General aviation pilot reported a traffic conflict with another aircraft in the traffic pattern at AVQ; a non-towered airport. The pilot identified the other aircraft closely behind on the downwind and maneuvered to increase the separation and landed.

Narrative

I was conducting pattern work at the airport. After a full stop taxi back; I lined up in front of Aircraft Y at the threshold of runway 12; who was still conducting their run up. I took off on runway 12. While still in the upwind; I heard Aircraft Y announce their takeoff on runway 12. Immediately following; another aircraft announced they were taking off on runway 21 and that the departing traffic would not be a factor. Shortly after; I made my left crosswind turn and announced my position. I looked back and couldn't see Aircraft Y; but I could see the aircraft on 21 accelerating down the crosswind runway. I assumed Aircraft Y was somewhere in the upwind behind me but was blending in with the terrain. I checked ForeFlight on my iPad on the panel and saw a red aircraft in the upwind. I made my downwind turn and call before looking for Aircraft Y and made visual contact. They were slightly lower at my 9 o'clock. The pilot announced their crosswind turn. At midfield in the downwind; I checked ForeFlight and noticed Aircraft Y was closer than was customary and I did not recall hearing a downwind radio call from them. As I reached abeam the numbers I saw Aircraft Y was getting very close and ForeFlight reported he was 100 ft above me. Aircraft Y announced they were departing the pattern from the downwind and that they had Aircraft Z in sight. Aircraft Z was over I-10 about three miles from the airport. I began my descent and knew that would only cause Aircraft Y to increase their close rate. Once I was established in the descent; I looked through the back windows and saw Aircraft Y and was alarmed at how close they were. I immediately made my base turn and my base turn call. I made a second call stating 'that was too close in the downwind.' Aircraft Y did not respond; but Aircraft Z pilot responded; 'I thought you were a flight of two.' My landing proceeded uneventfully. I believe the primary factors in the incident were the other pilot's failure to maintain situational awareness in the traffic pattern. Other aircraft conducting non-standard procedures made the situation more confusing than is customary. This lack of awareness caused the other pilot to fail to maintain appropriate distancing; requiring me to take evasive maneuvers.