It's not really tragedy of the commons, as there's no commons in play here, just a resource that a hunter-gatherer style group stumbles upon, then utilises, then moves on. Unlike human populations that destroy shared resources fully cognisant that they're doing themselves and their society future harm, it's not clear that birds or other animals conceive of time (in the planning or scheduling sense) the same way we do.

I do a bit of 'pottering on the land', and the inability to negotiate with animals is truly frustrating, as the damage done is objectively greater than the apparent benefit obtained (as per the wasted green fruit in TFA). Killing is undesirable, deterrents are often ineffective (incomplete, degrade over time) -- I'm drawn to the conclusion growing things in large cages is the most effective and humane way, though it's also the most expensive.