[R-sig-eco] parametric estimators for species richness in R

[Paulo Prado]

Dear Wenjing, 

Jari showed clearly that in doing modelling you always take assumptions, and
the key here is to be aware of them. I would add that 

> From this I gather that you may want to fit a regression on species
> accumulation against number of individuals or sampling units. 
1 - The usual algorithms to construct species-accumulation curves pick
randomly individuals from your sample to compose subsamples and then count
the species in these subsamples. Hence, the resulting data (to which you
will fit your model), is the expected richness for a given sample size if
sampling is random, or that the individuals are randonly and independently
dispersed.

>Some of these non-linear regression models may have a parameter that can be
> interpreted as the asymptotic (total, extrapolated) number of species. If
> this is the case, you can either directly use nonlinear regression models
> (function nls) which has inbuilt selfStart models for some cases, like
> Michaelis-Menten (SSmicmen). See appropriate help pages ?nls, ?selfStart,
> ?SSmicmen. 

2 - If you use nls to fit nonlinear models you are assuming that species
richness is a normal variate, which can be a good approximation if expected
species richness is high at all subsample sizes. If not, a Poisson model
(with glm or direct construction of your likelhood function, see the great
book on modelling in R by Ben Bolker) can be a better choice. I did not
check the new vegan functions that Jari mentioned, but if they fit some kind
of parametric model, an assumption on the underlying probability
distribution is certainly made.

3 - Fisher's alpha is also a parametric index, widely used and with a clear
biological meaning. If Fisher's logseries fit well to your data, you can try
it too.

Best wishes

Paulo 

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