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Genetics Unit 1: Mendelian Inheritance and Probability

This unit covers how single genes and pairs of genes are passed from parents to offspring, and the probability tools used to predict and test cross results.

Covers: Alleles, genotype and phenotype, Monohybrid crosses and segregation, Dihybrid crosses and independent assortment, Test crosses, Product, sum and binomial rules, Chi-square goodness of fit

Study guide

Mendel worked with pea plants that had clear either/or traits and true-breeding lines. When he crossed purple-flowered and white-flowered lines, all F1 plants were purple, but white returned in about one quarter of the F2. He explained this with paired hereditary factors that we now call alleles of a gene. A diploid organism carries two alleles for each gene, one from each parent. If the two alleles are the same, the organism is homozygous; if different, heterozygous. The genotype is the allele combination, and the phenotype is the observable trait. A dominant allele shows its phenotype in a heterozygote, and a recessive allele shows only when homozygous.

The law of segregation says the two alleles of a gene separate during gamete formation, so each gamete gets exactly one. A heterozygote Aa makes A and a gametes in equal numbers. Fertilization combines gametes at random, which is why a Punnett square works: Aa × Aa gives AA, Aa and aa in a 1:2:1 genotypic ratio and a 3:1 phenotypic ratio when A is completely dominant. A test cross mates a dominant-phenotype individual to a homozygous recessive. Because the recessive parent contributes only a, the offspring phenotypes directly reveal the gametes from the unknown parent: all dominant suggests AA, and a 1:1 ratio means Aa.

The law of independent assortment says alleles of different genes sort into gametes independently, as long as the genes are on different chromosomes (or very far apart on one). The physical reason is that each homologous pair orients randomly at metaphase I of meiosis. A dihybrid AaBb therefore makes four gamete types, AB, Ab, aB and ab, each 1/4 of the time. Crossing two dihybrids gives the famous 9:3:3:1 phenotypic ratio, which is simply two independent 3:1 ratios multiplied together. A dihybrid test cross, AaBb × aabb, gives a 1:1:1:1 ratio.

For crosses with several genes, Punnett squares become huge, so geneticists use probability. The product rule multiplies probabilities for independent events that must all happen ('and'). The sum rule adds probabilities for mutually exclusive outcomes ('or'). Break a multigene problem into one gene at a time, find each probability, then multiply. For questions about how many children in a family will have a trait, use the binomial formula: P = C(n,k) p^k q^(n−k), where the coefficient counts the possible birth orders. For 'at least one' questions, compute 1 minus the probability of none.

Real data rarely match ratios perfectly, so the chi-square test asks whether a deviation is larger than chance would produce. Compute expected counts from the hypothesis, then χ² = Σ (O − E)²/E using counts, not percentages. Degrees of freedom equal the number of phenotype classes minus one. If χ² is below the critical value (3.84 for 1 df, 5.99 for 2 df, 7.81 for 3 df at p = 0.05), you fail to reject the hypothesis; the deviation could be chance. If it is above, you reject the hypothesis and look for an explanation such as linkage or reduced viability.

Key ideas

• Each diploid individual carries two alleles per gene, and each gamete carries one.
• Heterozygote × heterozygote gives a 1:2:1 genotypic and 3:1 phenotypic ratio with complete dominance.
• Genes on different chromosomes assort independently because homologous pairs orient randomly at metaphase I.
• Multigene problems are solved one gene at a time and then multiplied.
• Use the binomial formula when the question asks how many of several offspring show a trait.
• A test cross to a homozygous recessive reveals the gametes of the unknown parent.
• The chi-square test can reject a hypothesis but never proves it true.

Formulas and rules

Common mistakes

• Using 1/2 instead of 2/3 for the chance that an unaffected child of two carriers is a carrier.
• Adding probabilities for an 'and' question or multiplying for an 'or' question.
• Forgetting the binomial coefficient when the order of births is not specified.
• Running chi-square on percentages instead of actual counts, or using the wrong degrees of freedom.
• Saying a chi-square result 'proves' a ratio instead of 'fails to reject' it.

Before the test, make sure you can

• Explain segregation and independent assortment and link each to meiosis.
• Predict genotypic and phenotypic ratios for monohybrid and dihybrid crosses.
• Use a test cross result to determine an unknown genotype.
• Calculate multigene probabilities with the product and sum rules.
• Calculate binomial probabilities for families of several children.
• Calculate the 2/3 carrier probability for unaffected siblings of affected individuals.
• Perform a chi-square test and interpret it with the correct degrees of freedom.

Words to know

Gene

A heritable unit of DNA at a particular chromosomal location that influences a trait.

Allele

One of the alternative versions of a gene.

Locus

The physical position of a gene on a chromosome.

Genotype

The combination of alleles an individual carries, such as Aa.

Phenotype

The observable trait produced by a genotype and environment.

Homozygous

Having two identical alleles at a locus (AA or aa).

Heterozygous

Having two different alleles at a locus (Aa).

Dominant allele

An allele whose phenotype appears in heterozygotes.

Recessive allele

An allele whose phenotype appears only when homozygous.

True-breeding

A line that produces only offspring like itself when self-fertilized, because it is homozygous.

F1 and F2

The first and second filial generations after a parental (P) cross.

Law of segregation

The two alleles of a gene separate so each gamete receives one.

Law of independent assortment

Alleles of different genes assort into gametes independently of each other.

Test cross

A cross of a dominant-phenotype individual to a homozygous recessive to find its genotype.

Monohybrid cross

A cross between individuals heterozygous for one gene.

Dihybrid cross

A cross between individuals heterozygous for two genes.

Chi-square test

A statistical test comparing observed counts with counts expected under a hypothesis.

Degrees of freedom

In a goodness-of-fit test, the number of classes minus one.

Sample practice questions

30 more questions like these, from level 1 to 5, are in the practice set.