State the Hardy-Weinberg principle and assumptions

5.5.1 · Biology › Population Genetics & Speciation

YEH HAI KYA?

HUM KYUN CARE KARTE HAIN? Kyunki yeh ek null hypothesis hai. Agar real genotype numbers Hardy-Weinberg predictions se match karti hain → toh gene shayad evolve nahi ho raha. Agar match nahi karti → toh koi force (selection, drift, migration, etc.) kaam kar raha hai, aur woh deviation hi hamein batata hai ki evolution ho raha hai.

HAME PEHLE PRINCIPLES SE KAISE DERIVE KARNA HAI?

$p^{2} + 2 pq + q^{2}$ ko yaad mat karo. Ise build karo.

Step 1 — Gene pool define karo. Socho poori population ke saare gametes (eggs + sperm) ek bucket mein daal diye. Fraction $p$ mein allele $A$ hai; fraction $q$ mein allele $a$ hai. Yeh step kyun? Random mating ka matlab hai ki offspring is bucket se do gametes randomly draw karke bante hain — toh genotype frequencies ek probability problem ban jaati hain.

Step 2 — Do gametes independently draw karo. Probability ki offspring hai:

$AA$ = P(pehla $A$ hai) × P(doosra $A$ hai) = $p \times p = p^{2}$
$aa$ = $q \times q = q^{2}$
$A a$ = $A$ phir $a$ , ya $a$ phir $A$ = $pq + q p = 2 pq$

Factor of 2 kyun? Kyunki heterozygotes do tarike se ban sakte hain — $A$ maa se aur $a$ baap se, ya ulta. Agar yeh miss karo toh tumhari frequencies 1 mein add nahi hongi.

Step 3 — Check karo ki yeh 1 mein sum hoti hain. $p^{2} + 2 pq + q^{2} = (p + q)^{2} = (1)^{2} = 1 ✓$ Yeh step kyun? Yeh algebraic guarantee hai ki humne har possible offspring cover ki hai — kuch missing nahi hai.

Step 4 — Dikhao ki yeh stable hai (actual "equilibrium"). Offspring generation mein $A$ ki allele frequency calculate karo. Har $AA$ mein $A$ ki 2 copies hain; har $A a$ mein 1: $p^{'} = \frac{2 p ^{2} + 2 pq}{2} = p^{2} + pq = p (p + q) = p (1) = p$ Toh $p^{'} = p$ . Allele frequency nahi badi. Woh constancy — generation dar generation — hi Hardy-Weinberg equilibrium hai.

Figure — State the Hardy-Weinberg principle and assumptions

5 Assumptions ("no-force" conditions)

Equilibrium tabhi hold karta hai jab paancho true hon. Har failed assumption ek evolutionary force ki definition hai.

Assumption	Agar violate ho →
No mutation ( $A \leftrightarrow a$ nahi hota)	naye alleles / $p, q$ badal jaate hain
No gene flow (migration) — koi allele andar/bahar nahi	frequencies migrants ki taraf shift hoti hain
Bahut badi population (ideally infinite)	random drift chance se $p, q$ badal deta hai
Random mating (koi mate preference nahi)	genotype ratios distort ho jaate hain (jaise inbreeding ↑ homozygotes)
No natural selection — saare genotypes equally survive aur reproduce karte hain	favoured alleles badhte hain

Worked Examples

Common Mistakes

Recall Feynman: 12-saal ke bachche ko explain karo

Socho ek bade jar mein laal aur neeli marbles hain (laal = allele $A$ , neeli = allele $a$ ). Baby banane ke liye, tum aankhein band karke do marbles random se nikaalte ho. Agar koi add nahi karta, nahi nikaalita, nahi rangta, ya favorites pick karke cheat nahi karta, toh jar mein laal vs neeli marbles ka fraction hamesha ke liye same rehta hai. Aur tum exactly predict kar sakte ho kitne babies ko do laal milte hain, do neele, ya ek ek — bas chances multiply karke. Woh "kuch nahi badlta" wala jar Hardy-Weinberg hai. Jab asli jar badalta hai, tum jaante ho koi marbles ke saath chhad kar raha tha — woh "chhad karna" hi evolution hai.

Active Recall Flashcards

Genotype frequencies ke liye Hardy-Weinberg equation bolo.

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

, with

p + q = 1

2 pq

kya represent karta hai aur factor of 2 kyun hai?

Heterozygotes (

A a

) ki frequency; 2 isliye hai kyunki

A a

do tarike se ban sakta hai (

A

a

a

A

Hardy-Weinberg equilibrium ki 5 assumptions list karo.

No mutation, no gene flow/migration, bahut badi (infinite) population, random mating, no natural selection.

Agar population ka 16%

aa

hai, toh

q

kya hai?

q = 0.16 = 0.4

HW ke under, generations mein allele frequencies ka kya hota hai?

Woh constant rehti hain (

p^{'} = p

q^{'} = q

Hardy-Weinberg ko "null hypothesis" kyun kehte hain?

Yeh frequencies predict karta hai jab evolution NAHI ho raha; isse deviation batata hai ki koi evolutionary force kaam kar rahi hai.

Kya dominance HW ke under allele ko zyada frequent banati hai?

Nahi — dominance phenotype masking affect karta hai, allele frequency nahi.

Genotype counts se allele frequency

p

kaise calculate karte hain?

p = \frac{2 ( AA ) + ( A a )}{2 \times total individuals}

Kaunsi violated assumption genetic drift se correspond karti hai?

Choti population size (finite population).

Dikhao ki

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

1 mein sum hoti hai.

Yeh

(p + q)^{2} = 1^{2} = 1

ke barabar hai.

Connections

Allele and Genotype Frequencies
Natural Selection — "no selection" assumption violate karta hai
Genetic Drift — "large population" violate karta hai
Gene Flow and Migration — "no gene flow" violate karta hai
Mutation as Source of Variation — "no mutation" violate karta hai
Non-random Mating and Inbreeding — genotype ratios distort karta hai
Speciation — tab hota hai jab populations shared HW equilibrium se diverge karti hain
Punnett Square — same gamete-drawing logic ka single-cross version