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Evolution

Origin of life, theories of evolution, Hardy-Weinberg.

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Theories of evolution

Lamarck, Darwin, modern synthesis.

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Hardy-Weinberg principle

p² + 2pq + q² = 1, deviations.

Hardy-Weinberg principle — and the 5 conditions that violate it
Notes

The Hardy-Weinberg principle (1908) states that allele and genotype frequencies in a large randomly mating population remain constant from generation to generation, in the absence of evolutionary forces.

Mathematical statement: if p = frequency of allele A and q = frequency of allele a (so p + q = 1), then in the next generation:

p² + 2pq + q² = 1

  • p² = frequency of homozygous dominant (AA)
  • 2pq = frequency of heterozygous (Aa)
  • q² = frequency of homozygous recessive (aa)

5 assumptions (any violation → evolution):

  1. No mutations. Mutation introduces new alleles.
  2. Random mating. Non-random mating (assortative, inbreeding) changes genotype frequencies (not allele frequencies, oddly).
  3. No genetic drift. Drift = random changes in allele frequency due to small population size. Severe in bottlenecks and founder effects.
  4. No gene flow (migration). Migrants change allele frequencies if their gene pools differ.
  5. No natural selection. Differential survival/reproduction changes allele frequencies.

Worked example. In a population, 16% of individuals are homozygous recessive (aa). Find p, q, and frequencies of AA and Aa.

q² = 0.16 → q = 0.4. p = 1 − 0.4 = 0.6.
AA: p² = 0.36. Aa: 2pq = 2(0.6)(0.4) = 0.48.

Check: 0.36 + 0.48 + 0.16 = 1. ✓

Worked example for X-linked traits. If 8% of males are colorblind (X-linked recessive), then q = 0.08.

Females: P(colorblind) = q² = 0.0064 = 0.64%. Carriers: 2pq = 2(0.92)(0.08) = 0.147 = ~14.7%.

This is why colorblindness is much rarer in females than males.

Evolutionary forces (the 5 forces of microevolution):

  1. Mutation — slow (~10⁻⁶ per locus per generation in humans) but the ultimate source of variation.
  2. Genetic drift — random; biggest in small populations. Bottleneck effect (catastrophe shrinks population) and founder effect (small group colonizes new area).
  3. Gene flow — migration between populations homogenizes them.
  4. Natural selection — directional (one extreme favored), stabilizing (intermediate favored), or disruptive (both extremes favored).
  5. Non-random mating — sexual selection, inbreeding, assortative mating.

Industrial melanism (peppered moth, Biston betularia): classic example of directional natural selection during the Industrial Revolution. Dark moths increased in soot-blackened Manchester; light moths returned when air quality improved.