conditional process
Kern AD & Schrider DR 2016 Discoal: flexible coalescent simulations with selection. Bioinf 32:3839-3841.
- conditioning on selected allele trajectories is performed in discoal one of two possible ways
- sweeps can follow deterministic trajectories or instead can be stochastic through the use of a conditional diffusion approach both using a model of genic (i.e. haploid) selection (Coop and Griffiths, 2004; Kim and Stephan, 2002)
- neutral fixation trajectories can also be simulated by discoal
- we use a stochastic jump process between small time steps, δt, to simulate the allele frequency, p, moving back in time from frequency 1.0 to frequency 1/2N such that the frequency of the neutral mutation in the next step, p', is given by
- p' = p + μ(p)δt + √(p(1 − p)δt) with probability 1/2
- p + μ(p)δt − √(p(1 − p)δt) with probability 1/2
- with μ(p) = − p (Ewens, 2004)
- this trajectory routine was tested for accuracy by calculating the expected time to fixation and by comparing simulation results to those from Tajima (1990)
- to model stochastic hard sweeps the selected allele frequency, p, is again modeled as a jump process as above, however in this case μ(p) is given by
- μ(p) = αp(1 − p) / tanh(αp)
- where α = 2Ns is the population scaled selection coefficient
