Dear all,

I have a question regarding the use of multi-model inference (specifically using the MuMIn package), based upon GAM models with an overdispersed poisson error structure. Briefly, I am interested in modelling the drivers of long-term change in populations of a lake zooplankton species ("Daph" below). In these models I need to capture the seasonal pattern of variation in "Daph" abundance before looking for long-term (among year) change, hence the smoother by day of year in the model below. I have then included a number of predictors (in the model below named "DAPHGlag_res", "Temp_res", "Chla_res", "PredThere", "FishNum_res"). While I figure that the identities of these variable are not relevant to the forum, I should say that each predictor is actually the residual variation in a particular variable, after using a GAM to "remove" the seasonal structure inherent in the data. Each predictor is allowed to interact with season, as the importance of different drivers may differ throughout the year. I also use a weighting function to down weight some rows of data (again I think this is probably not too relevant here). What I want to do is to find support for each predictor, using a multi-model approach.

My full/global model is:

Daph1<-gam(Daph~s(dayofyear,bs="cc")+Season+DAPHGlag_res+Temp_res+Chla_res+PredThere+FishNum_res+
           Season:Temp_res+Season:Chla_res+Season:PredThere+Season:FishNum_res,family=poisson(link="log"),weights=wts,data=zoodat)

This model is overdispersed; the dispersion parameter is approximately 18.8

I can extract a QAIC value for this model:

QAIC(Daph1,chat=(deviance(Daph1) / df.residual(Daph1)))

However, I'm wondering about the correct syntax for running dredge in MuMIn. Should I run the command as below, with the global model as a poisson (albeit overdispersed) model, but using the dispersion parameter extracted for this fit in conjunction with QAIC?

dredge.test<-dredge(global.model=Daph1,fixed=~s(as.numeric(DOY),bs="cc")+Season+DAPHGlag_res,eval=T,rank="QAIC",chat=(deviance(Daph1)/df.residual(Daph1)))

Or, should I directly fit a quasipoisson model, and treat this as the global model?

Any help would be much appreciated, I have not combined MuMIn and overdispersed models before!

Many thanks in advance

Steve Thackeray

Dr Stephen  Thackeray
Lake Ecosystem Group
Centre for Ecology and Hydrology
Lancaster Environment Centre
Library Avenue
Bailrigg
Lancaster
LA1 4AP
sjtr@ceh.ac.uk<mailto:sjtr@ceh.ac.uk>



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