Evolution, selection, Hardy-Weinberg

Mid-October 2026: in Year 5, at languages high schools as at almost all other licei, the biology in the syllabus generally turns to evolution between October and November, often after genetics. The oral test or written test arrives in five to nine weeks, between the end of November and mid-December. The topic also appears in the admission tests for medicine and the healthcare degrees, so it is worth understanding properly and not just memorising.

Questions on evolution are of two kinds: conceptual (explain natural selection, tell Lamarck and Darwin apart) and numerical (a Hardy-Weinberg exercise). The lowest marks almost always come from the first kind, because the phrasing “the organism adapts” is convenient and wrong. Here I give you the logical thread, the exercises with the calculations and the list of mistakes. For the genetics underneath you will find Mendelian genetics, Punnett squares and exercises and DNA: replication, transcription and translation.

Lamarck and Darwin: two explanations compared

Lamarck (early nineteenth century) proposes two ideas: characters are modified through the use and disuse of organs, and characters acquired during life are passed on to offspring. The classic example is the giraffe that stretches its neck to reach the high leaves and passes it on to its young. Today we know that the second idea is wrong: an acquired character (an athlete’s muscles, a scar) does not change the DNA of the gametes and so is not inherited.

Darwin (1859, On the Origin of Species) changes the point of view: the change does not happen in the single individual but in the population, over generations. Individuals do not transform themselves; those with more favourable characters leave more offspring. The long neck, in the Darwinian version, does not lengthen with effort: in the ancestral populations there were giraffes with slightly longer necks, these found more food, survived and reproduced more, and the characteristic spread.

If you have to give a single sentence: for Lamarck the individual changes and the change is passed on; for Darwin individuals do not change, the composition of the population does.

The four pillars of natural selection

Natural selection is a logical consequence of four observations:

Variation: the individuals of a population are not all the same (colour, size, resistance).
Heredity: part of these differences is passed on to descendants.
Overproduction: more individuals are born than the environment can support, so there is competition for limited resources.
Differential reproductive success: individuals with the characters best suited to that environment, on average, leave more offspring.

If these four conditions are true, the composition of the population changes over time. No “purpose” is needed: all you need is an environment that favours certain characters over others. Whoever writes “the organism developed X in order to survive” is writing in Lamarckian form; more correct: “individuals with X survived and reproduced more, so X spread”.

Another clarification: fitness in biology does not mean physical strength, but the number of fertile offspring left. A weak animal that has more young has higher fitness than a strong one that does not reproduce.

Three classic examples

The moths of the United Kingdom. Before the industrial revolution, light-coloured moths prevailed, camouflaged on lichen-covered trunks; dark ones were rare. Soot pollution blackened the trunks: the light ones became visible to predators, the dark ones did not. Within a few decades the fraction of dark moths became the majority in industrial areas. The colour already varied and was inherited: the environment changed which variant was favoured.

The finches of the Galápagos. On the different islands the finches have beaks of different shape and size, linked to the type of seeds available: robust beaks for hard seeds, thin ones for insects. A common ancestor gave rise to several species adapted to different resources.

Antibiotic resistance. In a population of bacteria, a few individuals have, through random mutation, a variant that makes them resistant. With the antibiotic the susceptible ones die, the resistant one survives and reproduces quickly, and after a few generations the population is almost all resistant. The antibiotic does not create the resistance: it selects a variant that was already present. It is the most useful example to cite in tests, because it can be observed over short timescales.

The modern synthesis

Darwin did not know about genes. The modern synthesis (early twentieth century) unites natural selection and genetics. It says that evolution is a change in the allele frequencies of a population over time. The sources of variation and the mechanisms of change are:

mutations: random changes in the DNA, the only source of new alleles;
recombination: the reshuffling during meiosis and sexual reproduction creates new combinations of alleles that already exist;
natural selection: the only mechanism that leads to adaptation;
genetic drift: random variation of allele frequencies, stronger in small populations (for example after a bottleneck or the founder effect). It does not produce adaptation;
gene flow: exchange of alleles between populations through the migration of individuals or gametes; it tends to make populations similar.

The difference between selection and drift is often asked: the first is directional and depends on the environment, the second is random and matters above all when the population is small.

Hardy-Weinberg: the population that does not evolve

To understand how frequencies change, you need a model of a population that does not change. This is the Hardy-Weinberg equilibrium. Consider a gene with two alleles: $A$ with frequency $p$ and $a$ with frequency $q$ . Since there are no others:

p + q = 1

If mating is random, the genotype frequencies in the next generation are

p^{2} + 2 pq + q^{2} = 1

where $p^{2}$ is the frequency of the $AA$ homozygotes, $2 pq$ of the $A a$ heterozygotes and $q^{2}$ of the $aa$ homozygotes. The equilibrium holds only if five conditions are met: a very large population, random mating, no mutations, no migration (gene flow), no selection. No real population meets them entirely; the model serves as a null hypothesis: if the data depart from it, an evolutionary factor is at work.

The trick in almost all exercises: the only genotype you can identify with certainty from the phenotype is the recessive one, so you start from $q^{2}$ , calculate $q$ with the square root and from there everything else.

Exercise 1: carriers of a recessive disease

A recessive genetic disease affects 1 person in 10 000 in a population in Hardy-Weinberg equilibrium. What is the frequency of heterozygous carriers?

Step 1: $q^{2}$ . The affected person is homozygous recessive, so

q^{2} = \frac{1}{10 000} = 0.0001

Step 2: $q$ .

q = 0.0001 = 0.01

Step 3: $p$ .

p = 1 - q = 1 - 0.01 = 0.99

Step 4: the carriers.

2 pq = 2 \cdot 0.99 \cdot 0.01 = 0.0198

Carriers are about $2%$ of the population, that is about 1 person in 50. It is the result that surprises most: a very rare disease (1 in 10 000) has one carrier in every 50, because the recessive allele “hides” in healthy heterozygotes. Check: $p^{2} = 0.9801$ , $2 pq = 0.0198$ , $q^{2} = 0.0001$ , and the sum is $1$ .

Exercise 2: is the population in equilibrium?

In a population of 100 individuals you count $50$ of genotype $AA$ , $20$ of genotype $A a$ and $30$ of genotype $aa$ . Calculate the allele frequencies and say whether the population is in equilibrium.

Step 1: the allele frequencies. Each individual has two alleles, so in total there are $200$ . The $A$ alleles are $2 \cdot 50 + 20 = 120$ , the $a$ alleles are $2 \cdot 30 + 20 = 80$ .

p = \frac{120}{200} = 0.6 q = \frac{80}{200} = 0.4

Step 2: the expected values at equilibrium.

p^{2} = 0.36 \to 36 individuals AA

2 pq = 2 \cdot 0.6 \cdot 0.4 = 0.48 \to 48 individuals A a

q^{2} = 0.16 \to 16 individuals aa

Step 3: comparison. Observed: $50, 20, 30$ . Expected: $36, 48, 16$ . There are far fewer heterozygotes than you would expect and far more homozygotes: the population is not in equilibrium. It may be due to non-random mating (for example between similar individuals), to selection or to division into subpopulations.

There is a useful detail: if in the next generation mating becomes random, in a single generation the genotype frequencies become $0.36$ , $0.48$ , $0.16$ , while $p$ and $q$ stay $0.6$ and $0.4$ . Allele frequencies do not change by themselves: only the combinations change.

Exercise 3: open question on antibiotics

A patient takes an antibiotic for three days and then stops; after a month the infection returns and the antibiotic no longer works. Explain with natural selection, without saying that “the bacteria got used to it”.

Solution.

In the bacterial population there is variation: through random mutations some individuals have a variant that makes them less sensitive to the antibiotic.
The resistance is heritable: it is passed on to daughter cells (and can also pass to other bacteria by exchange of DNA).
The antibiotic creates a selective pressure: the susceptible ones die, the less sensitive ones survive.
The survivors reproduce very quickly, with generation times of minutes, and after many generations the population is made up almost entirely of resistant bacteria.
So the antibiotic did not create the resistance: it selected it, and no bacterium “got used to it”. A course stopped too early leaves alive precisely the most resistant.

If the question asks which evolutionary factor is at work, the answer is natural selection; genetic drift does not explain so precise an adaptation.

Speciation and evidence for evolution

A species (biological concept) is a group of populations whose individuals can interbreed and produce fertile offspring, and are reproductively isolated from other groups. Speciation is the process by which one species gives rise to two.

Allopatric: a geographical barrier (an arm of the sea, a mountain range, a river that changes course) divides the population. The two parts evolve separately, with different mutations, selection and drift, until they can no longer interbreed. It is the most common mechanism and the case of the finches.
Sympatric: the new species forms in the same territory, without a geographical barrier, usually through reproductive isolation linked to ecology or through polyploidy, common in plants.

The evidence for evolution comes from several fields, and it is worth being able to cite one for each:

fossils: intermediate forms and succession in the rocks;
comparative anatomy: homologous structures (the forelimb of a human, a bat and a whale, with the same bones but different functions: they indicate a common origin) and analogous structures (the wing of a bird and that of an insect: same function, different origin);
embryology: vertebrate embryos very similar in the early stages;
molecular biology: the genetic code is practically universal and DNA and protein sequences are more similar between closer species;
biogeography: the distribution of species follows the history of continents and islands.

The mistakes that cost marks

“Evolution has a purpose.” There is no goal, nor progress towards a “more evolved” organism. What is selected is what works now, in that environment.
The individual that evolves. Populations evolve, not individuals. An individual does not change its own genes to adapt.
Lamarck in disguise. Phrases like “it adapted because it needed to” or “by using its neck it lengthened” are Lamarckian.
Survival of the fittest as strongest. What counts is the number of fertile offspring, not strength. The “fittest” is relative to the environment.
Hardy-Weinberg: forgetting the root. If the question gives the frequency of the disease, that number is $q^{2}$ , not $q$ . Then you take the square root.
Confusing allele frequency and genotype frequency. $q$ is the frequency of the allele, $q^{2}$ that of the recessive homozygotes, $2 pq$ that of the heterozygotes.
Mutation and selection swapped. Mutation is random and supplies the variation; selection is not random and chooses among the variants that already exist.

How to prepare

Write out the four pillars without looking and apply them to an example of your own. Then redo the three exercises, changing the data: another disease ( $q^{2} = 1/2500$ is good training), another population with other counts. To strengthen the genetics part, onto which Hardy-Weinberg is grafted, you can also use the Mendelian genetics simulator (questions in Italian). The picture of the other biology units, such as photosynthesis and cellular respiration, is in Science.

If you want a check before the oral test

If the concepts seem clear but your open answers do not come out in an orderly way, or Hardy-Weinberg always blocks you at the same step, it is a problem of method, which gets sorted in one or two sessions. Write to me from the contact page and we do a free introductory call: send me a question or an exercise that does not work out and I will tell you where it jams.

Evolution: Darwin, natural selection and Hardy-Weinberg