# User:R. Eric Collins/MBL/PAML

## Exercise 1

omega minimum at 0.067

## Exercise 2

Objective:

1. Test effect of transition / transversion ratio (κ)
• κ goes up when estimated
• S goes up when κ goes up
• omega goes up when κ goes up
2. Test effect of codon frequencies (π’s )
• log likelihoods: F61 (-756.57) < F3x4 (-842.21) < Fequal (-926.28)
3. Determine which assumptions yield the largest and smallest values of S, and what is the effect on ω
• largest S/largest ω: F61 + κ=1
• S = 165.8
• ω = 0.320
• smallest S/smallest: Fequal + κ=est
• S = 40.5
• ω = 0.063

## Exercise 3

Objective: Use LRTs to evaluate the following hypotheses:

1. The mutation rate of Ldh-C has increased relative to Ldh-A
• =H2: is omega of C0/1 greater than A0/1?
• omega_A 0.0755 omega_C 0.2394
• yes the mutation rate has increased, and it is significant (LRT = 66 >> 3.84)
2. A burst of positive selection for functional divergence occurred following the duplication event that gave rise to Ldh-C
• =H1: is omega of C0 greater than C1&A0/1?
• omega_A0 0.1319 omega_C0 0.192
• yes the mutation rate has increased, but it is not significant (LRT=2.12 < 3.84)
3. There was a long term shift in selective constraints following the duplication event that gave rise to Ldh-C
• = H3: is omega of C0/1 different from A0 and A1?
• omega_A0 = 0.0642 omega_A1 = 0.0949 omega_C0/1 = 0.2403
• A0 and A1 are slightly different and C0/1 is greater and may have relaxed constraints
• but it is not a significantly better explanation than H2 (LRT=3.05<3.84)