---
title: "Selection, Drift and Speciation"
book: "High School Biology"
subject: biology
language: en
chapter: 25
exercises: 15
source: https://one-course.com/books/biology/2/en/chapter/25-selection-drift-and-speciation
---

# Chapter 25 — Selection, Drift and Speciation

In 1848 a black form of the peppered moth was caught near an industrial city where every tree trunk was coated with soot; by 1895 nearly every moth in the region was black. A century later, with the soot gone and the trunks pale again, the black form had almost vanished. Nobody bred the moths; the birds that eat them did the sorting. The last two chapters described how variation arises; this one is about what happens to it in a [population](#def-g12-selection-drift-speciation-population) — how some [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) become common and others rare, by selection and by chance — and how, in the end, one [population](#def-g12-selection-drift-speciation-population) becomes two [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species).

## 25.1 Populations and their alleles

**Definition 25.1 (Population, allele frequency).**

A *population* is the set of individuals of one [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) living in the same place and breeding among themselves. Its genetic makeup is described by the *frequencies* of the [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) of each [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene): for a [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) with two [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) $A$ and $a$, the fraction $p$ of all copies that are $A$ and the fraction $q = 1 - p$ that are $a$. Evolution, at this scale, is a change of [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) frequencies from one generation to the next.

**Proposition 25.2 (Frequencies without any force).**

In a large [population](#def-g12-selection-drift-speciation-population) where mating is at random, where no [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) gives an advantage, and where no [mutation](https://one-course.com/books/biology/2/en/chapter/13-mutations-and-genetic-variation#def-g11-mutations-mutation) or migration occurs, the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) [frequencies](#def-g12-selection-drift-speciation-population) stay the same from generation to generation, and the [genotypes](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) appear in the proportions

$$
AA : Aa : aa = p^2 : 2pq : q^2 .
$$

This is the reference state: any departure from it, observed over the generations, is the sign that one of the conditions has failed — that selection, chance, migration or [mutation](https://one-course.com/books/biology/2/en/chapter/13-mutations-and-genetic-variation#def-g11-mutations-mutation) is at work.

**Proof.** Each gamete carries $A$ with probability $p$ and $a$ with probability $q$; two gametes drawn at random give $AA$ with probability $p^2$, $aa$ with $q^2$, and $Aa$ with $pq + qp = 2pq$. Counting the [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) of the new generation: $A$ copies make up $p^2 + \tfrac12 (2pq) =
p(p + q) = p$ of the total. The frequency is unchanged. ∎

![The genotype proportions of random mating, as areas. The square’s sides are the gamete frequencies; the four rectangles are the genotypes. The heterozygotes hold most of the rare allele’s copies.](https://one-course.com/images/onecourse/chapters/biology-2/g12-selection-drift-speciation/fig-56046f115b5a.svg)

*The [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) proportions of random mating, as areas. The square’s sides are the gamete [frequencies](#def-g12-selection-drift-speciation-population); the four rectangles are the [genotypes](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype). The heterozygotes hold most of the rare [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene)’s copies.*

**Example 25.3 (Counting alleles).**

Among 1000 people, 490 are $AA$, 420 $Aa$ and 90 $aa$. Copies of $a$: $420 + 2 \times 90 = 600$ out of 2000, so $q = 0.3$ and $p = 0.7$ — and the [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) counts are exactly $p^2$, $2pq$, $q^2$ of 1000: the [population](#def-g12-selection-drift-speciation-population) is at the reference state for this [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene). A [recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) disease affecting one newborn in 2500 ($q^2 = 1/2500$) implies $q = 1/50$ and carriers $2pq \approx 1/25$: the figures of [Chapter 16](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#ch-g11-genes-and-disease), derived.

## 25.2 Selection

**Definition 25.4 (Natural selection).**

*Natural selection* is the difference in reproduction between individuals that carry different [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), in a given environment: the carriers of one [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) leave, on average, more descendants than the carriers of another, and the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene)’s frequency rises from generation to generation. What is selected is the whole individual — its survival, its mating, its fertility — and the [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) ride along.

**Proposition 25.5 (Selection changes frequencies in a direction).**

An [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) whose carriers have even a slightly higher reproductive success spreads; one whose carriers have less becomes rare. The direction is set by the environment, and reverses if the environment does; the speed depends on the size of the advantage and on whether the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) is expressed in one copy ([dominant](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic), fast) or only in two ([recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic), slow at first, and never quite eliminated, since its rare copies hide in heterozygotes).

**Evidence.** The peppered moth: birds take the moths they see; on sooty trunks the pale form is seen, on clean ones the dark form; the frequency of the dark [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) rose from near zero to 98% in fifty years of pollution and fell back below 10% in forty years of clean air, tracking the trunks. [Antibiotic resistance](https://one-course.com/books/biology/2/en/chapter/18-bacteria-and-antibiotic-resistance#prop-g11-antibiotic-resistance-mechanisms) ([Chapter 18](https://one-course.com/books/biology/2/en/chapter/18-bacteria-and-antibiotic-resistance#ch-g11-antibiotic-resistance)): the resistant [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene)’s carriers alone reproduce in the presence of the drug. Lactase persistence ([Chapter 15](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#ch-g11-enzymes-and-phenotype)): the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) is common exactly where milk has been a food for adults for millennia. In each case the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene)’s fortune follows the environment. ∎

![Frequency of the dark form of the peppered moth near an industrial city (rounded from museum collections and catches). The rise tracks the blackening of the trunks; the fall, their cleaning. Selection reversed when the environment did.](https://one-course.com/images/onecourse/chapters/biology-2/g12-selection-drift-speciation/fig-6a1b54469875.svg)

*Frequency of the dark form of the peppered moth near an industrial city (rounded from museum collections and catches). The rise tracks the blackening of the trunks; the fall, their cleaning. Selection reversed when the environment did.*

![The two forms of the peppered moth on a soot-darkened trunk. Birds hunt by sight: on this bark the pale form is taken and the dark one survives; on a clean, lichen-covered trunk the reverse.](https://one-course.com/images/onecourse/chapters/biology-2/g12-selection-drift-speciation/img-bfd3a9054d52.jpg)

*The two forms of the peppered moth on a soot-darkened trunk. Birds hunt by sight: on this bark the pale form is taken and the dark one survives; on a clean, lichen-covered trunk the reverse.*

**Example 25.6 (Selection by the other sex).**

A peacock’s train makes it slower and more visible to predators, yet it is kept because peahens choose the males with the largest and most regular trains: an [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) that improves the train is passed on more often, whatever it costs in survival. *Sexual selection* — the choice of mates — produces the ornaments, songs and contests of animals, and can push a trait in a direction that survival alone would never favour.

## 25.3 Chance: genetic drift

**Proposition 25.7 (Genetic drift).**

In any [population](#def-g12-selection-drift-speciation-population) of finite size, the [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) of one generation are a random sample of the previous one: which individuals happen to reproduce, and which [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) their gametes happen to carry, fluctuate by chance. [Allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) [frequencies](#def-g12-selection-drift-speciation-population) therefore wander from generation to generation without any advantage being involved — *genetic drift*. The smaller the [population](#def-g12-selection-drift-speciation-population), the larger the wandering; in a small [population](#def-g12-selection-drift-speciation-population) an [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) can be lost, or reach 100%, by chance alone within a few generations, whatever its value.

**Evidence.** [Populations](#def-g12-selection-drift-speciation-population) founded by a few individuals — an island colonised by a handful of birds, a human community descended from a few dozen settlers — carry a distorted sample of the source [population](#def-g12-selection-drift-speciation-population)’s [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene): a rare disease [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) can be common in them, and much of the source’s diversity missing. [Species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) that passed through a *bottleneck* of very few survivors (the cheetah of [Chapter 5](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#ch-g10-biodiversity-scales), the northern elephant seal reduced to twenty animals in 1890) show almost no [genetic diversity](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-biodiversity) today, even after recovering to thousands. And in the laboratory, many small replicate [populations](#def-g12-selection-drift-speciation-population) started at the same frequency scatter in every direction within a few generations, while large ones stay put. ∎

![Simulated drift of a neutral allele starting at 50%. In populations of 20 individuals it is fixed or lost within a dozen generations, in a different direction each time; in a population of 5000 it barely moves.](https://one-course.com/images/onecourse/chapters/biology-2/g12-selection-drift-speciation/fig-c88c8a59844f.svg)

*Simulated drift of a neutral [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) starting at 50%. In [populations](#def-g12-selection-drift-speciation-population) of 20 individuals it is fixed or lost within a dozen generations, in a different direction each time; in a [population](#def-g12-selection-drift-speciation-population) of 5000 it barely moves.*

**Example 25.8 (A founder effect).**

An island community was founded by a few dozen settlers, one of whom carried an [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) for a rare disorder of the eye. Ten generations later the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene)’s frequency in the community is one in ten — a hundred times the mainland value — because one carrier among thirty founders is already 1.7% of the copies, and drift in a small, isolated [population](#def-g12-selection-drift-speciation-population) moved it further. The [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) confers no advantage; its abundance is an accident of who boarded the boat.

**Method 25.9 (Selection or drift?).**

Faced with a change of [allele frequency](#def-g12-selection-drift-speciation-population):

1. Estimate the [population](#def-g12-selection-drift-speciation-population) ’s size: drift is strong below a few hundred, negligible in millions.
2. Look for a direction that tracks the environment (selection), or for a random walk (drift). Replicate [populations](#def-g12-selection-drift-speciation-population) moving the same way indicate selection; moving in different directions, drift.
3. Look for a mechanism linking the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) to survival or reproduction; without one, suspect drift.
4. Remember that both act at once: selection sets a tendency, drift adds noise, and in small [populations](#def-g12-selection-drift-speciation-population) the noise can drown the tendency.

## 25.4 From population to species

**Proposition 25.10 (Speciation).**

Two [populations](#def-g12-selection-drift-speciation-population) of one [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) that stop exchanging [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) — separated by a barrier of geography, of behaviour or of timing — evolve apart: each accumulates its own [mutations](https://one-course.com/books/biology/2/en/chapter/13-mutations-and-genetic-variation#def-g11-mutations-mutation), is selected by its own environment and drifts its own way. When the divergence has gone far enough that individuals of the two [populations](#def-g12-selection-drift-speciation-population) no longer interbreed, or give sterile offspring, even when they meet again, two [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) exist where there was one. *Speciation* is this process; it usually takes thousands to millions of generations, though polyploidy ([Chapter 24](https://one-course.com/books/biology/2/en/chapter/24-diversification-of-living-things#ch-g12-diversification-of-life)) achieves it in one.

**Evidence.** Islands: each of the Galápagos islands carries its own finches, descended from a mainland [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) and closest to those of the neighbouring islands. Lakes: a single ancestral cichlid fish has given hundreds of [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) in one African lake within a few hundred thousand years, separated by habitat and by the females’ choice of male colour. Ring [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species): [populations](#def-g12-selection-drift-speciation-population) of a gull spread around the Arctic, interbreeding with their neighbours all the way round, until the two ends meet in Europe as forms that do not interbreed — a [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) boundary caught in the act of forming. And [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) separated recently, such as polar and brown bears, still produce fertile hybrids occasionally: the boundary is a matter of degree. ∎

![Speciation by separation. A barrier splits a population; each half evolves on its own; when they meet again, they no longer interbreed. The barrier may be a strait, a mountain, a change of habitat, or a preference in mating.](https://one-course.com/images/onecourse/chapters/biology-2/g12-selection-drift-speciation/fig-b709f13b3d16.svg)

*[Speciation](#prop-g12-selection-drift-speciation-speciation) by separation. A barrier splits a [population](#def-g12-selection-drift-speciation-population); each half evolves on its own; when they meet again, they no longer interbreed. The barrier may be a strait, a mountain, a change of habitat, or a preference in mating.*

**Proposition 25.11 (The species, reconsidered).**

A [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) is a [population](#def-g12-selection-drift-speciation-population), or a set of [populations](#def-g12-selection-drift-speciation-population), whose members interbreed among themselves and are genetically isolated from other such sets — a definition that works for most animals and plants at a given moment, but has edges: [populations](#def-g12-selection-drift-speciation-population) in the process of separating, [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) that still hybridise, organisms that reproduce without sex. A [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) is not a fixed type but a lineage in time: it begins when a [population](#def-g12-selection-drift-speciation-population) becomes isolated, exists while its members keep interbreeding, and ends by extinction or by splitting into new [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species). The [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) alive today are the tips of a tree whose branches are the subject of [Chapter 26](https://one-course.com/books/biology/2/en/chapter/26-reading-kinship-phylogenetic-trees#ch-g12-phylogenetic-trees).

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

**Remark 25.12 (Evolution, assembled).**

[Mutation](https://one-course.com/books/biology/2/en/chapter/13-mutations-and-genetic-variation#def-g11-mutations-mutation) and the shuffle supply variation; duplication, transfer, polyploidy, regulation and [symbiosis](https://one-course.com/books/biology/2/en/chapter/24-diversification-of-living-things#def-g12-diversification-of-life-symbiosis) supply more; selection sorts it by the environment, drift by chance; isolation lets [populations](#def-g12-selection-drift-speciation-population) diverge until they are [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species); extinction removes them. None of these steps has a goal, and none looks ahead; together, over the four billion years of the fossil record, they have produced the diversity of [Chapter 5](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#ch-g10-biodiversity-scales). The theory that names these steps and their interplay is the theory of evolution, and every chapter of this year has been a piece of its evidence.

## 25.5 Exercises

**Exercise 25.1 ★.**

Define [allele frequency](#def-g12-selection-drift-speciation-population), and give the [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) proportions of a [population](#def-g12-selection-drift-speciation-population) at the reference state with $p = 0.8$.

**Solution of Exercise 25.1.**

The fraction of all copies of a [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) in a [population](#def-g12-selection-drift-speciation-population) that are a given [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene). With $p = 0.8$, $q = 0.2$: $AA$ 64%, $Aa$ 32%, $aa$ 4%.

**Exercise 25.2 ★.**

Define [natural selection](#def-g12-selection-drift-speciation-selection) and [genetic drift](#prop-g12-selection-drift-speciation-drift), and state the essential difference between them.

**Solution of Exercise 25.2.**

Selection: a difference in reproduction between carriers of different [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), set by the environment, changing [frequencies](#def-g12-selection-drift-speciation-population) in a direction. Drift: random fluctuation of [frequencies](#def-g12-selection-drift-speciation-population) from the sampling of a finite [population](#def-g12-selection-drift-speciation-population), with no direction. Selection depends on what the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) does; drift does not.

**Exercise 25.3 ★.**

From the moth figure, read the frequency of the dark form in 1880 and in 1980, and name the environmental change behind each.

**Solution of Exercise 25.3.**

About 75% in 1880, when soot had blackened the trunks; about 30% in 1980, after clean-air laws had let the trunks pale again.

**Exercise 25.4 ★.**

Why does drift matter more in a small [population](#def-g12-selection-drift-speciation-population)?

**Solution of Exercise 25.4.**

The next generation’s [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) are a sample of the previous one’s; a small sample deviates more from the source than a large one, so the [frequencies](#def-g12-selection-drift-speciation-population) fluctuate more, and an [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) can be lost by chance.

**Exercise 25.5 ★.**

What is needed for one [population](#def-g12-selection-drift-speciation-population) to become two [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species)?

**Solution of Exercise 25.5.**

An interruption of [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) exchange between two [populations](#def-g12-selection-drift-speciation-population), long enough for them to diverge until they can no longer interbreed.

**Exercise 25.6 ★★.**

In a [population](#def-g12-selection-drift-speciation-population) of 500, 320 are $AA$, 160 $Aa$ and 20 $aa$. Compute $p$ and $q$, then the expected [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) numbers at the reference state, and compare.

**Solution of Exercise 25.6.**

Copies of $a$: $160 + 40 = 200$ of 1000, so $q = 0.2$, $p = 0.8$. Expected: $0.64 \times 500 = 320$, $0.32 \times 500 = 160$, $0.04
\times 500 = 20$ — exactly the census: the [population](#def-g12-selection-drift-speciation-population) is at the reference state.

**Exercise 25.7 ★★.**

A [recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) has frequency 0.01. What fraction of the [population](#def-g12-selection-drift-speciation-population) shows the [recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) trait, and what fraction carries the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) unseen? Why is the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) so hard to eliminate by selection against the trait?

**Solution of Exercise 25.7.**

$q^2 = 0.0001$: one in ten thousand shows the trait; $2pq \approx
0.02$: one in fifty carries it. Ninety-nine per cent of the copies sit in heterozygotes, on whom selection against the trait has no hold.

**Exercise 25.8 ★★.**

From the drift figure, in how many generations was the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) fixed or lost in the two small [populations](#def-g12-selection-drift-speciation-population) that reached the ends? Why did the third not?

**Solution of Exercise 25.8.**

Both reached an end at generation 12, one fixed at 100%, the other lost. The third wandered without touching either boundary in 20 generations — chance again; given more time it would.

**Exercise 25.9 ★★.**

Explain why the peppered moth’s dark [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) did not reach 100% during the sooty decades, using the moths that live and breed in the countryside.

**Solution of Exercise 25.9.**

Pale moths kept breeding in unpolluted countryside, where they were favoured, and moths fly: migrants carried the pale [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) back into the sooty region every generation, so it never disappeared.

**Exercise 25.10 ★★.**

Twenty seals survived a bottleneck; the [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) now numbers 100 000 but shows almost no [genetic diversity](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-biodiversity). Explain with drift.

**Solution of Exercise 25.10.**

Twenty individuals carry at most forty copies of each [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene), a tiny sample of the original [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene); most were lost in the bottleneck, and drift in the small [population](#def-g12-selection-drift-speciation-population) that followed lost more. Numbers came back; the [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) cannot, except by new [mutation](https://one-course.com/books/biology/2/en/chapter/13-mutations-and-genetic-variation#def-g11-mutations-mutation).

**Exercise 25.11 ★★.**

Apply [Method 25.9](#met-g12-selection-drift-speciation-which) to two cases: an [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) rising in ten separate lake [populations](#def-g12-selection-drift-speciation-population) at once after a new predator arrives; and an [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) reaching 80% in one island [population](#def-g12-selection-drift-speciation-population) of thirty birds.

**Solution of Exercise 25.11.**

Ten [populations](#def-g12-selection-drift-speciation-population) moving the same way, after the same environmental change, with a plausible mechanism: selection. One tiny [population](#def-g12-selection-drift-speciation-population) of thirty, with no reported cause: drift is the default explanation until a mechanism is shown.

**Exercise 25.12 ★★★.**

In a region with malaria, the sickle [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) has frequency 0.15 although $aa$ children rarely survive. Using the [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) proportions, compute the fractions of $AA$, $Aa$ and $aa$ newborns, and explain how the advantage of $Aa$ against malaria keeps the [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) common despite the loss of the $aa$.

**Solution of Exercise 25.12.**

$AA$ $0.85^2 \approx 72\%$, $Aa$ $2 \times 0.85 \times 0.15 \approx
26\%$, $aa$ $0.15^2 \approx 2\%$. The $aa$ die, removing copies of $a$; but the $Aa$, a quarter of the [population](#def-g12-selection-drift-speciation-population), survive malaria better than the $AA$ and pass on their copies of $a$. The loss from the $aa$ is balanced by the advantage of the $Aa$, and $a$ stays at 15%.

**Exercise 25.13 ★★★.**

Two cichlid [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) in one lake differ mainly in the males’ colour, and females of each choose their own colour. In turbid water, where colours cannot be seen, the two hybridise freely. What isolates the [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species), and what does the turbid case say about how recent the separation is?

**Solution of Exercise 25.13.**

Mate choice by colour: a behavioural barrier. In turbid water the barrier fails and the [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) hybridise, so no genetic incompatibility has yet accumulated: the separation is recent and still reversible.

**Exercise 25.14 ★★★.**

Explain why the ring [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) of gulls is an argument that speciation is gradual, and why the two ends meeting in Europe are nonetheless called two [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species).

**Solution of Exercise 25.14.**

Around the ring every [population](#def-g12-selection-drift-speciation-population) interbreeds with its neighbours, with only small differences between adjacent ones; the differences add up around the circle until the ends, meeting, do not interbreed. The whole gradient is visible at once: speciation is a matter of accumulated small steps. The two ends are called [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) because, where they meet, they behave as [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species): no [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) exchange.

**Exercise 25.15 ★★★.**

"Selection makes organisms better." Discuss in a paragraph: better at what, where, and compared with whom; and what drift, reversals and sexual selection add.

**Solution of Exercise 25.15.**

Selection makes carriers of some [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) reproduce more *here and now*: better at leaving descendants in this environment, compared with the other members of the [population](#def-g12-selection-drift-speciation-population) — not better in any absolute sense. When the environment changes, the direction reverses (the moths); drift makes [populations](#def-g12-selection-drift-speciation-population) differ for no reason of adaptation; sexual selection favours ornaments that hinder survival. Evolution has no direction of improvement, only local sorting.

## 25.6 Problem: The Mice of the Island

**Problem 25.1.**

Weekend problem — a population of mice on an island: its allele frequencies computed, a new predator’s selection followed, the drift of a tiny colony simulated, and the birth of a species foreseen

On a rocky island, mice carry a coat-colour [gene](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) with two [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene): $D$ (dark, [dominant](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic)) and $d$ (pale). A census of 2000 mice finds 720 dark mice of [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) $DD$, 960 dark $Dd$, and 320 pale $dd$.

**Part I — The [population](#def-g12-selection-drift-speciation-population) now.**

1. Compute the [frequencies](#def-g12-selection-drift-speciation-population) $p$ of $D$ and $q$ of $d$ by counting copies.
2. Compute the [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) numbers expected at the reference state and compare with the census. Is the [population](#def-g12-selection-drift-speciation-population) at the reference state?
3. What fraction of the dark mice are carriers of $d$ ?
4. Explain, from the previous answer, why removing all the pale mice from the island for one generation would lower $q$ only a little. Compute the new $q$ after such a removal, if the remaining mice breed at random.
5. Which of the four conditions of the reference state is most likely to fail on a small island, and with what effect?

**Part II — A predator arrives.** Owls colonise the island. On the pale rock, dark mice are seen and eaten twice as often: each generation, half the dark mice die before breeding while all the pale mice survive.

6. Starting from the census numbers, compute the number of mice of each [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) that survive to breed in the first generation.
7. Compute $p$ and $q$ among the survivors.
8. If the survivors mate at random, compute the [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) proportions of the next generation, then apply the owls again and compute $q$ among its survivors.
9. Repeat once more (two significant figures). Describe the trend of $q$ over the three generations.
10. Explain why $q$ rises steadily, and why $D$ , unlike a [recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) under the same selection, can be eliminated completely.

**Part III — A colony of six.** A storm carries six mice to a neighbouring islet: 2 $DD$, 3 $Dd$, 1 $dd$.

11. Compute $q$ in the colony and compare with the island.
12. In the first litter, by chance, only the two $DD$ and one $Dd$ breed. What are the possible values of $q$ in the next generation? What has happened to the [population](#def-g12-selection-drift-speciation-population) ’s variation?
13. Explain why, on the islet, an [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) can vanish in a few generations without owls or any advantage.
14. The islet has no owls. Predict the fate of $d$ there, and say why two neighbouring islands can end with different coat colours for no reason of adaptation.
15. Give the name of the process, and the feature of the colony that makes it [dominant](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) there.

**Part IV — Ten thousand years later.** The islet’s mice, isolated, have diverged: smaller, paler, breeding in a different season. Brought together with island mice in the laboratory, they rarely mate, and the few hybrids are sterile.

16. Are the islet’s mice a new [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) ? Justify with the definition.
17. Name the barrier that started the process and the two mechanisms that drove the divergence.
18. The season of breeding differs between the two. Explain how such a difference, once present, reinforces the isolation.
19. If the islet joined the island again tomorrow, would the two merge back into one [population](#def-g12-selection-drift-speciation-population) ? Distinguish the case of question 17 from an earlier stage, say after 100 years.
20. State the result: the frequency of $d$ on the island before and after three generations of owls, the fate of $d$ on the islet and the process responsible, and the number of [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) at the end.

**Solution of Problem 25.1.**

**1.** Copies of $D$: $2 \times 720 + 960 = 2400$; of $d$: $960 +
2 \times 320 = 1600$; out of 4000: $p = 0.6$, $q = 0.4$.

**2.** Expected $0.36 \times 2000 = 720$, $0.48 \times 2000 =
960$, $0.16 \times 2000 = 320$: exactly the census. Yes.

**3.** $960/1680 \approx 57\%$.

**4.** Most copies of $d$ are in the dark carriers. After removal: 1680 mice, $D$ copies 2400, $d$ copies 960: $q = 960/3360 \approx
0.29$ — a fall from 0.40, but far from elimination.

**5.** Large size: a small island [population](#def-g12-selection-drift-speciation-population) drifts, so [frequencies](#def-g12-selection-drift-speciation-population) wander by chance (and migration from the mainland is absent, [mutation](https://one-course.com/books/biology/2/en/chapter/13-mutations-and-genetic-variation#def-g11-mutations-mutation) negligible).

**6.** $DD$ 360, $Dd$ 480, $dd$ 320: 1160 breeders.

**7.** $D$: $720 + 480 = 1200$; $d$: $480 + 640 = 1120$; of 2320: $p \approx 0.52$, $q \approx 0.48$.

**8.** Next generation (per 2000): $DD$ $0.52^2 \approx 27\%$ (535), $Dd$ $\approx 50\%$ (999), $dd$ $\approx 23\%$ (466). After the owls: 267, 500, 466. $D$: $534 + 500 = 1034$; $d$: $500 + 932 =
1432$; $q \approx 0.58$.

**9.** With $q = 0.58$: $DD$ 18% (353), $Dd$ 49% (974), $dd$ 34% (673); survivors 176, 487, 673; $d$: $487 + 1346 = 1833$ of 2672: $q \approx 0.69$. Trend: 0.40, 0.48, 0.58, 0.69 — rising by about 0.1 per generation.

**10.** Every carrier of $D$ is dark and exposed to the owls, so selection acts on every copy of $D$ at every generation; $q$ rises steadily. A [recessive](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) would hide in heterozygotes once rare, but a [dominant](https://one-course.com/books/biology/2/en/chapter/16-genetic-variation-and-disease#def-g11-genes-and-disease-genetic) one never hides: $D$ can be driven to zero.

**11.** $D$: $4 + 3 = 7$; $d$: $3 + 2 = 5$; $q = 5/12 \approx
0.42$, close to the island’s 0.40 by luck of the draw.

**12.** Among the breeders $D$ has 5 copies and $d$ 1: $q$ in the next generation is $1/6$ on average, but the single $d$ copy may be passed to none of the young ($q = 0$) or to several; the $dd$ [genotype](https://one-course.com/books/biology/2/en/chapter/15-enzymes-and-the-phenotype#def-g11-enzymes-and-phenotype-phenotype) has already vanished, and with it much of the variation.

**13.** With so few breeders, which [alleles](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) are passed on is a matter of chance at every generation; a rare [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) can be lost in a single unlucky litter.

**14.** $d$ will drift, and within some generations be fixed or lost — either outcome by chance. A neighbouring islet, from the same start, may end with the opposite [allele](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene): the two islands differ in coat colour for no adaptive reason.

**15.** [Genetic drift](#prop-g12-selection-drift-speciation-drift); the tiny size of the colony.

**16.** Yes: they rarely interbreed with island mice and the hybrids are sterile — reproductive isolation.

**17.** The sea, a geographic barrier; selection in a different environment (no owls, other conditions) and [genetic drift](#prop-g12-selection-drift-speciation-drift) in a small [population](#def-g12-selection-drift-speciation-population).

**18.** Mice that breed at different seasons never meet as partners: even without any barrier of geography, no [genes](https://one-course.com/books/biology/2/en/chapter/3-dna-a-universal-genetic-molecule#def-g10-universal-dna-gene) flow, and the [populations](#def-g12-selection-drift-speciation-population) continue to diverge.

**19.** Not now: they are isolated by behaviour and sterility and would remain two [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) side by side. After only 100 years they would still have interbred freely and merged back into one [population](#def-g12-selection-drift-speciation-population).

**20.** $q$ from 0.40 to about 0.69 after three generations of owls; on the islet $d$ was fixed or lost by [genetic drift](#prop-g12-selection-drift-speciation-drift); two [species](https://one-course.com/books/biology/2/en/chapter/5-biodiversity-at-every-scale#def-g10-biodiversity-scales-species) in the end.