The running is the male scarpering away as quickly as possible after the deed is done, which shows they are not as stupid a bird as commonly thought.
Usually I don't have a problem with promiscuity but pigeons only give it a rest to do two other things: 1) Fight about who's to do it next. 2) Do a passable impression of a flying cow-pat dispenser. They sit on the gable end of my house with their rear ends over the edge and let fly. Where did they get the taste for vindaloo every night? I hate them with a passion - as you may have noticed.
Why do they call them seagulls.........the way they hang around land acting as an early morning alarm clock...........stealing from unaware fish and chip eaters.........they should be called landmuggers...or even landbuggers.