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Large grasslands are good for raptors, especially in September. At the one I work at in Massachusetts, I've seen merlins, kestrels, peregrines, ospreys, Cooper's, red-shoulders, and red-tails all in a single day. And they all seem to hate each other.
Yesterday I saw a peregrine and a Cooper's hawk terrorizing a pair of harriers, which seemed slow and cumbersome in comparison. And they weren't just chasing, but actually making full-speed, talons-forward attacks. The harriers would roll over, talons up, to defend themselves - a common response of larger birds in response to such pestering. But mostly they just seemed to want to be left alone.
It could be a between-species competition thing...or maybe a small bird, large bird thing. But I don't think so. A few years ago (same site, same time of year), I saw a harrier and a peregrine working together, relentlessly attacking a second, perched peregrine (see photos).
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It could be a between-individual competition thing. I'd say it probably is most of the time. A crowded field of hawks, hungry and cranky from migration.
But, intriguingly, it also could be cannibalism of a sort. A common site around the grasslands is merlins (notoriously cranky, even for raptors) swiftly pursuing kestrels in the same "I-want-to-kill-you" way. I've never seen one caught yet, but if I do I won't be surprised.
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Harrier wins.