Sharedchao results in wiki examples

Theory behind mothur
1

Hi there!

First of all, thanks for mothur! It’s awesome!

I have one question about sharedchao and the examples given in the wiki. This is where sharedchao is explained:
http://www.mothur.org/wiki/Sharedchao

According to that page, you used the Amazonian dataset to calculate a sharedchao richness estimate of 24.5

Now, on the wiki page of Sorest (http://www.mothur.org/wiki/Sorest) and Jest (http://www.mothur.org/wiki/Jest) you use the exact same dataset.
There you briefly mention “Elsewhere, we used the sharedchao calculator to estimate that the shared richness was 69.5 OTUs”.

So on the sharedchao page you get a shared richness of 24.5 and on the Jest and Sorest page you say you got a shared richness of 69.5. Am I missing something here? What did you do different to get the those results?

Thanks a lot in advance,
Rene

2

I took a look at the wiki and there appears to be an error in the table that shows the abundance data. The table differs from the abundance lines above. I have fixed the table. Let’s look at the hand calculations:

All OTUs:
0.10 forest 55 1 1 1 1 1 1 3 3 2 2 1 1 3 2 1 1 1 1 2 1 1 2 5 1 1 1 1 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.10 pasture 55 0 0 0 1 1 0 1 0 0 5 0 0 0 0 0 2 0 0 0 3 0 0 2 1 0 1 0 0 0 0 0 0 1 2 1 1 1 1 1 7 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1

SharedOTUs:
0.10 forest 10 1 1 3 2 1 1 5 1 1 1
0.10 pasture 10 1 1 1 5 2 3 2 1 1 1

For sharedChao:
f11 = 5
f1+ = 7
f2+ = 1
f+1 = 6
f+2 = 2
f22 = 0

sharedChao = numSharedOTUs + (f1+(f1±1))/2(f2++1) + (f+1(f+1-1))/2(f+2+1) + (f11(f11-1)/4(f22+1)
sharedChao = 10 + (7(6)/2(2)) + (6(5)/2(3)) + (5(4)/4(1))
sharedChao = 10 + (42/4) + (30/6) + (20/4)
sharedChao = 10 + 10.5 + 5 + 5 = 30.5

Sabund Info:
0.10 forest 7 24 5 1 0 1 0 1
0.10 pasture 5 23 6 3 0 1

For Chao:
pasture:
sobs = 33
n1 = 23
n2 = 6
Chao = Sobs + (n1(n1-1)/2(n2+1)
Chao = 33 + (23(22))/2(7) = 69.1428

forest:
sobs = 32
n1 = 24
n2 = 5
Chao = Sobs + (n1(n1-1)/2(n2+1)
Chao = 32 + (24(23))/2(6) = 78

Jest = 1 - (sharedChao / (chaoForest+chaoPasture - shareChao))
Jest = 1 - (30.5 / (78 + 69.1 - 30.5)) = 0.7384

Sorest = 1- (2(sharedChao) / (chaoForest+chaoPasture))
Sorest = 1 - (2*30.5 / (78 + 69.1)) = 0.5853

3

Thanks a lot for your reply! Now it all makes sense!