Figure 1.
Clones under of Dirac, Log-normal, and Exponential models.
The Log-normal distribution has been adjusted on Kelly and Rahn's data. All three distribution have been scaled to have unit growth rates. Clones were simulated up to time 5.
Figure 2.
Boxplots of estimates of α and ρ, using the exponential and the Dirac models.
Red horizontal lines mark true values of the parameters. For each of the 9 sets of parameters (rows) and
(columns), 10000 samples of size 100 of the
were simulated, F being the Log-normal distribution adjusted on Kelly and Rahn's data. The estimates of α and ρ were calculated with the two models Dirac and exponential. Each boxplot represents the distribution of the 10000 estimates obtained by the Dirac model (left) and the exponential model (right).
Table 1.
Mean biases on estimates of alpha and rho.
Table 2.
Proportion of success for 95% confidence intervals.
Figure 3.
Relative bias on α between the exponential and the Dirac models.
Ten thousand samples of size 100 were simulated for the for alpha between 1 and 10 (left panel), then between 10 and 100 (right panel) and
. The estimate of α was computed using the
, then averaged over all samples. The relative bias was calculated as the difference between the mean estimate and the true value of α, divided by the true value of α. Results are plotted as red points. The results for the opposite experiment (i.e. simulating the
, and estimating using the
) are plotted as green points.
Table 3.
Confidence intervals for published data sets.
Table 4.
Kolmogorov-Smirnov goodness-of-fit tests for published data sets.
Figure 4.
Densities of Gamma, Log-normal, and Inverse Gaussian.
All densities have been rescaled to have unit growth rates. The dashed curve is the density of the exponential distribution with rate 1. The dashed vertical line locates the Dirac distribution at log 2.
Table 5.
Characteristics of three families of distribution.
Figure 5.
Adjusted distributions for Kelly and Rahn's data on Bacterium aerogenes [15].
On the left panel, the histogram of the data, and the three densities are superposed; the Gamma distribution appears in red, the Log-normal distribution in blue, the Inverse Gaussian in green. The blue and green curves are very close. On the right panel, the densities have been rescaled to unit growth rate. The dashed curve is the density of the exponential distribution, the dashed vertical line locates the Dirac distribution at log 2.
Table 6.
Adjusted distributions for Kelly and Rahn's data on Bacterium aerogenes [15].
Figure 6.
Ratios for GF estimators of the relative fitness ρ.
Ratios as functions of ρ, for
and
. The ratios depend on the division time distribution: exponential (solid black), Dirac (dashed black), Gamma (red), Log-normal (blue), Inverse Gaussian (green). The realistic distributions are close together, and closer to the Dirac case than to the exponential case. This explains why the classical Luria-Delbrück model induces a positive bias on the estimation of ρ, and why the Dirac model yields better results.