Communicating extraterrestrial intelligence (CETI) interaction models based on the Drake equation

The Drake equation has proven fertile ground for speculation about the abundance, or lack thereof, of communicating extraterrestrial intelligences (CETIs) for decades. It has been augmented by subsequent authors to include random variables in order to understand its probabilistic behaviour. However, in most cases, the emergence and lifetime of CETIs are assumed to be independent of each other. In this paper, we will derive several expressions that can demonstrate how CETIs may relate to each other in technological age as well as how the dynamics of the concurrent CETI population change under basic models of interaction, such as the Allee effect. By defining interaction as the change in the expected communication lifetime with respect to the density of CETI in a region of space, we can use models and simulation to understand how the CETI density can promote or inhibit the longevity and overall population of interstellar technological civilizations.