Archiver > GENEALOGY-DNA > 2010-11 > 1289766524

From: James Heald <>
Subject: Re: [DNA] Explaining Haplogroup Success
Date: Sun, 14 Nov 2010 20:28:44 +0000
References: <00ec01cb8433$d1e05690$c2482dae@Ken1>
In-Reply-To: <00ec01cb8433$d1e05690$c2482dae@Ken1>

Interesting, but you need to compare this zero growth situation against
what happens when a new lineage is surfing a major range expansion and
population increase.

As an example, I've looked at the Heald surname a bit. In the U.K.
there are lots of different lineages, largely (though without DNA
testing so far) apparently unconnected.

On the other hand, there was a Heald who emigrated across the Atlantic
in 1640, who then had about a dozen children, most of whom also had
similar number of children.

Of course there was some later Heald emigration; but because of that
initial head start, today almost all the Heald families in the United
States can be traced either to that John Heald from 1640, or (probably)
cousins of his that emigrated in 1703.

If a single lineage gets injected in a zero-population growth
population, the chances are (as you have found) that it will disappear
-- as we know from curves of the Galton-Watson process. But if a single
lineage gets injected just before a population undergoes a burst of very
rapid growth and range expansion, the chances are much higher that it
will survive. The converse can also be made: the chances that a
lineage has survived, so that it can be found (or even has grown
dominant today) are much higher if that lineage emerged into a sudden
burst of population expansion, than if it emerged into a static
zero-growth set up.

On 14/11/2010 19:40, Ken Nordtvedt wrote:
> Both academic papers and hobbyists try very hard to come up with casual/historic/anthropological/selection reasons as to why some y haplogroups demographically succeed (as seen today) and others less so or barely at all (and don't forget the mostly out of sight not at all). Though such causative reasons could be in play, I often get the feeling folks are trying too hard, and probably statistical luck is more at work in determining haplogroup demographic winners than we think.
> Suppose we consider some haplogroup MRCA (a single male individual) living thousands of years ago in an era of negligible overall population growth rate and immersed within a population large enough so that his line's success won't perturb the overall crowding of his niche. One can do simulations of how many surviving males, if any, his line will have at some later generation, given some basic probability assumptions of each male having 0, 1, 2, .... male offspring. I have run many of these in the past, both to gain some feeling for what happens and to confirm some analytic results one can derive for this stuff.
> Here's a typical case: Reproduction probabilities are set so the population is under zero growth situation. We look 30 generations (900 years) into the future after the MRCA. I run through this 300 independent times in order to gather some distribution for outcomes from this MRCA. 273 of the 300 trials led to extinction of that MRCA's line before the 30th generation.
> For the 27 trials which led to the MRCA having male descendants in the 30th generation, here are the numbers for such descendants:
> 5, 1, 8, 11, 5, 9, 36, 32, 11, 10, 2, 3, 7, 31, 26, 16, 2, 3, 9, 5, 2, 9, 1, 3, 1, 9, 3
> (and don't forget the 273 cases of 0!!!!!!)
> There are wild variations from one trial run to the next independent trial run through the generations, caused solely by the basic chance nature for a father's number of sons each generation.
> Now suppose in that original generation there had been two different haplogroup MRCAs living. And we are talking about haplogroups still seen 30 generations later. We see that the ratio of the sizes of these surviving haplogroups will not concentrate around one. Based on pure chance the norm will be a substantial ratio in the success (size) of the two surviving haplogroup populations 30 generations later.
> I am reprogramming my program to produce the distribution of this RATIO of size success and will show it in due course.
> Every haplogroup starts with a single male. Most of this luck factor in its size as seen way down the road takes place in the early generations when the statistical flucuations are necessarily large --- this is an unavoidable piece of every haplogroup's history.
> This leads me to migrate my thinking more to the issue of why some haplogroups maintain their frequency success over much larger geographical regions than others?
> This seems a more fruitful area of inquiry for which explanations of the type we typically call "causes" might be there?
> Ken
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