The video was captured by Captain Dave's Dolphin and Whale Watching Safari and has garnered thousands of views.
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The crew said as the boat approached the whale, the newborn calf came up to the surface and started learning how to swim as it bonded with its mother.
"For a minute, many of us thought it may be a shark or predatory event. But no, instead of the end of life, it was the beginning of a new one!" read the video's caption on YouTube.
The whale watching group said gray whales prefer to give birth in the warm and protected lagoons of Baja California, Mexico.
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The lagoons offer safety from predators like orcas, as well as warm water for calves.
Editor's note: This report was originally published in January 2023.