Evolution

The Hardy-Weinberg principle (G.H. Hardy, mathematician, and W. Weinberg, physician, both 1908) states that in an idealised population, the allele and genotype frequencies remain constant from generation to generation. The principle provides a baseline — a null hypothesis — against which to test whether a real population is evolving.

The two equations.

For a gene with two alleles in the population, let:

• $p$ = frequency of the dominant allele
• $q$ = frequency of the recessive allele

Equation 1 — allele frequencies: $p + q = 1$ (because every copy of the gene is either dominant or recessive, so they must sum to 1).

Equation 2 — genotype frequencies (after one generation of random mating): $p^2 + 2pq + q^2 = 1$ where:

• $p^2$ = frequency of homozygous dominant (e.g. AA)
• $2pq$ = frequency of heterozygous (e.g. Aa) — the factor of 2 is because Aa and aA are equivalent
• $q^2$ = frequency of homozygous recessive (e.g. aa)

Derivation (intuitive). If alleles are sampled at random from the gene pool for fertilisation, the probability of an AA offspring is $p \times p = p^2$; aa is $q \times q = q^2$; and Aa or aA is $p \times q + q \times p = 2pq$. The three probabilities sum to $(p + q)^2 = 1$.

Why $q^2$ is the most useful quantity. Many genetic diseases (cystic fibrosis, phenylketonuria, sickle-cell anaemia) are caused by homozygous recessive genotypes (aa). The observed disease frequency therefore directly gives $q^2$. From there:

1. $q = \sqrt{q^2}$ (take the square root).
2. $p = 1 - q$.
3. Carrier (heterozygous) frequency = $2pq$.

This calculation is widely used in genetic counselling to estimate the chance that an apparently healthy person carries a disease allele.

Worked example — phenylketonuria (PKU). PKU affects 1 in 10,000 newborns in some populations (autosomal recessive).

• $q^2 = 1/10{,}000 = 10^{-4}$
• $q = \sqrt{10^{-4}} = 0.01$ (PKU allele frequency = 1%)
• $p = 1 - 0.01 = 0.99$
• $2pq = 2(0.99)(0.01) = 0.0198 \approx 0.02$ (carrier frequency = 2%, or about 1 in 50 people)

Note that carriers vastly outnumber affected individuals (2% vs 0.01% = 200× more carriers). This is why recessive disease alleles persist — most copies hide in heterozygotes who are themselves healthy.

Hardy-Weinberg equilibrium holds only when five conditions are simultaneously satisfied. Each condition, if violated, drives evolution (a change in allele frequencies).

1. No mutation. Mutation creates new alleles (or destroys existing ones), changing the gene pool. For H-W to hold, no new mutations may occur at the locus.

2. No natural selection. All genotypes must have equal fitness (equal survival and reproductive success). Any selection advantage will shift allele frequencies.

3. No gene flow (no migration). No alleles may enter the population by immigration nor leave by emigration. Migration brings in new alleles or removes existing ones, altering frequencies.

4. Random mating. Mating must be random with respect to genotype — no assortative mating (mating with similar phenotypes) and no inbreeding (mating with close relatives). Non-random mating changes genotype frequencies even when allele frequencies stay constant.

5. Large population (no genetic drift). The population must be large enough that chance fluctuations in allele frequency from one generation to the next are negligible. In small populations, genetic drift causes appreciable random changes.

Mnemonic: Mad Scientists Make Random Laws (Mutation, Selection, Migration, Random mating, Large population).

Why H-W is useful even though no real population meets all five conditions.

(a) Null hypothesis for evolution. Hardy-Weinberg describes a population in which no evolution is occurring. By comparing observed allele/genotype frequencies with those predicted by H-W, biologists can:

• Detect that evolution is occurring.
• Identify which condition is being violated. For example:
  • Excess homozygotes → inbreeding or selection against heterozygotes.
  • Allele frequencies changing over time → selection or drift.
  • Sudden allele appearance → migration or mutation.

(b) Carrier frequency calculations. From observed disease incidence ($q^2$), the carrier frequency ($2pq$) can be calculated for genetic counselling, public-health planning and screening programmes.

(c) Conservation genetics. Departures from H-W flag inbreeding in endangered species, helping conservationists design breeding programmes that preserve heterozygosity.

(d) Forensic and ancestry genetics. Population allele frequencies (calculated by assuming H-W equilibrium at a given locus) are used in DNA profiling probability calculations.

In short, H-W is a powerful idealisation — not a literal description of real populations, but a benchmark that lets us measure how and why real populations deviate.

Species (biological species concept) = a group of organisms that can interbreed in the wild to produce fertile offspring, and is reproductively isolated from other such groups. Speciation is the formation of a new species from an existing one — requiring reproductive isolation between the diverging populations so they no longer exchange alleles.

Reproductive isolating mechanisms fall into two categories: pre-zygotic (preventing fertilisation) and post-zygotic (preventing successful hybrid reproduction).

Pre-zygotic mechanisms (act before fertilisation):

Mechanism	How it works	Example
Geographical	Physical separation (mountain, river, ocean)	Galapagos islands
Temporal	Populations breed at different times of year	Spring vs autumn breeding frogs
Behavioural	Different courtship songs, displays, pheromones	Cichlid fish mating colours
Mechanical	Incompatible genitalia or flower morphology	Some insects, orchid–pollinator pairs
Gametic	Sperm cannot fertilise eggs of other species	Marine invertebrates with species-specific gamete recognition
Ecological	Populations occupy different habitats/niches	Apple maggot fly host-shifting

Post-zygotic mechanisms (act after fertilisation):

Mechanism	How it works	Example
Hybrid inviability	Zygote forms but dies during development	Many cross-species crosses
Hybrid sterility	Hybrid survives but cannot produce gametes	Mule (horse × donkey) — meiosis fails because chromosome numbers differ
Hybrid breakdown	F₁ hybrids fertile but F₂ generation weak/sterile	Some plant crosses

The classic post-zygotic example: the mule. A horse (Equus caballus, 64 chromosomes) crossed with a donkey (Equus asinus, 62 chromosomes) produces a mule with 63 chromosomes. The mule is vigorous and useful as a working animal, but its chromosomes cannot pair correctly in meiosis because the homologues don't match — so it produces no viable gametes and is sterile. The two parent species are therefore reproductively isolated.

Outcome of speciation. Once reproductive isolation is complete (by any combination of mechanisms), the gene pools of the populations evolve independently. Mutation, selection and drift in each population accumulate differences. Over time, the populations become so different that they are recognisable as separate species by morphology, behaviour and DNA.

Allopatric speciation (Greek allos = different, patris = homeland) is the formation of new species from a single ancestral population that has been geographically separated by a physical barrier. It is the most common mode of speciation in animals.

The process — five stages.

1. Initial population. A single interbreeding ancestral population shares a common gene pool. All members can in principle exchange alleles by mating.

2. Geographical isolation. Subpopulations become separated by a physical barrier — a mountain range, river, ocean or even a new highway. Once the barrier appears, gene flow ceases — alleles can no longer be exchanged between the subpopulations.

3. Different selection pressures + mutation + drift. Each isolated population experiences a different environment. Natural selection drives each population towards its local optimum, mutation creates new alleles independently in each, and genetic drift (especially strong in small island populations) randomly changes allele frequencies.

4. Divergence. Over many generations, the gene pools of the subpopulations become progressively more different — in anatomy, physiology, behaviour and the underlying DNA. Pre-zygotic isolating mechanisms (different courtship displays, different breeding times) often emerge first.

5. Reproductive isolation complete. Eventually the populations diverge enough that, even if they were brought back together, they could no longer interbreed to produce fertile offspring. They are now separate species.

Classic example: Darwin's finches. Around 2–3 million years ago, a single ancestral grassquit (probably Tiaris from the South American mainland) colonised the Galapagos archipelago. The islands were geographically separated by ocean, and each island offered different food resources.

• On islands with large hard seeds, selection favoured large beaks capable of cracking them. Today these birds include the large ground finch Geospiza magnirostris.
• On islands with insects in tree bark, selection favoured slender, pointed beaks suited to probing crevices. These became the warbler finches.
• On islands with cactus flowers, selection favoured long, slender beaks for sipping nectar. These became cactus finches.

Genetic drift in small founding island populations further accelerated divergence. Different mating songs emerged on different islands (a pre-zygotic isolating mechanism). Today there are 14–18 species of Darwin's finch on the Galapagos, each adapted to its niche. All descended from the same single ancestor in just 2–3 million years.

Other classic examples. Kaibab and Albert squirrels (separated by the Grand Canyon); London Underground mosquito (Culex pipiens molestus, evolved in the isolated underground tunnels since the 19th century); marine snails on opposite sides of the Isthmus of Panama (separated when the isthmus closed 3 million years ago).

Sympatric speciation (Greek sym = together) is the formation of new species without geographical separation — the populations live in the same area but become reproductively isolated by other mechanisms. Although rarer than allopatric speciation overall, sympatric speciation is hugely important in plants, where polyploidy provides a single-step route to reproductive isolation.

Routes to sympatric speciation:

1. Polyploidy (the most common route in plants). An individual ends up with more than two complete sets of chromosomes — for example, a tetraploid (4n) instead of the diploid (2n) of its parents. The polyploid cannot interbreed successfully with its diploid parents because their offspring would be triploid (3n), with chromosomes that cannot pair in meiosis. Reproductive isolation is therefore instantaneous.

Example: bread wheat (Triticum aestivum). Modern bread wheat is a hexaploid (6n = 42 chromosomes) that arose by two successive polyploidisation events involving three different diploid wild grass ancestors:

• Diploid (AA) × diploid (BB) → tetraploid (AABB) = emmer/durum wheat.
• Tetraploid (AABB) × diploid (DD) → hexaploid (AABBDD) = bread wheat.

Many other crops are polyploids: cotton (4n), banana (often 3n, sterile), strawberry (8n), oats (6n), sugar cane (variable), and many cultivated potato varieties.

Why polyploidy works in plants but rarely in animals. Plants can often self-pollinate or reproduce vegetatively, so a new polyploid plant can give rise to a viable population even from a single individual. In animals, the chromosomal imbalance usually disrupts sex determination and development, making polyploids inviable. Exceptions exist — some fish, frogs and lizards are polyploid — but they are rare.

2. Behavioural isolation. In the same habitat, two populations may evolve different mating songs, courtship displays or pheromones. Mating is no longer random. African cichlid fishes in lakes Victoria, Malawi and Tanganyika provide spectacular examples — hundreds of species have evolved within single lakes, often distinguished only by colour and courtship behaviour.

3. Temporal isolation. Populations in the same area breed at different times (different seasons, different times of day). Magicicada periodical cicadas, for example, have 13-year and 17-year broods that almost never co-emerge.

4. Mechanical isolation. Incompatible morphology — incompatible genitalia in insects, incompatible flower structures in plants — prevents successful mating even when the populations attempt to interbreed.

5. Gametic incompatibility. Sperm cannot fertilise eggs even if mating occurs. Common in marine invertebrates that broadcast-spawn into water — species-specific recognition proteins prevent inter-species fertilisation.

6. Habitat specialisation. Populations within the same broad area exploit different niches — different host plants, different microhabitats — and rarely encounter each other. The apple maggot fly (Rhagoletis pomonella) is a classic case: originally a parasite of hawthorn fruit in North America, a population switched to apples (introduced by European settlers in the 1800s). The two host-races now mate on their respective host plants and rarely interbreed — sympatric speciation in progress.

Genetic drift is the random change in allele frequencies from one generation to the next due to chance — not natural selection. It happens because gametes are sampled from a finite gene pool, and any small sample can deviate from the parent frequencies just by chance.

Why drift matters in small populations. Imagine tossing a fair coin. In 10 tosses, you might easily get 7 heads and 3 tails (70% vs 50% expected) — a large deviation just from chance. In 10,000 tosses, you will get very close to 5,000 of each — chance deviations average out in large samples. The same applies to allele sampling: in a small population, chance deviations from one generation to the next are large, and alleles can be fixed (frequency 1.0) or lost (frequency 0) in only a few generations, purely by accident and independently of fitness. In a large population, drift is too small to matter much.

Two specific scenarios of strong drift:

1. Founder effect. When a small group of individuals establishes a new population — for example, a few birds blown to an oceanic island, a small human group emigrating to settle a new region, or a few microbes colonising a new host — the founders carry only a subset of the parent population's gene pool. Some alleles may by chance be over-represented; others may be missing entirely. The new population grows from this biased starting point, and its allele frequencies remain very different from the parent population's.

Examples of the founder effect:

• Amish polydactyly — the high incidence of polydactyly (extra fingers/toes) among the Amish of Pennsylvania traces back to a single founding couple in the 18th century who happened to carry the allele.
• Pingelap colour blindness — total colour blindness (achromatopsia) affects about 10% of the population on the tiny Pacific island of Pingelap. The condition traces to a typhoon in 1775 that killed most of the population; one survivor happened to carry the recessive allele.
• Galapagos finches — each island's founding population carried only a sample of the mainland allele variation, contributing to the rapid divergence seen during allopatric speciation.

2. Bottleneck effect. When a population is dramatically reduced by a catastrophic event — disease, hunting, severe habitat loss, volcanic eruption, climate change — and then recovers, the survivors are a random sample of the original gene pool. Rare alleles, which may have been carried in only one or a few individuals, are likely to be lost. The recovered population can grow large again but with markedly reduced genetic diversity.

Examples of the bottleneck effect:

• Northern elephant seal — hunted to about 20 individuals in the 1890s before protection. Today's population of ~150,000 descends from those 20 survivors and shows extremely low genetic variability.
• Cheetah — a population bottleneck around 10,000 years ago (likely climate-related) reduced cheetahs to such low numbers that all modern cheetahs are genetically as similar as siblings. Tissue grafts between unrelated cheetahs are accepted with little rejection — astonishing for outbred mammals.
• European bison (wisent) — reduced to about 50 individuals after World War I; today's ~7,000 wisent all descend from 12 founders of those 50.

Consequences of drift. Both founder and bottleneck effects produce populations with reduced genetic diversity and allele frequencies that may have shifted drastically from the original. Crucially, drift can fix harmful alleles purely by chance — small endangered populations are therefore vulnerable to:

• Loss of adaptive flexibility (less variation to respond to environmental change).
• Increased frequency of harmful recessive alleles.
• Inbreeding depression when small populations cannot avoid mating between relatives.
• Reduced disease resistance.

This is why conservation genetics treats genetic diversity as a critical resource and seeks to maintain effective population sizes large enough to minimise drift.