Evolgen and Popgen Ramblings have put up posts where they criticize a parameter of the acceleration paper. John Hawks responds in the comments. But I thought this line was priceless:
Nah, you're not a dirty anti-adaptationist! All these labels are nonsense; all that is important is understanding the math involved -- something Gould never really seemed very interested in. The problem with purely verbal arguments is that there is no scorekeeper.: it's like Olympic ice dancing, or something.
A lot of the formalism in population genetics isn't that mentally taxing (although the derivations may be!). For example, the famous (or infamous) Hardy-Weinberg Equilibrium, p2 + 2pq + q2 = 1, requires about a middle school level of mathematical knowledge (grade 7 or 8). And one can describe it in words, but by doing so one removes its algebraic utility and clear precision of communication. A non-formal Hardy-Weinberg Equilibrium could never have become one of the pillars upon which population genetic theory was built, to use programming terminology, verbal arguments are often far less extensible than mathematical ones. In the short term verbal description of population genetic theory is much clearer to those who are not used to thinking in terms of variables, but over the long term they leave a lot to be desired in generating a contingent & systematic model. I also think that when scientists communicate and debate it wastes a lot of time when you argue in words because without any magnitude placed upon the implicit variables people easily talk past each other and generate mountains of repetitive prose.
Update: See comments for a clarification.
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I wasn't criticizing the parameters so much as referencing the criticism posted at popgen ramblings. I felt obligated to post something after Hawks replied to my previous post. I don't know enough about human demography to say whether or not hawks et al's parameters are reasonable.
The harmonic-mean population average will not tell what you want to know about the number of sweeping alleles today: adaptive genes move to high frequencies, fixation even, and aren't easily lost in a bottleneck.
As for the idea that the effective population size (for any purpose) of the human race (or Europe, or for that matter Italy) in the middle Holocene was 10,000 - well, we're talking early recorded history. Sumer and Egypt existed, it's not controversial.
I also noticed John's "understanding the math" line. It reminded of J.B.S.Haldane's:
"An ounce of algebra is worth of a ton of verbal argument."
"An ounce of algebra is worth of a ton of verbal argument."
The Genetical Theory of Natural Selection
Hardcover: 318 pages
Publisher: Oxford University Press, USA; 1 edition (March 24, 2000)
Language: English
The Structure of Evolutionary Theory
Hardcover: 1464 pages
Publisher: Belknap Press (March 21, 2002)
Language: English
;-)
Natural languages are perfectly able to be used precisely... but unless they're forced to the sparseness and precision of mathematical symbols, most people don't seem able to take advantage of this.
The best way to describe (and teach) Hardy-Weinberg Equilibrium is neither mathematically nor verbally but graphically, using a drawing that's like a Punnett Square with allele frequencies replacing the alleles. I've posted an example on my teaching blog.
Viewed this way, HWE is so obvious and so intuitive that there's no need for ps and qs at all. (And there never was any need for the apparent complication of q, as it's just 1-p.) The axes are simply labeled with the actual allele frequencies, and the areas they create are the genotype frequencies in the next generation.
Of course math will be needed to deal with the deviations from HWE produced by selection and other factors, but starting with this graphical explanation helps beginning students see how simple and inevitable HWE is. (My freshman class on this is titled "The incredible tedium of Hardy-Weinberg equilibrium.)
It's interesting to note that a few of the most insightful observations about the evolutionary process were first promulgated verbally, then later proven mathematically (unlike H-W equilibrium). These include runaway sexual selection (first adumbrated by Fisher, then shown mathematically possible by Lande and Kirkpatrick), the handicap principle (first adumbrated by Zahavi, then--finally--shown to be mathematically possible by Grafen), and, of course, natural selection (first adumbrated by what's-his-face, then formalized by Wright, Fisher, and later Price, among others). And of course, all of these topics were debated back-n-forth until the math made them more clear.