Table 1. Summary of the symbols in this article.

Symbol	Description
Nt	Number of tumor cells at time t
C	Internal state of a cell
E	External environment of a cell
w	Waiting time for a next event on a cell
f(w)	Probability density function of waiting time (Eq 1)
k	Shape parameter for the gamma distribution of waiting time
β	Birth rate (see Eq 5)
δ	Death rate (see Eq 12)
ρ	Migration rate (see Eq 13)
ps	Probability of symmetric division (0 ≤ ps ≤ 1)
ω	Number of cell division allowed for a TAC
s	Effect of driver mutation (Eq 6)
$\overline{s},\sigma$	Mean and standard deviation of mutation effect
$\overrightarrow{p}=(x,y,z)$	Coordinate of a cell in a lattice (Eq 7)
ϕ	Proportion of empty nodes in the adjacent sites (Eq 8)
lmin	Minimum distance to the nearest empty site