There is a requirement from the studbook keeper at Cobenhavn Zoo, that allows Western Chimpanzee females having 5 babys in their lifetime depending on their parentage. These was made to preserve high genetic diversity.
According to their website info, one of the Edinburgh (western) females has had a lot of offspring (but it doesn't say how many surviving?) So presumbly those in Edinburgh's group that have few or no offspring will be the ones allowed/encouraged to breed.