AIC number of parameter

Dear all, I am new in this forum.

I m facing a problem with my AIC.

I m using model selection framework (Akaike’s weights) with various type of "Abundance-occupancy" model. It is a family of model which uses mean abundance of species to predict the probability of occurrence.

One of these models, called trivariate model, is Oc = 1-(Ab/Var)^(Ab^2/(Var-Ab) [1] with Oc = occupancy, Ab = mean Abundance and Var = Variance of Abundance. As you can see, there is no free parameters in the model, BUT the variance is not the observed variance but the predicted variance from the power model Var = a * Ab ^b [2]. This model was developed to connect these 3 variables (Ab, Var and Oc) and the efficiency of the model was clearly shown (e.g. Gaston at al., 2006, Journal of Animal Ecology).

for the AIC of my Abundance-Occupancy model [1] , I use the Residual sum-of-square and k= the number of parameter (of course)...but for k , I have a uncertainty: basically the number of parameter should be 0 but indirectly, the predicted variance Var was estimated by 2 parameters a and b from the power model [2].

k = 0 or 2 ?? or something else?

Thanks you for your help