How fast can a bird search a tree?

I was wondering if you could help me figure something out: what is the algorithmic complexity of a bird searching a tree for food?
Over the years I've had the pleasure of watching a lot of cute little birds feed in our oak trees. I've noticed they have a search pattern.
A bird will hop from branch to branch looking for insects. They don't hop on a branch and explore every square inch of it, so it's not an exhaustive search. They'll take a couple hops, peck at a branch a few times, and hop to a nearby branch. Birds also search the underside of branches, so the whole surface area of a tree is game.
I've often marveled in wonder at how efficient this whole process is. They scour huge trees in no time. Then they'll move on to the next tree and repeat the process until they fly away to a completely different area.
My dog when searching for a ball seems to follow a similar Lévy flight sort of pattern. Search a local area by bouncing around for bit and then take a bee-line for a completely different area and repeat the process.
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