Explain polygenic inheritance — Hinglish notes

3.2.4 · Biology › Extensions of Mendelian Genetics

Polygenic inheritance KYA hai?

Ise compare karo (taaki kabhi confuse na ho):

Term	Meaning
Polygenic	EK trait ← BAHUT saare genes
Pleiotropy	EK gene → BAHUT saare traits
Multiple alleles	EK gene, 2 se ZYADA allele versions (e.g. ABO)

"Bahut saare genes" smooth bell curve KAISE banate hain?

Pehle principles se derivation — counting argument

Maan lo ek trait $n$ genes se control hoti hai. Har gene ke do alleles hain:

ek contributing allele (1 unit add karta hai), ise uppercase kaho,
ek non-contributing allele (0 add karta hai), ise lowercase kaho.

Ek person ke paas total $2 n$ alleles hain. Contributing alleles ki sankhya, $k$ , $0$ se $2 n$ tak range karti hai.

Distribution middle mein peak kyon karta hai? Theek $k$ contributing alleles dene wale genotypic combinations ki sankhya binomial coefficient hai:

$ways (k) = (k 2 n)$

Ye formula kyon? Hum choose kar rahe hain ki $2 n$ allele slots mein se kaun se $k$ contributing version hain — ek pure "choose $k$ from $2 n$ " count. 0 contributing rakhne ka exactly ek tarika hai ( $(0 2 n) = 1$ ) lekin half rakhne ke bahut saare tarike hain ( $(n 2 n)$ sabse bada hai).

Agar har allele equally likely hai (heterozygous parents, frequency $\frac{1}{2}$ ), toh phenotype class $k$ ki probability hai:

$P (k) = (k 2 n) (\frac{1}{2})^{2 n}$

$(1/2)^{2 n}$ kyon? $2 n$ alleles mein se har ek independently probability $\frac{1}{2}$ se contributing hai; $2 n$ independent halves ko multiply karo.

Jaise-jaise $n$ badhta hai, ye binomial bars itne zyada aur itne finely spaced ho jaate hain ki wo ek continuous bell curve mein merge ho jaate hain (Central Limit Theorem in action).

Worked Example 1 — Wheat kernel colour (classic, $n = 2$ )

Do genes ( $A$ aur $B$ ) redness control karte hain. Har uppercase allele red pigment ki ek "dose" add karta hai. Do dihybrid plants cross karo: $A a B b \times A a B b$ .

Step 1 — Har genotype mein contributing alleles count karo. Kyon? Phenotype depend karta hai ki kitne uppercase alleles hain, kaunsa gene nahi.

Step 2 — Class sizes ke liye $(k 4)$ use karo ( $2 n = 4$ ):

Uppercase alleles $k$	$(k 4)$	Phenotype	Fraction
4	1	sabse dark red	1/16
3	4	medium-dark	4/16
2	6	intermediate	6/16
1	4	light	4/16
0	1	white	1/16

Ratio $= 1 : 4 : 6 : 4 : 1$ . Ye step kyon? Ye Pascal's triangle ki row 4 hai = $(k 4)$ .

Step 3 — Phenotype classes ki sankhya $= 2 n + 1 = 5$ . ✔ Table se match karta hai. Extreme fraction $= 1/ 4^{2} = 1/16$ pure white ke liye (aur 1/16 sabse dark). ✔

Worked Example 2 — Human skin colour predict karna ( $n = 3$ )

Maan lo 3 genes, har ek melanin add karta hai. Do log jo teeno mein heterozygous hain unhe cross karo: $A a B b C c \times A a B b C c$ .

Step 1 — $2 n = 6$ alleles, toh classes $= 2 n + 1 = 7$ shades. Kyon? 0 se 6 contributing alleles tak.

Step 2 — Ratio = $(k 6)$ : $1 : 6 : 15 : 20 : 15 : 6 : 1$ (sum $= 64 = 4^{3}$ ). 64 kyon? Total combinations $= 4^{n} = 4^{3} = 64$ .

Step 3 — Sabse pale child (0 contributing) ka chance = $1/64$ . Kyon? 64 outcomes mein sirf ek genotype $aabb cc$ hai.

Step 4 — Sabse common = middle class ( $k = 3$ ): $20/64 \approx 31%$ . Kyon? Sabse bada binomial coefficient, $(3 6) = 20$ .

Worked Example 3 — $n$ ko reverse engineer karna

Ek trait mein do heterozygotes ke cross mein offspring mein 9 distinct phenotype classes dikhte hain. Kitne genes?

Step 1 — Use karo $2 n + 1 = 9 \Rightarrow n = 4$ genes. Kyon? Classes ki sankhya directly $2 n + 1$ deti hai. Step 2 — Extreme fraction $= 1/ 4^{4} = 1/256$ . Kyon? $n = 4$ ko $1/ 4^{n}$ mein plug karo.

Common mistake Common errors ko steel-man karo

Mistake 1: "Polygenic = pleiotropy." Ye sahi kyon lagta hai: dono mein "many" + "genes" hai, toh blur ho jaate hain. Fix: Polygenic = bahut saare genes → ek trait. Pleiotropy = ek gene → bahut saare traits. Arrow direction opposite hai.

Mistake 2: "Continuous variation matlab koi genetics nahi, sirf environment hai." Ye sahi kyon lagta hai: smooth curve measurement noise ki tarah lagti hai. Fix: Curve genetic hai (additive alleles) plus ek environmental spread. Dono ise shape karte hain; genes hatao aur trait collapse ho jaata hai.

Mistake 3: $2 n + 1$ ko genotypes ki sankhya samajhna. Ye sahi kyon lagta hai: ye sahi counting style hai. Fix: $2 n + 1$ phenotype classes ki sankhya hai. Genotypes bahut zyada hote hain (jaise $3^{n}$ genotype combinations).

Mistake 4: Alleles ko additive ki jagah dominant/recessive treat karna. Ye sahi kyon lagta hai: Mendelian habit — "uppercase, lowercase ko mask karta hai." Fix: Classic polygenic models mein alleles add karte hain, dominate nahi; $A a$ ek intermediate phenotype deta hai, homozygote phenotype nahi.

Recall Feynman: ek 12-saal ke bacche ko explain karo

Imagine karo tum paint mix kar rahe ho. Red ki ek drop zyada change nahi laati — lekin agar tumhare paas bahut saari choti red-dropper bottles hain, aur tum randomly kuch use karo, toh pale pink, deeper pink, ya full red mil sakta hai. Zyaadatar bacche randomly lagbhag aadhi bottles use karenge, toh zyaadatar paints medium pink dikhenge, aur sirf kuch pure white ya full red honge. Isliye human heights aur skin colours ek smooth range mein aate hain, na ki sirf "lamba ya chhota." Bahut saare tiny gene-drops add up ho jaate hain!

Flashcards

Polygenic inheritance kya hai?

Ek trait jo do ya zyada genes se control hoti hai jinke effects add hote hain, jo continuous (quantitative) variation produce karte hain.

n polygenes ke liye do heterozygotes ke cross se kitne phenotype classes bante hain?

2 n + 1

n genes ke liye extreme (sab- ya koi nahi-contributing) phenotype dikhane wale offspring ka fraction kya hai?

1/ 4^{n}

Polygenic inheritance bell-shaped curve kyon deta hai?

Contributing alleles ki moderate numbers bahut saare combinations mein form ho sakti hain (bade binomial coefficients) jabki extremes sirf ek tarike se bante hain, isliye middle phenotypes sabse common hain.

2-gene (AaBb × AaBb) additive cross ke liye phenotype ratio?

1:4:6:4:1.

Polygenic inheritance aur pleiotropy mein kya fark hai?

Polygenic = bahut saare genes ek trait affect karte hain; pleiotropy = ek gene bahut saare traits affect karta hai.

Polygene alleles dominant/recessive hain ya additive?

Additive — har contributing allele ek chota equal increment add karta hai.

Ek cross 7 phenotype classes deta hai; kitne genes?

2 n + 1 = 7 \Rightarrow n = 3

genes.

Binomial coefficient

(k 2 n)

yahan kya represent karta hai?

Theek

k

contributing alleles produce karne wale genotype combinations ki sankhya (phenotype class

k

ki size).

Connections

Mendelian Inheritance — polygenic, Mendel ko multiple additive loci tak extend karta hai.
Pleiotropy — mirror-image concept (ek gene, bahut saare traits).
Multiple Alleles — ek aur extension; ABO blood groups.
Incomplete Dominance — intermediate phenotypes bhi deta hai (lekin single gene).
Quantitative Traits & QTL — polygenic traits ka modern genetics naam.
Normal Distribution / Central Limit Theorem — kyon additive genes ek bell curve dete hain.
Environmental Influence on Phenotype — variation curve ko broaden karta hai.