Next, we examined the neutral evolution mode by analyzing the “neutral” model, where we considered only neutral mutations that do not affect cell division and death. In a unit time, a cell divides into two daughter cells with a constant probability *g*_{0} without dying. Similarly to driver mutations in the driver model, in each cell division, each of the two daughter cells acquires *k*_{n} ∼ Pois(*m*_{n}/2) neutral mutations. We assumed that neutral mutations acquired by different division events occur at different genomic positions and each cell can accumulate *N*_{n} mutations at maximum. In this study, we set *N*_{n} = 1000, which is sufficiently large that no cell reaches at the upper limit, except in a few exceptional cases. The simulation started from one cell without mutations and ended when population size *p* reached *P* or time *t* reached *T*.

Furthermore, the neutral model is exteneded to the “neutral-s model", which assumes that two types of cell exist: stem and differentiated. Stem cells divide with a probability *g*_{o} without dying. For each cell division of stem cells, a symmetrical division generating two stem cells occurs with a probability *s*, while an asymmetrical division generating one stem cell and one differentiated cell occurs with a probability 1 − *s*. A differentiated cell symmetrically divides to generate two differentiated cells with a probability *g*_{0} but dies with a probability *d*_{0}^{d}. The means of accumulating neutral mutations in the two types of cell is the same as that in the original neutral model, which means that the neutral-s model is equal to the original neutral model when *s* = 0 or *d*_{0}^{d}=0.

Information of variables and parameters are listed in Tables 1 and 2.
For MASSIVE, we defined *δ* = log_{10}(*d*_{0}^{d}/*g*_{0}) and converted *m*_{n}, *s* and *P* to log scale, i.e., *m*_{n}' = log_{10} *m*_{n}',
*s*' = log_{10} *s* and *P*' = log_{10} *P*. We then tested every combination of
*δ* ∈ {-0.5, -0.25, 0, 0.25, 0.5},
*m*_{n}' ∈ {-2, -1, 0, 1},
*s*' ∈ {-2, -1.5, -1, -0.5, 1} and
*P*' ∈ {3, 4, 5}.
All results are explorable in the focused and comparative view modes of the MASSIVE viewer.

Table 1. a list of the variabes

symbol | description |
---|---|

k_{n} |
number of neutral mutations obtained in a cell division |

n_{n} |
number of neutral mutations accumulated in a cell |

p |
population size |

t |
number of time steps |

Table 1. a list of the parameters

symbol | description | value |
---|---|---|

m_{n} |
expected number of neutral mutations generated per cell division | {10^{-2}, 10^{-1.5}, 10^{-0.5},...,10^{1}} |

N_{n} |
maximum number of neutral mutations accumulated in a cell | 1000 |

g_{0} |
base cell division probability | 10^{-2} |

d_{0}^{d} |
base cell death probability for differentiated cells | {10^{-2.5}, 10^{-2.25}, 10^{-2},10^{-1.75}, 10^{-1.5}} |

s |
symmetric division probability | {10^{-2}, 10^{-1.5}, 10^{-1.0},10^{-0.5}, 10^{0}} |

P |
maximum population size | {10^{3}, 10^{4}, 10^{5}} |

T |
maximum number of time steps | 10^{6} |