In the real world, prey animals reproduce rapidly because they're constantly being eaten by predators. But Zootopia's whole premise is that such savagery is a thing of the past -- prey animals face no more danger than the average American. Some will die prematurely of disease and accidents, but it will be a statistically insignificant number in the grand scheme of things. Furthermore, Zootopia's animals have human lifespans. Judy's in her early 20s, while her parents are middle-aged. We see lemmings running a bank and a shrew running a criminal empire, neither of which could be accomplished with their natural two-year lifespans. All animals in Zootopia, regardless of their species, have a life expectancy no different than yours. Well, in 2013, the United States had about 2.6 million deaths, giving the country a sustainable ratio of 1.5 births per death. In Zootopia, human death rates combined with animal birth rates produce a ratio that's laughably unsustainable.
It gets worse. Judy's hometown of Bunnyburrow, despite being 81 million strong, is considered a backwater Podunk. Zootopia's co-director called it the Yonkers to Zootopia's New York City. Well, NYC has 42.6 times the population of Yonkers, so Zootopia's population is implicitly just shy of 3.5 billion -- 3,469,165,080, to be exact. Are they all reproducing at their respective species' natural rates? It seems like they're instinctively driven to, if Judy's parents are any indication.
Zootopia has lots of predators, who reproduce conservatively, but we also see scores of prey, who mate at a pretty healthy clip -- lemmings, mice, shrew, deer. Even if these are career deer and mice who keep their reproduction rate down relative to the boonies, a single litter of, say, lemmings, produces an average of seven babies. With no predators to eat some of them, it won't take long for Zootopia's population to careen out of control, even if most animals show relative restraint. Especially since, while the animals have developed human lifespans, they've kept their original pregnancy cycles. Judy's mom simply couldn't have pumped out 275 kids if each one took nine months, and we see Fru Fru, a shrew, go from her wedding night to heavily pregnant in a matter of days.
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Animals also still have their original nutritional requirements. We see itty-bitty plates of food at Fru Fru's wedding, while Judy and Nick meet in an ice cream parlor serving giant portions to elephants. At first, that makes Zootopia appear sustainable -- the animals with humble dietary requirements vastly outnumber the heavy eaters. But Australia once had a rabbit population of 10 billion, and this was the result: