A good part of a squirrel’s strength can be traced to its elaborately veined tail, which, among other things, serves as a thermoregulatory device, in winter helping to shunt warm blood toward the squirrel’s core and in summer to wick excess heat off into the air. Rodents like rats and mice are nocturnal and have poor vision, relying on whiskers to navigate their world. The gray squirrel is diurnal and has the keen eyesight to match. “Its primary visual cortex is huge,” said Jon H. Kaas, a comparative neuroscientist at Vanderbilt University, A squirrel’s peripheral vision is as sharp as its focal eyesight, which means it can see what’s above and beside it without moving its head. While its color vision may only be so-so, akin to a person with red-green colorblindness who can tell green and red from other colors but not from each other, a squirrel has the benefit of natural sunglasses, pale yellow lenses that cut down on glare.

Gray squirrels use their sharp, shaded vision to keep an eye on each other. Michael A. Steele of Wilkes University in Pennsylvania and his colleagues have studied the squirrels’ hoarding behavior, which turns out to be remarkably calculated and rococo. Squirrels may be opportunistic feeders, able to make a meal of a discarded cheeseburger, crickets or a baby sparrow if need be, but in the main they are granivores and seed hoarders. They’ll gather acorns and other nuts, assess which are in danger of germinating and using up stored nutrients, remove the offending tree embryos with a few quick slices of their incisors, and then cache the sterilized treasure for later consumption, one seed per inch-deep hole.

But the squirrels don’t just bury an acorn and come back in winter. They bury the seed, dig it up shortly afterward, rebury it elsewhere, dig it up again. “We’ve seen seeds that were recached as many as five times,” said Dr. Steele. The squirrels recache to deter theft, lest another squirrel spied the burial the first X times. Reporting in the journal Animal Behaviour, the Steele team showed that when squirrels are certain that they are being watched, they will actively seek to deceive the would-be thieves. They’ll dig a hole, pretend to push an acorn in, and then cover it over, all the while keeping the prized seed hidden in their mouth. “Deceptive caching involves some pretty serious decision making,” Dr. Steele said. “It meets the criteria of tactical deception, which previously was thought to only occur in primates.”

Squirrels are also master kvetchers, modulating their utterances to convey the nature and severity of their complaint: a moaning “kuk” for mild discomfort, a buzzing sound for more pressing distress, and a short scream for extreme dismay. During the one or two days a year that a female is fertile, she will be chased by every male in the vicinity, all of them hounding her round and round a tree with sneezelike calls, and her on top, refusing to say gesundheit. A squirrel threatened by a serious predator like a cat, dog, hawk or wayward toddler will issue a multimodal alarm, barking out a series of loud chuk-chuk-chuks with a nasally, penetrating “whaa” at the end, while simultaneously performing a tail flag — lifting its fluffy baton high over its head and flicking it back and forth rhythmically.

Sarah R. Partan of Hampshire College in Amherst, Mass., and her students have used a custom-built squirrel robot to track how real squirrels respond to the components of an alarm signal. The robot looks and sounds like a squirrel, its tail moves sort of like a squirrel’s, but because its plastic body is covered in rabbit fur it doesn’t smell like a squirrel. Yet squirrels tested in Florida and New England have responded to the knockoff appropriately, with alarm barks of their own or by running up a tree. Human passers-by have likewise been enchanted. “People are always coming over, asking what we’re doing,” said Dr. Partan. “We’ve had to abandon many trials halfway through.” An iSquirrel? Now that’s something even a New Yorker might love.