Difference between revisions of "Haldane 1937"
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The student's ''t''-test comparison of two populations of equal size with equal variance and a mean difference of 0.001 is | The student's ''t''-test comparison of two populations of equal size with equal variance and a mean difference of 0.001 is | ||
| − | <math>t = \frac{0.001}{\sqrt{2}\sqrt{2/1.6\times10^7}} =2</math>. | + | <math>t = \frac{\bar{x}_1 - \bar{x}_2}{\sigma \sqrt{2/n}} \frac{0.001}{\sqrt{2}\sqrt{2/1.6\times10^7}} =2</math>. |
| − | However, this is the size of each group being compared. Detecting this difference would require a comparison of the number of offspring of 32 million individuals, half with the genotype and half without. | + | However, this (''n'') is the size of each group being compared. Detecting this difference would require a comparison of the number of offspring of 32 million individuals, half with the genotype and half without. |
==Paragraph Three== | ==Paragraph Three== | ||
Revision as of 18:03, 9 September 2018
Contents
Citation
Haldane, J. B. S. (1937). The effect of variation of fitness. The American Naturalist, 71(735), 337-349.
Links
- https://www.journals.uchicago.edu/doi/abs/10.1086/280722
- https://www.jstor.org/stable/2457289
- http://hawaiireedlab.com/pdf/haldane1937.pdf (internal lab link only)
Notes
Paragraph One
Haldane points out the distinction between Darwinian evolution (novel adaptation) and stabilizing selection (or purifying selection or "maintenance" selection).
Paragraph Two
The change in frequency of alleles resulting in novel adaptation can be very slow in human terms; however, extremely fast on a geologic timescale. Very small fitness differences in numbers of offspring could be virtually impossible to detect by direct observation yet have a very real evolutionary effect.
"In order that an observed viability difference of 0.1 per cent. should exceed twice its standard error, we should have to observe at least sixteen million individuals." If the average number of offspring per individual is two, for a population at constant size, this is expected to be Poisson distributed with a variance of two. The student's t-test comparison of two populations of equal size with equal variance and a mean difference of 0.001 is
[math]t = \frac{\bar{x}_1 - \bar{x}_2}{\sigma \sqrt{2/n}} \frac{0.001}{\sqrt{2}\sqrt{2/1.6\times10^7}} =2[/math].
However, this (n) is the size of each group being compared. Detecting this difference would require a comparison of the number of offspring of 32 million individuals, half with the genotype and half without.
Paragraph Three
Again, adaptive evolution is expected to be very slow and not observable on a time-scale of human lifetimes (however, today we know of exceptions to this where observable evolution can happen quite rapidly). Except, Haldane says, possibly in cases of adapting to changes in the environment many of which are human caused, "agriculture, fishing and industry". "The balance of nature has recently been upset in a manner probably without precedent in our planet's history; and hence on the Darwinian theory we should expect that evolution was proceeding with extreme and abnormal speed."
Paragraph Four
To be continued ...
Terms
Facies - appearance. https://en.wiktionary.org/wiki/facies
