Re: Drift and fixation simulated

[Mark Isaak]

On 7/6/12 10:22 AM, Greg Guarino wrote:
> On 6/13/2012 11:07 PM, Mark Isaak wrote:
>
>>
>> Here is the command line and the output, albeit with most of the
>> intermediate lines omitted to save space and tedium:
>>
>> ===== Begin output
>> =27 a.out -r2000
>> drift: crude simulation of genetic drift
>> Population size: 1000; Mutations: 8 per individual per generation
>> Sexual recombination of new generations
>> Run for 500000 generations, Report every 2000.
>> Using genome buffers of 4915200 bits
>>
>> Gen. 2000: 15363704 fixations, 3098 of them mutants, 636296 SNPs
>> Gen. 4000: 31321792 fixations, 16379 of them mutants, 678208 SNPs
>> Gen. 6000: 47313480 fixations, 31936 of them mutants, 686520 SNPs
>> Gen. 8000: 63327136 fixations, 48187 of them mutants, 672864 SNPs
>> Gen. 10000: 79314808 fixations, 63830 of them mutants, 685192 SNPs
>> Gen. 12000: 95319288 fixations, 80033 of them mutants, 680712 SNPs
>> Gen. 14000: 111319864 fixations, 96211 of them mutants, 680136 SNPs
>> Gen. 16000: 127322688 fixations, 112369 of them mutants, 677312 SNPs
>> Gen. 18000: 143319280 fixations, 128274 of them mutants, 680720 SNPs
>> Gen. 20000: 159320824 fixations, 143980 of them mutants, 679176 SNPs
>> . . .
>> Gen. 496000: 3967311376 fixations, 3950459 of them mutants, 688624 SNPs
>> Gen. 498000: 3983318232 fixations, 3966792 of them mutants, 681768 SNPs
>> Gen. 500000: 3999318968 fixations, 3982775 of them mutants, 681032 SNPs
>> Final: 3999878832 fixations, 3982903 of them mutants
>> ===== End output
>>
>> As you can see, after 500,000 generations, 3,982,903 mutations have
>> drifted to fixation, very close to the predicted 4,000,000. The
>> shortfall can be explained by the fact that we started with genomes with
>> no mutations at all, and it took 5000 generations or so to build up a
>> sizable number of mutations in the population.
>
> <snip>
>>
>> Every so often, we check the population for fixed loci -- if all beings
>> have the same value in the same locus, we do not have to keep it in the
>> active genome anymore; we add to the number of fixations, and if it is a
>> one (meaning a mutation), we add to the number of fixed mutations also.
>
> I'd like to try to understand your results better. I'm confused by the
> first number in each line: "fixations". What does that count exactly?

The program only watches sites where a mutation has been introduced. In
time, each site drifts to a fixed state, i.e. where everyone in the
population has the same value at that site. The first number (after
"Gen.") is the number of mutated sites that have drifted to fixation;
the second is the subset of those in which the mutation was the fixed state.

The total number of mutations is mutations/individual/gen (8) *
population (1000) * generations (500000) = 4e9, of which 3,999,878,832
had become fixed at the end of the run above, leaving 121,168 sites
where some of the population had mutations and some did not. As I
explained earlier somewhere, the number of fixations in all lines but
the Final one is incomplete, since they only count fixations where eight
consecutive sites have become fixed (because it is a lot faster to
compare bytes at a time than bits).

--
Mark Isaak eciton (at) curioustaxonomy (dot) net
"It is certain, from experience, that the smallest grain of natural
honesty and benevolence has more effect on men's conduct, than the most
pompous views suggested by theological theories and systems." - D. Hume

[Greg Guarino]

On 7/9/2012 2:03 PM, Mark Isaak wrote:
>> I'd like to try to understand your results better. I'm confused by the
>> first number in each line: "fixations". What does that count exactly?
>
> The program only watches sites where a mutation has been introduced. In
> time, each site drifts to a fixed state, i.e. where everyone in the
> population has the same value at that site. The first number (after
> "Gen.") is the number of mutated sites that have drifted to fixation;
> the second is the subset of those in which the mutation was the fixed
> state.

So in the 2000th generation, 15 million of the sites that had undergone
a mutation had become fixed at the original base and 3098 had become
fixed at the mutated base. After the 400th generation, we get
approximately 16000 fixed mutations every 2000 generations. That is very
close to [mutations/individual/generation]*[number of generations],
(8*2000), which I think is what the theory predicts.

With the EV program, I put in the following values:

genome length: 256
population: 64
no selection
1 mutation every 10,000 bases
random one survives
single founder

I counted 154 fixed mutations after 20000 generations. The prediction
would be 512, I think. I'm aware that EV actually works by Kleinman's
odd logic; first it picks a site for a "mutation", then assigns any one
of the FOUR bases to that site. Thus 1 out of every 4 "mutations" is not
a mutation. That would conceivably bring my number up to 200. I wouldn't
think the "ramp up" at the beginning would last very long in a
population of only 64. Still I'm at about 1/2 the prediction. I believe
that the prediction is merely a mean value. Is that perhaps the
explanation?