null models with continuous abundance data

Many thanks again Carsten.

ensure that a decent number

don't think it would be a

continuous abundance data

0]) )

of

mostly

suggestion, I came up with a simple (read na?ve) R

a binary matrix obtained by commsimulator

work relatively well, though it's

algorithm fills the matrix one individual at a

problem of one individual which had

site (i.e. the row sum) was

disappears, i.e. goes

but it's the

algorithm

of

of

I don't see this as being a
real

definitely

algorithm, as well as some code to

compare it to Vazquez's

function(x){

rowsum <- rowSums(x)

method = "quasiswap")

colSums(nullbin)

ind <- rep(1:nsp, colsum)

sum(rowsum)

indsel <- ind[selinds[j]]

if (length(ress[ress %in% sitepot]) > 0 ){

sample(ress[ress %in% sitepot], 1)

sitesel)[1] ]

+ 1

function

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,

total number of individuals

"stuck" with no ressources...

999

null matrices?

individuals in m?

individuals getting stuck with no ressources

as.numeric(lapply(nulls, sum, simplify = T))

had 29 or 30 individuals

Dormann a ?crit :
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


V?zquez,
D. P., Meli?n, C. J., Williams, N. M., Bl?thgen, 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
Lalibert? 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 ?crit :

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

P?ter S?lymos

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 Lalibert? 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