Ab10 frequencies

starting allele frequency of Ab10 is \(p=0.01\). Let’s say drive is 80%.

p=0.01
d=0.8

\(p\) in the next generation (\(p'\)) is the average of male (\(p_m\)) and female (\(p_f\)) allele frequencies:

\(p'=\frac{p_m+p_f}{2}\)

And in the next generation, we have:

\(p_m'=p_mp_f+\frac{p_m(1-p_f)+pf(1-p_m)}{2}\)

\(p_f'=p_mp_f+\frac{(1+d)(p_m(1-p_f)+pf(1-p_m))}{2}\)

With these we can iterate the change in allele frequency over generations.

pf=p
pm=p
pvec=as.numeric()
pvec[1]=p
for(i in 1:100){
  ppm=pm*pf+(pm*(1-pf))/2+(pf*(1-pm))/2
  ppf=pm*pf+(1+d)*(pm*(1-pf)+pf*(1-pm))/2
  pp=(ppm+ppf)/2
  pm=pp
  pf=pp
  pvec[i+1]=pp
}

No we plot the frequency of Ab10, and note it goes to 100% (fixes) in about 20 generations!

plot(pvec,pch=19,xlab="generations",ylab="Ab10 frequency")

But what about other values? You can try any other values you want here.

The short of it is: for almost any plausible range of values, Ab10 should not be found segregating in any population!