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THEORY II 129

Figure 7.5 uses n = 7 stages; Figure 7.6 provides similar plots but with
n = 10 stages.
In summary, a mutant genotype that increases transition rates will
cause a rise in ΔLLA when compared with the wild type. This increase in
ΔLLA occurs even though the number of rate-limiting stages is the same
for mutant and wild-type genotypes. The amount of the rise with age in
ΔLLA depends most strongly on the increase in transition rates caused
by the mutant and on the number of independent lines of progression
in the tissue.

CONCLUSIONS
The ratio of normal to mutant incidence provides one of the best tests
for the role of genetics in progression dynamics. Figures 7.3 and 7.4
show predictions for this ratio under simple assumptions about pro-
gression. Similar predictions could be derived by analyzing the ratio
of incidences in other models of progression, such as those developed
in earlier sections. In Chapter 8, I analyze data on the observed ratio
of incidences between normal and mutant genotypes. Those ratio tests
provide the most compelling evidence available that particular inherited
mutations reduce the number of rate-limiting stages in progression.

7.3 Continuous Genetic and
Environmental Heterogeneity

Quantitative traits include attributes such as height and weight that
can differ by small amounts between individuals, leading to nearly con-
tinuous trait values in large groups (Lynch and Walsh 1998). All quan-
titative traits vary in populations. With regard to cancer, studies have
demonstrated wide variability in DNA repair efficacy (Berwick and Vineis
2000; Mohrenweiser et al. 2003), which influences the rate of progres-
sion. Probably all other factors that determine the rate of progression
vary significantly between individuals.
Variation in quantitative traits stems from genetic differences and
from environmental differences. The genetic side arises mainly from
polymorphisms at multiple genetic loci that contribute to inherited poly-
genic variability. The environmental side includes all nongenetic factors
that influence variability, such as diet, lifestyle, exposure to carcinogens,
and so on.