Page 143 - 20dynamics of cancer

128 CHAPTER 7

n = 10
0 (a) 4 (e)
Incidence 1 2 LLA 3 2

3 1
0
0 (b) 4 (f)
Incidence 1 2 LLA 3 2 1

3
0
0 (c) 4 (g)
Incidence 1 2 LLA 3 2

3 1
0
0 (d) 4 (h)
Incidence 1 2 LLA 3 2

3 1
0
20 40 80 20 40 80
Age

Figure 7.6 Comparison between genotypes with different transition rates. As-
sumptions are the same as in Figure 7.5, except that n = 10 and δ = 3 i/4 for
i = 1,..., 4.

remaining; thus, the log-log incidence slopes remain near n − 1 for both
wild-type and mutant genotypes.
0
The top right panel, Figure 7.5e, uses L = 10 independent lines of
progression within the tissue. With small L, the few lineages at risk
tend to progress with age through at least the early stages, causing a
reduction in the number of remaining stages and a drop in the log-log
incidence slope. The mutants, with faster transition rates, advance more
quickly through the early stages and so, at a particular age, have fewer
stages remaining to cancer. With fewer stages remaining, those mu-
tants have lower log-log incidence slopes, and therefore the difference
in slopes, ΔLLA, between wild-type and mutant genotypes increases.