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Manual Rarefaction and CI's

1 message · Jari Oksanen

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Nicholas,

Your approach looks perfectly OK. However, rarefied sampling is normally done *without* replacement. 

It looks to me that a similar analysis could be done with vegan::specaccum function. However, that uses sampling without replacement.

About your specific questions: you can use quantile() function in base R to get desired confidence intervals. The CIs should be given as argument probs to quantile(). For quantile function you should return a vector of richness values instead of a table. You can get similar with table output as well, but you may need to write that yourself.

It is excepted that the CI gets narrower as the subsample size increases. In classic rarefaction sampling without replacement, there is only one "subsample" of the original sample size and therefore there is no variance but you get the observed data. As the subsampled proportion approaches 1, the number of possible samples decreases and so does the variance of subsamples. With replacement this may not happen as some units are there twice or more and some are missing. Subsample of original size with replacement should contain 63.2% of your original units. This also means that because you duplicate (or multiplicate) some sampling units and omit some, you will systematically underestimate richness when you subsample with replacement. This is why we normally use subsampling without replacement. However, the larger subsamples tend to become more similar, in particular with data set like you described. This is necessary and correct. 

This is the most annoying thing in CIs in rarefaction to me. The rarefaction variation *only* describes the randomness of subsampling from a fixed sample. It does not describe the variance of that fixed sample, or the real variance of your observed richness. With real variability I mean the variance you observe if you replicate your sampling in Nature and get completely new, independent samples from the same real community. I am afraid people use those rarefaction CIs and variances as measures of sample variability which is really misleading -- they actually describe only the artifactual variance of subsampling from fixed samples, when these fixed samples are regarded as error-free and to have zero variance of species richness. Using these variances to infer differences in species richness in Nature is wrong and misleading. I have tried to spell out that warning in vegan manual pages, but people seem to ignore those parts of the text. 

cheers, Jari Oksanen
On 28/05/2014, at 20:05 PM, Nicholas J. Negovetich wrote: