Mendelian Genetics and the Chromosomal Basis of Inheritance

Why do two brown eyed parents sometimes have a blue eyed child, why are color blind men so much more common than color blind women, and why does a single extra chromosome change the course of a whole life? The answers come from a set of rules first worked out in a monastery garden with pea plants and later traced to the behavior of chromosomes during meiosis. This chapter teaches you those rules, shows you how to calculate the odds of any genetic outcome, and then follows the many ways real inheritance bends and breaks the simple patterns.

Section 1Mendel's experiments and the laws of segregation and independent assortment

The problem Mendel solved

Before the 1860s, most naturalists explained heredity with the blending hypothesis: the traits of two parents mix in their offspring the way blue and yellow paint mix to make green. Blending has an obvious flaw. If it were true, variation would shrink every generation until a population became uniform, and a trait that disappeared in one generation could never come back. Farmers and breeders knew better. A white flowered plant could appear among the offspring of purple flowered parents, and a calf could resemble its grandmother more than either parent.

Gregor Mendel, a monk trained in physics and mathematics, replaced blending with a particulate hypothesis. He proposed that parents pass on discrete heritable factors, which we now call genes, and that these factors keep their identity from generation to generation even when they are hidden. He reached this conclusion not by clever argument but by counting thousands of offspring and treating the counts mathematically, an approach that was unusual for biology at the time.

Why the garden pea was a good choice

Mendel worked with the garden pea, Pisum sativum, and his choice of organism mattered as much as his method.

• Peas come in many varieties with clear either or characters: a character is a heritable feature such as flower color, and a trait is one variant of it, such as purple or white.
• Peas normally self fertilize, because the pollen producing stamens and egg producing carpel are enclosed together in the same flower. This let Mendel start with true breeding lines, plants that produce only offspring like themselves when they self.
• He could also force cross pollination by cutting away the immature stamens of one plant and dusting its carpel with pollen from another. That gave him full control over which plants mated.

Mendel also made two smart experimental decisions. He followed characters that came in only two clearly different forms, and he tracked them for at least three generations. The true breeding parents are the P generation (parental). Their hybrid offspring are the F₁ generation (first filial), and the offspring produced when F₁ plants self or cross with one another are the F₂ generation.

The monohybrid cross

In a typical experiment, Mendel crossed a true breeding purple flowered plant with a true breeding white flowered plant. Every F₁ plant had purple flowers. The white trait had not blended into a pale lavender; it had simply vanished. When he let the F₁ plants self pollinate, white flowers reappeared in the F₂ in roughly one quarter of the plants: 705 purple to 224 white, close to 3:1. A cross between parents that differ in one character, followed into the F₂, is a monohybrid cross, and the F₁ plants are monohybrids (heterozygous for one gene).

Mendel saw the same pattern for all seven characters in the table above. He called the trait that appeared in the F₁ dominant and the trait that was hidden in the F₁ and reappeared in the F₂ recessive. To explain the 3:1 ratio, he built a model with four parts. Translated into modern terms:

1. Alternative versions of a gene explain variation in inherited characters. These versions are alleles. The gene for flower color has a purple allele and a white allele. Each gene sits at a specific place, its locus (plural loci), on a particular chromosome.
2. An organism inherits two copies of each gene, one from each parent. The two copies sit at the same locus on a pair of homologous chromosomes. They may be identical, as in true breeding plants, or different, as in the F₁ hybrids.
3. If the two alleles differ, the dominant allele determines appearance and the recessive allele has no noticeable effect. By convention, a capital letter stands for the dominant allele (P for purple) and the lowercase letter for the recessive allele (p for white).
4. The two alleles for a character separate (segregate) during gamete formation and end up in different gametes. An egg or a sperm carries only one allele for each character. This is the law of segregation.

Vocabulary that makes problems easier

An organism with two identical alleles for a gene, such as PP or pp, is homozygous for that gene. One with two different alleles, Pp, is heterozygous. The genotype is the genetic makeup (PP, Pp or pp); the phenotype is the observable appearance (purple or white), which also includes physiological and biochemical traits. Two organisms can share a phenotype but differ in genotype: PP and Pp plants are both purple. That is why the F₂ phenotype ratio is 3:1 while the genotype ratio is 1 PP : 2 Pp : 1 pp.

A Punnett square is a grid that lists the possible gametes of one parent along the top and those of the other along the side. Each box is one possible fertilization, and because each gamete type is equally likely, each box is equally likely.

The testcross

A purple flowered plant could be PP or Pp. To find out which, breed it with a homozygous recessive plant (pp). This is a testcross. If all offspring are purple, the mystery parent was almost certainly PP, because a Pp parent would have given about half white offspring. If any white offspring appear, the parent must be Pp. The testcross works because the recessive parent contributes only recessive alleles, so the offspring phenotypes directly reveal the gametes of the unknown parent.

The dihybrid cross and independent assortment

Mendel next asked whether the alleles of two different genes travel together or separately. He crossed true breeding plants with round yellow seeds (RRYY) and true breeding plants with wrinkled green seeds (rryy). The F₁ were all round and yellow, and they were dihybrids, RrYy. Two hypotheses predicted different F₂ results.

• If the alleles stayed together as they had arrived from each parent (dependent assortment), an F₁ plant would make only two kinds of gametes, RY and ry, and the F₂ would show a 3:1 ratio of round yellow to wrinkled green, with no new combinations.
• If the alleles of each gene sorted independently, an F₁ plant would make four kinds of gametes in equal numbers, RY, Ry, rY and ry, and a 4 × 4 Punnett square would give 16 equally likely combinations.

Mendel's F₂ counts were 315 round yellow, 108 round green, 101 wrinkled yellow and 32 wrinkled green, very close to 9:3:3:1. The new combinations (round green and wrinkled yellow) proved that the two genes had sorted independently. Notice that each character on its own still gave 3:1: round to wrinkled was 423:133, and yellow to green was 416:140. The 9:3:3:1 ratio is simply (3:1) × (3:1). This led to the law of independent assortment: each pair of alleles segregates independently of each other pair during gamete formation.

Independent assortment has an important limit. It holds for genes on different chromosomes and for genes so far apart on the same chromosome that crossing over separates them about half the time. Genes close together on one chromosome are linked and tend to be inherited together (Section 4). Mendel was fortunate: the seven characters he reported are controlled by genes that either sit on different chromosomes or are far enough apart to behave as if they were.

The physical basis: meiosis

Mendel had no idea what his factors were made of. Decades later, cytologists watching cells divide noticed that chromosomes behave exactly the way Mendel's factors must. The match is the heart of the chromosome theory of inheritance.

• Segregation happens because homologous chromosomes, one from each parent, separate in anaphase I of meiosis. Each daughter cell receives one homolog, and therefore one allele, for every locus. (If crossing over has swapped the alleles between sister chromatids, the final separation of alleles occurs at anaphase II.)
• Independent assortment happens because each pair of homologs lines up at the metaphase plate in metaphase I independently of every other pair. Whether the maternal or paternal homolog of chromosome 1 faces a given pole has no effect on which homolog of chromosome 2 faces that pole.

Section 2Probability and genetic problems

Why genetics is a probability science

Segregation and fertilization are random events, much like coin tosses. A heterozygote makes P and p gametes in equal numbers, but which gamete reaches a particular egg is a matter of chance. That is why Mendel's counts were close to 3:1 but never exactly 3:1, and why a family with four children can easily have no affected children even when each child faces a one in four risk. A probability is a number from 0 (the event never happens) to 1 (it always happens), and the probabilities of all possible outcomes of an event add up to 1. Each new child, like each new coin toss, is an independent event: earlier outcomes do not change the odds for the next one.

The multiplication rule

The multiplication rule states that the probability that two or more independent events all occur together is the product of their separate probabilities. The key words are "and" or "both." For an Rr × Rr cross, the chance that the egg carries r is 1/2 and the chance that the sperm carries r is 1/2, so the chance of an rr offspring is 1/2 × 1/2 = 1/4. The same rule tells you that the chance that two children in a row will both be rr is 1/4 × 1/4 = 1/16.

The addition rule

The addition rule states that the probability that any one of two or more mutually exclusive events will occur is the sum of their individual probabilities. The key word is "or." Mutually exclusive means the events cannot happen together: a single offspring cannot be both Rr made by an R egg and r sperm and Rr made by an r egg and R sperm. Each of those ways has probability 1/4, so the probability of a heterozygous offspring is 1/4 + 1/4 = 1/2.

Solving multigene problems without giant Punnett squares

A trihybrid cross would need a 64 box Punnett square. Instead, because independently assorting genes behave like separate monohybrid crosses, break the problem into one gene at a time, find the probability for each, and multiply.

Worked example. In the cross AaBbCcDd × AaBbccDd, what fraction of offspring will be AaBbccdd?

• Aa × Aa gives Aa with probability 1/2.
• Bb × Bb gives Bb with probability 1/2.
• Cc × cc gives cc with probability 1/2.
• Dd × Dd gives dd with probability 1/4.
• Multiply: 1/2 × 1/2 × 1/2 × 1/4 = 1/32.

Worked example with "or." In the cross PpYyRr × Ppyyrr, what fraction of offspring will show at least two recessive traits? List the genotypes that qualify and calculate each one with the multiplication rule, then add. The qualifying genotypes are ppyyRr, ppYyrr, Ppyyrr, PPyyrr and ppyyrr, which give 1/16 + 1/16 + 2/16 + 1/16 + 1/16 = 6/16, or 3/8. The pattern is always the same: multiply within a combination, add across combinations.

The binomial expression: "exactly k of n"

Families raise a different kind of question: in a family of three children, what is the chance that exactly two are affected by a recessive condition when both parents are carriers? The two affected children could be the first and second, first and third, or second and third. Each specific birth order has probability (1/4)(1/4)(3/4) = 3/64, and there are three orders, so the answer is 3 × 3/64 = 9/64. The general form is the binomial expression:

P(exactly k of n) = [n! / (k!(n − k)!)] × p^k × q^n−k

Here p is the probability of the event in one trial and q = 1 − p. The fraction with factorials counts the number of orders. For "at least one" questions, the fastest route is often to subtract from 1: the probability that at least one of four children is affected is 1 − (3/4)⁴ = 1 − 81/256 = 175/256.

Conditional probability: the two-thirds rule

Sometimes information you already have changes the odds. Suppose two carrier parents (Aa × Aa) have a son who does not have the recessive disorder. What is the chance he is a carrier? Without any information, the probabilities are 1/4 AA, 1/2 Aa and 1/4 aa. But we know he is not aa, so only the AA and Aa outcomes remain, in a ratio of 1:2. The chance he is a carrier is therefore 2/3, not 1/2. This conditional probability appears constantly in genetic counseling problems involving the unaffected siblings of affected people.

Pedigree analysis

Geneticists cannot arrange human matings, so they study families that already exist. A pedigree is a family tree that shows how a trait passes through generations. Squares are males and circles are females; a filled symbol is an affected person; a horizontal line joins mates; a vertical line drops to their children, who are listed left to right in birth order. Generations are numbered with Roman numerals and individuals with Arabic numerals, so II-3 is the third person in the second generation.

To identify the mode of inheritance, look for a few decisive clues rather than trying every possibility at once.

Testing whether data fit a ratio: the chi-square test

Mendel's 315:108:101:32 is close to 9:3:3:1, but how close is close enough? The chi-square (χ²) goodness of fit test asks whether the difference between observed (O) and expected (E) counts is small enough to be explained by chance alone. The null hypothesis is that the data fit the predicted ratio and any deviation is random.

1. Calculate expected counts from the total and the predicted ratio. For 556 seeds and 9:3:3:1: 312.75, 104.25, 104.25 and 34.75.
2. For each class, compute (O − E)²/E and add them: 0.016 + 0.135 + 0.101 + 0.218 = χ² = 0.47.
3. Find the degrees of freedom: the number of classes minus 1, here 4 − 1 = 3.
4. Compare with the critical value at p = 0.05. If χ² is smaller than the critical value, you fail to reject the null hypothesis; the deviation is consistent with chance.

Mendel's value of 0.47 is far below 7.81, so the data fit independent assortment well. A large χ² does not prove the model wrong, but it signals that something other than chance, such as linkage or reduced survival of one genotype, is probably at work.

Section 3Extensions: dominance, multiple alleles, epistasis, polygenic traits

Mendel's rules still hold; the relationships get richer

Mendel chose characters in which one allele was completely dominant and each character was controlled by one gene with two alleles. Most traits are not that tidy. The patterns in this section can look as if they break Mendel's laws, but they do not. Alleles still segregate and genes still assort independently. What changes is the relationship between genotype and phenotype: how two alleles of the same gene interact, how many alleles exist in a population, how genes interact with one another and how the environment shapes the outcome.

Degrees of dominance

With complete dominance, the heterozygote and the dominant homozygote look the same. With incomplete dominance, the heterozygote has a phenotype intermediate between the two homozygotes. Crossing red snapdragons (C^RC^R) with white snapdragons (C^WC^W) gives all pink F₁ flowers. This might look like blending, but the F₂ settles the question: it contains red, pink and white in a 1:2:1 ratio, so the red and white alleles came through intact. In incomplete dominance the phenotype ratio equals the genotype ratio because every genotype has its own look. The molecular reason is usually dosage: one functional allele makes only enough red pigment to tint the petals pink.

With codominance, the heterozygote fully and separately expresses both alleles. The human MN blood group is the classic case. The M and N alleles specify slightly different forms of a glycoprotein on red blood cells. People who are MN have both forms on their cells, not an intermediate molecule. The AB blood type, discussed below, is another example.

Dominance can also depend on the level at which you look. In Tay-Sachs disease, children with two defective alleles cannot break down a membrane lipid (GM2 ganglioside) in brain cells and die in early childhood. At the level of the whole organism, the allele is recessive, because heterozygotes are healthy. At the biochemical level, heterozygotes have about half the normal enzyme activity, which looks like incomplete dominance. At the molecular level, both normal and defective enzyme molecules are made, which is codominance. Dominance describes phenotype, so it always depends on which phenotype you measure.

Multiple alleles

Any one diploid individual carries at most two alleles of a gene, but a population can carry many. The ABO blood group has three common alleles: I^A, I^B and i. I^A encodes an enzyme that adds the sugar N-acetylgalactosamine to a carbohydrate on the red cell surface, forming the A antigen; I^B encodes an enzyme that adds galactose, forming the B antigen; i encodes no functional enzyme. I^A and I^B are codominant with each other, and both are completely dominant over i. Six genotypes give four phenotypes.

Rabbit coat color shows a dominance series of four alleles: full color (C) > chinchilla (c^ch) > Himalayan (c^h) > albino (c). The Himalayan allele produces a temperature sensitive version of tyrosinase, the enzyme that starts melanin synthesis. The enzyme works only below body temperature, so pigment forms on the cool ears, nose, feet and tail. The same allele explains the color points of Siamese cats.

Pleiotropy and lethal alleles

Many genes affect more than one phenotypic character, a property called pleiotropy. The sickle cell allele changes one amino acid in the β chain of hemoglobin. In people homozygous for it, red cells sickle when oxygen is low, which leads to anemia, pain crises, organ damage, stroke risk and a damaged spleen. One base change, many effects. Marfan syndrome, a dominant disorder of the connective tissue protein fibrillin-1, affects the skeleton (long limbs), the eyes (dislocated lenses) and the aorta (dilation and dissection).

Some alleles are lethal when homozygous. In mice, the dominant yellow coat allele A^Y gives yellow fur in heterozygotes, but A^YA^Y embryos die. A cross of two yellow mice therefore gives yellow and agouti (wild type) offspring in a 2:1 ratio rather than 3:1, because the expected quarter of A^YA^Y offspring never appears. The A^Y allele is dominant for coat color but recessive for lethality, a reminder that dominance is defined per trait.

Epistasis: one gene masks another

In epistasis (Greek for "standing upon"), the phenotype produced by one gene depends on the genotype at a second gene. Labrador retrievers make a clear example. Gene B controls the type of pigment: B (dominant) makes black eumelanin and b makes brown. A second gene, E, controls whether pigment is deposited in the hair at all. Dogs with at least one E allele deposit pigment; ee dogs deposit almost none in the hair and are yellow whatever their B genotype. Gene E is said to be epistatic to gene B.

Cross two dogs that are both BbEe. The 16 combinations still form, in the familiar 9:3:3:1 genotype classes: 9 B_E_, 3 bbE_, 3 B_ee, 1 bbee. But the last two classes look the same, so the phenotype ratio becomes 9 black : 3 chocolate : 4 yellow. When a dihybrid cross gives a ratio whose numbers add to 16 but that is not 9:3:3:1, suspect two genes interacting.

The 9:7 ratio is worth understanding in terms of a pathway. Suppose a white precursor is converted to an intermediate by enzyme C and the intermediate to purple pigment by enzyme P. A plant needs at least one working allele of both genes (C_P_, 9/16) to make purple. Any plant that is cc, pp or both (3 + 3 + 1 = 7/16) is white. Crossing two different white strains (CCpp × ccPP) can therefore give all purple F₁ plants, a complementation result that tells geneticists the two white mutations are in different genes.

Polygenic inheritance and quantitative traits

Mendel's characters came in discrete either or forms. Height, skin color, blood pressure, birth weight and the number of grains on a wheat head vary continuously along a scale. These quantitative characters usually reflect polygenic inheritance, the additive effect of two or more genes on one phenotype.

A simplified model of skin pigmentation imagines three genes, each with a "dark" allele (A, B, C) that adds one unit of darkness and a "light" allele (a, b, c) that adds none. A person who is AaBbCc has three dark units. If two such people have children, offspring can carry anywhere from 0 to 6 dark alleles, giving seven phenotypic classes in the proportions 1:6:15:20:15:6:1 out of 64. Most children fall near the middle and few at the extremes. Add more genes and environmental effects such as sun exposure, and the steps blur into a smooth bell shaped curve.

Nature and nurture

Genotype rarely fixes a phenotype exactly. The range of phenotypes one genotype can produce across environments is its norm of reaction. Hydrangeas of the same genotype bloom blue in acidic soil and pink in neutral or basic soil, because soil pH controls how much aluminum the plant absorbs. Human height depends on nutrition as well as genes. Traits shaped by many genes plus the environment, such as heart disease, type 2 diabetes, many cancers and some mental illnesses, are called multifactorial.

Two more terms describe how consistently a genotype shows itself. Penetrance is the proportion of individuals with a genotype who show the expected phenotype at all; if only 80 percent of people with a dominant polydactyly allele have extra digits, penetrance is 80 percent (incomplete penetrance). Expressivity is the degree to which a phenotype is expressed in those who show it; in neurofibromatosis type 1, one family member may have a few pale brown skin spots while another has many tumors along nerves (variable expressivity).

Section 4Sex linkage, linked genes and recombination

The chromosome theory and Morgan's white eyed fly

Around 1902, Walter Sutton and Theodor Boveri independently noted the parallels between Mendel's factors and chromosomes: both come in pairs, both separate during gamete formation and both assort independently. The chromosome theory of inheritance proposed that genes occupy specific loci on chromosomes and that chromosome behavior in meiosis explains Mendel's laws. The first solid evidence tying a specific gene to a specific chromosome came from Thomas Hunt Morgan's work with the fruit fly Drosophila melanogaster, an ideal organism that breeds every two weeks, produces hundreds of offspring and has only four pairs of chromosomes.

Wild type flies have red eyes. (The wild type is the phenotype most common in natural populations; alleles for other phenotypes are mutant alleles.) Morgan found a male with white eyes and crossed it with a red eyed female. All F₁ flies had red eyes, so red was dominant. In the F₂, the familiar 3:1 ratio appeared, but with a twist: every white eyed fly was male. Half the F₂ males had white eyes and none of the females did. Morgan concluded that the eye color gene lies on the X chromosome and that the Y chromosome carries no allele for it. A male, with one X, shows whatever allele that X carries.

Sex determination

In humans and other mammals, females are XX and males are XY. The Y chromosome is small and carries relatively few genes, but one of them, SRY (sex determining region of Y), triggers development of testes in the embryo; without it, the gonads develop as ovaries. Other organisms use other systems.

Inheritance of X linked genes

Genes on a sex chromosome are sex linked; in humans, the term usually means X linked, because the X carries about 1,000 genes and most have nothing to do with sex. A male has only one copy of each X linked gene and is called hemizygous. That single fact explains the pattern of X linked recessive disorders.

• A male who inherits one recessive X linked allele shows the trait, because no second allele can mask it. A female must inherit two copies, which is much rarer. If an allele has frequency 1/10 in a population, about 1 in 10 males but only 1 in 100 females will be affected.
• A father passes his X to all his daughters and his Y to all his sons, so an affected father never passes an X linked trait to a son, but all his daughters become carriers.
• A carrier mother (X^AX^a) passes the allele to half her children: half of her sons will be affected and half of her daughters will be carriers.

Important X linked recessive disorders include red-green color blindness (about 8 percent of males of northern European ancestry), hemophilia A (lack of clotting factor VIII), Duchenne muscular dystrophy (absence of the muscle protein dystrophin, causing progressive weakness from early childhood) and G6PD deficiency (red cells that break down under oxidative stress).

X inactivation

Females have two X chromosomes, yet they do not make twice as much of each X linked protein as males. Early in embryonic development of a female mammal, one X in each cell condenses into a compact Barr body that lies along the inside of the nuclear envelope and is mostly silent. The choice of which X to inactivate is random and independent in each embryonic cell, but once made, all descendants of that cell keep the same inactive X. A female is therefore a mosaic of two cell populations. Inactivation depends on the XIST gene, which is expressed only from the chromosome that will become the Barr body; its RNA coats that X and recruits proteins that modify chromatin and shut it down.

The tortoiseshell or calico cat shows mosaicism on the outside. An X linked gene has an orange allele and a black allele. A heterozygous female has patches of orange fur where the black X is inactive and patches of black where the orange X is inactive (white patches come from a separate gene). Male cats with these colors are almost always XXY. In humans, a carrier female for an X linked condition can show mild symptoms if, by chance, most cells in a relevant tissue inactivated the normal X.

Linked genes

Each chromosome carries hundreds or thousands of genes. Genes on the same chromosome tend to be inherited together and are called linked genes. (Do not confuse linked genes, which share any chromosome, with sex linked genes, which are on a sex chromosome.) Morgan studied two Drosophila genes: body color (b⁺ gray, b black) and wing size (vg⁺ normal, vg vestigial). He crossed F₁ dihybrid females (b⁺b vg⁺vg) with tester males that were black and vestigial (bb vgvg). If the genes assorted independently, the four phenotype classes would appear 1:1:1:1. Instead he got:

• 965 gray, normal wings and 944 black, vestigial wings: the parental types, matching the combinations in the P generation.
• 206 gray, vestigial and 185 black, normal: the recombinant types, new combinations.

The excess of parental types meant the genes were on the same chromosome. But the recombinants meant the linkage was incomplete. Morgan proposed that crossing over between non-sister chromatids during prophase I of meiosis occasionally exchanges segments, creating chromosomes with new allele combinations. The recombination frequency is the percentage of offspring that are recombinant: (206 + 185) / 2,300 = 17 percent.

Genetic maps

Morgan's student Alfred Sturtevant reasoned that the farther apart two genes are on a chromosome, the more places a crossover can occur between them, and the higher their recombination frequency. He defined one map unit (now also called a centimorgan, cM) as a 1 percent recombination frequency and used the values to build a linkage map, a map of the relative order and spacing of genes. For example, the b to cn (cinnabar eye) distance is 9 map units, cn to vg is 9.5, and b to vg is 17. The order must be b, cn, vg, with cn in the middle. The b to vg value (17) is slightly less than the sum (18.5) because some chromatids have two crossovers between b and vg, which restore the parental combination and go uncounted.

Two rules keep map problems straight. First, recombination frequency can never exceed 50 percent. Genes far apart on the same chromosome cross over so often that they behave like unlinked genes and show a 1:1:1:1 testcross ratio; they are still physically linked but genetically unlinked. Second, in a three point cross, the rarest phenotype classes are the double crossovers; comparing them with the parental classes reveals which gene is in the middle. Map units measure recombination, not physical length, so they are only roughly proportional to base pairs, because crossing over is more frequent in some regions than others.

Section 5Chromosomal alterations and human disorders

Nondisjunction and abnormal chromosome number

Meiosis normally delivers exactly one copy of each chromosome to each gamete. Occasionally the members of a homologous pair fail to separate in meiosis I, or sister chromatids fail to separate in meiosis II. This is nondisjunction. One gamete gets an extra copy of a chromosome and another gets none. If an abnormal gamete is fertilized by a normal one, the zygote has an abnormal number of that chromosome, a condition called aneuploidy. A zygote with three copies of a chromosome (2n + 1) is trisomic; one with only one copy (2n − 1) is monosomic. Nondisjunction during mitosis early in development produces a mosaic, with a mix of normal and aneuploid cells.

Most aneuploid embryos do not survive; aneuploidy is a major cause of first trimester miscarriage. The few that survive to birth involve the smallest autosomes or the sex chromosomes. Sex chromosome aneuploidies are tolerated better than autosomal ones because X inactivation silences extra X chromosomes and the Y carries few genes.

About 95 percent of Down syndrome cases result from nondisjunction, most often in the mother's meiosis I. Human oocytes begin meiosis before birth and pause in prophase I for decades, which may let the proteins holding homologs together weaken; that may explain why risk rises from roughly 1 in 1,500 births at age 20 to about 1 in 100 at age 40. Roughly 4 percent of cases come from a translocation and about 1 percent are mosaics.

Polyploidy

Sometimes an entire set of chromosomes is added, producing polyploidy: triploid (3n), tetraploid (4n) and so on. Polyploidy is rare and lethal in animals with chromosomal sex determination but is common and important in plants. Bread wheat is hexaploid (6n), descended from three ancestral species. Triploid organisms are usually sterile because three sets cannot pair evenly in meiosis; growers exploit this to produce seedless bananas and seedless watermelons.

Changes in chromosome structure

Breakage of a chromosome can produce four kinds of structural change.

• A deletion removes a segment. Deletion of part of the short arm of chromosome 5 causes cri du chat syndrome ("cry of the cat"), with intellectual disability and a high pitched, cat like cry in infancy.
• A duplication repeats a segment, often after unequal crossing over. Duplications are an important raw material of evolution because the extra copy can acquire a new function.
• An inversion reverses a segment within a chromosome. A pericentric inversion includes the centromere; a paracentric inversion does not. Carriers may be healthy but can produce unbalanced gametes when crossing over occurs within the inverted loop.
• A translocation moves a segment to a nonhomologous chromosome. In a reciprocal translocation two nonhomologous chromosomes exchange pieces. In a Robertsonian translocation the long arms of two acrocentric chromosomes (such as 14 and 21) fuse. A carrier of a balanced 14/21 translocation is healthy but can pass on an extra chromosome 21 arm, causing familial Down syndrome.

Exceptions to Mendelian inheritance

In genomic imprinting, certain genes are expressed differently depending on whether they were inherited from the mother or the father. Imprints are set during gamete formation by methylation of DNA and are reset each generation. A deletion in region 15q11 to q13 shows the effect vividly: if the deletion is on the chromosome inherited from the father, the child has Prader-Willi syndrome (poor muscle tone in infancy, then excessive eating and obesity, intellectual disability); if it is on the chromosome from the mother, the child has Angelman syndrome (severe intellectual disability, seizures, jerky movements and frequent laughter). The same deletion, two diseases, depending only on which parent it came from.

Genes in mitochondria and plastids are inherited outside the nucleus. Because the egg supplies almost all the cytoplasm of the zygote, mitochondrial genes pass from a mother to all her children and are not transmitted by fathers. Mitochondrial DNA mutations often affect tissues with high energy needs, such as the eye, brain and muscle (for example, Leber hereditary optic neuropathy). A cell can contain a mixture of normal and mutant mitochondria (heteroplasmy), so severity varies among siblings.

Words worth knowing