At about 6pm on Thursday, Davison killed his mother Maxine Davison, 51, who he shot in a house in the Keyham area of the City in what is believed to be a domestic-related incident.
He left the property on a shooting rampage and shot three-year-old Sophie Martyn and her father Lee Martyn, 43.
The gunman then walked along nearby Biddick Drive where he shot at two local residents, a man aged 33 and a 53-year-old woman, who suffered significant injuries not believed to be life-threatening. The man has been named locally as Ben Parsonage and the woman is reported to be his mother - though her name is not yet known.
Davison - who held a firearms licence - then walked through some nearby woodland, where he shot and killed Stephen Washington, 59. His final victim was Kate Shepherd, 66, who was killed outside a hair salon.
Eye-witnesses told police Davison, who held a firearms licence, then turned the gun on himself.