## August 12, 2013

### Population growth and the linkage disequilibrium curve

The concluding paragraph:
The European LD curve is steeper than either of the equilibrium curves in Fig. 10, suggesting a history of population expansion. This might re- ﬂect the spread of modern humans into Europe, the spread of farmers during the Neolithic, or the spread of Indo-European speakers. I evaluate these alternatives in a separate publication
arXiv:1308.1984 [q-bio.PE]

How Population Growth Affects Linkage Disequilibrium

Alan R. Rogers

Linkage disequilibrium (LD) is often summarized using the "LD curve," which relates the LD between pairs of sites to the distance that separates them along the chromosome. This paper shows how the LD curve responds to changes in population size. An expansion of population size generates an LD curve that declines steeply, especially if that expansion has followed a bottleneck. A reduction in size generates an LD curve that is high but relatively flat. In European data, the curve is steep, suggesting a history of population expansion. These conclusions emerge from the study of $\sigma_d^2$, a measure of LD that has never played a central role. It has been seen merely as an approximation to another measure, $r^2$. Yet $\sigma_d^2$ has different dynamical behavior and provides deeper time depth. Furthermore, it is easily estimated from data and can be predicted from population history using a fast, deterministic algorithm.

1. Of course, at least as far back as Roman times, there is enough decent data points in written records to make credible estimates of European population sizes. Abundant archaeological data and ancient DNA data provide methodologically independent checks on these estimates and provide meaningful estimates of population size and effective population size well into human pre-history in Europe. Any LD based estimates that seriously contradict these historical data points deserve strict scrutiny.

2. Also, while I understand the incentives for doing so, I have to say that I am not a fan of breaking up parts of substantial studies of the same data set with the same methods into multiple papers. Let's leave sequels and trilogies to popular culture, thank you very much.

3. Also, while I understand the incentives for doing so, I have to say that I am not a fan of breaking up parts of substantial studies of the same data set with the same methods into multiple papers. Let's leave sequels and trilogies to popular culture, thank you very much.

IMO it's better for stuff to be published as soon as possible. If a research devotes 2 man-years on an analysis, but can break it down into four pieces, then the public can read 1/4 of his work in six months, 2/4 in a year, 3/4 in 1.5 years, and 4/4 in 2 years. So, other research that builds on or is enabled by some of these results can start (and finish) earlier.

4. @andrew

How can you affirm that "ancient DNA data provide methodologically independent checks on these estimates and provide meaningful estimates of population size and effective population size well into human pre-history" in Europe or anywhere else ?
All the methods are approximation, estimation, prediction, evaluation. Nothing factual nor historical.

5. Ancient DNA data is absolutely factual and has a solid scientific foundation that is very well understood and has been used successfully many times. Of course, by definition, when it comes from pre-history it isn't "historical", i.e. it isn't based on written records. But, it provides a very rich source of information in a non-human language (DNA) about the nature of people who died in a particular time and place typically established by other means (e.g. carbon dating or stratiography).

The fact that each of multiple methods have uncertainties and hidden assumptions means that it is especially important to corroborate evidence from different methods to be sure that you have a robust result, so that you can be sure that your conclusion is not just an artifact of a particular quirk of a particular methodology that is not well understood.

But, if multiple methods, each with their own quirks, reach the same result, this greatly reduces the risk that your conclusion is the result of systemic error. Conclusions confirmed by multiple independent methodologies are the gold standard of ancient history and the study of human pre-history.

The reality that a fact is imprecisely known does not cause it to cease to be a fact. All facts of some degree of imprecision. Every single data point in the Particle Physics Groups thousands of pages long catalog of physical constants has an error margin attached, for example (except in cases where there aren't enough data points to accurately estimate margin of error). The question is, can we quantify the risk of error enough and get a result sufficiently precise to be useful. If so, it's all good.

Historical records likewise has risks of systemic errors that need to be understood.

Lack of omnipotence is no reason to call off the enterprise of scientific investigation.

A head in the sand rejection of a kind of evidence because it involves approximation, estimation, prediction and evaluation is unscientific and wrongheaded.

Stay on topic. Be polite. Use facts and arguments. Be Brief. Do not post back to back comments in the same thread, unless you absolutely have to. Don't quote excessively. Google before you ask.