This is a problem from capture-mark-recapture study. I specify a model where parameters $c$ and $p$ have equal intercept. In MARK, a design matrix would look like

and I would name it as $c=p(.)$.
Extending this model with an individual covariate, a design matrix for $c=p(.)\cdot sp$ would be

I'm trying to rerun this analysis in R using the RMark package.
I have tried the following method, but I can't put my finger on what I'm doing wrong.
tr.models <- function() {
# specify models
c.pequal.dot <- list(formula = ~ 1, share = TRUE)
c.pequal.dot.sp <- list(formula = ~ sp, share = TRUE)
# collect models and run
cml <- create.model.list("Huggins")
tr.result <- mark.wrapper(cml, data = tr.process, ddl = tr.ddl, adjust = FALSE)
return(tr.result)
}
Result of RMark:
model npar AICc DeltaAICc weight Deviance
2 p(~1)c(~sp) 3 1543.523 0.000000 0.99162194 1537.504
1 p(~1)c(~1) 2 1553.070 9.547451 0.00837806 2358.903
The number of parameters in MARK method is 1 and 2, and 2 and 3 in RMark, respectively. Any input on how to use formula specification in RMark to make the design matrix mimic the one from MARK?