Oh, ok. I thought the blobs died each generation. A shrinking population. Instead they go into nursing homes. A growing population which stabilizes once everyone is geriatric.

Got it. Wei pretty clearly has the solution. Negative Binomial distribution

The negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of Bernoulli trials before a specified (non-random) number r of failures occurs.

Pretty damned obvious, actually, that (P-N) is distributed as a negative binomial where r is set to N; failure = failure to reproduce; success = birth.