Jost D, Wright Fst, Weir & Cockerham Fst(theta)
Linda Rutledge
Thursday, 17 September 2009 16:09 UTC
Hi,
I have been using Jost’s D to look at differentiation. I understand why it is so much better than Wright’s Fst which is based on heterozygosity, but the newer estimates like Weir & Cockerham’s Fst (theta) are based on variance in allele frequencies. So W&C should pick up differences based on shared alleles. Also, I think the scale for W&C is -1 to +1 technically.
I am wondering if W&C estimates on a -1 to 1 scale would show more similar estimates to Jost’s D on a 0 to 1 scale? I have found when comparing various estimates of differentiation that putting a secondary axis on Fst like estimates show similar trends among all estimators. So, on a relative scale they seem to be the same (in my dataset anyway where heterozygosity is about 0.7). I also find that Jost’s D is almost exactly the same as Nei’s, which he has said in a previous post is not unusual, but I am wondering then why Jost’s D is superior to Nei’s?
I haven’t noticed a post about this but sorry if it is a repeat question. I’m looking forward to input on this question. Thanks.
Linda Rutledge
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Replies
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Hi Linda,
There are legitimate measures of differentiation besides D, but the ones you mentioned are not among them. There are some simple tests you can do to see if a given software program is using a legitimate measure of differentiation. To do these tests, make sure you set the option to use alleles as the unit of analysis (there is a checkbox to that effect in some programs such as Arlequin).Test 1: Use two demes. The demes have the following allele counts (all at a single locus).
First count is for Deme 1, second count or column is for Deme 2:
Allele 1: 45, 0
Allele 2: 30, 0
Allele 3: 50, 0
Allele 4: 46, 0
Allele 5: 20, 0
Allele 6: 5, 0
Allele 7: 70, 0
Allele 8: 60, 0
Allele 9: 65, 0
Allele 10: 55,0
Allele 11: 0, 34
Allele 12: 0, 45
Allele 13: 0, 67
Allele 14: 0, 40
Allele 15: 0, 45
Allele 16: 0, 46
Allele 17: 0, 24
Allele 18: 0, 39
Allele 19: 0, 46
Allele 20: 0, 60
The sample sizes from each deme are equal, and the demes share no alleles. Under these conditions a legitimate measure of differentiation will give unity if you are using the theoretical formula (eg my D), and a number close to or equal to unity if the formula incorporates statistical estimators (like my D_est). Nei’s Gst will give a low number, which is why it is not a legitimate measure of differentiation. I hope you report back with the values of Theta for this dataset as calculated by your favorite program.Test 2: Here is another test, which looks at the other end of the spectrum, high similarity among demes but low heterozygosity. For this test, create 100 demes. Demes 1-99 have 500 individuals of Allele 1, and no individuals of Allele 2. Deme 100 has no individuals of Allele 1, and 500 individuals of Allele 2. This set of demes is very homogeneous, since 99/100 demes are genetically identical. A legitimate measure of differentiation should be close to zero. Yet Nei’s Gst is 1.00, indicating maximum differentiation. This is another very strong reason to abandon Gst. I do not know how your software will handle this example, so please report the results.
I hope other readers will report the results of these tests using their favorite software and formulas. Make sure that you are using alleles as the unit of analysis!
I mentioned that there are other legitimate measures of differentiation besides my D. Some of these are derived in Jost (2007), Partitioning diversity into independent alpha and beta components. Ecology 88: 2427-2439. (In ecological jargon, alpha diversity is within-group diversity, and beta diversity is between-group diversity.) A good article on legitimate entropy-based differentiation measures is Sherwin et al (2006), Measurement of biological information with applications from genes to landscapes, Molecular Ecology 15:2857-2869.
Finally, as the above tests show, your comment that Gst and D often give the same results is not generally correct. If the heterozygosities of all populations are equal, then the ranking of populations according to their degree of differentiation will be similar between Gst and D. But to have exactly equal heterozygosities among all species or loci is very unusual. Also, even if the populations are correctly ranked, Gst gives you no clue about the magnitide of the differentiation. A value of 0.01 could mean complete differentiation, near-identity, or anything in between. Better to use a measure that does not confound within-group heterozygosity with differentiation. That mathematical property is what distinguishes D.
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I should clarify that the Ecology article I cited focusses on measures of similarity rather than differentiation. The two are complementary concepts; most of the similarity measures I give in the Ecology article can be converted to measures of relative differentiation by subtracting them from unity. Some of the measures I discuss in the Ecology article are only valid for two demes. The generalization to multiple demes is given in Chao et al (2008), A two-stage probabilistic approach to multiple-community similarity indices, Biometrics 64: 1178-1186.
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Hi Lou,
Thank you for this. I will look do the exercise sometime in the near future. I was finding that Nei’s unbiased genetic distance (D) was quite similar to Jost D. The figure attached has the Fst and Gst values on the secondary axis whereas the other estimators are on the primary axis.
!/Users/lindarutledge/Desktop/Genetic Differentiation.jpg!Thanks again.
Linda
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Oops. I guess you can only attach url images.
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When you posted your first post, I thought you were referring to Gst when you said “Nei’s” behaves the same as my D. Yes, Nei’s genetic distance (rather than his Gst) is closely related to my D, as I showed in my 2009 Molecular Ecology paper responding to Ryman and Leimar (2009) and Heller and Seigismund (2009).
I look forward to your tests, Lou
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