Biology — Complete Formula Sheet

All cells of the female gametophyte are haploid; the central cell has two polar nuclei that later fuse.

One male gamete fuses with the egg to form a diploid zygote.

The Primary Endosperm Nucleus (PEN) is triploid and develops into the endosperm.

One microspore mother cell (pollen mother cell) gives four haploid pollen grains arranged as a tetrad.

Only the chalazal (functional) megaspore survives and forms the embryo sac (monosporic development).

Cell breakdown: 1 egg + 2 synergids (egg apparatus) + 3 antipodals + 1 central cell (with 2 polar nuclei).

Seed coat and perisperm are of maternal (sporophytic) origin; only endosperm is triploid.

2-celled at shedding in most species; 3-celled when the generative cell has already divided to give two male gametes.

Sporopollenin resists high temperature, strong acids/alkalis and enzymes — the reason pollen fossilises so well.

Apomictic seeds are genetically identical to the mother — useful in hybrid seed technology.

$T_{\text{testes}}$: Temperature of the testes (°C) · $T_{\text{body}}$: Normal internal body temperature (°C)

The testes lie outside the abdominal cavity in the scrotum, which keeps them 2–2.5 °C below normal internal body temperature — needed for spermatogenesis.

Seminiferous tubules are lined by spermatogonia and Sertoli cells. Leydig (interstitial) cells lie outside the tubules and secrete androgens.

Spermatogonia multiply by mitosis; some become primary spermatocytes (2n = 46), which undergo meiosis. Spermatids become sperms by spermiogenesis; release of sperms from the tubules is spermiation.

$N_{\text{sperms}}$: Number of sperms (equal to number of spermatids) · $N_{\text{primary}}$: Number of primary spermatocytes · $N_{\text{secondary}}$: Number of secondary spermatocytes

Each primary spermatocyte gives 4 sperms; each secondary spermatocyte gives 2. Number of spermatids = number of sperms.

GnRH from the hypothalamus makes the anterior pituitary release LH and FSH. Androgens stimulate spermatogenesis; FSH makes Sertoli cells secrete factors that help spermiogenesis.

Both conditions must hold for normal fertility. Seminal plasma comes from the seminal vesicles, prostate and bulbourethral glands.

Both divisions are unequal: the oocyte keeps the bulk of the nutrient-rich cytoplasm. Meiosis I finishes in the tertiary follicle; meiosis II finishes only after a sperm enters.

$N_{\text{ova}}$: Number of ova formed · $N_{\text{primary oocytes}}$: Number of primary oocytes completing oogenesis

One ovum per primary oocyte, compared with four sperms per primary spermatocyte. The extra nuclei go into polar bodies.

Only 60,000–80,000 primary follicles are left in each ovary at puberty. The tertiary follicle has a fluid-filled cavity called the antrum; the secondary oocyte forms the zona pellucida.

NCERT gives the average interval between menstruations as about 28/29 days. One ovum is released in the middle of each cycle. The reproductive cycle of female primates (monkeys, apes, humans) is the menstrual cycle. Menarche is the first menstruation at puberty; menopause is around 50 years of age.

Menstrual flow lasts 3–5 days. The follicular (proliferative) phase regenerates the endometrium; the luteal phase is when the corpus luteum is active. Day numbers are for an idealised 28-day cycle.

The LH surge ruptures the Graafian follicle. Progesterone from the corpus luteum maintains the endometrium. With no fertilisation the corpus luteum degenerates, the endometrium breaks down and menstruation follows.

All ova carry X; half the sperms carry X and half carry Y. So the father's sperm decides the sex, with a 50% chance of each.

Fertilisation happens in the ampullary region of the oviduct. Cleavage (mitosis) starts as the zygote moves through the isthmus towards the uterus.

The trophoblast attaches to the endometrium; the inner cell mass becomes the embryo. Embedding of the blastocyst in the endometrium is implantation, which leads to pregnancy.

Levels of estrogens, progestogens, cortisol, prolactin and thyroxine also rise in maternal blood during pregnancy. Relaxin comes from the ovary, not the placenta.

First movements of the foetus and hair on the head usually appear in the fifth month. By 24 weeks (end of the second trimester) the body has fine hair, eyelids separate and eyelashes form.

The signal comes from the fully developed foetus and the placenta. Oxytocin causes stronger contractions, which cause more oxytocin release — a positive loop until the baby is delivered.

Cross Tt × Tt: dominant phenotype : recessive phenotype.

Only visible when a test cross is made — Tt × tt gives 1:1 tall to dwarf.

Two independently segregating pairs. 9 dominant-dominant : 3 dominant-recessive : 3 recessive-dominant : 1 recessive-recessive.

Used to expose the genotype of an individual showing the dominant phenotype.

Phenotypic ratio equals genotypic ratio (e.g. Mirabilis: red : pink : white).

Multiple alleles; Iᴬ and Iᴮ are codominant; both dominant over i.

Grasshopper follows XX/XO. In humans the father is always the sex-determining parent.

22 pairs autosomes + 1 pair sex chromosomes.

Extra copy of chromosome 21 due to non-disjunction during meiosis.

Klinefelter is male with an extra X; Turner is female with a missing X (sterile).

Purines equal pyrimidines in any double-stranded DNA (holds across species).

B-form DNA, right-handed helix.

About 2 metres of DNA is packed into every human diploid nucleus (only a few micrometres wide).

Proved by Meselson-Stahl (1958) via density gradient centrifugation of ¹⁵N-labelled DNA.

Nucleoside = sugar + base only. Adding phosphate makes a nucleotide.

In prokaryotes RNA polymerase reads the template strand 3' → 5' and builds mRNA 5' → 3'.

Triplet, degenerate, unambiguous, universal, non-overlapping, commaless.

Reverse transcription (RNA → DNA) is an addition proposed by Temin and Baltimore in retroviruses.

5' cap = methyl guanosine; 3' tail = ~200 adenylates; splicing removes introns and joins exons.

Less than 2% of the genome codes for protein; the rest was earlier called 'junk DNA'.

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.

S.L. Miller recreated early-Earth conditions in a closed flask. Formation of amino acids supported chemical 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.

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.

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.

Darwin's two key ideas are branching descent and natural selection. 'Fit' means leaving more offspring, not being physically stronger.

Hugo de Vries worked on evening primrose. He held that mutations, not small heritable variations, cause speciation in single large steps.

$p$: 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.

$p^2$: Frequency of homozygous dominant AA · $2pq$: 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.

$q$: 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.

$N_{AA},N_{Aa},N_{aa}$: 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.

Any of these changes allele frequencies, which means evolution is taking place. A drifted population that becomes a new species shows the founder effect.

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.

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.

Y-shaped molecule; each arm has an antigen-binding site (Fab); stem is Fc.

IgG crosses placenta; IgA in secretions; IgM first responder in primary response; IgE in allergies; IgD B-cell receptor.

Active immunity is slow but long-lasting; passive is fast but short-lived.

Retrovirus — reverses the central dogma to make DNA from RNA.

Detects anti-HIV antibodies in patient's blood; confirmed by Western blot.

Benign tumours stay put; malignant tumours invade and spread through blood/lymph.

Molecular biology techniques detect genes with cancer predisposition.

Morphine binds opioid receptors; cocaine blocks dopamine reuptake.

Cytokine of the innate immune system; enhances antiviral state.

Induces active immunity without causing disease.

Restriction enzyme cuts both — DNA ligase seals the sticky ends.

First letter of genus + first two of species (italicised) + strain + Roman numeral.

Reads the same 5' → 3' on both strands. Eco RI cuts between G and A leaving sticky ends.

After n cycles the template is amplified 2ⁿ-fold. 30 cycles ⇒ about 10⁹-fold amplification.

ori = origin of replication; MCS = multiple cloning site; selectable marker distinguishes transformants.

Provides optimum temperature, pH, aeration and substrate to microbes.

Antibiotic resistance genes let researchers select cells with recombinant vector.

The steps after fermentation that give the marketable product.

Nature's own genetic engineer — used to make transgenic crops.

Smaller fragments move farther. Visualised with ethidium bromide under UV light.

$N$: Population density (individuals per unit area or volume)

Total number is not always meaningful: one huge banyan tree versus 200 Parthenium plants. Then per cent cover or biomass is a better measure. Relative density (fish caught per trap) or indirect signs (tiger pug marks and fecal pellets) are also used.

$b$: Per capita birth rate (births per individual per unit time)

A per capita rate. Example from NCERT: 8 new lotus plants added to 20 gives 8/20 = 0.4 offspring per lotus per year.

$d$: Per capita death rate (deaths per individual per unit time)

A per capita rate. Example from NCERT: 4 of 40 fruit flies die in a week gives 4/40 = 0.1 individuals per fruit fly per week.

Age groups are pre-reproductive, reproductive and post-reproductive. An expanding pyramid has a broad base (many young); a declining one has a narrow base. Sex ratio is another attribute, e.g. 60% females and 40% males.

$N_t$: Population density at time t · $N_{t+1}$: Population density one time step later · $B$: Number of births (natality) · $I$: Number of immigrants (same species coming in) · $D$: Number of deaths (mortality) · $E$: Number of emigrants (leaving the habitat)

Population increases if (B + I) > (D + E) and decreases if (B + I) < (D + E). Births and deaths matter most normally; immigration can dominate when a new habitat is being colonised.

$N$: Population size (density) · $r$: Intrinsic rate of natural increase, r = b − d (per unit time) · $b,d$: Per capita birth and death rates

Applies when resources are unlimited. Each species then realises its full innate potential to grow, and the curve is J-shaped.

$N_t$: Population density after time t · $N_0$: Population density at time zero · $e$: Base of natural logarithms (2.71828) · $t$: Time elapsed

Use for the population after time t under unlimited resources. Keep r and t in matching time units.

r measures how quickly a population can grow under ideal conditions. These are the values quoted in NCERT; they are useful for comparison questions.

$N$: Population density at time t · $r$: Intrinsic rate of natural increase · $K$: Carrying capacity — the maximum population the habitat can support

Applies when resources are limited. Growth slows as N approaches the carrying capacity K, giving an S-shaped (sigmoid) curve. NCERT calls this the more realistic model.

When the population is small the logistic curve looks exponential; at N = K growth stops and the curve reaches its asymptote.

Plot population density N on the y-axis and time t on the x-axis. Mark K as a horizontal dashed line on the logistic curve.

Some organisms produce many small offspring (oysters, pelagic fishes); others produce a few large ones (birds, mammals). Populations evolve to maximise reproductive fitness in their habitat.

+ means benefit, − means harm, 0 means unaffected. Mutualism: lichens, mycorrhizae, fig and wasp. Commensalism: orchid on a mango branch, barnacles on a whale, cattle egret and cattle, clown fish and sea anemone. Brood parasitism: cuckoo (koel) laying eggs in a crow's nest.

The competitively inferior species is eliminated eventually. Species can co-exist by resource partitioning, as MacArthur showed for five warbler species feeding on the same tree.

Primary production is the biomass made per unit area by plants during photosynthesis. The rate of biomass production is productivity, so it carries a per-time unit.

$\text{GPP}$: Gross primary productivity (g m⁻² yr⁻¹ or kcal m⁻² yr⁻¹) · $R$: Respiration losses of the producers (same units) · $\text{NPP}$: Net primary productivity (same units)

GPP is the rate of production of organic matter in photosynthesis. Plants use part of it in respiration (R). NPP is the biomass available to heterotrophs (herbivores and decomposers).

Primary productivity depends on the plant species, environmental factors, nutrient availability and the photosynthetic capacity of plants.

Dry weight of organic matter per year. Oceans cover about 70% of the surface but give only about 55 of the 170 billion tons.

Detritivores (earthworm) fragment detritus; water-soluble nutrients leach into the soil and precipitate as unavailable salts; bacterial and fungal enzymes catabolise detritus; humus forms; humus is mineralised to release inorganic nutrients. The steps operate simultaneously.

Humification and mineralisation happen in the soil. Humus resists microbial action, which is why it decomposes at an extremely slow rate.

Decomposition is an oxygen-requiring process. Chemical composition of detritus and climatic factors (temperature, soil moisture) control the rate.

Decomposers (mainly fungi and bacteria) are saprotrophs. In aquatic ecosystems the GFC is the major conduit for energy; on land a much larger fraction of energy flows through the DFC.

Herbivores are primary consumers; carnivores feeding on them are secondary consumers. Food chains interconnect to form a food web.

Except for deep-sea hydrothermal ecosystems, the sun is the only source of energy. This small captured fraction sustains the entire living world.

Ecosystems obey the second law of thermodynamics: they need a constant input of energy to counteract the tendency towards disorder.

$E_n$: Energy at trophic level n (J or kcal) · $E_{n+1}$: Energy transferred to the next trophic level

Only about 10% of the energy at one trophic level is transferred to the next; the rest is lost, mostly as heat. This limits the number of trophic levels.

$E_1$: Energy fixed by producers (J or kcal) · $n$: Trophic level number (producers are n = 1)

Repeated application of the 10% law. Going down the chain, divide by 0.1 for each step: E₁ = Eₙ/(0.1)ⁿ⁻¹.

Measured as biomass or as number per unit area. Biomass in dry weight is more accurate than fresh weight.

Pyramid of biomass in the sea is generally inverted because the biomass of fishes far exceeds that of phytoplankton. Energy is always lost as heat at each step, so the energy pyramid can never be inverted.