My first post to this list- please forgive any convention missteps :)
Comparing species abundance distribution models (SADs), I am trying to reconstruct expected abundances for each rank, for the SAD models that I compared the fits of using radfit in vegan.
I have the ML parameter estimates from the radfit output, but have questions about the parameter estimates for the lognormal and zipf-mandelbrot models.
For the lognormal- where expected abundance at rank r " a[r] = exp(log(mu) + log(sigma) * N), where N is a Normal deviate", the entries in the table for parameters are mu and sigma, according to the document "Vegan: ecological diversity", and I figure these are mu=mean of the log(abundance) and sigma of same.  If I use the parameters directly in the table (which in this case are 1.2867 and 1.7127), with the above formula, as a[1] = exp(log(1.2867) + (log(1.7127))*(1.875, an appropriate normal deviate here), I get an expected abundance that is by far too small.  If instead I use a[1] = exp(1.2867+(1.7127*1.875)) I get a value that makes sense, and is in the ballpark of the expected first-rank abundances from other models.  Should I then take that a[r] = exp(mu+(sigma*N)), as mu and sigma are of log(abundances)?
For the Zipf-Mandelbrot, I have parameter estimates of 1.7837, -1.8897, and 1.456, which should be c, beta, and gamma.  If expected abundances are a[r] = J*c*(r+beta)^gamma, and J=438, the values are increasing across ranks, rather than decreasing, and are in the tens of thousands, which is not sensible.  But the model did not fail, and the fit is not bad, and on the radfit plot output it looks good.  Where am I going wrong here?
Thank you very much for any help,
Dan

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