The route history, that is, how the Greater Dayton RTA came to be, is quite complicated. Five separate horsecar and streetcar operating companies, along with nine interurban lines paved the way for the Rather than try to explain it with words, see the graphic below to get an idea of where and when the various street railway companies, starting with horsecars, progressing to streetcars, and then trolleybuses, came to be. At some future point, I'll update this with the various interurban lines.
The following links give an idea of how the streetcar system, route by route, changed to trolley coach, and then how several of the trolley coach lines became diesel
Dayton ETB Route History until 1947
Dayton ETB Route History after 1947