I know this is morbid but

Where do pigeons go when they die?
I don't mean, like, do they go to pigeon purgatory for crappin all over the place and being annoying but like, why don't we see more dead pigeons around?
Pigeons peck rampantly all over New York City, like rats (though MUCH less bothersome, in my opinion) but they don't have the rat-like ability to hide under subway trains or scurry to places I don't even want to think about. Pigeons are out there, doing their business all day, every day and at some point, these lil birdies must get old and die, right?
You see the occasional hit and run pigeon that pecked it's way too far into the crosswalk but why aren't we stepping over pigeons in the streets?
Is there a dead pigeon picker upper that's employed by the city?
Does whole foods scoop them up and market them as locally grown poultry?
Do the other pigeons carry off their dead? with what arms?
Someone, anyone?