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VOL. 76 (2), 189-208, 2010 THE IGNORED STOWAWAYS: WORLDWIDE...

culture number of resistant cells is found (variance/mean > 1), it
means that resistant cells appeared by random mutations occurring
before selection, and the flask-to-flask variation would not be
consistent with the Poisson model. Resistant-mutants occurred
during the time in which the cultures reached Nt from N0 cells, prior
to TBT exposure (Figure 1, set 1B). The set 2 cultures serve as the
experimental control of the fluctuation analysis (Figure 1). Variance
is expected to be low, because set 2 samples the variance of the
parental population. Thus, if a similar variance/mean ratio between
set 1 and set 2 is found, resistant cells arose induced during the
exposure to the TBT. If the variance/mean ratio of set 1 is
significantly greater than the variance/mean ratio of set 2
(fluctuation), resistant cells arose by rare mutations that occurred
before exposure to the TBT.

The fluctuation analysis also allows estimation of the rate of
appearance of resistant cells. The proportion of set 1 cultures
showing non-resistant cells after TBT exposure (P0 estimator) was
used to calculate the mutation rate (µ) as follows:

P0 = e –µ (Nt - N0) (23)

where P0 is the proportion of cultures showing no resistant cells, N0
and Nt are the initial and the final cell number respectively and µ is
the mutation rates (in mutants per cell division).

If the mutation from a normal wild-type TBT-sensitive allele to
a TBT-resistant allele is recurrent, and the TBT-resistant allele is
detrimental to fitness in the absence of TBT, then new mutants arise
in each generation, but most of these mutants are eliminated sooner
or later by natural selection, if not by chance (21). At any one time
there will be a certain number of resistant mutants that are not
yet eliminated. The balance between m and the rate of selective
elimination (s) will determine the average number of such mutants:

q = µ / (µ + s) (24)

where q is the frequency of the TBT-resistant allele and s is the
coefficient of selection against TBT-resistant allele calculated as
follows:

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