CBSE · Class 12 · Biology · Chapter 6

Evolution — Formula Sheet

Board Formulas

14 formulas

1.Time Scale of Life
$Universe \approx 13.8 billion yr; Earth \approx 4.5 billion yr; life \approx 4 billion yr ago$
The current NCERT reprint gives the age of the universe as almost 13.8 billion years (older reprints said 20 billion). Life appeared about 500 million years after the Earth formed. Oparin and Haldane proposed that the first life came from pre-existing non-living organic molecules after a phase of chemical evolution.
2.Miller's Experiment (1953)★
$CH_{4} + H_{2} + NH_{3} + H_{2} O (vapour) electric discharge, 80 0^{\circ} C amino acids$
S.L. Miller recreated early-Earth conditions in a closed flask. Formation of amino acids supported chemical evolution.
3.Homology and Analogy★
$Homologous organs \Rightarrow divergent evolution; Analogous organs \Rightarrow convergent evolution$
Homologous: forelimbs of whale, bat, cheetah and human; thorn of Bougainvillea and tendril of Cucurbita. Analogous: wings of butterfly and bird; eyes of octopus and mammals; flippers of penguin and dolphin; sweet potato and potato.
4.Adaptive Radiation
$One ancestral stock (one area) \to many species adapted to different habitats$
Examples: Darwin's finches of the Galapagos, and Australian marsupials. More than one adaptive radiation in an isolated area (placental mammals and marsupials in Australia) is convergent evolution.
5.Industrial Melanism
$1850s: white-winged > dark-winged; 1920: dark-winged > white-winged$
Before industrialisation, white lichen covered tree trunks and white moths were camouflaged. After industrialisation, smoke and soot darkened the trunks, so dark moths escaped predators. Selection changed the proportion; no new moth was created.
6.Darwinian Fitness
$Fitness = reproductive fitness (leaving more progeny)$
Darwin's two key ideas are branching descent and natural selection. 'Fit' means leaving more offspring, not being physically stronger.
7.Mutation Theory (de Vries)
$Mutation: large, sudden, random, directionless (saltation) vs Darwinian variation: small, directional$
Hugo de Vries worked on evening primrose. He held that mutations, not small heritable variations, cause speciation in single large steps.
8.Sum of Allele Frequencies
$p + q = 1$
$p$ : Frequency of allele A (dimensionless, 0 to 1) · $q$ : Frequency of allele a (dimensionless, 0 to 1)
For a gene with two alleles A and a, the frequencies of all alleles in the gene pool add up to 1.
9.Hardy–Weinberg Equation★
$p^{2} + 2 pq + q^{2} = 1$
$p^{2}$ : Frequency of homozygous dominant AA · $2 pq$ : Frequency of heterozygous Aa · $q^{2}$ : Frequency of homozygous recessive aa
Genotype frequencies of AA, Aa and aa in a population at genetic equilibrium. It is the binomial expansion of (p + q)² = 1.
10.Recessive Allele from Phenotype
$q = q^{2} = frequency of aa$
$q$ : Frequency of the recessive allele a
Only aa individuals can be recognised directly by their phenotype, so start every numerical with q². Valid only if the population is in equilibrium.
11.Allele Frequency by Counting
$p = \frac{2 N _{AA} + N _{A a}}{2 N}, q = \frac{2 N _{aa} + N _{A a}}{2 N}$
$N_{AA}, N_{A a}, N_{aa}$ : Number of individuals of each genotype · $N$ : Total number of individuals
Each diploid individual carries two alleles, so the denominator is 2N. Use this when genotype counts are given; it needs no equilibrium assumption.
12.Factors Affecting Hardy–Weinberg Equilibrium★
$Gene flow, genetic drift, mutation, genetic recombination, natural selection$
Any of these changes allele frequencies, which means evolution is taking place. A drifted population that becomes a new species shows the founder effect.
13.Types of Natural Selection
$Stabilising (mean favoured); Directional (one extreme favoured); Disruptive (both extremes favoured)$
Stabilising: more individuals take the mean value and the peak gets taller. Directional: the peak shifts to one side. Disruptive: more individuals at both ends, giving two peaks.
14.Brain Capacity in Human Evolution
$Homo habilis : 650 to 800 cc; Homo erectus \approx 900 cc; Neanderthal \approx 1400 cc$
Homo habilis was the first human-like hominid; Homo erectus lived about 1.5 million years ago; Neanderthal man lived 1,00,000–40,000 years ago in the near east and central Asia.