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The aerial hunting behaviours of birds are strongly influenced by flight morphology and ecology, but little is known of how this relates to the behavioural algorithms guiding flight. Here, we used GPS loggers to record the attack trajectories of captive-bred gyrfalcons ( Falco rusticolus ) during their maiden flights against robotic aerial targets, which we compared with existing flight data from peregrine falcons ( Falco peregrinus ). The attack trajectories of both species were well modelled by a proportional navigation (PN) guidance law, which commands turning in proportion to the angular rate of the line-of-sight to target, at a guidance gain N However, naive gyrfalcons operate at significantly lower values of N than peregrine falcons, producing slower turning and a longer path to intercept. Gyrfalcons are less manoeuvrable than peregrine falcons, but physical constraint is insufficient to explain the lower values of N we found, which may reflect either the inexperience of the individual birds or ecological adaptation at the species level. For example, low values of N promote the tail-chasing behaviour that is typical of wild gyrfalcons and which apparently serves to tire their prey in a prolonged high-speed pursuit. Likewise, during close pursuit of typical fast evasive prey, PN will be less prone to being thrown off by erratic target manoeuvres at low guidance gain. The fact that low-gain PN successfully models the maiden attack flights of gyrfalcons suggests that this behavioural algorithm is embedded in a guidance pathway ancestral to the clade containing gyrfalcons and peregrine falcons, though perhaps with much deeper evolutionary origins., Competing Interests: Competing interestsC.H.B., K.E.C. and G.K.T. declare no competing interests. N.C.F. is CEO of Wingbeat Ltd, which supplied and piloted the Roprey in this study., (© 2021. Published by The Company of Biologists Ltd.)