But little else is known about the two animals, because they live at such great ocean depths.
Both creatures spend much of their lives in the ocean's mesopelagic zone, 650 to 3,300 feet (200 to 1,000 meters) below sea level.
The tagging of the animals was conducted near Santa Rosalia, a coastal Baja California town, in the fall of 2004 by two separate teams of researchers. One group, led by Gilly, tagged three squid, while another group, led by Randall Davis, a professor of marine biology at Texas A&M University, Galveston, tagged five sperm whales.
(Gilly's research was partly funded by the National Geographic Society. National Geographic News is a division of the National Geographic Society.)
The study's findings have helped clear up some longstanding mysteries.
"No one has ever seen a sperm whale feeding, so most of our information on hunting behavior is circumstantial," Davis said. "Nevertheless, our study provides some new insights into how they may capture a very active prey at depth."
During the day the whales and squid spent about 75 percent of their time at depths ranging from 600 to 1,300 feet (180 to 400 meters).
At night, the tagged squid spent at least half of their time above 600 feet (180 meters), most likely following small fish and other prey that migrate toward the surface at night and then return to deeper waters during the day.
Unlike the squid, however, the sperm whales only slightly altered their diving pattern at night, continuing to spend most of their time at lower depths.
"The whales are not diving to eat where the squid are the most abundant," Gilly, of Stanford University, said.
Researchers do know, however, that squid often make rapid nighttime dives from the surface to deeper waters, possibly to recover from spending too much energy in warmer waters or to avoid long exposure to the higher oxygen levels found near the surface.
During their deep nighttime foraging, the squid may be recovering from stress after their recent surface activity and may be more susceptible to predation by sperm whales.
"A stressed-out squid may be an easy target for hungry sperm whales waiting below," Gilly said.
The reaction times of squid may also slow down at low-oxygen levels, making them easier to catch.
Still, just how the whales manage to catch the squid is a mystery. They might sneak up on their prey or perhaps use sonar to catch them, scientists say.
One thing is clear: There's plenty of food for the whales.
Analysis of the tagging data showed that the whales were traveling up to 60 miles (100 kilometers) a day within a relatively small area, suggesting that they easily found an abundant supply of squid to eat.
"We're beginning to realize how many squid there are," Gilly said. "It may be like a cocktail party for the whales down there."
Jumbo squid are the target of a thriving commercial fishery in Baja California and are now found from Chile to Alaska.
"They're incredibly adaptable in diet and can tolerate temperature extremes as well as low oxygen levels," Gilly said.
"It's just an awesome animal and an unbelievably important player in the ecosystem of the eastern Pacific," he added. "Their abundance is a good news story for the oceans."
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