1. Resources on the initial planet
2. The will to create a daughter civilization
3. Interstellar space travel
4. Planetary conditions on the target planet
5. Raw materials on the target planet
6. Environmental conditions on the target planet
7. Technology to keep at least 10000 living beings alive
8. Organization to manage such a community of life

Daughter civilizations depend on v conditions.
I.e. they form the set V of civilization prerequisites for daughter civilizations.

Then each element contributes to the overall probability. A differentiation of the individual parts is still obtained by weighting the individual elements.
The total probability of establishing a subsidiary civilization is then the sum of the weighted individual probabilities.

17.3.1 Equation

An expansion rate for civilizations can thus be defined:

Then the overall probability for a daughter civilization can be converted into an expansion rate for civilizations as follows:

This results in the number of daughter civilizations in a period of T

That goes for one civilization. Now the sum of all old civilizations has to be made to get the total number of daughter civilizations in the galaxy.

Then is the total number of daughter civilizations in the galaxy within the time span T

17.3.6 Equation

A simple rough calculation can be made. According to Theorem 15.3.5, up to 14 ancient civilizations could exist in the galaxy. If each produces 1 to 2 daughter civilizations per century, that is a maximum of 30 colonies per century. After 1000 years there are about 300 daughter civilizations and that is exactly as many civilizations as there are already. (According to Theorem 15.3.2 there are 336 technological civilizations).

An old civilization that forms expansive daugther civilizations would, after a few thousand years, have populated larger parts of the galaxy, with at least one hundred planetary systems.

If a civilization has a long history of interstellar spaceflight, it is quite possible that it will go all the way into space. It can therefore be taken into account that extraterrestrial civilizations exist that prefer life in space, on their generational spaceships or flying cities or the like on planets. So also create additional homes

Civilizations that are technologically advanced enough could not only colonize planets similar to the home planet, but could also do geoengineering or terraforming. So make planets fit.

All in all, old civilizations have a multitude of dispersal possibilities. According to Theorem 15.3.4, 82 space travelling civilizations are added to their larger areas. Therefore, most of the space in the galaxy is likely already occupied. On the basis of the data in this book, a rough estimate can be made.

According to Theorem 15.1.2, between 5,748 and 9,642 uninhabited, but animate earth-like planets could exist in the galaxy. Thus rounded 5000 to 10,000. The mean distance of these systems to each other then amounts to 1360-1700 light years.

According to Theorem 15.3.5, up to 14 ancient civilizations could exist in the galaxy. If each of them has founded 100 daughter civilizations, that is already 1400 systems. In addition, according to Theorem 15.3.4, there are 82 spacefaring civilizations. Makes a total of 1500 inhabited star systems rounded. Then each system has a latitude or terretorium of 2560 light years.
Our terretorium would therefore only contain one uninhabited planet similar to Earth. I.e. for larger expansion plans of mankind in the galaxy it will not be easy or not possible at all, because in worst case too little free space is available.

A consequence of this galactic civilisational situation is that something like a galactic order must exist in which each species at least recognises the space of another species. As in any association, individual parties will have formed here as well. They act with each other or against each other.
As galactic freshmen, we don't know which interest group an alien belongs to. Therefore, future encounters (e.g. of the third kind) should be made with caution. You never know who you're dealing with. For reasons of self-preservation alone, we should be suspicious of alien civilizations.