To evaluate different demographic scenarios (e.g. constant population sizes or population expansion from the time of the prehistoric sample), we simulated an extant sample and a prehistoric sample using the program COMPASS [ 17].
For each sample, we simulated 10 million and 30 million 100-bp single-end (CAST and DO) or paired-end (CAST only) reads with a standard error model (0.028% average mutations per sequence, 34.96 quality).
Since both resting-state fMRI dataset (Baltimore dataset) and task-based fMRI dataset (false belief fMRI dataset) are fully sampled, we simulated undersampled k-space data ({mathbf{Y }}) in (2) by computing the Fourier transform of Casorati matrix ({mathbf{X }}) and then, retrospectively undersampling in the k-space using measurement matrix ({mathbf {Phi }}).
In both samples, we simulated data according to a 1-factor model with factor loadings equal to.5.
To estimate the fraction of amino-acid mutations that would have been sampled, we simulated randomly selecting 85% of the mutant codons from the HA sequence, and determined that these codons encoded ≈97% of the amino-acid mutations.
For each dataset, and for a range of sub-sample sample sizes, we simulated a case control study and the two two-phase designs described above.
For that fixed set of parameters and sample size, we simulate 10,000 sets of data.
The probability of state change is calculated as shown in (2) P → (t + n Δ t ) = Q t n P → t, where P → denotes a vector signifying the state of the calcium channel, Δ t denotes the sampling time of the simulation, and n denotes how many samples ahead we simulate (for this study every time sample was simulated; therefore n = 1).
For each CG site in each simulated sample, we then simulated the reads (C if methylated or T if unmethylated) based on the average methylation level (Pm) from all real samples at this CG site.
To account for variation in sample size, we simulated the actual distribution of sample sizes in the observed data.
