuals differ.

A gene is a segment of DNA that contributes to a biological function or trait. Alternative DNA sequences of the same gene are alleles. In a diploid organism, the two alleles of a gene occupy corresponding loci on homologous chromosomes. An offspring usually receives one allele from each parent.

The distinction between genotype and phenotype is essential:

• Genotype describes the allele combination, such as $YY$, $Yy$, or $yy$.

• Phenotype describes an observable or measurable characteristic, such as seed color.

• Homozygous means that the two alleles are identical.

• Heterozygous means that the two alleles are different.

• A carrier possesses a disease-associated recessive allele but does not show the recessive phenotype under the model being used.

A dominant allele affects the phenotype when present in one or two copies under a particular model. A recessive phenotype generally appears only when two recessive alleles are present. Dominance does not mean that an allele is more common, more adaptive, or biologically superior.

Takeaway: Track the alleles an individual carries separately from the phenotype that individual displays.

Mendelian Laws and Single-Gene Crosses

Mendelian inheritance begins with the behavior of chromosomes during meiosis. The Law of Segregation states that the two alleles for a gene separate during gamete formation, so each gamete receives only one allele. Fertilization then combines one allele from each parent.

For a heterozygous parent with genotype $Yy$, the expected gametes are:

• $Y$ in approximately $1/2$ of gametes

• $y$ in approximately $1/2$ of gametes

Independent assortment describes the distribution of alleles of different genes into gametes. It applies most directly when genes are on different chromosomes or sufficiently far apart on the same chromosome. For a parent with genotype $AaBb$, the expected gamete types are $AB$, $Ab$, $aB$, and $ab$ when the genes assort independently.

A monohybrid cross illustrates both segregation and dominance. For $Yy \times Yy$, the possible offspring genotypes are $YY$, $Yy$, $Yy$, and $yy$. Therefore:

If $Y$ is completely dominant, the expected phenotype ratio is:

These are expected proportions across many offspring, not guarantees for a small family. Closely linked genes do not assort independently in the simple way described above, although crossing over can generate recombinant chromosomes.

Takeaway: Meiosis explains why each gamete carries one allele per gene, while fertilization restores paired alleles in the offspring.

Punnett Squares and Genetic Probability

A Punnett square places one parent's gametes along one edge and the other parent's gametes along the other edge. Each cell combines one gamete from each parent. Record genotype probabilities first, then translate them into phenotype probabilities.

For two heterozygous genes, $AaBb \times AaBb$, each parent can produce $AB$, $Ab$, $aB$, and $ab$ when independent assortment applies. With complete dominance at both genes, the expected phenotype ratio is:

For large crosses, probability rules are often more efficient than a $16$-cell grid.

Probability rules

The product rule gives the probability that independent events both occur:

For example, in $Yy \times Yy$, the probability of $yy$ for one child is $1/4$. The probability that two independently conceived children are both $yy$ is:

The sum rule combines mutually exclusive outcomes:

The genotype $Yy$ can result from $Y$ from the first parent and $y$ from the second, or the reverse. Thus:

The complement rule is useful for questions such as “at least one”:

If each of three children has an affected probability of $1/4$, then:

Conditional probability uses additional information to revise a probability. If two carriers have an unaffected child, that child cannot be $aa$. The remaining genotype possibilities are $AA$ and $Aa$, with:

Takeaway: Choose the product, sum, or complement rule according to the wording and independence assumptions in the problem.

Pedigrees and Inheritance Patterns

A pedigree is a diagram that shows how a trait or condition occurs across generations. Begin with observable transmission patterns rather than assuming a genotype immediately. Family history may be incomplete, and small family size, misclassification, adoption, early death, or reduced penetrance can obscure a pattern.

Common symbols include:

• A square for a male

• A circle for a female

• A shaded symbol for an individual expressing the trait

• An unshaded symbol for an individual not expressing the trait

• A horizontal line for a mating relationship

• A vertical line connecting parents to offspring

• Roman numerals for generations and Arabic numerals for individuals within a generation

Comparing inheritance patterns

Autosomal dominant inheritance often appears in successive generations, affects males and females at similar frequencies, and permits father-to-son transmission. A heterozygous affected parent and an unaffected parent have the cross $Aa \times aa$, giving an expected affected probability of $1/2$ for each child.

Autosomal recessive inheritance can skip generations. Affected individuals may have unaffected parents, and males and females are generally affected at similar frequencies. Two unaffected carrier parents have the cross $Aa \times Aa$, which gives:

X-linked recessive inheritance often affects males more frequently because males typically have one X chromosome. An affected father does not transmit the allele to sons, because sons receive his Y chromosome. A carrier mother with genotype $X^AX^a$ and an unaffected father with genotype $X^AY$ can produce carrier daughters, unaffected daughters, unaffected sons, and affected sons.

For X-linked dominant inheritance, an affected father transmits the trait to all daughters and no sons in the simplest model. A heterozygous affected mother has an expected transmission probability of $1/2$ to each child.

Y-linked inheritance passes from father to son. Only males are affected, and an affected father transmits the allele to all biological sons.

Mitochondrial inheritance usually follows maternal transmission through the egg cytoplasm. An affected mother may transmit a mitochondrial variant to all children, whereas an affected father generally does not transmit it. Expression can vary when cells contain different proportions of mitochondria with and without the variant.

Takeaway: Use the pattern of transmission, sex distribution, and parent-to-child pathways together; no single clue should be treated as conclusive.

Variation Beyond Simple Mendelian Models

Simple dominant-recessive models are useful starting points, but many traits do not follow them exactly.

• Incomplete dominance: the heterozygote has an intermediate phenotype. For example, $RR$ may produce red flowers, $rr$ white flowers, and $Rr$ pink flowers.

• Codominance: both alleles are expressed in the heterozygote. The human ABO system illustrates codominance between $I^A$ and $I^B$, while $i$ is recessive.

• Multiple alleles: a gene can have more than two alleles in a population, although an individual generally carries no more than two alleles at an autosomal locus.

• Epistasis: an allele at one gene alters or masks the expression of another gene.

• Polygenic inheritance: many genes contribute to a trait, often producing continuous variation such as variation in height.

• Sex-influenced inheritance: an allele has different effects in males and females.

• Sex-limited inheritance: a trait is expressed in only one sex even though the genes may be present in both.

• Penetrance: the proportion of individuals with a genotype who express the phenotype.

• Expressivity: the degree or range to which a phenotype is expressed.

A mutation is a change in DNA sequence. Mutations may be neutral, harmful under particular conditions, beneficial in a particular environment, or conditional. Changes can include base substitutions, insertions, deletions, duplications, inversions, and larger chromosome rearrangements. Mutations in germ cells can be inherited, while mutations in somatic cells generally remain within the individual's body tissues.

Genetic variation also arises through crossing over, independent assortment, and random fertilization. These processes create new combinations of existing alleles even when no new mutation occurs. Phenotypic variation can be summarized as:

Takeaway: Genotype does not always predict phenotype with certainty because allelic relationships, gene interactions, environmental conditions, and variable expression can all matter.

A Reliable Problem-Solving Method

Use a consistent sequence when solving an inheritance problem.

1. Identify the inheritance model. Decide whether the problem involves autosomal or sex-linked inheritance, dominant or recessive expression, incomplete dominance, codominance, linkage, mitochondrial inheritance, or Y-linked inheritance.

2. Define allele symbols. State what each symbol means. For an X-linked trait, include the chromosome, such as $X^A$ and $X^a$.

3. Infer parental genotypes. Use phenotype and family information. If a dominant phenotype could be either $AA$ or $Aa$, write A_ until further evidence resolves the ambiguity.

4. List possible gametes. A homozygous individual produces one allele type for that gene; a heterozygous individual produces two expected allele types.

5. Combine gametes. Use a Punnett square, branching diagram, or probability multiplication.

6. Convert genotype probabilities to phenotype probabilities. Do not skip this distinction.

7. Check the result. Probabilities should sum to $1$, or $100\%$. Also check sex chromosomes, independence, linkage, penetrance, and environmental effects.

Worked reasoning

If two unaffected parents have a child with an autosomal recessive condition, the affected child is $aa$. Each parent must therefore have contributed an $a$ allele. Under the simple model, the parental cross is $Aa \times Aa$, so the risk for each subsequent child is:

The previous child's outcome does not determine the next child's genotype; it provides evidence that both parents are carriers. For two additional children, the probability that both are unaffected is:

For a dihybrid cross $AaBb \times AaBb$, the probability of $aabb$, assuming independent assortment, is:

Frequent errors to avoid

• Confusing dominant with common

• Treating probability as certainty

• Ignoring genotype ambiguity

• Assuming previous births determine the next birth

• Applying independent assortment to closely linked genes

• Assuming every pedigree is complete

• Equating phenotype with genotype

• Ignoring which parent supplies an X or Y chromosome

Final takeaway: Define the model, assign symbols, infer genotypes, list gametes, calculate combinations, translate genotype into phenotype, and then test whether the assumptions fit the biological situation.