[R-sig-eco] ZINB or density data models with lots of zeros

[tavery]

I have completed zero-inflation negative binomial (ZINB) models on count 
data for the absolute counts of ectoparasites on fish where there are 
lots of zeros (everything worked well using Zuur et al. and a host of 
other sources). The fish are of different sizes with corresponding 
differences in surface areas of fins etc. and I would now like to 
compare density of parasites among each area. Densities were calculated 
by dividing the counts for each parasite by the surface area of the fin 
(etc.) and surface areas were different for each individual i.e. scaled 
for size of fish.

The comparisons are then of non-integer values that do not play nice 
with Poisson or Negative Binomial models. However, the issue of having 
lots of zeros remains and will affect mean values if I were to use some 
sort of ANOVA based analysis.

Does anyone have any suggestions on how to deal with the many zeros for 
the density data (assuming I was to use an ANOVA type analysis)? I have 
also thought to just include fish size as a covariate in the ZINB 
models, but a) have not seen an example of such, b) do not want to over 
complicate the analysis, and/or c) this will only scale the counts to 
overall fish size, not to fin etc. surface areas. Of course, fin surface 
areas probably scale linearly and, if so, body size might be an 
appropriate covariate to remove the effect from the ZINB comparisons of 
counts on fins i.e. essentially the same comparison (density = ZINB with 
fish size covariate). Does that make sense?

This ZINB model works well (yes, the 'false' zeros are independent of 
factors hence the "| 1"). Where would I insert the fish size covariate?
location_on_body = where parasites were found (7 body areas)
location = site of fish capture (2 sites)

zinb2<-zeroinfl(caligus_elongatus~location_on_body+location | 1, 
dist="negbin", link="logit", data=sturg)

I would assume this:

zinb2<-zeroinfl(caligus_elongatus~fish_size+location_on_body+location | 
1, dist="negbin", link="logit", data=sturg)

thanks in advance,
trevor