You are correct, there is no discussion of the APM, either as ADFM or DTLM theories. This is because they are unproven theories, first described in 1866 and largely reported in common literature though frequently challenged scientifically. Recent research on European Starlings has suggested that for this species at least the theory is false. See “Experimental Analysis of Perching in the European Starling” by Galton and Shepherd 2012. Earlier research has also failed to find any automatic mechanism in other species such as Rock Doves and American Crows. That said, I will try and add something on how birds sleep in the future.