Gait Adaptation?

For quite some time I have wondered if the off and on pacing gait these horses travel with means anything. Pacing is when both legs land and rise on the same side, working as a lateral pair, as opposed to the more regular diagonal lifting and landing of the legs. Some information I have discovered offers a hypothesis; they say it is a sign of greater fitness when horses that are not naturally gaited breeds travel this way, even if only in a brief or random frequency. Oldtimers say a “running walk” is the sign of a sturdier horse and is essential for efficient mileage. I don’t know. Two beat, three beat and four beat patterns all occur naturally in horses depending on speed but horses with freedom over uneven terrain exhibit an unusual mixture of them all.