[R-sig-eco] null models with continuous abundance data

Etienne Laliberté etiennelaliberte at gmail.com
Tue Jan 12 20:42:28 CET 2010 

Thanks again Peter,

I'm running the latest development version of vegan. Indeed, you are
right that "abuswap" is the closest algorithm to what I wanted. Not
quite what I was after, but perhaps close enough...

Cheers

Etienne


Le lundi 11 janvier 2010 à 00:30 -0700, Peter Solymos a écrit :
> Etienne,
> 
> Good points, thanks for summarizing! I think that points 2 and 3 are
> related somewhat, and a balance should be found between the too
> constrained (small sample space) and the non-realistic (few
> constraints) ends with respect to the data set. Point 1 is rather
> technical, and there are some diagnostics to check sequential
> algorithms for independence and randomness.
> 
> Going back to your original problem, I just realized the huge lag
> between the public and the developmental versions of permatswap in
> vegan. Actually, there are two more algorithms that implement some
> features which might be of interest. By using permatswap, you can
> achieve these constraint combinations:
> 
> 1) "swap"/"quasiswap": marginal totals and matrix fill fixed (but not
> col/row occurrences);
> 2) "swsh": row and column occurrences (not totals) fixed (thus fill, too);
> 3) "abuswap": row and column occurrences (and so the fill) fixed, and
> row OR column totals (this latter algorithm was published by Hardy
> 2008 J Ecol 96, 914-926).
> 
> Maybe this "abuswap" is the closest to the one you wanted.
> 
> Yours,
> 
> Peter
> 
> Péter Sólymos
> Alberta Biodiversity Monitoring Institute
> Department of Biological Sciences
> CW 405, Biological Sciences Bldg
> University of Alberta
> Edmonton, Alberta, T6G 2E9, Canada
> Phone: 780.492.8534
> Fax: 780.492.7635
> 
> 
> 
> 2010/1/10 Etienne Laliberté <etiennelaliberte at gmail.com>:
> > Many thanks again Carsten for your answer.
> >
> > >From this interesting discussion, it seems that there are three
> > different and somewhat distinct potential problems with null model
> > approaches. Here's my attempt at summarizing them. Please correct me if
> > I'm wrong.
> >
> > 1) non-randomness of null matrices: This can happen for example in
> > sequential algorithms, where a null matrix may be quite similar to the
> > previous one. I think this was the main point raised by Peter, and seems
> > to be primarily linked to the nature of the algorithm (and not the
> > constraints). For example, permatswap(..., method = "swap") vs.
> > permatswap(..., method = "quasiswap"). His function summary.permat is a
> > good way of checking this.
> >
> > 2) not enough unique matrices obtained: one should check how many unique
> > null matrices are obtained. A small matrix with many constraints may
> > lead to few unique null matrices. This does not imply that the algorithm
> > has the problem described in #1 though. Having few unique matrices may
> > make P-values obtained in tests meaningless. This was the main point
> > raised by Carsten.
> >
> > 3) non-realism of null model: it is easy to build null models that are
> > too null and biologically irrelevant. In that case it becomes very easy
> > to detect significant patterns, and to some extent this could maybe be
> > compared to a type-I error? Adding constraints is required to isolate
> > the feature we want to test as much as possible, but too many
> > constraints can sometimes make the test overly conservative (could maybe
> > compare this to a type-II error?), and can increase the likelihood of
> > problem #2.
> >
> > I *think* this was the point Jari raised about r2dtable(), i.e. that is
> > is too null and leads to null matrices with lower variance than the
> > observed matrix because it tends to fill the zeros (and in doing so
> > reduce the high abundances because marginal sums need to be respected),
> > which has nothing to do with problem #1 or #2.
> >
> > Feebdack would be appreciated. I think it's important not to confuse
> > these different problems.
> >
> > Cheers
> >
> > Etienne
> >
> > Le vendredi 08 janvier 2010 à 08:32 +0100, Carsten Dormann a écrit :
> >> Dear Etienne,
> >>
> >> although certainly not as thorough as Peter/Jari's approach would be, I
> >> find that "problematic" null models become noticeable when you produce
> >> only few of them (say 100 or so) and table (or plot the density) of
> >> their indices (say for example the Shannon diversity of entries or
> >> alike). What often happens with "problematic" null models is that they
> >> show only very few alternative "random" combinations, i.e. that I see 2
> >> to 5 humps of the density curve. That clearly indicates that only very
> >> few alternative combinations are possible and hence that the null model
> >> is too constrained.
> >> Using 1000s of null models might blur this picture a bit but should give
> >> the same idea.
> >>
> >> Jari, did I understand you right that think the r2dtable doesn't
> >> randomly and unbiasedly sample the space of possible combinations? You
> >> wrote about "too regular" matrices. I took r2dtable (or rather the
> >> Patefield algorithm) for granted, since it apparently is also under the
> >> hood of Fisher's test etc.
> >> That should be relatively easy to find out, for a given matrix, by
> >> creating endless numbers of null models and tabulating their unique
> >> frequencies. Ideally, this should show a uniform distribution.
> >>
> >> require(bipartite)
> >> data(Safariland)
> >> nulls <- r2dtable(10000, r=rowSums(Safariland), c=colSums(Safariland))
> >>
> >> # this takes a few minutes:
> >> nonsame <- 1:3
> >> for (i in 1:10000){
> >>     nonsame[i] <- sum(sapply(nulls, function(x) identical(x, nulls[[i]])))
> >> }
> >> table(nonsame-1)
> >> #       0
> >> #10000
> >>
> >> This means, there are no two identical random matrices. Encouraging (for
> >> this example)!
> >>
> >> HOWEVER, this does not mean that the whole sample space is covered.
> >> Furthermore, these null models may still be similarly "regular". But at
> >> least the r2dtable samples a large set of matrices. Maybe a value of 1e6
> >> to 1e9 would be better, and then some ordination of the matrices to
> >> visualise the coverage of the matrix space?
> >>
> >>
> >> Best wishes,
> >>
> >> Carsten
> >>
> >>
> >>
> >> On 07/01/2010 21:42, Etienne Laliberté wrote:
> >> > Many thanks Jari for your input.
> >> >
> >> > I'll have a look at this backtracking method and see how I could
> >> > implement it.
> >> >
> >> > Ensuring that the null matrices are indeed random is clearly good
> >> > advice, and I'd need to do this, but do you have any suggestions on how
> >> > to do this in practice? A copy of the script you've used to test Peter's
> >> > null model algorithms would be very useful.
> >> >
> >> > Thanks
> >> >
> >> > Etienne
> >> >
> >> >
> >> > Le jeudi 07 janvier 2010 à 22:24 +0200, Jari Oksanen a écrit :
> >> >
> >> >> On 07/01/2010 21:48, "Etienne Laliberté"<etiennelaliberte at gmail.com>  wrote:
> >> >>
> >> >>
> >> >>> Many thanks again Carsten.
> >> >>>
> >> >> Yes, you're right that care must be taken to
> >> >>
> >> >>> ensure that a decent number
> >> >>>
> >> >> of unique random matrices must be obtained. I
> >> >>
> >> >>> don't think it would be a
> >> >>>
> >> >> problem in my case given that transforming my
> >> >>
> >> >>> continuous abundance data
> >> >>>
> >> >> to count by
> >> >>
> >> >> mat2<- floor(mat * 100 / min(mat[mat>
> >> >>
> >> >>> 0]) )
> >> >>>
> >> >> can quickly lead to a very large number of individuals (hundreds
> >> >>
> >> >>> of
> >> >>>
> >> >> thousands if not>  million in some cases). The issue then becomes
> >> >>
> >> >>> mostly
> >> >>>
> >> >> one of computing speed, but that's another story.
> >> >>
> >> >> Following your
> >> >>
> >> >>> suggestion, I came up with a simple (read naïve) R
> >> >>>
> >> >> algorithm that starts with
> >> >>
> >> >>> a binary matrix obtained by commsimulator
> >> >>>
> >> >> then fills it randomly. It seems to
> >> >>
> >> >>> work relatively well, though it's
> >> >>>
> >> >> extremely slow.
> >> >>
> >> >> In addition, because the
> >> >>
> >> >>> algorithm fills the matrix one individual at a
> >> >>>
> >> >> time, I sometimes ran into the
> >> >>
> >> >>> problem of one individual which had
> >> >>>
> >> >> nowhere to go because "ressources" at the
> >> >>
> >> >>> site (i.e. the row sum) was
> >> >>>
> >> >> already full. In that case, this individual
> >> >>
> >> >>> disappears, i.e. goes
> >> >>>
> >> >> nowhere. This is a bit drastic and clearly sub-optimal,
> >> >>
> >> >>> but it's the
> >> >>>
> >> >> only way I could quickly think of yesterday to prevent the
> >> >>
> >> >>> algorithm
> >> >>>
> >> >> from getting stuck. The consequence is that often, the total number
> >> >>
> >> >>> of
> >> >>>
> >> >> individuals in the null matrix is a bit less than total number
> >> >>
> >> >>> of
> >> >>>
> >> >> individuals in the observed matrix.
> >> >>
> >> >> Etienne,
> >> >>
> >> >> This is the same problem as filling up a binary matrix: you get stuck before
> >> >> you can fill in all presences. The solution in vegan::commsimulator was
> >> >> "backtracking" method: when you get stuck, you remove some of the items
> >> >> (backtrack to an earlier stage of filling) and start again. This is even
> >> >> slower than initial filling, but it may be doable. The model application of
> >> >> backtracking goes back to Gotelli&  Entsminger (Oecologia 129, 282--291;
> >> >> 2001) who had this for binary data, but the same idea is natural for
> >> >> quantitative null models, too. The vegan vignette discusses some details of
> >> >> implementation which are valid also for quantitative filling.
> >> >>
> >> >> I would like to repeat the serious warning that Carsten Dormann made: you
> >> >> better be sure that your generated null models really are random. Péter
> >> >> Sólymos developed some quantitative null models for vegan, but we found in
> >> >> our tests that they were not random at all, but the constraints we put
> >> >> produced peculiar kind of data with regular features although there was
> >> >> technically no problem. Therefore we removed code worth of huge amount of
> >> >> developing work as dangerous for use. I do think that also the r2dtable
> >> >> approach is more regular and less variable (lower variance) than the
> >> >> community data, and you very easily get misleadingly significant results
> >> >> when you compare your observed community against too regular null models.
> >> >> This is something analogous to using strict Poisson error in glm or gam when
> >> >> the data in fact are overdispersed to Poisson. Be very careful if you want
> >> >> to claim significant results based on quantitative null models. Would I be a
> >> >> referee or an editor for this kind of ms, I would be very skeptical ask for
> >> >> the proof of the validity of the null model.
> >> >>
> >> >> Cheers, Jari Oksanen
> >> >>
> >> >>
> >> >>> I don't see this as being a
> >> >>> real
> >> >>>
> >> >> problem with the large matrices I'll deal with though, but
> >> >>
> >> >>> definitely
> >> >>>
> >> >> something to be aware of.
> >> >>
> >> >> If you're curious, here's the simple
> >> >>
> >> >>> algorithm, as well as some code to
> >> >>>
> >> >> run a test below. I'd be very interested to
> >> >>
> >> >>> compare it to Vazquez's
> >> >>>
> >> >> algorithm!
> >> >>
> >> >> Thanks again
> >> >>
> >> >> Etienne
> >> >>
> >> >> ###
> >> >>
> >> >> nullabun<-
> >> >>
> >> >>> function(x){
> >> >>>
> >> >>     require(vegan)
> >> >>     nsites<- nrow(x)
> >> >>     nsp<- ncol(x)
> >> >>
> >> >>
> >> >>> rowsum<- rowSums(x)
> >> >>>
> >> >>     colsum<- colSums(x)
> >> >>     nullbin<- commsimulator(x,
> >> >>
> >> >>> method = "quasiswap")
> >> >>>
> >> >>     rownull<- rowSums(nullbin)
> >> >>     colnull<-
> >> >>
> >> >>> colSums(nullbin)
> >> >>>
> >> >>     rowsum<- rowsum - rownull
> >> >>     colsum<- colsum - colnull
> >> >>
> >> >>
> >> >>> ind<- rep(1:nsp, colsum)
> >> >>>
> >> >>     ress<- rep(1:nsites, rowsum)
> >> >>     total<-
> >> >>
> >> >>> sum(rowsum)
> >> >>>
> >> >>     selinds<- sample(1:total)
> >> >>        for (j in 1:total){
> >> >>
> >> >>
> >> >>> indsel<- ind[selinds[j]]
> >> >>>
> >> >>           sitepot<- which(nullbin[, indsel]>  0)
> >> >>
> >> >>
> >> >>> if (length(ress[ress %in% sitepot])>  0 ){
> >> >>>
> >> >>              sitesel<-
> >> >>
> >> >>> sample(ress[ress %in% sitepot], 1)
> >> >>>
> >> >>              ress<- ress[-which(ress ==
> >> >>
> >> >>> sitesel)[1] ]
> >> >>>
> >> >>              nullbin[sitesel, indsel]<- nullbin[sitesel, indsel]
> >> >>
> >> >>> + 1
> >> >>>
> >> >>             }
> >> >>        }
> >> >> return(nullbin)
> >> >> }
> >> >>
> >> >>
> >> >> ### now let's test the
> >> >>
> >> >>> function
> >> >>>
> >> >> # create a dummy abundance matrix
> >> >> m<-
> >> >>
> >> >>> matrix(c(1,3,2,0,3,1,0,2,1,0,2,1,0,0,1,2,0,3,0,0,0,1,4,3), 4,
> >> >>> 6,
> >> >>>
> >> >> byrow=TRUE)
> >> >>
> >> >> # generate a null matrix
> >> >> m.null<- nullabun(m)
> >> >>
> >> >> # compare
> >> >>
> >> >>> total number of individuals
> >> >>>
> >> >> sum(m) #30
> >> >> sum(m.null) #29: one individual got
> >> >>
> >> >>> "stuck" with no ressources...
> >> >>>
> >> >> # to generate more than one null matrix, say
> >> >>
> >> >>> 999
> >> >>>
> >> >> nulls<- replicate(n = 999, nullabun(m), simplify = F)
> >> >>
> >> >> # how many unique
> >> >>
> >> >>> null matrices?
> >> >>>
> >> >> length(unique(nulls) ) # I found 983 out of 999
> >> >>
> >> >> # how many
> >> >>
> >> >>> individuals in m?
> >> >>>
> >> >> sum(m) # there are 30
> >> >>
> >> >> # how bad is the problem of
> >> >>
> >> >>> individuals getting stuck with no ressources
> >> >>>
> >> >> in null matrices?
> >> >> sums<-
> >> >>
> >> >>> as.numeric(lapply(nulls, sum, simplify = T))
> >> >>>
> >> >> hist(sums) # the vast majority
> >> >>
> >> >>> had 29 or 30 individuals
> >> >>>
> >> >>
> >> >> Le jeudi 07 janvier 2010 à 10:34 +0100, Carsten
> >> >>
> >> >>> Dormann a écrit :
> >> >>> Hi Etienne,
> >> >>>
> >> >>> I'm afraid that swap.web cannot easily
> >> >>> accommodate this constraint.
> >> >>> Diego Vazquez has used an alternative approach
> >> >>> for this problem, but I
> >> >>> haven't seen code for it (it's briefly described in
> >> >>> his Oikos 2005
> >> >>> paper). While swap.web starts with a "too-full" matrix and
> >> >>> then
> >> >>> downsamples, Diego starts by allocating bottom-up. There it should be
> >> >>>
> >> >>> relatively easy to also constrain the row-constancy of connectance.
> >> >>>
> >> >>> I
> >> >>> can't promise, but I will hopefully have this algorithm by the end
> >> >>> of next
> >> >>> week (I'm teaching this stuff next week and this is one of the
> >> >>> assignments).
> >> >>> If so, I'll get it over to you.
> >> >>>
> >> >>> The problem that already arises with
> >> >>> swap.web for very sparse matrices
> >> >>> is that there are very few unique
> >> >>> combinations left after all these
> >> >>> constraints. This will be even worse for
> >> >>> your approach, and plant
> >> >>> community data are usually VERY sparse. Once you
> >> >>> have produced the
> >> >>> null models, you should assure yourself that there are
> >> >>> hundreds
> >> >>> (better thousands) of possible randomised matrices. Adding just
> >> >>> one
> >> >>> more constraint to your null model (that of column AND row constancy
> >> >>>
> >> >>> of 0s) will uniquely define the matrix! Referees may not pick it up,
> >> >>> but it
> >> >>> may give you trivial results.
> >> >>>
> >> >>> Best wishes,
> >> >>>
> >> >>> Carsten
> >> >>>
> >> >>>
> >> >>> Vázquez,
> >> >>> D. P., Melián, C. J., Williams, N. M., Blüthgen, N., Krasnov,
> >> >>> B. R., Poulin,
> >> >>> R., et al. (2007). Species abundance and asymmetric
> >> >>> interaction strength in
> >> >>> ecological networks. Oikos, 116, 1120-1127.
> >> >>>
> >> >>> On 06/01/2010 23:57, Etienne
> >> >>> Laliberté wrote:
> >> >>>
> >> >>>> Many thanks Carsten and Peter for your suggestions.
> >> >>>>
> >> >>>>
> >> >>>
> >> >>>> commsimulator indeed respects the two contraints I'm interested in, but>
> >> >>>> only allows for binary data.
> >> >>>>
> >> >>>> swap.web is *almost* what I need, but
> >> >>>>
> >> >>> only overall matrix fill is kept
> >> >>>
> >> >>>> constant, whereas I want zeros to move
> >> >>>>
> >> >>> only between rows, not between
> >> >>>
> >> >>>> both columns and rows. In others words, if
> >> >>>>
> >> >>> the initial data matrix had
> >> >>>
> >> >>>> three zeros for row 1, permuted matrices
> >> >>>>
> >> >>> should also have three zeros
> >> >>>
> >> >>>> for that row.
> >> >>>>
> >> >>>> I do not doubt that
> >> >>>>
> >> >>> Peter's suggestions are good, but I'm afraid they
> >> >>>
> >> >>>> seem a bit overly
> >> >>>>
> >> >>> complicated for my particular problem. All I'm after
> >> >>>
> >> >>>> is to create n
> >> >>>>
> >> >>> randomly-assembled matrices from an observed species
> >> >>>
> >> >>>> abundance matrix to
> >> >>>>
> >> >>> compare the observed functional diversity of the
> >> >>>
> >> >>>> sampling sites to a null
> >> >>>>
> >> >>> expectation. To be conservative, this requires
> >> >>>
> >> >>>> that I hold species
> >> >>>>
> >> >>> richness constant at each site, and keep row and
> >> >>>
> >> >>>> column marginals fixed.
> >> >>>>
> >> >>>
> >> >>>> Could swap.web or permatswap(..., method = "quasiswap") be easily
> >> >>>>
> >> >>>>
> >> >>> tweaked to accomodate this? The only difference really is that matrix
> >> >>>
> >> >>>> fill
> >> >>>>
> >> >>> should be kept constant *but also* be constrained within rows.
> >> >>>
> >> >>>> Thanks
> >> >>>>
> >> >>> again for your help.
> >> >>>
> >> >>>> Etienne
> >> >>>>
> >> >>>> Le 7 janvier 2010 08:17, Peter
> >> >>>>
> >> >>> Solymos<solymos at ualberta.ca>  a écrit :
> >> >>>
> >> >>>>
> >> >>>>
> >> >>>>> Dear Etienne,
> >> >>>>>
> >> >>>>>
> >> >>>> You can try the Chris Hennig's prablus package which have a parametric
> >> >>>>
> >> >>>>>
> >> >>> bootstrap based null-model where clumpedness of occurrences or
> >> >>>
> >> >>>>>
> >> >>> abundances (this might allow continuous data, too) is estimated from
> >> >>>
> >> >>>>> the
> >> >>>>>
> >> >>> site-species matrix and used in the null-model generation. But
> >> >>>
> >> >>>>> here, the
> >> >>>>>
> >> >>> sum of the matrix will vary randomly.
> >> >>>
> >> >>>>> But if you have
> >> >>>>>
> >> >>> environmental covariates, you might try something more
> >> >>>
> >> >>>>> parametric. For
> >> >>>>>
> >> >>> example the simulate.rda or simulate.cca functions in
> >> >>>
> >> >>>>> the vegan package,
> >> >>>>>
> >> >>> or fit multivariate LM for nested models (i.e.
> >> >>>
> >> >>>>> intercept only, and with
> >> >>>>>
> >> >>> other covariates) and compare AIC's, or use
> >> >>>
> >> >>>>> the simulate.lm to get
> >> >>>>>
> >> >>> random numbers based on the fitted model. This
> >> >>>
> >> >>>>> way you can base you
> >> >>>>>
> >> >>> desired statistic on the simulated data sets, and
> >> >>>
> >> >>>>> you know explicitly
> >> >>>>>
> >> >>> what is the model (plus it is good for continuous
> >> >>>
> >> >>>>> data that you have).
> >> >>>>>
> >> >>> By using the null-model approach, you implicitly
> >> >>>
> >> >>>>> have a model by
> >> >>>>>
> >> >>> defining constraints for the permutations, and
> >> >>>
> >> >>>>> p-values are
> >> >>>>>
> >> >>> probabilities of the data given the constraints (null
> >> >>>
> >> >>>>> hypothesis), and
> >> >>>>>
> >> >>> not probability of the null hypothesis given the data
> >> >>>
> >> >>>>> (what people
> >> >>>>>
> >> >>> usually really want).
> >> >>>
> >> >>>>> Cheers,
> >> >>>>>
> >> >>>>> Peter
> >> >>>>>
> >> >>>>>
> >> >>>>>
> >> >>> Péter Sólymos
> >> >>>
> >> >>>>> Alberta Biodiversity Monitoring Institute
> >> >>>>> Department
> >> >>>>>
> >> >>> of Biological Sciences
> >> >>>
> >> >>>>> CW 405, Biological Sciences Bldg
> >> >>>>> University
> >> >>>>>
> >> >>> of Alberta
> >> >>>
> >> >>>>> Edmonton, Alberta, T6G 2E9, Canada
> >> >>>>> Phone:
> >> >>>>>
> >> >>> 780.492.8534
> >> >>>
> >> >>>>> Fax: 780.492.7635
> >> >>>>>
> >> >>>>>
> >> >>>>>
> >> >>>>> On Wed, Jan 6,
> >> >>>>>
> >> >>> 2010 at 2:18 AM, Carsten Dormann<carsten.dormann at ufz.de>  wrote:
> >> >>>
> >> >>>>>
> >> >>>>>
> >> >>>
> >> >>>>>> Hi Etienne,
> >> >>>>>>
> >> >>>>>> the double constraint is observed by two
> >> >>>>>>
> >> >>> functions:
> >> >>>
> >> >>>>>> swap.web in package bipartite
> >> >>>>>>
> >> >>>>>>
> >> >>>>>>
> >> >>> and
> >> >>>
> >> >>>>>> commsimulator in vegan (at least in the r-forge
> >> >>>>>>
> >> >>> version)
> >> >>>
> >> >>>>>> Both build on the r2dtable approach, i.e. you have,
> >> >>>>>>
> >> >>> as you propose, to turn
> >> >>>
> >> >>>>>> the low values into higher-value integers.
> >> >>>>>>
> >> >>>>
> >> >>>>>
> >> >>>>>> The algorithm is described in the help to swap.web.
> >> >>>>>>
> >> >>>>>>
> >> >>>>
> >> >>>>>
> >> >>>>>> HTH,
> >> >>>>>>
> >> >>>>>> Carsten
> >> >>>>>>
> >> >>>>>>
> >> >>>>>>
> >> >>>>>>
> >> >>>>>>
> >> >>> On 06/01/2010 08:55, Etienne Laliberté wrote:
> >> >>>
> >> >>>>>>
> >> >>>>>>
> >> >>>>>>> Hi,
> >> >>>>>>>
> >> >>>>
> >> >>>>>>
> >> >>>>>>> Let's say I have measured plant biomass for a total of 5
> >> >>>>>>>
> >> >>> species from 3
> >> >>>
> >> >>>>>>> sites (i.e. plots), such that I end with the
> >> >>>>>>>
> >> >>> following data matrix
> >> >>>
> >> >>>>>>> mat<- matrix(c(0.35, 0.12, 0.61, 0,
> >> >>>>>>>
> >> >>> 0, 0.28, 0, 0.42, 0.31, 0.19, 0.82,
> >> >>>
> >> >>>>>>> 0, 0, 0, 0.25), 3, 5, byrow =
> >> >>>>>>>
> >> >>> T)
> >> >>>
> >> >>>>>>> dimnames(mat)<- list(c("site1", "site2", "site3"),
> >> >>>>>>>
> >> >>> c("sp1", "sp2",
> >> >>>
> >> >>>>>>> "sp3", "sp4", "sp5"))
> >> >>>>>>>
> >> >>>>>>> Data is
> >> >>>>>>>
> >> >>> therefore continuous. I want to generate n random community
> >> >>>
> >> >>>>>>> matrices
> >> >>>>>>>
> >> >>> which both respect the following constraints:
> >> >>>
> >> >>>>>>> 1) row and
> >> >>>>>>>
> >> >>> column totals are kept constant, such that "productivity" of
> >> >>>
> >> >>>>>>> each
> >> >>>>>>>
> >> >>> site is maintained, and that rare species at a "regional" level
> >> >>>
> >> >>>>>>> stay
> >> >>>>>>>
> >> >>> rare (and vice-versa).
> >> >>>
> >> >>>>>>> 2) number of species in each plot
> >> >>>>>>>
> >> >>> is kept constant, i.e. each row
> >> >>>
> >> >>>>>>> maintains the same number of zeros,
> >> >>>>>>>
> >> >>> though these zeros should not stay
> >> >>>
> >> >>>>>>> fixed.
> >> >>>>>>>
> >> >>>>>>> To
> >> >>>>>>>
> >> >>> deal with continuous data, my initial idea was to transform the
> >> >>>
> >> >>>>>>>
> >> >>> continuous data in mat to integer data by
> >> >>>
> >> >>>>>>> mat2<-
> >> >>>>>>>
> >> >>> floor(mat * 100 / min(mat[mat>   0]) )
> >> >>>
> >> >>>>>>> where multiplying
> >> >>>>>>>
> >> >>> by 100 is only used to reduce the effect of rounding
> >> >>>
> >> >>>>>>> to nearest
> >> >>>>>>>
> >> >>> integer (a bit arbitrary). In a way, shuffling mat could now
> >> >>>
> >> >>>>>>> be seen
> >> >>>>>>>
> >> >>> as re-allocating "units of biomass" randomly to plots. However,
> >> >>>
> >> >>>>>>>
> >> >>> doing so results in a matrix with large number of "individuals" to
> >> >>>
> >> >>>>>>>
> >> >>> reshuffle, which can slow things down quite a bit. But this is only part
> >> >>>
> >> >>>>> of the problem.
> >> >>>>>
> >> >>>>>>> My main problem has been to find an
> >> >>>>>>>
> >> >>> algorithm that can actually respect
> >> >>>
> >> >>>>>>> constraints 1 and 2. Despite
> >> >>>>>>>
> >> >>> trying various R functions (r2dtable,
> >> >>>
> >> >>>>>>> permatfull, etc), I have not
> >> >>>>>>>
> >> >>> yet been able to find one that can do
> >> >>>
> >> >>>>>>> this.
> >> >>>>>>>
> >> >>>>>>>
> >> >>>>>>>
> >> >>> I've had some kind help from Peter Solymos who suggested that I try the
> >> >>>
> >> >>>>> aylmer package, and it's *almost* what I need, but the problem is that
> >> >>>>>
> >> >>>>
> >> >>>>>> their algorithm does not allow for the zeros to move within the
> >> >>>>>>
> >> >>> matrix;
> >> >>>
> >> >>>>>>> they stay fixed. I want the number of zeros to stay constant
> >> >>>>>>>
> >> >>> within each
> >> >>>
> >> >>>>>>> row, but I want them to move freely betweem columns.
> >> >>>>>>>
> >> >>>>
> >> >>>>>>
> >> >>>>>>> Any help would be very much appreciated.
> >> >>>>>>>
> >> >>>>>>>
> >> >>>>>>>
> >> >>> Thanks
> >> >>>
> >> >>>>>>>
> >> >>>>>>>
> >> >>>>>>>
> >> >>>>>> --
> >> >>>>>> Dr. Carsten
> >> >>>>>>
> >> >>> F. Dormann
> >> >>>
> >> >>>>>> Department of Computational Landscape Ecology
> >> >>>>>>
> >> >>>>>>
> >> >>> Helmholtz Centre for Environmental Research-UFZ
> >> >>>
> >> >>>>>> Permoserstr. 15
> >> >>>>>>
> >> >>>>>
> >> >>>> 04318 Leipzig
> >> >>>>
> >> >>>>>> Germany
> >> >>>>>>
> >> >>>>>> Tel: ++49(0)341 2351946
> >> >>>>>>
> >> >>>>>
> >> >>>> Fax: ++49(0)341 2351939
> >> >>>>
> >> >>>>>> Email: carsten.dormann at ufz.de
> >> >>>>>>
> >> >>>>>>
> >> >>> internet: http://www.ufz.de/index.php?de=4205
> >> >>>
> >> >>>>>>
> >> >>>>>>
> >> >>> _______________________________________________
> >> >>>
> >> >>>>>> R-sig-ecology mailing
> >> >>>>>>
> >> >>> list
> >> >>>
> >> >>>>>> R-sig-ecology at r-project.org
> >> >>>>>>
> >> >>>>>>
> >> >>> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
> >> >>>
> >> >>>>>>
> >> >>>>>>
> >> >>>>>>
> >> >>>
> >> >>>>
> >> >>>>
> >> >>>>
> >> >>> --
> >> >>> Dr. Carsten F. Dormann
> >> >>> Department of
> >> >>> Computational Landscape Ecology
> >> >>> Helmholtz Centre for Environmental
> >> >>> Research-UFZ
> >> >>> Permoserstr. 15
> >> >>> 04318 Leipzig
> >> >>> Germany
> >> >>>
> >> >>> Tel: ++49(0)341
> >> >>> 2351946
> >> >>> Fax: ++49(0)341 2351939
> >> >>> Email: carsten.dormann at ufz.de
> >> >>> internet:
> >> >>> http://www.ufz.de/index.php?de=4205
> >> >>>
> >> >>
> >> >>
> >> >
> >> >
> >>
> >
> >
> > --
> > Etienne Laliberté
> > ================================
> > School of Forestry
> > University of Canterbury
> > Private Bag 4800
> > Christchurch 8140, New Zealand
> > Phone: +64 3 366 7001 ext. 8365
> > Fax: +64 3 364 2124
> > www.elaliberte.info
> >
> >


-- 
Etienne Laliberté
================================
School of Forestry
University of Canterbury
Private Bag 4800
Christchurch 8140, New Zealand
Phone: +64 3 366 7001 ext. 8365
Fax: +64 3 364 2124
www.elaliberte.info

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