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I am very confused about how to interpret Table 8.3 in Smith's Evolutionary Genetics.

Is the GST in the table the same as the G,ST (with the comma), which is defined (pg. 156; Box 8.3) as "the probability that two genes drawn at random from the same deme are identical"? If so, is it not the same as Hs, the probability that two homologous genes from the same deme are identical? If it is the same, why do they differ?

And why would Hr be larger than Hs? That is, why would a gene be more likely to be identical with a gene from a different deme than the same deme? Doesn't this suggest negative assortment?

Thank you very much to anyone who can help!

This is the table:
enter image description here

David
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sterid
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  • Welcome to Biology.SE. Can you please just display the figure directly on the post (screenshot the image from the pdf and add the image using the icon dedicated to adding images). Users don't want to click on a link, load a pdf, screen through 362 pages trying to find Table 8.3! – Remi.b Nov 13 '16 at 07:20
  • The title is really not informative. You could ask "What is the difference between Hs and Gst". Also, can you please use the > symbol for quotation and indicated where (what page, what column, what paragraph) the quote comes from. – Remi.b Nov 13 '16 at 07:23
  • GST or GST' (I've never seen G,ST) is not "the probability that two genes drawn at random from the same deme are identical". This definition matches $H_s$ (as you figured out). $GST = \frac{H_t - H_s}{H_t}$. I have never seen $H_r$. Hopefully, there is a definition of $H_r$ in the text. It could be defined as $H_r = H_t - H_s$ given what you seem to say but please make sure to quote the book on that definition. – Remi.b Nov 13 '16 at 07:26
  • I apologize to you. After zooming in on the text, I found that what I thought was the definition for Hr was actually the definition for Ht. I did a text search: that was the only mention of "Hr" in the book. So, I do not know the definition for Hr. So by that definition of GST, if GST is positive, does it mean assortment is negative? Which of these measures would represent "relatedness" in Hamilton's rule? (Or would there be a combination necessary?) Thank you! – sterid Nov 13 '16 at 08:18
  • The link given appears to be to an illegal copy of a book. I have deleted it and vote to close. – David Nov 13 '16 at 08:50
  • I'm voting to close this question as off-topic because cites pirated text. – David Nov 13 '16 at 08:52
  • The text was cited by an article I am reading. I am trying to complete a paper (not for school). I do not currently live near a university library and therefore cannot get it via interlibrary loan. The cost of the text is prohibitive, since I am only interested in one page of it. I believe voting to close would be unnecessarily severe. – sterid Nov 13 '16 at 09:06
  • I would appreciate an answer to my questions. That would be a productive way of responding. – sterid Nov 13 '16 at 09:09
  • If it makes a difference, I do not expect to be paid in any way for said paper. – sterid Nov 13 '16 at 09:10
  • Is Hs equivalent to Hamilton's relatedness? Thank you. – sterid Nov 13 '16 at 09:36
  • No $H_S$ is not equivalent to $r$ (relatedness). $r$ comes from the field of quantitative genetics for which you need to consider a phenotype, while $H_S$ comes from classical population genetics and is independent of the phenotype. You can find book recommendation here for a good intro to population genetics. – Remi.b Nov 14 '16 at 06:07
  • Remi, I thank you very much and I am very sorry. I didn't realize I had a response. I guess we don't receive an email notification. After asking this question, it occurred to me that Hs would be equivalent to relatedness if one omits intergroup effects? I have a couple of intro to population genetics texts (the Gillespie text and the Hartl text), but Hs is not in the index of either of them. Does it go by another term? I do not understand the distinction you made between considering a phenotype and independent of phenotype. Can relatedness be calculated from a combination of Hs and GST? – sterid Nov 20 '16 at 08:02
  • For context, Schonmann, VIcente & Caticha, 2013 says the following, "For these games, the condition for altruism to proliferate is Hamilton’s classical rule...Therefore, in this setting, altruism can only spread when either relatedness is large, or the cost/benefit ratio is low. And since relatedness is often low [28] (Table 8.3), [30], [31] (Tables 6.4 and 6.5), [32], [33](Table 4.9), exceptionally low cost/benefit ratios are required, as observed for instance in [34]." The measures listed in the citations are: hr, hs, gst, and fst. How can relatedness be determined from these measures? – sterid Nov 20 '16 at 10:49

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