Lecture 8
- 1. Maximum Likelihood Estimation Lecture – 8 Nafis Neehal, Lecturer, Department of CSE, DIU
- 2. CONTENTS 1. Maximum Likelihood Estimation 2. Calculate Maximum Likelihood of a Phylogenetic Tree with known history
- 3. 1. Maximum Likelihood Estimation Computing Likelihood if History is Known
- 4. Maximum Likelihood Estimation Data (Given) 1. Tree Topology with Branch Lengths (Given) 3. Substitution Rate Matrix (Given) • Denoted by Q • QAC means substitution rate of A to C = 0.541 (From Q Matrix) (EXTRA) Probability ( A -> C ) = ( QAC ) / ( QAC + QAG + QAT ) = 0.541 / ( 0.541 + 0.787 + 0.588 ) = 0.541 / 1.916 = 0.282 2. Stationary Probabilities (Given) πa = 0.138 πc = 0.188 πg = 0.495 πt = 0.179
- 5. Maximum Likelihood Estimation Data (Example) πA = 0.138, πC = 0.188, πG = 0.495, πT = 0.179 History (Given) Branch Length (Given) = Maximum Likelihood
- 6. Maximum Likelihood Estimation Data (Example Explained) ▹πT for Root’s Stationary Probability ▹For each branch which has same start and end point, multiply e (branch length) x Q (start alphabet, end alphabet) ▹For one branch (as you can see, the 3rd branch) there is a transition in history. Started from T, then transitioned from T to G then finally G to G from that transition point ▹For this kind of branch, you have to multiply and extra (-QTT) for the T-T transition from initial point to transition point and another extra (-QTG/QTT) ratio as it changing from T to G for the G-G transition = Maximum Likelihood ▹ Up to T-G transition point in 3rd branch, the T-T branch length is 0.045 ▹ Total branch length is 0.15 ▹ So G-G branch length will be (0.15-0.045) = 0.105
- 7. 1 Million Years agoHuman beings left Africa 50,000 years ago Humans navigated in the Indian Ocean in boats Neanderthan You may be a part of it Evolution Its Still HAPPENING !!!
- 8. Final-Done