4. Population Genetics statistics

library(mobster)
library(tidyr)
library(dplyr)

Population Genetics statistics can be extracted from a MOBSTER model.

data('fit_example', package = 'mobster')
print(fit_example$best)
#> ── [ MOBSTER ] My MOBSTER model n = 5000 with k = 2 Beta(s) and a tail ─────────
#> ● Clusters: π = 55% [C1], 31% [Tail], and 14% [C2], with π > 0.
#> ● Tail [n = 1370, 31%] with alpha = 1.2.
#> ● Beta C1 [n = 2784, 55%] with mean = 0.48.
#> ● Beta C2 [n = 846, 14%] with mean = 0.15.
#> ℹ Score(s): NLL = -5671.5; ICL = -10359.09 (-11266.35), H = 907.26 (0). Fit
#> converged by MM in 75 steps.

evolutionary_parameters(fit_example)
#> # A tibble: 1 x 7
#>      mu exponent  time subclonefrequency subclonemutations cluster     s
#>   <dbl>    <dbl> <dbl>             <dbl>             <dbl> <chr>   <dbl>
#> 1  73.5     2.25  5.98             0.298              695. C2      0.177

The mutation rate mu (cell division units) scaled by the probability of lineage survival \(\beta\), \(\mu/\beta\), is given by: \[ \mu/\beta = \dfrac{M} {(\frac{1}{f_\text{min}} - \frac{1}{f_\text{max}})} \] Where \(f_\text{min}\) is the minimum VAF and \(f_\text{max}\) is the maximum, and \(M\) is the number of mutations between \(f_\text{min}\) and \(f_\text{max}\).

Selection is defined as the relative growth rates of host tumour cell populations (\(\lambda h\)) vs subclone (\(\lambda s\)): \[ 1+s= \dfrac{\lambda h}{ \lambda s} \]

The mathematical details of these computations are described in the main paper, and baesd on the population genetics model of tumour evolutionin Williams et al. 2016 and 2018 (Nature Genetics).

Giulio Caravagna

29 October, 2020