The 6ft (1.83m) rhea, a tall flightless bird native to South America, went missing from a private collection in Carlton-in-Lindrick, Nottinghamshire, on Tuesday and has not been seen since.
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"We are warning local people and particularly those with small children to be on their guard and not to approach the bird, which poses a very real threat to the public due to its size, aggressive nature and the unfamiliar surroundings it could find itself in," said Inspector Paul Peatfield of Nottinghamshire police.
However, bird experts have said the ominous warning might be over-egged.
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"It's a bird that will peg it (run away) as soon as it sees you ... it's been very overrated in terms of the dangerous aspect of it," David Lindo, a broadcaster and writer about birds, told the BBC.
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