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

[Eik Vettorazzi]

Hi Jasper,
maybe its not a very R'ish solution but the following could be a 
starting point:
First, notice that every combination you are looking for can be 
represented as an integer in binary notation where each bit stands for a 
specific community.
So looping through all combinations is the same as looping through 
0:(2^n-1) , eg. 7=2^0+2^2, so community 1 and 3 (natural numbering) are 
"set" in the corresponding subset.

#some auxillary functions are needed to extract the bits set in a given 
combination
#get bit returns presence/absence vector of species for given subset x
get.bit<-function(x,n)  x%/%(2^(0:(n-1)))%%2

#index of data columns included in subset x
get.index<-function(x,n)  x%/%(2^(0:(n-1)))%%2==1

n<-15 # number of communities
dta<-matrix(1:(12*n),ncol=n) # some sample data

#looping thru *all* possible combinations of n communities.
#will work, but it is in fact *very*! time consuming for n=25
for (i in 0:(2^n-1))  {
 sub.index<-get.index(i,n)
 # subsetting your dataset using this index and do subset analysis
 # dta[,sub.index]
}

hth



jasper slingsby schrieb:
> 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
>
>