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

[Peter Solymos]

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
>
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