5.3 Mendelian Genetics

A gene is a stretch of DNA that codes for a product, usually a protein, that affects a trait, and an allele is one version of that gene. A diploid organism has two alleles of each gene, one on each homolog. Your genotype is the set of alleles you have (for example Pp). Your phenotype is the trait you can observe (purple flowers). If both alleles are the same (PP or pp), you're homozygous; if they're different (Pp), you're heterozygous.

A dominant allele shows its phenotype in a heterozygote and is written with a capital letter (P). A recessive allele shows only when there's no dominant allele present, so the genotype must be pp. Dominant doesn't mean more common or better; it only describes what the heterozygote looks like.

The law of segregation says the two alleles of a gene separate when gametes form, so each gamete carries just one allele. This happens because homologs separate in anaphase I. A Pp plant makes half P gametes and half p gametes.

The law of independent assortment says alleles of different genes are sorted into gametes independently of each other, as long as the genes are on different chromosomes. It comes from the random orientation of homologous pairs in metaphase I. A plant that is AaBb makes AB, Ab, aB and ab gametes in equal amounts. Genes close together on the same chromosome break this rule (see linkage in 5.4).

Fertilization joins two haploid gametes and restores the diploid number, creating new allele combinations in the zygote. A Punnett square lists one parent's gametes across the top and the other's down the side, and each box is a possible offspring.

Two rules (both on the AP formula sheet) let you skip big Punnett squares. Multiplication rule: if two events are independent, P(A and B) = P(A) × P(B). Addition rule: if two outcomes are mutually exclusive (they can't both happen), P(A or B) = P(A) + P(B).

Because unlinked genes assort independently, you can treat each gene as its own monohybrid cross and multiply. For AaBb × AaBb, the chance of an aabb offspring is ¼ × ¼ = 1/16. The chance a Pp × Pp offspring is heterozygous is P(P from mom and p from dad) + P(p from mom and P from dad) = ¼ + ¼ = ½.

A test cross tells you whether an organism showing the dominant phenotype is homozygous or heterozygous: cross it with a homozygous recessive. If any offspring show the recessive phenotype, the parent must be heterozygous. If many offspring are all dominant, the parent is very likely homozygous dominant.

A pedigree is a family tree for a trait: squares are males, circles are females, filled shapes are affected, and a horizontal line between a male and a female is a mating. Useful clues: if two unaffected parents have an affected child, the trait is recessive. If an affected child always has at least one affected parent and the trait appears in every generation, it's likely dominant. Two affected parents with an unaffected child means the trait must be dominant. Sex-linked patterns are covered in 5.4.

Real crosses never hit ratios exactly, so you use a chi-square (χ²) test to decide whether the difference is just chance. The null hypothesis says there's no real difference between observed and expected results (the data fit the predicted ratio). Compute χ² = Σ (o − e)² / e, using counts, not percentages. Degrees of freedom = number of categories − 1. Compare χ² with the critical value at p = 0.05 from the formula sheet (3.84 for 1 df, 5.99 for 2, 7.81 for 3). If χ² is larger than the critical value, reject the null hypothesis; if it's smaller, fail to reject it.