6.4.6
Intuition Badi picture (WHY hum trees banate hain?)Species, genes aur proteins common ancestors share karte hain. Agar do sequences bahut similar hain, toh woh probably haal hi mein alag hue; agar bahut different hain, toh bahut pehle alag hue. Ek phylogenetic tree bas ek tarika hai "kaun kiske sabse close hai" ko draw karne ka, taaki branch lengths evolutionary distance encode karein aur branching pattern (topology) shared ancestry encode kare . Poora game yeh hai: sequence differences ki ek table lo aur ek aisa tree banao jo unhe best explain kare.
Definition Core vocabulary
Leaf (tip / taxon): ek observed sequence/species (present-day).Internal node: ek hypothetical common ancestor.Branch length: evolutionary change ki matra (substitutions per site).Topology: shape — kaun se taxa saath group karte hain.Rooted tree: time ki direction hoti hai (ek node sabka ancestor hota hai).Unrooted tree: relationships dikhata hai par time ki direction nahi.Outgroup: ek door se related taxon jo tree ko root karne ke liye deliberately add kiya jaata hai.
Algorithms ki do broad families hain:
Family
Input
Idea
Distance-based ek distance matrix D ij
pehle closest cheezein cluster karo (UPGMA, Neighbor-Joining)
Character-based aligned sequences khud
ek aisi tree dhoondo jo har column ko best explain kare (Maximum Parsimony, Maximum Likelihood, Bayesian)
Intuition WHY hume pehle distances chahiye hoti hainRaw sequences ko directly compare nahi kar sakte; pehle hum unhe align karte hain, phir differences count karte hain. Sabse simple distance p-distance hai:
p = total aligned sites number of differing sites
Lekin p underestimate karta hai kyunki multiple hits hote hain (ek site A→G→A mutate ho sakti hai aur unchanged lagti hai). Jukes–Cantor correction isko fix karti hai.
Worked example Corrected distance compute karnaDo sequences 300 sites mein se 60 par differ karti hain ⇒ p = 0.20 d = − 4 3 ln ( 1 − 3 4 ( 0.2 )) = − 0.75 ln ( 0.7333 ) = 0.2326 Yeh step kyun? 0.2326 > 0.20
U nweighted P air G roup M ethod with A rithmetic mean.
Intuition WHY yeh kaam karta hai / WHAT yeh assume karta haiBaar baar do closest clusters ko join karo aur unka ancestor unke beech mein halfway rakho. Yeh molecular clock assume karta hai (constant substitution rate), toh saare leaves root se equidistant hain (ek ultrametric tree).
HOW (the loop):
Sabse chhota D ij ( i , j )
Unhe cluster u D ij /2
Cluster sizes ke weighted average se distances update karo:
D ( u ) k = n i + n j n i D ik + n j D j k Tab tak repeat karo jab tak ek cluster na reh jaaye.
Worked example 4 taxa par UPGMAD
Sabse chhota = A-B (2) aur C-D (2). A-B join karo → node height 1 par. Kyun? closest pair pehle merge hoti hai.
C-D join karo → node height 1 par.
Distance (AB)-(CD) = A-C, A-D, B-C, B-D ka average = 4. Height 2 par join karo.
Result: ((A,B),(C,D)), ultrametric. ✔
Common mistake Steel-man: "UPGMA safe default hai."Kyun sahi lagta hai: simple hai aur hamesha rooted tree deta hai. Kyun galat hai: agar lineages alag rates par evolve karein, toh clock assumption fail hoti hai aur UPGMA fast-evolving taxa ko galat group karta hai (long-branch problems). Fix: Neighbor-Joining use karo, jo clock assume nahi karta.
Intuition WHY yeh UPGMA se better haiSirf "closest pair" ki jagah, NJ woh pair choose karta hai jo close ho aur baaki sab se door bhi ho, ek correction term use karke. Yeh minimum-evolution (sabse chhoti total branch length waali) tree deta hai aur unequal rates ke saath bhi kaam karta hai.
Worked example Ek NJ step (4 taxa)D n = 4 R A = 23 , R B = 25 , R C = 27 , R D = 27 Q A B = ( 2 ) ( 5 ) − 23 − 25 = − 38 Q A B A,B kyun join karein? Most negative Q δ A u = 2 1 ( 5 ) + 4 1 ( 23 − 25 ) = 2 δ B u = 3 D u C = 2 1 ( 9 + 10 − 5 ) = 7 D u D = 7
Occam's razor: woh tree prefer karo jo aligned columns explain karne ke liye sabse kam evolutionary changes (mutations) maange. HOW: har candidate topology ke liye, Fitch's algorithm (bottom-up set operations) use karke har column ke liye minimum substitutions count karo, columns par sum karo, sabse chhota total pick karo.
Worked example Ek column, tree((A,B),(C,D)), states A=C, B=A, C=G, D=G.
Node(A,B): { C } ∩ { A } = ∅ ⇒ { C , A }
Node(C,D): { G } ∩ { G } = { G }
Root: { C , A } ∩ { G } = ∅ ⇒ + 1 Kyun: jab bhi possible tha hum ne intersections choose kiye taaki extra mutations na invent karni padein.
Common mistake Steel-man: "Kam changes hamesha = true tree."Kyun sahi lagta hai: simplicity elegant hai. Kyun fail hota hai: high divergence mein parsimony long-branch attraction suffer karta hai — unrelated fast-evolving taxa group ho jaate hain kyunki coincidental identical states shared ancestry jaisi lagti hain. Fix: model-based Maximum Likelihood .
Intuition WHY probabilistic model use kareinSirf count karne ki jagah, ML ek substitution model (JC, K2P, GTR) use karta hai compute karne ke liye
L ( tree ) = P ( data ∣ topology , branch lengths , model ) maximize karein. Yeh explicitly multiple hits aur rate variation model karta hai, isliye sabse accurate hai (par computationally heavy — trees ki sankhya explode karti hai).
Bootstrap: alignment columns ko replacement ke saath resample karo, tree kai baar rebuild karo; ek clade dikhane waale replicates ka % = uska support (≥70% ≈ reliable).
Recall Woh 20% jo 80% deta hai
Distance methods (UPGMA, NJ) = fast, matrix chahiye; NJ practical default hai.
UPGMA molecular clock assume karta hai (rooted, ultrametric); NJ nahi karta (unrooted).
Character methods (Parsimony, ML, Bayesian) raw columns use karte hain; ML = sabse accurate.
JC correction multiple-hit underestimation fix karta hai.
Long-branch attraction classic failure mode hai.
Bootstrap / posterior = statistical support.
Recall Ek 12-saal ke bacche ko explain karo (hidden)Socho kuch dost ek story copy kar rahe the aur choti spelling mistakes kar rahe the. Agar do doston ki galtiyan almost same hain, toh unhone haal hi mein copy kiya. Hum copies ka ek family tree draw karte hain: matching mistakes wale dost ek chhoti branch par saath baithte hain. UPGMA sirf do sabse similar doston ko pair karta rehta hai. Neighbor-Joining smarter hai — yeh yeh bhi check karta hai ki sab ke mukable mein kaun weird hai. Parsimony woh tree pick karta hai jisme sab explain karne ke liye sabse kam nayi spelling mistakes chahiye. Likelihood is baat ke probability rules use karta hai ki letters kitni baar change hote hain taaki sabse believable tree mile.
Mnemonic Chaar algorithms yaad rakho"U Never Play Loud" → U PGMA, N eighbor-Joining, P arsimony, L ikelihood — simple→sophisticated order mein (distance → character → statistical).
Phylogenetic tree mein ek branch length kya represent karta hai? Us lineage mein evolutionary change ki matra (substitutions per site).
UPGMA kaun si assumption karta hai jo NJ nahi karta? Molecular clock (constant substitution rate), jo ek ultrametric rooted tree deta hai.
P-distance true evolutionary distance ko kyun underestimate karta hai? Yeh ek hi site par multiple substitutions ignore karta hai (hidden back/parallel mutations).
Jukes–Cantor distance formula batao. d = − 4 3 ln ( 1 − 3 4 p )
Neighbor-Joining mein kaun si pair join ki jaati hai? Woh pair jo Q-matrix mein minimum value rakhti hai Q ij = ( n − 2 ) D ij − ∑ k D ik − ∑ k D j k
Maximum Parsimony ka goal kya hai? Woh tree dhoondo jo sabse kam total evolutionary changes maange (Occam's razor).
Parsimony mein har column ke minimum changes count karne ke liye kaun sa algorithm use hota hai? Fitch's algorithm (set intersection/union, bottom-up).
Long-branch attraction kya hai? Coincidental shared states ki wajah se unrelated fast-evolving taxa ka artificial grouping.
Maximum Likelihood kya maximize karta hai? P(data | topology, branch lengths, substitution model).
Unrooted tree ko usually kaise root kiya jaata hai? Ek outgroup include karke — ek jaana-maana door se related taxon.
90% bootstrap value ka matlab kya hai? 90% resampled datasets ne woh clade recover kiya — strong support.
UPGMA cluster-distance update formula kya hai? D ( u ) k = n i + n j n i D ik + n j D j k
Sequence Alignment — aligned columns/distance matrix provide karta hai.Substitution Models (JC, K2P, GTR) — distance correction & ML ko power dete hain.Molecular Clock Hypothesis — UPGMA ke peeche assumption.Bootstrap and Resampling Statistics — branch support.Occam's Razor and Parsimony — MP ka logical basis.Homology vs Homoplasy — tree building mein signal vs noise.
UPGMA and Neighbor-Joining
Parsimony, Likelihood, Bayesian
