Figure 7.8. Acceleration for different levels of phenotypic heterogeneity in transition rates.

Figure 7.8

Acceleration for different levels of phenotypic heterogeneity in transition rates. Each curve shows the acceleration in the population when aggregated over all individuals, calculated by Eq. (7.9). I used a log-normal distribution for f(u) to describe the heterogeneity in transitions rates, in which ln(u) has a normal distribution with mean m and standard deviation s. To get each curve, I set a value of s and then solved for the value of m that caused 1−b = 0.1 of the population to have cancer by age 80 (see Eq. (7.7)). With this calculation, 95% of the population has u values that lie in the interval (em−1.96s,em+1.96s) (see Figure 7.7). For all curves, I used n = 10 and L = 107. For the curves, from top to bottom, I list the values for (m,s) : low–high, where low and high are the bottom and top of the 95% intervals for u values: (−4.64,0) : 0.0097 – 0.0097; (−4.77,0.2) : 0.0057 – 0.013; (−5.00,0.4) : 0.0031 − 0.0015; (−5.25,0.6) : 0.0016 – 0.017; (−5.50,0.8) : 0.00085 − 0.020; and (−5.75,1) : 0.00045 − 0.023. I tagged the curve with s = 0.6 to highlight that case for further analysis in Figure 7.9.

From: Chapter 7, Theory II

Cover of Dynamics of Cancer
Dynamics of Cancer: Incidence, Inheritance, and Evolution.
Frank SA.
Princeton (NJ): Princeton University Press; 2007.
Copyright © 2007, Steven A Frank.

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