Biology · AP Biology
Heredity
meiosis and Mendel
A parent passes on half of its chromosomes. Which half is a matter of chance, and that chance is what Mendel counted.
In the figure a cell with four chromosomes makes four cells with two. The red chromosomes came from the cell’s mother, the blue ones from its father. Each new cell gets one of each pair, but which one is random.
This chapter follows chromosomes through meiosis, shows how meiosis shuffles them, and uses probability to predict the offspring of a cross. Then it turns to the patterns Mendel’s ratios do not describe, to the environment’s part in a phenotype, and to what happens when chromosomes are sorted wrongly.
one diploid cell, four haploid cells
Meiosis makes gametes (eggs and sperm) with half the parent’s chromosome number.
A diploid cell (2n) holds two sets of chromosomes, one set from each parent. The two chromosomes of a pair are homologous chromosomes: the same length, the same genes in the same order, possibly with different versions (alleles) of those genes. Human body cells have 2n = 46; human gametes are haploid, n = 23.
Before meiosis the DNA is copied, so each chromosome is two identical sister chromatids joined at a centromere. Then there are two divisions:
Meiosis I separates homologues. The pairs line up together in the middle of the cell and one of each pair goes to each pole. Each of the two cells is now haploid, though its chromosomes still have two chromatids.
Meiosis II separates sister chromatids, much as mitosis does. Result: four haploid cells.
| in the figure | cells | chromosomes per cell | chromatids each | DNA per cell |
|---|
| before meiosis I | 1 | 4 | 2 | 4 |
| after meiosis I | 2 | 2 | 2 | 2 |
| after meiosis II | 4 | 2 | 1 | 1 |
DNA per cell is in units of one gamete’s. Mitosis keeps the chromosome number and makes identical cells; meiosis halves it and makes cells that differ. Fertilization joins two haploid gametes and restores 2n.
homologues trade segments
While homologues are paired at the start of meiosis I, non-sister chromatids exchange matching segments. This is crossing over.
The paired homologues, four chromatids together, form a tetrad. A chromatid of the red homologue and one of the blue break at the same place and rejoin to each other. The point where they cross is a chiasma.
In the figure, gene A lies above the crossover and gene B below it. The red homologue carried A and B, the blue one a and b. After meiosis the four chromatids carry:
| A B | A b | a B | a b |
| parental | recombinant | recombinant | parental |
The recombinant chromatids carry combinations of alleles that neither of the parent’s chromosomes had. Crossing over is why each chromosome a gamete gets is a patchwork of the two homologues, not a copy of either.
Two genes far apart on a chromosome are more likely to have a crossover fall between them than two genes close together (5.4).
more combinations than people
At metaphase I each homologous pair lines up with its mother’s chromosome on one side or the other, independently of every other pair. This is independent assortment.
In the figure, the long pair carries gene A and the short pair gene B. One lining-up sends A B to one pole and a b to the other. Its mirror image sends A b and a B. Over many meioses the four kinds of gamete are equally common.
With n pairs there are 2n combinations. For a human, n = 23:
Random fertilization. Any one of these eggs can meet any one of these sperm, so one couple could make ≈ 7.0 × 1013 different zygotes, before crossing over adds more.
Crossing over, independent assortment and random fertilization together make each offspring of sexual reproduction genetically unique (identical twins aside), and give natural selection variation to act on.
one allele from each parent
Mendel crossed pea plants and counted the offspring. When he crossed the hybrids of round-seeded and wrinkled-seeded plants, the next generation (F2) was about 3 round : 1 wrinkled.
| trait | dominant | recessive | ratio |
|---|
| seed shape | 5,474 round | 1,850 wrinkled | 2.96 : 1 |
| seed colour | 6,022 yellow | 2,001 green | 3.01 : 1 |
| flower colour | 705 purple | 224 white | 3.15 : 1 |
A gene comes in alleles: R (round) and r (wrinkled). An organism’s pair of alleles is its genotype; the trait it shows is its phenotype. RR and rr are homozygous, Rr heterozygous. R is dominant: Rr seeds are round. r is recessive: it shows only in rr.
The law of segregation. The two alleles of a gene separate into different gametes, half the gametes carrying each. That is meiosis I: the homologues that carry them go to opposite poles.
The Punnett square crosses each kind of egg with each kind of sperm: Rr × Rr gives 1 RR : 2 Rr : 1 rr, so 3 round : 1 wrinkled.
A round seed may be RR or Rr. A testcross to an rr plant tells which: RR gives all round offspring, Rr half wrinkled.
9 : 3 : 3 : 1
Genes on different chromosomes are inherited independently of each other: Mendel’s law of independent assortment, the result of the pairs lining up independently (5.2).
So two genes can be treated one at a time and combined with two rules:
Product rule. For independent events, P(A and B) = P(A) × P(B).
Sum rule. For events that exclude each other, P(A or B) = P(A) + P(B).
Example. RrYy × RrYy, with yellow (Y) dominant over green (y). Each gene alone gives 3/4 dominant, 1/4 recessive:
| phenotype | round yellow | round green | wrinkled yellow | wrinkled green |
|---|
| of 16 | 9 | 3 | 3 | 1 |
|---|
The sum rule finds a heterozygote: from Rr × Rr, Rr arises as R egg with r sperm or r egg with R sperm, ¼ + ¼ = ½.
The rules scale where a Punnett square would not: from AaBbCc × AaBbCc, P(aabbcc) = (¼)³ = 1/64.
In the figure each seed’s shape is its shape; white stands for yellow and grey for green.
is the difference just chance?
Real counts never match a predicted ratio exactly. The chi-square test asks whether the difference is small enough to be chance.
where o is each observed count and e the count expected. The null hypothesis here: the two genes assort independently, so the F2 is 9 : 3 : 3 : 1. Mendel counted 556 seeds:
| o | e | (o − e)²/e |
|---|
| round yellow | 315 | 312.75 | 0.016 |
| round green | 108 | 104.25 | 0.135 |
| wrinkled yellow | 101 | 104.25 | 0.101 |
| wrinkled green | 32 | 34.75 | 0.218 |
| total | 556 | 556 | χ² = 0.47 |
|---|
Degrees of freedom = classes − 1 = 3. From the formula sheet the critical value at p = 0.05 is 7.81. Since 0.47 < 7.81, we fail to reject the null hypothesis: deviations this size are what chance gives.
A χ² above the critical value would reject it: the genes may be linked (5.4), or one genotype may survive less well. Use counts, never percentages; and failing to reject supports a hypothesis but does not prove it.
genes that travel together
Genes close together on the same chromosome are linked: they tend to be inherited together, and do not assort independently.
Only a crossover between them separates them. In the figure, a crossover between A and B makes recombinant chromatids; one outside that stretch leaves the combinations as they were.
Testcross. A fly that got A B from one parent and a b from the other is crossed to aabb. If the genes assorted independently the four classes would be 1 : 1 : 1 : 1. They are not:
| offspring | number | |
|---|
| A B / a b | 415 | parental |
| a b / a b | 405 | parental |
| A b / a b | 92 | recombinant |
| a B / a b | 88 | recombinant |
RF is the recombination frequency. One map unit (centimorgan) is 1% recombination, so A and B are 18 map units apart. Farther apart, more crossovers fall between: higher frequency. It never exceeds 50%, which is what unlinked genes give.
Mapping. If A–B is 18, B–C 7 and A–C 25, then 18 + 7 = 25: the order is A–B–C.
sons get their X from their mother
In humans and fruit flies, females are XX and males XY. Genes on the X chromosome are X-linked; the small Y carries few genes.
A male has one X, so whatever allele it carries shows, dominant or recessive. A female shows a recessive X-linked trait only if both her X’s carry it; with one copy she is a carrier.
Morgan’s flies. White eyes (r) is a recessive X-linked allele. A carrier female XRXr × a red-eyed male XRY:
| daughters | sons |
|---|
| red eyes | all (half carriers) | half |
| white eyes | none | half |
A father gives his X to every daughter and his Y to every son. So an X-linked recessive trait is far more common in males, usually reaches them through carrier mothers, and is never passed from father to son.
Human examples: red–green colour blindness and hemophilia.
many patterns of inheritance
Mendel’s ratios assume one gene, two alleles, one dominant, and one trait. Many traits break one of those.
| pattern | what happens | example |
|---|
| incomplete dominance | the heterozygote is in between | red × white snapdragons give pink; F2 1 red : 2 pink : 1 white |
| codominance | both alleles show in full | IAIB: type AB blood |
| multiple alleles | more than two alleles in the population | ABO: IA, IB, i |
| polygenic | several genes add up | human height, skin colour |
| pleiotropy | one gene affects several traits | the sickle-cell allele |
Polygenic. In the figure three genes each add one unit of a trait per capital allele. AaBbCc × AaBbCc gives 64 equally likely combinations, and the number of capital alleles falls in a bell shape, 1 : 6 : 15 : 20 : 15 : 6 : 1. With more genes, and the environment, the steps blur into continuous variation.
Pleiotropy. The sickle-cell allele changes one amino acid of hemoglobin. Its effects include sickled red blood cells, anemia, pain, damage to several organs, and, in heterozygotes, resistance to malaria.
Such traits do not give Mendel’s ratios; a chi-square test against 3 : 1 or 9 : 3 : 3 : 1 will reject them.
mitochondria come with the egg
Mitochondria and chloroplasts have their own DNA. Their genes do not follow Mendel’s laws.
These organelles are not divided by meiosis. They are shared out at random to daughter cells and gametes, with the cytoplasm.
In humans and other animals the zygote’s mitochondria come from the egg. The sperm brings its nucleus; its few mitochondria, in the midpiece, are destroyed in the egg. So a trait coded in mitochondrial DNA is maternally inherited:
| parent with the trait | children who can inherit it |
|---|
| mother | sons and daughters |
| father | none |
Example: Leber’s hereditary optic neuropathy, a loss of vision caused by mutations in mitochondrial genes.
In plants, chloroplasts sorted at random to cells can give leaves patches of green and white (variegation).
one genotype, more than one phenotype
A phenotype is made by genes and environment together. One genotype giving different phenotypes in different environments is phenotypic plasticity.
Temperature and sex. Many turtles have no sex chromosomes; the temperature of the egg during development sets the sex. In the figure’s model species, eggs below the pivotal temperature, 29 °C, hatch mostly male, above it mostly female: at 27 °C, 2.6% female; at 31 °C, 97.4%.
| environment | effect |
|---|
| soil pH | hydrangeas flower blue in acid soil, pink in alkaline |
| temperature | Himalayan rabbits grow dark fur where skin is cold (ears, nose, paws) |
| season | arctic foxes grow a white coat in winter, brown in summer |
| diet | a low-phenylalanine diet prevents the intellectual disability of PKU |
| nutrition | human height |
The rabbit’s pigment enzyme is temperature-sensitive: it works only where the body is cool. The PKU genotype is unchanged by the diet; the phenotype is not.
when meiosis mis-sorts
Genes sit on chromosomes, and chromosomes’ movements in meiosis explain Mendel’s laws: this is the chromosome theory of inheritance. When those movements go wrong, gametes get the wrong number.
Nondisjunction is a failure to separate: homologues in meiosis I, or sister chromatids in meiosis II.
| fails in | gametes |
|---|
| meiosis I | two n + 1, two n − 1 |
| meiosis II (one cell) | two n, one n + 1, one n − 1 |
An n + 1 gamete fertilized by a normal one gives a trisomy (2n + 1); an n − 1 gamete gives a monosomy (2n − 1).
| condition | chromosomes |
|---|
| Down syndrome, trisomy 21 | 47 |
| Turner syndrome, one X | 45, X |
| Klinefelter syndrome | 47, XXY |
Most other changes in chromosome number are lethal before birth. The risk of trisomy 21 rises with the mother’s age.
reading inheritance from a family
A pedigree charts a trait through a family: squares are males, circles females, filled symbols affected; a horizontal line joins parents, and a vertical one leads to their children.
Working it out. II-2 is affected, but his parents are not. So the trait is recessive, and he is aa. Each parent gave him an a while showing A: both are Aa. His children are unaffected but got an a from him: Aa.
His unaffected sister II-1 is AA or Aa. Of the children of Aa × Aa who are unaffected, 2 in 3 are Aa:
| pattern | signs | example |
|---|
| autosomal recessive | skips generations; affected children of unaffected parents | cystic fibrosis, sickle-cell disease |
| autosomal dominant | every affected person has an affected parent | Huntington’s disease |
| X-linked recessive | mostly males, through carrier mothers | hemophilia |
| mitochondrial | from mothers to all their children | LHON |
Genetic testing and counselling raise ethical, social and medical questions: who should know a result, and what to do with it.
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