The Butterfly Effect was a theory that a butterfly could flap its wings in one place and greatly affect events in another place. This was a concern in time travel that travelling to the past and crushing a butterfly could drastically change the future.
The Seventh Doctor contemplated a butterfly flapping its wings in Mettula Orionis as having great consequences elsewhere in the universe (NA: Transit). The Eighth Doctor confused the theory, mentioning how a bat flaps its wing and causes a tropical storm. (BFA: Invaders from Mars)