This is a typical problem which should be solved with zero-inflated models (or, if they do not fit well, Hurdle-models), since there are two different processes wich generate your data: A Binomial process regarding the question if there are offspring or not (success/failure). And the second process - the number of offspring - is based on a Poisson distribution (or, if you have overdispersion, also a negative-Binomial distribution can be used). The advantage of zero-inflated models is, that you don't have to artificially split your data into different parts and that it is the "most natural" description of such a process.

I have no experiences with SPSS, in R you could use hurdle() or zeroinfl() from the package pscl.