how to subsample all possible combinations of n species taken 1:n at a time?

sample(33554432,100)

Hello

I apologise for the length of this entry but please bear with me.

In short:
I need a way of subsampling communities from all possible communities of n
taxa taken 1:n at a time without having to calculate all possible
combinations (because this gives me a memory error - using
combn() or expand.grid() at least). Does anyone know of a function? Or can
you help me edit the
combn
or
expand.grid
functions to generate subsamples?

In long:
I have been creating all possible communities of n taxa taken 1:n at a time
to get a presence/absence matrix of species occurrence in communities as
below...

Rows are samples, columns are species:

? ?A ? ?B ? ?C ? D ? ? . ? ? . ? ?. ? ?.
? ?1 ? ?0 ? ?1 ? ?1 ? ?1 ? ?0 ? ?0 ? ?0 ? ?1 ? ? 1 ? ? 1 ? ? 1 ? ? 0 ? ? 0
0 ? ? 0
? ?0 ? ?1 ? ?1 ? ?1 ? ?1 ? ?0 ? ?0 ? ?0 ? ?1 ? ? 1 ? ? 1 ? ? 1 ? ? 0 ? ? 0
0 ? ? 0
? ?1 ? ?1 ? ?1 ? ?1 ? ?1 ? ?0 ? ?0 ? ?0 ? ?1 ? ? 1 ? ? 1 ? ? 1 ? ? 0 ? ? 0
0 ? ? 0
? ?0 ? ?0 ? ?0 ? ?0 ? ?0 ? ?1 ? ?0 ? ?0 ? ?1 ? ? 1 ? ? 1 ? ? 1 ? ? 0 ? ? 0
0 ? ? 0
? ?1 ? ?0 ? ?0 ? ?0 ? ?0 ? ?1 ? ?0 ? ?0 ? ?1 ? ? 1 ? ? 1 ? ? 1 ? ? 0 ? ? 0
0 ? ? 0
? ?0 ? ?1 ? ?0 ? ?0 ? ?0 ? ?1 ? ?0 ? ?0 ? ?1 ? ? 1 ? ? 1 ? ? 1 ? ? 0 ? ? 0
0 ? ? 0
? ?1 ? ?1 ? ?0 ? ?0 ? ?0 ? ?1 ? ?0 ? ?0 ? ?1 ? ? 1 ? ? 1 ? ? 1 ? ? 0 ? ? 0
0 ? ? 0
? ?0 ? ?0 ? ?1 ? ?0 ? ?0 ? ?1 ? ?0 ? ?0 ? ?1 ? ? 1 ? ? 1 ? ? 1 ? ? 0 ? ? 0
0 ? ? 0

...but the number of possible communities increases exponentially with each
added taxon.

n<-11 ? ? #number of taxa
sum(for (i in 0:n) choose(i, k = 0:i)) #number of combos

So all possible combinations of 11 taxa taken 1:11 at a time is 2048, all
combos of 12 taken 1:12 is 4096, 13 taken 1:13 = 8192...etc etc such that
when I reach about 25 taken 1:25 the number of combos is 33554432 and I get
a memory error.

I have found that the number of combos of x taxa taken from a pool of n
creates a very kurtotic unimodal distribution,...

x<-vector("integer",20)
for (i in 1:20) {x[i]<-choose(20,i)}
plot(x)

...but have found that limiting the number of samples for any community size
to 1000 is good enough for the further analyses I wish to do.
My problem lies in sampling all possible combos without having to calculate
all possible combos. I have tried two methods but both give memory errors at
about 25 taxa.

The expand.grid() method:

n <- 11
toto <- vector("list",n)
titi <- lapply(toto,function(x) c(0,1))
tutu <- expand.grid(titi)

The combn() method (a slightly lengthlier function):

samplecommunityD<- function(n,numsamples)
{
super<-mat.or.vec(,n)
for (numspploop in 1:n)
{
?minor<-t(combn(n,numspploop))
?if (dim(minor)[1]<numsamples)
?{
? ?minot<-mat.or.vec(dim(minor)[1],n)
? ?for (loopi in 1:dim(minor)[1])
? ?{
? ? ?for (loopbi in 1:dim(minor)[2])
? ? ?{
? ? ? ?minot[loopi,minor[loopi,loopbi]] <- 1
? ? ?}
? ?}
? ?super<-rbind(super,minot)
? ?rm(minot)
?}
?else
?{
? minot<-mat.or.vec(numsamples,n)
? for (loopii in 1:numsamples)
? {
? ? thousand<-sample(dim(minor)[1],numsamples)
? ? ? for (loopbii in 1:dim(minor)[2])
? ? ? {
? ? ? minot[loopii,minor[thousand[loopii],loopbii]] <- 1
? ? ? }
? }
? super<-rbind(super,minot)
? rm(minot)
?}
}
super<-super[!rowSums(super)>n-1&!rowSums(super)<2,]
return(super)
}

samplecommunityD(11,1000)


So unless anyone knows of another function I could try my next step would be
to modify the combn or expand.grid functions to generate subsamples, but
their coding beyond me at this stage (I'm a 3.5 month newbie). Can anyone
identify where in the code I would need to introduce a sampling term or
skipping sequence?

Thanks for your time
Jasper

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