AP Biology · Lesson 2

Mendel's rules, probability and the environment

Know Know it

A gene comes in versions called alleles. A diploid organism has two alleles of each autosomal gene: homozygous if they match (RR or rr), heterozygous if they differ (Rr). The genotype is the alleles; the phenotype is the trait that shows. A dominant allele shows its trait in a heterozygote; a recessive allele shows only when it is the only allele present.

Segregation: the two alleles of a gene go into different gametes, because homologs separate in meiosis I. So Rr x Rr gives offspring in the ratio 1 RR : 2 Rr : 1 rr, a 3 : 1 phenotype ratio when R is dominant. Independent assortment: genes on different chromosomes sort into gametes independently, so AaBb x AaBb gives a 9 : 3 : 3 : 1 phenotype ratio. A test cross with a homozygous recessive reveals an unknown genotype: Rr x rr gives half dominant and half recessive offspring.

Ratios are probabilities. The product rule: the chance that two independent events both happen is the product of their chances. The sum rule: the chance that one of two exclusive events happens is the sum of their chances. Work each gene on its own, then multiply. For AaBb x AaBb, the chance of aabb is 1/4 x 1/4 = 1/16.

A chi-square test checks whether counts fit a predicted ratio. For each class, compute (observed - expected) squared, divided by expected, and add the results. The degrees of freedom are the number of classes minus 1. At the usual p = 0.05 level the critical values are 3.84 for 1 degree of freedom, 5.99 for 2 and 7.81 for 3. If chi-square is larger than the critical value, reject the hypothesis that only chance explains the gap. If it is smaller, the data are consistent with the hypothesis.

Phenotype also depends on the environment. One genotype can give different phenotypes under different conditions: phenotypic plasticity. In some mammals a pigment enzyme works only at cooler temperatures, so fur is darker on the ears and paws. In some reptiles, the temperature of the eggs decides the sex of the young. A person with the genotype for phenylketonuria who eats a diet low in phenylalanine from birth can avoid most of its harmful effects.

Trap A ratio is a chance, not a count

A 3 : 1 ratio means each offspring has a 3 in 4 chance of showing the dominant trait. Four offspring will not always be three and one, and two heterozygotes can have four recessive offspring in a row. That is why counts are compared with expected numbers using chi-square, and why small samples wander from the ratio.

Worked example Easy

In a fictional plant, red flowers (R) are dominant to white (r). Two Rr plants are crossed. What fraction of the offspring are expected to have white flowers?

  1. 1/4Answer
  2. 1/2
  3. 3/4
  4. 1/3

How to solve it

  1. Each Rr parent makes gametes that are half R and half r.
  2. White needs rr: an r from each parent.
  3. 1/2 x 1/2 = 1/4.

Why each choice is right or wrong

  • A. Correct. Each parent gives r half the time, so rr has a chance of 1/2 x 1/2 = 1/4.
  • B. Incorrect. 1/2 is the expected fraction of heterozygous Rr offspring, which have red flowers, not white.
  • C. Incorrect. 3/4 is the expected fraction with red flowers (RR plus Rr), the dominant phenotype.
  • D. Incorrect. 1/3 is the share of red-flowered offspring that are RR, not the share with white flowers.

Explain Explain it

Task verbs: calculate, explain

For a cross with two or more genes, calculate one gene at a time. Write the chance for each gene's part of the genotype or phenotype you want, then multiply, because genes on different chromosomes assort independently. In an explanation, name the rule you used and why it applies.

Worked example Medium

In a fictional pea-like plant, purple flowers (A) are dominant to white (a), and round seeds (B) are dominant to wrinkled (b). The genes are on different chromosomes. What fraction of the offspring of AaBb x Aabb are expected to have purple flowers and round seeds?

  1. 3/16
  2. 3/8Answer
  3. 9/16
  4. 1/8

How to solve it

  1. Flower color: Aa x Aa gives purple (AA or Aa) with a chance of 3/4.
  2. Seed shape: Bb x bb gives round (Bb) with a chance of 1/2.
  3. The genes assort independently, so multiply: 3/4 x 1/2 = 3/8.

Why each choice is right or wrong

  • A. Incorrect. 3/16 would come from multiplying 3/4 by 1/4, but Bb x bb gives round seeds half the time, not a quarter.
  • B. Correct. Purple from Aa x Aa is 3/4, round from Bb x bb is 1/2, and 3/4 x 1/2 = 3/8.
  • C. Incorrect. 9/16 is the share for AaBb x AaBb; here the second parent is bb, so round seeds are less likely.
  • D. Incorrect. 1/8 is the chance of white flowers with wrinkled seeds (1/4 x 1/2), the opposite phenotype.

Calculate Your turn

In a fictional beetle, a shiny shell (S) is dominant to dull (s), and long antennae (T) are dominant to short (t). The genes are on different chromosomes. Calculate the chance that one offspring of Ss Tt x ss Tt is dull with short antennae (ss tt). Show the chance for each gene, then explain why you can combine them the way you did.

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Compare with a model answer

A full answer does this

  • Gives a chance of 1/2 for ss and 1/4 for tt, and multiplies them to get 1/8
  • Explains that the chances can be multiplied because the two genes are on different chromosomes and so assort independently (the product rule)

Model answer

For the shell gene, Ss x ss gives ss half the time, so the chance is 1/2. For the antenna gene, Tt x Tt gives tt a quarter of the time, so the chance is 1/4. The chance of ss tt is 1/2 x 1/4 = 1/8. I can multiply because the two genes are on different chromosomes, so they assort independently: the allele a gamete gets for one gene does not affect the allele it gets for the other. By the product rule, the chance of two independent events both happening is the product of their chances.

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