Secrets of Bat Machismo
magazine, May 2006, p. 17: A species of bat has been discovered with very large testicles and very small brains. This is explained as follows: "Testicles are almost always bigger in animals species in which females mate with multiple partners.... When females are promiscuous, the sperm of different males must compete to fertilize each egg. Because males with more sperm have a better chance of producing offspring, the frequency of large testicles in those species increases. The pattern holds among all animals, including primates. Gorillas, who keep their harem close, have small testicles, while libertine chimpanzees have large ones. Those of humans, whose mating habits fall in between, are midsize."
The connection to brain size is that both a large brain and large testicles take a lot of metabolic resources. So we would expect that bats that need big testicles to gain an advantage in reproducing would have smaller brains to compensate.
Evidence was collected for 334 bat species. "In species with unfaithful females, males invest almost five times as much in testicles and 27 percent less in brains."