We applied BARCE to the two sequence alignments mosaic structure A, tree height 0.1, and mosaic structure A, tree height 0.2, and we chose very short equilibration and sampling times of 10,000 MCMC steps each. This took only a few minutes on a SUN Ultra 60. Now, such short burn-in and sampling periods are not recommended, and the purpose of this experiment was solely to explore how much improvement can be obtained with the annealing scheme. Recall that for infinitely long sampling times, annealing is irrelevant since the Markov chain is guaranteed to converge, irrespective of the details of the sampling process (assuming the system is ergodic). For short sampling times, however, annealing may improve results considerably due to improved mixing and convergence of the chain. This was, in fact, borne out in the experiment: While simulations without annealing led to suboptimal results, simulations with annealing gave accurate predictions in spite of the short equilibration and sampling periods. The details are given below. We start with a reminder of the true mosaic structure, where the horizontal axis shows the position in the DNA sequence alignment, and the vertical axis represents the three possible tree topologies.
Each of the figures below contains three graphs, which show the posterior probabilities for the three possible tree topologies, plotted along the DNA sequence alignment (the horizontal axis represents sites in the alignment).
Results of the simulation experiments:
| Tree height 0.1, no annealing |
| Tree height 0.1, simulated annealing |
| Tree height 0.2, no annealing |
| Tree height 0.2, simulated annealing |
Length of the burn-in period
|
B
|
10000
|
Length of the sampling period
|
.
|
10000
|
Number of points to return
|
N
|
100
|
Thinning interval
|
I
|
100
|
Annealing scheme for lambda
|
Q
|
none
|
Otherwise, the default settings were used.
Monitor the equilibration process
Result suboptimal: No recombination event is detected.
Length of the burn-in period
|
B
|
10000
|
Length of the sampling period
|
.
|
10000
|
Number of points to return
|
N
|
100
|
Thinning interval
|
I
|
100
|
Annealing scheme for lambda
|
Q
|
PAR
|
Otherwise, the default settings were used.
Monitor the equilibration process
Result: Both recombinant regions are detected and classified correctly.
Length of the burn-in period
|
B
|
10000
|
Length of the sampling period
|
.
|
10000
|
Number of points to return
|
N
|
100
|
Thinning interval
|
I
|
100
|
Annealing scheme for lambda
|
Q
|
none
|
Otherwise, the default settings were used.
Monitor the equilibration process
Result suboptimal: The first recombinant region is misclassified.
Length of the burn-in period
|
B
|
10000
|
Length of the sampling period
|
.
|
10000
|
Number of points to return
|
N
|
100
|
Thinning interval
|
I
|
100
|
Annealing scheme for lambda
|
Q
|
PAR
|
Otherwise, the default settings were used.
Monitor the equilibration process
Result: Both recombinant regions are detected and classified correctly.
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