[R-sig-eco] question about appropriate model for abundance studies

[Gavin Simpson]

On Sun, 2011-03-27 at 20:18 +0100, Gavin Simpson wrote:
<snip />
> 
> I think you are confusing the error structure with the model or
> systematic structure? Yes, Poisson errors are expected with count
> abundance data, or if there is more dispersion than expected under the
> Poisson, then a negative binomial error might be appropriate or failing
> that ZIP, ZINB or burdle models.

LOL - I meant a "hurdle" model! [If the OP is interested in those, then
they could do a lot worse than look at the pscl package.]

Thanks Roman.

G

> To fit a bell shaped response curve, you need to fit a quadratic
> equation in the response; say no3 + no3^2. The Guassian model of species
> abundance is IIRC correctly specified if a Possion error distribution
> with a log link is specified.
> 
> Say you have species abundances and you wish to model them using a
> Gaussian response model, then in R you could do:
> 
> mod <- glm(abund ~ no3 + I(no3^2), data = dat, family = poisson)
> 
> where `mod` will contain the fitted model, `abund` is the variable with
> the single species counts, `dat` is the data frame containing `abund`
> and `no3`.
> 
> This is fine if you want to use this model to extract the optimum, max
> fitted abundance and tolerance of the response, but if you are just
> interested in the fitting the response curve then using orthogonal
> polynomials should be more computationally robust. 
> 
> You can test whether the bell shaped response is a better fit to a
> sigmoid (monotonic) increasing or decreasing response (say where you
> have only sampled a part of the gradient of relevance to a particular
> species or the gradient space/environment is truncated in some way), by
> comparing the quadratic model with one that includes the no3 term, eg:
> 
> mod2 <- glm(abund ~ no3, data = dat, family = poisson)
> 
> then
> 
> anova(mod2, mod, test = "Chisq").
> 
> HTH
> 
> G

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