[R] nlme model

[Daniel O'Shea]

I am having trouble figuring out the right form for the nlme arguments.  I do have examples in Modern and Applied Statistics with S and from other sources, but I still can't figure it out. 

I am trying to estimate species richness (sr) in streams across minnesota.  My predictor variables are depth (d), habitat diversity (habdiv), drainage area (da) and an indicator variable representing the watershed/basins that the streams are in (bas: there are 10 watersheds).  The variable explaining the greatest amount of variation appears to be da.  I have used a log(da) to linearize the relationship, but an asymptotic relationship is more appropriate. I have used nls:

B<-c(.007,1,3,2,2,2,2,2,2,2,2,2,.05,.001,.8)
st<-list(ad=B[1],ahabdiv=B[2],abas=B[3:12],b=B[13],c=B[14],z=B[15])
modnls.a<-nls(sr~ad*log(d)+ahabdiv*habdiv+abas[bas]+(b/(c+(da^-z))),
    start=st,trace=T)

I next used a random slope and intercept model using lmer from the package (lme4). 

modlme<-lmer(y~d+habdiv+log(da)+(log(da)|bas),method='ML')

What I would like to do is use a similar model to the modlme, but use (b/(c+(da^-z))) instead of log(da).  Keeping d and habdiv as fixed effects and the sr-da relationship for each basin as a random effect.  For the life of me I can not figure out the proper form of nlme.  Any help would be greatly appreciated.  

Fsr<-function(da,b,c,z){b/(c+(da^-z}
modnlme<-nlme(sr~d+habdiv+Fsr(da,b,c,z),
    fixed=,
    random=,
    start=)