---
title: "Meiosis and Genetic Shuffling"
book: "High School Biology"
subject: biology
language: en
chapter: 23
exercises: 15
source: https://one-course.com/books/biology/2/en/chapter/23-meiosis-and-genetic-shuffling
---

# Chapter 23 — Meiosis and Genetic Shuffling

Two parents, each with 46 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), produce a child with 46 — not 92. Somewhere between the parents’ bodies and the child, the count is halved, and it is halved in a way that deals each child a hand no sibling has ever held: the same parents, forty years of children, and no two alike except identical twins. The halving is a special division called [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis); the dealing is what it does with the [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) on the way. This chapter follows one [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) through [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis), counts the combinations it can produce, and reads the results of crosses that reveal, from the outside, what happened inside.

## 23.1 Halving the set

**Definition 23.1 (Diploid, haploid, meiosis).**

A [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) carrying two copies of each [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) — one from each parent, the two forming a pair of *homologous chromosomes* — is *diploid*, written $2n$ ($2n = 46$ in humans). A [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) carrying one copy of each is *haploid*, written $n$. *Meiosis* is the sequence of two divisions by which one diploid [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell), after a single replication of its [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), produces four haploid [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) — the gametes, or their precursors. *Fertilisation* unites two haploid gametes and restores the diploid number: the alternation of meiosis and fertilisation is the cycle of every sexually reproducing [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species).

**Proposition 23.2 (The two divisions).**

Before [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) is replicated: each [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) has two [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome). Then:

- *First division* ( [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I, *reductional* ): the homologous chromosomes pair up, two by two, on the equator; the members of each pair are pulled to opposite poles. Each daughter [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) receives *one [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) of each pair* , still made of two [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) : $n$ [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) , [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) amount $q$ (the amount of a [diploid](#def-g12-meiosis-genetic-shuffling-meiosis) [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) before replication).
- *Second division* ( [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) II, *equational* ): like a [mitosis](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-cycle) , the [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) of each [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) separate. Each of the four [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) receives $n$ [single-chromatid](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) , [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) amount $q/2$ .

The first division halves the number of [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information); the second halves the amount of [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) back to one [chromatid](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) per [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome).

**Proof.** *Admitted at this level.* ∎

![Meiosis in a cell with two pairs of chromosomes (2n = 4); dark and pale shades mark the two members of each pair, from the two parents. The first division separates the homologues, the second the chromatids. Here the dark long chromosome went with the pale short one: one of the two possible deals.](https://one-course.com/images/onecourse/chapters/biology-2/g12-meiosis-genetic-shuffling/fig-5336e58b9630.svg)

*[Meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) in a [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) with two pairs of [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) ($2n = 4$); dark and pale shades mark the two members of each pair, from the two parents. The first division separates the homologues, the second the [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome). Here the dark long [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) went with the pale short one: one of the two possible deals.*

![DNA per cell through meiosis. One replication, then two divisions without replication between them: the gametes hold a quarter of the DNA the mother cell held after S, and half of what a diploid cell holds at rest.](https://one-course.com/images/onecourse/chapters/biology-2/g12-meiosis-genetic-shuffling/fig-2fd18c5b92d0.svg)

*[DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) per [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) through [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis). One replication, then two divisions without replication between them: the gametes hold a quarter of the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) the mother [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) held after S, and half of what a [diploid](#def-g12-meiosis-genetic-shuffling-meiosis) [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) holds at rest.*

**Example 23.3 (Human numbers).**

A germ [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) of the testis, $2n = 46$, replicates to 46 [two-chromatid](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) ($2q$); after [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I, two [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) of 23 [two-chromatid](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) ($q$); after [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) II, four sperm [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) of 23 [single-chromatid](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) ($q/2$). At fertilisation, $23 + 23 =
46$ and $q/2 + q/2 = q$: the zygote is back to a [diploid](#def-g12-meiosis-genetic-shuffling-meiosis) [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) at rest. In the ovary, the same divisions produce one large egg [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) and three tiny [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) that are discarded; the arithmetic is identical.

## 23.2 The shuffle

**Proposition 23.4 (Independent assortment).**

At metaphase I, each pair of homologues lines up on the equator independently of the other pairs: which member of a pair goes to which pole is decided by chance, pair by pair. A [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) with $n$ pairs can therefore produce $2^n$ different combinations of paternal and maternal [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) in its gametes — $2^{23} \approx 8.4 \times 10^{6}$ in a human. Fertilisation, uniting two such gametes at random, yields $2^{23}
\times 2^{23} \approx 7 \times 10^{13}$ combinations of [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) for one couple’s children, before any other source of variety is counted.

**Proof.** *Admitted at this level.* ∎

**Proposition 23.5 (Crossing-over).**

While the homologues are paired, early in [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I, two non-sister [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) break at the same point and rejoin crosswise: a *crossing-over*. Each [chromatid](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) beyond the exchange point now carries the other homologue’s [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene). The [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) that reach the gametes are therefore not the parents’ [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) but *recombined* ones, mixing along their length the [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) received from the two grandparents. One to three exchanges occur on every pair at every [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis), at variable positions: the number of possible gametes is, in practice, unlimited.

**Evidence.** Under the microscope, paired homologues in [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I show crossed points, *chiasmata*, where two [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) visibly swap partners. Crosses in which two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) lie on the same [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) give, among the offspring, a minority carrying new combinations of the two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene)’ [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) — combinations neither parent carried — in a proportion that depends on the distance between the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene); [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) far apart on a [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) recombine as often as [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) on different [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information). Molecular markers followed through families show the segments of each [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) switching between grandparental origins at one or two points per [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) per generation. ∎

![Crossing-over between two genes A and B on the same chromosome. Two of the four chromatids exchange their ends; of the four gametes, two carry the parental combinations (AB, ab) and two new ones (Ab, aB).](https://one-course.com/images/onecourse/chapters/biology-2/g12-meiosis-genetic-shuffling/fig-36d32f4d76c3.svg)

*[Crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) between two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) $A$ and $B$ on the same [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome). Two of the four [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) exchange their ends; of the four gametes, two carry the parental combinations ($AB$, $ab$) and two new ones ($Ab$, $aB$).*

![Cells of a lily anther in meiosis, stained: in some, the paired homologues line up across the middle of the cell; in others they have been pulled to the two poles. The stages of the schematic, seen in the tissue that makes pollen.](https://one-course.com/images/onecourse/chapters/biology-2/g12-meiosis-genetic-shuffling/img-ba571316886f.jpg)

*[Cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) of a lily anther in [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis), stained: in some, the paired homologues line up across the middle of the [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell); in others they have been pulled to the two poles. The stages of the schematic, seen in the tissue that makes pollen.*

**Example 23.6 (Three sources of variety, in order).**

A child of two parents is new in three ways: [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) rebuilt each [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) of each gamete from the two grandparental copies; independent assortment dealt one recombined [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) of each pair into the gamete, among $2^{23}$ deals; fertilisation joined one such gamete to another drawn from the other parent’s $2^{23}$. [Mutation](https://one-course.com/books/biology/2/en/chapter/13-mutations-and-genetic-variation#def-g11-mutations-mutation), which created the [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) being shuffled, acts on a far slower timescale: the shuffle is what makes every generation new from the same deck.

## 23.3 Reading the shuffle in a cross

![Gregor Mendel, who counted the offspring of pea crosses in a monastery garden in the 1860s and found the ratios — 3:1 for one character, 9:3:3:1 for two — that meiosis, unknown to him, produces. Photograph, public domain.](https://one-course.com/images/onecourse/chapters/biology-2/g12-meiosis-genetic-shuffling/img-909aa9da2921.jpg)

*Gregor Mendel, who counted the offspring of pea crosses in a monastery garden in the 1860s and found the ratios — 3:1 for one character, 9:3:3:1 for two — that [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis), unknown to him, produces. Photograph, public domain.*

**Method 23.7 (The test cross).**

To see what gametes an individual makes, cross it with a partner carrying only [recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) (a *test cross*): each offspring then shows exactly the [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) the tested parent’s gamete carried. For two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), with the tested parent $AaBb$ and the partner $aabb$:

1. Count the four kinds of offspring: $AB$ , $Ab$ , $aB$ , $ab$ (each also carrying $ab$ from the partner).
2. If the four are equally frequent ( $1:1:1:1$ ), the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) lie on different [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) and assort independently.
3. If two kinds (the parental combinations) are much commoner than the other two (the recombinants), the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) lie on the same [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) ; the recombinants come from [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) , and their proportion measures the distance between the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) .
4. Recombinants are always the minority and always come in two equal classes; parentals likewise.

**Example 23.8 (Two crosses in the fruit fly).**

Fly A, heterozygous for body colour and wing shape, test-crossed: 254 grey-normal, 248 black-vestigial, 251 grey-vestigial, 247 black-normal — four equal classes, the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) are on different [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information). Fly B, heterozygous for body colour and eye colour: 412 grey-red, 405 black-purple, 44 grey-purple, 39 black-red — two parental classes of about 45% each and two recombinant classes of about 5%: the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) are on the same [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome), close together, separated by a [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) in 9% of meioses.

![The gametes of two heterozygous flies, read from test crosses. Equal classes mean independent assortment; two large and two small classes mean the genes are linked, with the small classes produced by crossing-over.](https://one-course.com/images/onecourse/chapters/biology-2/g12-meiosis-genetic-shuffling/fig-8327ccccd3f5.svg)

*The gametes of two heterozygous flies, read from test crosses. Equal classes mean independent assortment; two large and two small classes mean the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) are linked, with the small classes produced by [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover).*

## 23.4 When the shuffle goes wrong

**Proposition 23.9 (Errors of meiosis).**

Occasionally a pair of homologues fails to separate at [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I, or two [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) at [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) II: one gamete receives two copies of a [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) and another none. Fertilised, they give a zygote with three copies (*trisomy*) or one (*monosomy*). Most such zygotes do not develop; those that do carry a set of characteristic features. Trisomy 21 (about one birth in 700) causes intellectual disability and heart defects and is the commonest; its frequency rises steeply with the mother’s age. An unequal [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) — [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) exchanging unequal segments — produces a [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) with a duplicated [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) and one with a deletion: the mechanism by which the [opsin](https://one-course.com/books/biology/2/en/chapter/21-the-eye-and-its-photoreceptors#def-g11-the-eye-photoreceptors) [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) of [Chapter 21](https://one-course.com/books/biology/2/en/chapter/21-the-eye-and-its-photoreceptors#ch-g11-the-eye) were multiplied, and by which new [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) arise ([Chapter 24](https://one-course.com/books/biology/2/en/chapter/24-diversification-of-living-things#ch-g12-diversification-of-life)).

**Proof.** *Admitted at this level.* ∎

![Frequency of trisomy 21 at birth against the mother’s age. The egg cells are formed before a woman’s birth and paused in meiosis I for decades; the longer the pause, the likelier a failure to separate the homologues.](https://one-course.com/images/onecourse/chapters/biology-2/g12-meiosis-genetic-shuffling/fig-ac0f7bb5cf0d.svg)

*Frequency of trisomy 21 at birth against the mother’s age. The egg [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) are formed before a woman’s birth and paused in [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I for decades; the longer the pause, the likelier a failure to separate the homologues.*

**Example 23.10 (Sex chromosomes miscounted).**

A gamete with no sex [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) fertilised by an X-bearing one gives an XO zygote: a girl of short stature whose ovaries do not develop. An XX egg fertilised by a Y sperm gives XXY: a boy whose testes stay small and make no sperm. In both, [SRY](https://one-course.com/books/biology/2/en/chapter/19-becoming-male-or-female#prop-g11-becoming-male-female-sry) decides the gonad as in [Chapter 19](https://one-course.com/books/biology/2/en/chapter/19-becoming-male-or-female#ch-g11-becoming-male-female); the number of X [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) decides much of the rest, which is why these are the mildest of the chromosomal errors.

**Remark 23.11 (Why sex).**

A bacterium copies itself; a rose can grow from a cutting. Sexual reproduction is costlier — two parents, [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis), the search for a mate — and its product is a set of offspring each different from its parents and from each other. That difference is the point: in an environment that changes, and against parasites that evolve, a population of varied individuals is likelier to contain some that survive than a population of copies. The shuffle of this chapter is the raw material that the next two chapters’ selection will sort.

## 23.5 Exercises

**Exercise 23.1 ★.**

Define [diploid](#def-g12-meiosis-genetic-shuffling-meiosis) and [haploid](#def-g12-meiosis-genetic-shuffling-meiosis), and state what [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) does to the [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) number and to the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) amount.

**Solution of Exercise 23.1.**

[Diploid](#def-g12-meiosis-genetic-shuffling-meiosis): two copies of each [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) ($2n$); [haploid](#def-g12-meiosis-genetic-shuffling-meiosis): one ($n$). [Meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) halves the [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) number, from $2n$ to $n$, and reduces the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) from $2q$ (after replication) to $q/2$ per gamete.

**Exercise 23.2 ★.**

What separates at [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I? At [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) II? Which division is the reductional one?

**Solution of Exercise 23.2.**

[Meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I separates the homologous chromosomes of each pair; [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) II separates the two [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) of each [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome). The first is reductional.

**Exercise 23.3 ★.**

A [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) has $2n = 8$ and [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) $2q$ at the start of [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis). Give the [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) number and [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) amount of the [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) after [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I and after [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) II.

**Solution of Exercise 23.3.**

After [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I: 4 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) (two [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) each), [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) $q$. After [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) II: 4 [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) (one [chromatid](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) each), [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) $q/2$.

**Exercise 23.4 ★.**

How many [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) combinations can the gametes of a [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) with $2n = 8$ show by independent assortment alone?

**Solution of Exercise 23.4.**

$2^4 = 16$.

**Exercise 23.5 ★.**

What is a test cross, and what does the proportion of recombinant offspring reveal?

**Solution of Exercise 23.5.**

A cross with a partner carrying only [recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), so that each offspring shows the tested parent’s gamete. The proportion of recombinants reveals whether two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) are on the same [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) and, if so, how far apart.

**Exercise 23.6 ★★.**

From the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) figure, read the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) per [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) of a [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) in [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I, of a [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell) between the two divisions, and of a gamete. Explain why there is no S phase between the divisions.

**Solution of Exercise 23.6.**

[Meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I: $2q$; between the divisions: $q$; gamete: $q/2$. Without an intervening S phase, the second division halves the [DNA](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) again, which is what brings the gamete to half a [diploid](#def-g12-meiosis-genetic-shuffling-meiosis) [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell)’s content.

**Exercise 23.7 ★★.**

A test cross gives 300 $AB$, 298 $ab$, 302 $Ab$, 300 $aB$. Are the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) linked? What are the parent’s gametes?

**Solution of Exercise 23.7.**

Four equal classes: not linked, on different [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information). Gametes $AB$, $Ab$, $aB$, $ab$, a quarter each.

**Exercise 23.8 ★★.**

A test cross gives 460 $AB$, 455 $ab$, 42 $Ab$, 43 $aB$. Are the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) linked? Which classes are recombinant, and what fraction do they make?

**Solution of Exercise 23.8.**

Linked: two large classes ($AB$, $ab$, parental) and two small ($Ab$, $aB$, recombinant). Recombinants $85/1000 = 8.5\%$.

**Exercise 23.9 ★★.**

In the [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) figure, which two gametes would you obtain if the exchange took place *above* both [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene)? Explain.

**Solution of Exercise 23.9.**

Only $AB$ and $ab$: an exchange above both [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) swaps segments that carry neither, so the combinations of $A/a$ and $B/b$ are unchanged. Recombination between two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) requires an exchange between them.

**Exercise 23.10 ★★.**

From the trisomy figure, read the frequency at 25, 35 and 42 years, and compute the factor between 25 and 42.

**Solution of Exercise 23.10.**

About 0.8, 2.9 and 16 per 1000: a factor of 20 between 25 and 42.

**Exercise 23.11 ★★.**

Explain how a non-disjunction at [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I differs from one at [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) II in the gametes it produces (consider all four [cells](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell)).

**Solution of Exercise 23.11.**

At [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I, both homologues go to one [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell): two gametes with two copies and two with none. At [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) II, both [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) of one [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) go to one [cell](https://one-course.com/books/biology/2/en/chapter/2-cells-the-common-unit-of-life#def-g10-cells-common-unit-cell): one gamete with two copies, one with none, and two normal.

**Exercise 23.12 ★★★.**

Two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) on the same [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) recombine in 2% of meioses; two others on the same [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) in 48%. Explain what each figure says about their distance apart, and why the second pair behaves almost like independent [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene).

**Solution of Exercise 23.12.**

Recombination is proportional to distance: 2% means the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) are very close, so an exchange rarely falls between them; 48% means far apart, with an exchange between them in nearly every [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis). Since one exchange gives 50% recombinant gametes, distant linked [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) recombine as freely as independent ones.

**Exercise 23.13 ★★★.**

A plant has $2n = 4$, one pair carrying $A/a$ and the other $B/b$. List all the gametes of an $AaBb$ plant with their frequencies, without [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover); then say what [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) would change.

**Solution of Exercise 23.13.**

$AB$, $Ab$, $aB$, $ab$, a quarter each, by independent assortment of the two pairs. [Crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) changes nothing for these [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene): it recombines [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) along one [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome), and these are on different ones.

**Exercise 23.14 ★★★.**

Identical twins share all their [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene); ordinary siblings share half on average. Explain the "half" with [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) and fertilisation, and why it is an average.

**Solution of Exercise 23.14.**

Each parent passes each child one of two [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) at every [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), chosen at random; at a given [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), two siblings received the same [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) from a parent with probability $1/2$. Over many [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) the fraction shared averages $1/2$, but for any one pair of siblings it varies around it.

**Exercise 23.15 ★★★.**

Some plants reproduce by seeds formed without [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) or fertilisation. Explain what their offspring are genetically, what such a plant gains, and what it loses in the long run.

**Solution of Exercise 23.15.**

Clones of the mother plant, genetically identical to it and to each other. The plant gains a fast, sure multiplication of a [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) that works here and now; it loses the variety that would let some descendants survive a change of environment or a new parasite.

## 23.6 Problem: The Geneticist’s Flies

**Problem 23.1.**

Weekend problem — two genes followed through meiosis and a test cross: the gametes counted, linkage decided, the recombination measured, and the number of hands a couple can deal

In the fruit fly, the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) $b$ (black body) is [recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) to $b^+$ (grey), and $vg$ (vestigial wings) [recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) to $vg^+$ (normal). A grey, normal-winged female whose parents were pure grey-normal and pure black-vestigial is crossed with a black, vestigial male. Offspring: grey-normal 965, black-vestigial 944, grey-vestigial 206, black-normal 185.

**Part I — The cross.**

1. Give the [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) of the female and of the male, [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) by [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) .
2. What gametes does the male produce? Why does that make the cross a test cross?
3. List the four gametes the female could produce, and the offspring each gives.
4. Compute the percentage of each class among the 2300 offspring.
5. Are the two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) on the same [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) or on different ones? Justify from the proportions.

**Part II — Inside the female’s [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis).**

6. Which two classes are the parental combinations, and where do they come from in the female’s [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) ?
7. Which two are recombinant? By what event of [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) I did they arise?
8. Compute the recombination frequency (recombinants over the total). What fraction of the female’s meioses had a [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) between the two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) ?
9. Explain why the two recombinant classes are nearly equal, and why the two parental classes are.
10. The same two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) , in a female whose parents were pure grey-vestigial and pure black-normal: predict the four classes and their frequencies.

**Part III — A third [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene).** A third [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), $cn$ (cinnabar eyes), is test-crossed with $b$ in another female: recombinants 9%. Test-crossed with $vg$: recombinants 8%.

11. Is $cn$ on the same [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) as $b$ and $vg$ ?
12. Using the three recombination frequencies (17% for $b$ – $vg$ , 9% for $b$ – $cn$ , 8% for $cn$ – $vg$ ), place the three [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) in order along the [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) .
13. Explain why the frequencies add up (nearly), and what this says about the relation between recombination and distance.
14. Two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) at opposite ends of a long [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) give 50% recombinants. Explain why the frequency cannot exceed 50%.
15. A fourth [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) gives 50% recombinants with all three. What can you conclude, and what can you not?

**Part IV — The size of the deck.** The fruit fly has $2n = 8$.

16. How many [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) combinations can a fly’s gametes show by independent assortment alone? And a fly couple’s offspring?
17. With one [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) at a variable position on each pair, explain why the number of distinct gametes becomes practically unlimited.
18. For a human couple, compute the number of [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) combinations of their children by assortment alone, and compare with the number of humans who have ever lived (about $10^{11}$ ).
19. Explain why two siblings are nevertheless more alike than two strangers, in terms of the [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) they can have received.
20. State the result: the recombination frequency between $b$ and $vg$ , what it measures, and the two mechanisms of [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) that make every gamete of the female different.

**Solution of Problem 23.1.**

**1.** Female $b^+b$, $vg^+vg$, with $b^+vg^+$ on one [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) and $b\,vg$ on the other (from her two pure parents). Male $bb$, $vg\,vg$.

**2.** Only $b\,vg$ gametes: the male contributes [recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) only, so each offspring’s [phenotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) reveals the female’s gamete.

**3.** $b^+vg^+$ (grey-normal), $b\,vg$ (black-vestigial), $b^+vg$ (grey-vestigial), $b\,vg^+$ (black-normal).

**4.** Grey-normal 42%, black-vestigial 41%, grey-vestigial 9%, black-normal 8%.

**5.** On the same [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome): two large and two small classes instead of $1:1:1:1$.

**6.** Grey-normal and black-vestigial: the combinations carried by her two homologues, inherited intact from her pure parents.

**7.** Grey-vestigial and black-normal, from a [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) between the two [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) in prophase I.

**8.** $(206 + 185)/2300 \approx 17\%$. A [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) between the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) makes two of the four [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) recombinant, so 17% recombinant gametes means an exchange in about 34% of meioses.

**9.** A single exchange produces the two recombinant [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) together, one of each kind; and the two homologues go to the gametes equally, so the two parental classes match too.

**10.** Parental classes now grey-vestigial and black-normal, about 41.5% each; recombinants grey-normal and black-vestigial, about 8.5% each.

**11.** Yes: recombination well below 50% with both.

**12.** $b$ — $cn$ — $vg$: 9 and 8 add up to 17.

**13.** The chance of an exchange in an interval is proportional to its length, so the frequencies of adjacent intervals add: recombination frequency measures distance along the [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome).

**14.** One exchange gives two recombinant [chromatids](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) out of four: 50% at most; additional exchanges reshuffle but never raise the recombinant fraction above half.

**15.** It is on another [chromosome](https://one-course.com/books/biology/2/en/chapter/12-the-cell-cycle-and-mitosis#def-g11-cell-cycle-mitosis-chromosome) or very far along the same one; the crosses cannot tell which.

**16.** $2^4 = 16$ gametes; $16 \times 16 = 256$ combinations.

**17.** Every exchange produces [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information) that never existed before, at a position that varies from one [meiosis](#def-g12-meiosis-genetic-shuffling-meiosis) to the next; the number of distinct [chromosomes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-information), hence of gametes, has no practical limit.

**18.** $2^{23} \times 2^{23} \approx 7 \times 10^{13}$: seven hundred times more combinations than the number of humans who have ever lived, and that before [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover).

**19.** Siblings draw their [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) from the same four sets (two per parent) and share, on average, half of them; strangers draw from different sets.

**20.** 17%, the fraction of the female’s gametes recombined between $b$ and $vg$, measures the distance between the [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene); independent assortment of the pairs and [crossing-over](#prop-g12-meiosis-genetic-shuffling-crossingover) within each pair make every gamete different.