The "Letter" is the standard "paper" format for Nature, and the vast majority of Nature papers are "Letters". "Letter" simply describes the length and format, and "Letters" undergo rigorous peer-review identical to "Article" submissions.
I didn't know that. I stand corrected.
You seem to be stuck on a simple point here - you have genealogical ancestors whose genomes have contributed absolutely zero to your genome. It isn't a simple halving of a genome at each step.
You inherit 50% of your genome (in a simple sense) from your mother and 50% from your father. When you go back to grandparents however, you don't inherit 25% of your genome from each grandparent, due to variability in recombination and chromosome segregation. Potentially (though very improbably), one of your grandparents may have contributed zero to your genome.
I figured that out from nwr's posts since last go round. The irony (to me) is that now we are talking about someone who was (potentially) totally insignificant to most people alive today then eh?
This becomes no more significant than having "six degrees of separation" between all living individuals. Whoopie: my dad shook hands with Nixon (reluctantly) so that leaves me connected to how many people?
Now perhaps we can get back to the maths issue ...
I still have a LOT of trouble with treating (any) mathematical model like this as anything more than a faint possiblity at best. It may help define limits within which reality acts, at best, and is
totally dependent on getting all the input factors correct to end up with the correct results. My hackles are also raised when they use terminology like "would have lived" when they can really only mean "could
at a minimum have lived" at best, and thus give a false sense of {truth\validity} to what is at best a very hypothetical and untested result.
This model assumes a random mating of individuals - mating is not random with males and females mating at every chance meeting (and even if they did there would be regional selection due to distance between populations). There is structure in reproductive behavior. They go from 600 years ago for a purely random result based on 1 million people (why one million?) to 5000 years by applying "more realistic" factors ... how do we know it shouldn't be 30,000 years ago? The upper limit would logically be the younger of the {matrilineal\patrilinial} ancestor (here the 60,000 to 90,000 years ago of yDNA Adam)
They apply "structure" by dividing the world up:
... consider a population of size n divided into randomly mating subpopulations that are linked by occasional migrants.
Whoops, they still use random mating within each sub-population?
They then get involved in modeling hypothetical migration numbers and percentages ... and conclude:
Arguably, this simulation is far too conservative, especially given its prediction that, even in densely populated Eurasia, only 55.3 people will leave each country per generation in AD 1500. If the migration rate among towns is increased to 20%, the local port users are reduced to 80%, and the migration rates between countries and continents are scaled up by factors of 5 and 10, respectively, the mean MRCA date is as recent as AD 55 and the mean IA date is 2,158 BC.
The biggest hole in this is using random mating in the subpopulations. Judging by what we know from history, traditions and anthropological evidence it seems to me that the smaller the population gets the more it would be modeled by a completely structured pattern of mating behavior than a random one - that random would best apply to the chance interaction between structured sub-populations.
Now consider that social conventions and taboos act as a control on random mating to a certain level. If nothing else, a basic human pattern is for sexually active individuals to have several children with the same mate. Every additional child by the same parents cuts severely into the random equation. If we assume a minimum structured mating pattern holds over a 2 generation period then the MCRA 'advances' n/2=2/2=1 generation during those 2 generation periods.
How does this affect the overal calculation? It would make the time period develop like n/2 half the time and like log
2n half the time.
It seems to me that log
2n is a more logical lower limit and that n/2 (for a purely structured population that matches matrilineal\patrilinial ancestry) is an upper limit: 5,000 to 90,000 years ... that's a pretty big range.
If I take half of one and half of the other (to simulate the effect of structure over two generations per above) I get 47,500 years.
It almost appears that they stopped evaluating the results when they got the 5000 year figure. That's not a good feeling.
migration rates and patterns ...
The model uses a simplified migration system in which each person has a single opportunity to migrate from his or her town of birth. The probabilities of leaving a town or a country are set at various levels to reflect different migration patterns.
It seems from the letter that the only real attempts to input historical data is by setting date limits at certain bottlnecks and in introducing population loss due to disease introduction post columbus. They do say that:
Actual migration rates among populations are very poorly known and undoubtedly have varied considerably in different times and places.
They briefly discuss the effect of changing the migration rate at one locus, but do not say what happens when you change all of them.
There is no mention of testing their modelled migration rates against any known migration pattern to ground truth their assumptions.
A mathematical model that hasn't been ground-truthed is worthless.
I also have a LOT of trouble with the "MRCA" terminology. You suggested MRCP, but nwr takes exception to that.
Most people seem to assume a single ancestor from the term (see Randman's post for example) in spite of explanations to the contrary. This means the term contributes to the confusion.
Not sure what to do about that. Last Universal Connection?
Enough for tonight.
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