The first proof that the biggest brains could be the fittest was provided by a study that investigated the influence of brain size in the survival of guppies.

"We have provided the first experimental proof that a large brain offers an evolutionary advantage," explained first author Alexander Kotrschal from the Stockholm University in Sweden.
In this study, the researchers investigated the influence of brain size in survival of guppies, a species of freshwater aquarium fish whose natural range is in the Caribbean region.
They conducted an artificial selection experiment and successfully generated large- and small-brained guppies.
The researchers released 4,800 guppies from these selection lines into large semi-natural streams, which also contained a natural predator.
About half a year later, significantly more guppies with large brains had survived.
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"Our findings support the hypothesis that large brains provide a survival benefit under predation pressure," co-author Dustin Penn from the University of Veterinary Medicine Vienna, Austria.
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Source-Medindia