4.3 Mendelian inheritance and population genetics

Mendelian Inheritance

Gregor Mendel's pea plant experiments revealed the basic rules of how traits pass from parents to offspring. Through controlled breeding and careful statistical analysis, he identified principles that form the foundation of modern genetics.

These principles connect directly to population genetics, which zooms out from individual crosses to ask: how do allele frequencies behave across entire populations over time?

Principles of Mendelian Inheritance

Dominance and recessiveness: A dominant allele masks the effect of a recessive allele. Recessive traits only show up when an individual carries two copies of the recessive allele (homozygous recessive). In Mendel's pea plants, tall (T) was dominant over short (t), so both TT and Tt plants were tall, while only tt plants were short.

Law of Segregation: During gamete formation, the two alleles for each gene separate so that each gamete carries only one allele. When a Tt plant produces gametes, half carry T and half carry t. This explained why crossing two Tt plants could produce short offspring (tt) even though both parents were tall.

Law of Independent Assortment: Genes for different traits are inherited independently of each other, as long as they're on different chromosomes. Mendel showed this by tracking flower color and seed shape at the same time: inheriting purple flowers didn't determine whether seeds were round or wrinkled.

Punnett squares are the standard tool for predicting offspring genotypes and phenotypes. They lay out every possible allele combination from both parents in a grid format.

• Monohybrid crosses track one trait with two alleles (e.g., pea plant height: Tt × Tt)
• Dihybrid crosses track two traits simultaneously (e.g., seed color and shape: RrYy × RrYy)

Probability in Genetic Crosses

Two rules drive most genetics probability calculations:

• Product rule: Multiply probabilities of independent events. If the chance of being tall is $3/4$ and the chance of being yellow-seeded is $3/4$, the chance of being both tall and yellow-seeded is $3/4 \times 3/4 = 9/16$.
• Sum rule: Add probabilities of mutually exclusive events. If there are two different ways to get a heterozygous genotype, you add their individual probabilities.

Monohybrid cross ratios: A cross of two heterozygotes (Aa × Aa) yields a genotype ratio of $1/4$ AA : $1/2$ Aa : $1/4$ aa, which produces a 3:1 phenotypic ratio (dominant : recessive).

Dihybrid cross ratios: A cross of two double heterozygotes (AaBb × AaBb) yields the classic $9:3:3:1$ phenotypic ratio. Mendel observed this with round/wrinkled and yellow/green peas.

Test crosses determine whether an organism showing a dominant phenotype is homozygous (AA) or heterozygous (Aa). You cross it with a homozygous recessive individual (aa). If any offspring show the recessive phenotype, the parent must be heterozygous.

Pedigree analysis traces inheritance patterns through family trees. It's especially useful for identifying carriers of recessive alleles who don't show the trait themselves.

Concepts in Population Genetics

Population genetics shifts focus from individual crosses to entire populations. Instead of asking "what will this cross produce?" you ask "how common is each allele in this group?"

Allele frequency is the proportion of a specific allele in a population. For a gene with two alleles, these frequencies are labeled $p$ and $q$, where $p + q = 1$.

Genotype frequency describes the proportion of individuals with each genotype. Under certain conditions, genotype frequencies can be calculated from allele frequencies:

• Homozygous dominant: $p^2$
• Heterozygous: $2pq$
• Homozygous recessive: $q^2$

This relationship is captured by the Hardy-Weinberg equation:

$p^2 + 2pq + q^2 = 1$

Hardy-Weinberg equilibrium describes a population where allele frequencies stay constant across generations. It holds only when all five of these conditions are met:

1. No mutation
2. No migration (gene flow)
3. Large population size (no genetic drift)
4. Random mating
5. No natural selection

No real population meets all five conditions perfectly, which is exactly the point. Hardy-Weinberg serves as a null model: if observed genotype frequencies don't match the predicted values, something evolutionary is happening. For example, comparing observed ABO blood type frequencies to Hardy-Weinberg predictions can reveal whether non-random mating or selection is at work.

Factors Affecting Allele Frequencies

When Hardy-Weinberg conditions are violated, allele frequencies change. That change is evolution at the population level. Here are the main forces driving it:

Natural selection occurs when individuals with certain heritable traits reproduce more successfully than others. It takes several forms:

• Directional selection shifts the population toward one extreme (e.g., antibiotic resistance increasing in bacteria)
• Stabilizing selection favors intermediate traits and reduces variation
• Disruptive selection favors both extremes over the middle

Genetic drift is random change in allele frequencies, and it hits small populations hardest. Two notable examples:

• Founder effect: a small group colonizes a new area, carrying only a subset of the original population's alleles
• Bottleneck effect: a population crash drastically reduces genetic diversity (cheetahs have extremely low genetic variation due to a historical bottleneck)

Mutation introduces new alleles or modifies existing ones. Types include point mutations, insertions, deletions, and larger chromosomal rearrangements. Mutation is the ultimate source of all genetic variation, though any single mutation is rare. The sickle cell allele (HbS) arose from a single point mutation in the hemoglobin gene.

Gene flow is the transfer of alleles between populations through migration. It can introduce new alleles to a population or shift existing frequencies. Pesticide resistance genes spreading between insect populations is a well-studied example.

Non-random mating doesn't change allele frequencies directly, but it reshuffles genotype frequencies:

• Inbreeding (mating between close relatives) increases homozygosity, which can expose harmful recessive alleles. Purebred dog breeds often show health problems for this reason.
• Assortative mating (choosing mates with similar phenotypes, like height in humans) increases homozygosity for the traits involved without changing overall allele frequencies.

Genetic hitchhiking occurs when a neutral or even slightly harmful allele increases in frequency because it's physically linked on the same chromosome to an allele under positive selection. Coat color variation in mice has been linked to this process.

Meiotic drive is the preferential transmission of certain alleles during meiosis, violating the usual 50/50 segregation. The t-haplotype in mice is a classic case: it gets transmitted to more than 50% of offspring from heterozygous males, even though homozygous tt individuals have reduced fitness.