Heredity & Genetics

Mendel's Laws of Inheritance

Gregor Mendel's work with garden peas established two foundational principles. The Law of Segregation states that each organism carries two alleles for every gene, and these alleles separate during gamete formation so each gamete receives only one. The Law of Independent Assortment states that alleles at different loci sort into gametes independently of each other, provided the genes are on separate chromosomes or far apart on the same chromosome.

A monohybrid cross (Aa x Aa) tracks a single gene and produces a 3:1 phenotypic ratio when dominance is complete. A dihybrid cross (AaBb x AaBb) tracks two genes simultaneously and yields the classic 9:3:3:1 ratio. Understanding these ratios is essential for predicting offspring probabilities and recognizing departures from Mendelian expectations.

Punnett Squares and Probability

Punnett squares organize all possible gamete combinations in a grid format, making it straightforward to derive genotypic and phenotypic ratios. For a monohybrid cross of two heterozygotes the grid is 2x2; for a dihybrid it expands to 4x4 with 16 cells. Each cell represents an equally likely fertilization event.

The multiplication rule applies when calculating the probability of two independent events occurring together (multiply individual probabilities). The addition rule applies when calculating the probability of either of two mutually exclusive outcomes (add individual probabilities). Combining both rules lets you solve complex multi-gene problems without drawing every cell of a large Punnett square.

Dominance Patterns

Not every trait follows simple complete dominance. Recognizing the pattern matters for predicting phenotypic ratios, especially on free-response questions where you must justify your cross.

Multiple Alleles - ABO Blood Types

The ABO blood group demonstrates multiple alleles (three alleles - I^A, I^B, and i - at one locus) combined with codominance. I^A and I^B are codominant to each other, and both are dominant over i. This produces four phenotypic blood types: A, B, AB, and O. Blood-type problems are common on the AP exam because they require understanding of both codominance and multiple alleles simultaneously.

Beyond Simple Mendelian Ratios

Polygenic traits are controlled by two or more genes, each contributing a small additive effect. Skin color, height, and grain color in wheat are classic examples. Polygenic traits produce a continuous distribution of phenotypes (bell curve) rather than discrete categories.

Pleiotropy occurs when a single gene influences multiple phenotypic traits. Sickle cell disease illustrates pleiotropy: the HBB gene mutation affects hemoglobin shape, oxygen transport, red blood cell morphology, and organ function.

Epistasis occurs when one gene masks or modifies the expression of another gene at a different locus. In Labrador coat color, the E gene determines whether pigment is deposited at all, while the B gene determines pigment color (black vs brown). A dog homozygous recessive at the E locus (ee) is yellow regardless of its B genotype, producing a modified 9:3:4 ratio instead of the expected 9:3:3:1.

Sex-Linked Inheritance and Linked Genes

Genes carried on the X chromosome show X-linked inheritance. Males (XY) express X-linked recessive traits more frequently because they have only one X. Hemophilia and red-green color blindness are classic X-linked recessive disorders. In pedigrees, X-linked recessive traits skip generations and appear predominantly in males.

Linked genes are located near each other on the same chromosome and tend to be inherited together, violating independent assortment. Recombination frequency between linked loci is used to construct genetic maps; the farther apart two genes are, the higher the crossover frequency, up to a maximum of 50% (which mimics independent assortment).

Chi-Square Analysis

The chi-square goodness-of-fit test determines whether observed offspring ratios differ significantly from expected Mendelian ratios. The formula is:

Degrees of freedom equal the number of phenotypic classes minus one. Compare the calculated value to the critical value at the 0.05 significance level. If X^2 is less than or equal to the critical value, you fail to reject the null hypothesis, meaning the observed data are consistent with the expected ratio. If X^2 exceeds the critical value, the deviation is statistically significant and something other than chance (linkage, epistasis, selection) may be operating.