Note: I have not delineated between "full" and "basketball only" members in the graphics, mostly because that would turn them from "visually interesting" to "Oh my God! MY EYES!!!"
Conference USA has probably seen the most large-scale changes to its composition over time, so there's a lot to cover. It started as Cincinnati, DePaul, Louisville, Marquette, Saint Louis, USF, UNC-Charlotte, Southern Miss, UAB, Memphis and Tulane (look familiar?) in 1995, and was also a basketball-only conference.
The next year, Houston joined for all sports, and Tulane, Memphis, Southern Miss, Louisville and Cinci all added football. A year later, ECU joined for football, the next year Army did the same, and the year after that UAB added football. By January of 2000, CUSA was a 12 team basketball conference and a 14 team football conference.
That was only the beginning of the change, though. The next year East Carolina joined for all sports, as did Texas Christian; this made the numbers odd, but this was 2001 when nobody cared nearly as much about that. This was followed by a whopping four years of relative peace, where the only change was South Florida adding a football program in 2003. Then came 2005, and the mass exodus.
Cincinnati, De Paul, Louisville, Marquette and South Florida all departed for the Big East, Saint Louis and Charlotte left for the Atlantic 10, TCU left for the Mountain West, and Army decided to return to being an FBS Independent program (for football). This left the conference with only six programs and in dire need of a membership influx. That's when Conference USA welcomed Central Florida, Southern Methodist, Tulsa, Marshall, Rice and Texas-El Paso into the fold.
This returned them to a nice even 12 members until the Big East dissolution and formation of the American Athletic Conference, which cost them Memphis, Houston, UCF and SMU, but regained them Charlotte as a basketball-only member. They also poached from the Sun Belt, where some planning ahead gained them more members than they lost in the form of Florida Atlantic, Florida International, Middle Tennessee State, Louisiana Tech, North Texas, and Texas-San Antonio, along with Old Dominion as a basketball only member. That planning ahead was wise, since this past offseason saw East Carolina, Tulsa and Tulane depart for The American, with Western Kentucky now joining from the Sun Belt and Old Dominion adding football starting this season - next year Charlotte will do the same.
So follow this chain. The American has 11 current members, nine of whom were members of Conference USA at some point prior to their current affiliation. Additionally, of the 18 teams who can call themselves former members of the Sun Belt Conference, 11 of those are now members of either Conference USA or The American.
So at least in terms of conference affiliation, the borders that delineate these teams are wafer-thin and have been crossed numerous times before, such that really they're all just one, big, happy family.