There is no pure math in this space - just hand-waving and conjecture.
We have exactly no information about xeno-evolution. It's not even a given that aliens would be motivated to colonise the galaxy, or that they'd do it in a way that would be recognisable to us.
It's hard enough to predict where human civilisation is going to be fifty years from now. The idea that we have any clue what an alien civilisation will do over millions of years is... unconvincing.
We have exactly no information about xeno-evolution. It's not even a given that aliens would be motivated to colonise the galaxy, or that they'd do it in a way that would be recognisable to us.
It's hard enough to predict where human civilisation is going to be fifty years from now. The idea that we have any clue what an alien civilisation will do over millions of years is... unconvincing.