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As laboratory animal
Pigs were used for a variety of experiments, likely due to their prevalence and biological features similar to humans. In the 1930s, the Cult of Skaro turned the less intelligent people they captured into pig slaves, humanoids with pig-like features, to work for them. (TV: Daleks in Manhattan/Evolution of the Daleks)
In 2006, a pig was augmented into a bipedal creature by the Slitheen family as part of an alien invader hoax. It was then planted in a ship to act as a diversion from the family. (TV: Aliens of London)
Pork was a popular foodstuff on Earth, eaten by humans and other predators. It was also eaten by the Doctor. His second self once chose pork when confronted by a food machine on a rocket. (TV: The Wheel in Space) A pig's head with an apple in its mouth was one of the foods served to the sons of Grekk. (PROSE: The Sons of Grekk)
Cultural references to pigs
English speakers sometimes used the phrase "when pigs fly" to indicate the certain impossibility of a thing. However, the Eleventh Doctor once declared that a number of planets were home to a variety of pig that could fly. (COMIC: The Only Good Dalek)