I think it just depends on the number of generations. This is not steady state. I"m not sure what the cutoff for seeing this is exactly, but is certainly several times longer than 6,000 years for human populations. That much we know, but perhaps 200,000 years might be enough. That is less clear.
Still there are many more than four alleles in common between us and chimps at several places in the genome. That is a very difficult to explain puzzle if we start from a single couple, unless God is specifically introducing chimp DNA into early humans. That is very hard to square with reality.
@glipsnort can you give us your graphs without scaling to total population? That might help.
That is the extreme and it is unlikely. I am talking about the more common outcomes. The bigger you are, the bigger steps your random walk takes each generation, and that is what gives rise to the power law distribution in this case. You intuition should be built around that basic logic. It doesn’t have to be “large” fluctuation, but a “larger” fluctuation.
We are not at steady state. I"m not sure what you mean by absorbing barrier.
Also, this is not steady state. There are a steadily growing number of mutations. We are just looking at the relative distribution of SNPs. There is a relationship between the total number of mutations and mutation rate and generation time, but this distribution does not. I think the old population has more generations, that’s it.
Average time to fixation (which is closely related to this) is proportional to N, not N^2. Rate of fixation is independent of N and just depends on mutation rate R.
Your analogy is not really right.
Which is exactly what happens in LD analysis, as described by @DennisVenema in his book so well .
It does not work to “rule out” a pair as much estimate the effective population size. The estimates will be proportional to the geometric mean of the true value, and are therefore biased a bit upwards from the arithmetic mean, but “effective size” so biased down from the “census size”.
An easier to understand and minimum to the population size is from looking of ancient alleles shared by both humans and chimps. In normal circumstances, an individual will carry 2 alleles at a time. If we see more than 4 alleles (e.g. versions of gene) shared between us and chimps, that means we need more than 2 ancestors to carry all that variation. Otherwise, how did human magically get chimp DNA into our genomes that wasn’t in Adam or Eves?
A good study on this is by Fransico Ayala,
Exon 2 of the DRBJ gene consists of 270 nucleotides that
specify all the (3-chain amino acids involved in peptide
binding. No fewer than 58 distinct human alleles have been
identified that differ in their exon 2 nucleotide sequences.
Fig. 3 is a phylogenetic reconstruction of the 58 alleles.
The time scale has been determined by the "minimumminimum"
method (39, 40), which is based on the comparison
between pairs of species that share the same divergence
node, such as the three pairs orangutan-human, orangutangorilla,
and orangutan-chimpanzee. The minimum distance
observed in such a set of comparisons will correspond to
alleles that diverge at, or close to, the time of the species
divergence. (Alleles that were polymorphic at the time of the
species divergence will show larger distances than the minimum-minimum
value.) A plot of minimum-minimum distances
versus the correspondent divergence times gives an
estimate of rate of evolution.
As can be seen in Fig. 3, all 58 DRBJ alleles have persisted
through the last 500,000 years, but coalesce into 44 ancestral
lineages by 1.7 Myr before present (B.P.), 21 lineages by 6
Myr B.P., and 10 lineages by 13 Myr B.P. It is apparent that
the DRBI polymorphism is ancient, so that numerous alleles
have persisted through successive speciation events. In order
to pass 58 alleles through the generations, no fewer than 29
individuals are required at any time. As we shall presently
see, the size of the human populations needs to be much
greater than that in order to retain the DRBJ polymorphisms
over the last few million years.
To account for the variation this exon alone, there were always more than 29 individuals in the human population.
If you didn’t catch that, there are 58 versions of the DRBJ exon shared by humans, orangutans and chimps. They are identical amongst all three of us. How did they get there if we do not share a common ancestor?
God can do anything, so is certainly possible that God introduced these mutations into Adam and Eve’s children over several generations. It is also possible that he made them mosaics, with different genomes in each of their eggs/sperm. If he did this, he was introducing chimpanzee DNA into our genomes outside the natural order. Either way, the DNA evidence (and the Biblical account) points to a larger population than a single couple.