[R-sig-eco] R: vegan/permute: additional level of nesting for pseudoreplicates

[Guillaume Adeux]

Hi everyone,
I am trying to investigate how to set up a permutation scheme for community
data originating from a split plot experiment with pseudoreplicates at the
lowest level.
A theoretical design could be the following:
4 blocks
2 tillage strips nested within each block (main plot)
2 cover crop species nested within tillage strips (subplot)
2 pseudoreplicates at the subplot level

I think I am able to do what I want with the R software if I average the
two pseudoreplicates (so as to avoid the pseudoreplication level), as
follows:

require("vegan")
require("permute")
data(mite)

*# tillage strip nested in blocks, cover crop nested within tillage strip,
only one observation per combination of blcks:tillage:covcrop*
trt=expand.grid(blcks=c("B1","B2","B3","B4"),tillage=c("CT","NT"),covcrop=c("C","VV"))
com=mite[1:16,]
dat=cbind(trt,com)
h <- how(within = Within(type = "free"),plots = Plots(strata =
interaction(dat$blcks,dat$tillage), type = "free"),blocks =
dat$blcks,nperm=999)
pcoa=capscale(com~tillage*covcrop+Condition(blcks),method="bray",data=dat)
anova(pcoa,by="terms",perm=h)

Now what I wish to do is to add an additional level of nesting so as to
permute group of observations (pseudoreplicates: named quadrat_ID in the
following script) at the lowest level:

*# same design but pseudoreplication at the subplot level, i.e. two
observations per combination of blcks:tillage:covcrop*
trt2=expand.grid(blcks=c("B1","B2","B3","B4"),tillage=c("CT","NT"),covcrop=c("C","VV"),quadrat_ID=c(1,2))
com2=mite[1:48,]
dat2=cbind(trt2,com2)
h <- ?????
pcoa=capscale(com~tillage*covcrop+Condition(blcks),method="bray",data=dat)
anova(pcoa,by="terms",perm=h)

Thank you very much for your help.
Best.
Guillaume ADEUX

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