This story, which inspired Herman Melville's Moby Dick, has always troubled me. I have heard of modern day survival stories where castaways survived much longer out at sea by fishing, and hunting birds. I understand that fresh water was also a concern, but instead of cannibalizing their crew, why didn't they turn to hunting and fishing more?
Of all the misfortunes suffered by the crew of the Essex, the precise spot in the Pacific where the ship was attacked and sank may have been some of the worst (aside from being nearly killed by an angry whale, of course).
Start by looking at a map showing where the various whaleboats sailed/drifted after the Essex was destroyed. If you're interested in their plight, you might as well find a copy of Nathaniel Philbrick's In the Heart of the Sea, which is a great chronicle of the voyage. But Philbrick explains that this particular spot in the ocean was "notoriously sterile," so much so that 19th century cartographer and pioneering oceanographer Matthew Fontaine Maury called it "the desolate region."
Except for flying fish, gooseneck barnacles would be the only marine life the Essex crew would manage to harvest from the open ocean. Indeed, these twenty whalemen were singularly unsuccessful in catching the fish that castaways normally depend on for survival. Part of the problem was that their search for the band of variable winds had taken them into a notoriously sterile region of the Pacific.
For an ocean to support life, it must contain the nutrients necessary for the production of phytoplankton, the organism at the base of the ocean’s food chain. These nutrients come from two places: the land, through rivers and streams, and from the organic material on the ocean floor. The region into which the Essex crew had now ventured was so far removed from South America that the only source of nutrients was at the bottom of the sea.
Cold water is denser than warm water, and when the surface waters of the ocean cool in the winter months, they are replaced by the warmer water underneath, creating a mixing action that brings the nutrient-rich waters at the bottom up to the surface. In the subtropical region, however, the temperature is fairly constant throughout the year. As a result, the ocean remains permanently divided into a warm upper layer and a cold lower layer, effectively sealing off the bottom nutrients from the surface.
Over the next few decades seamen became well aware that the waters in this portion of the Pacific were almost devoid of fish and birds. In the middle of the nineteenth century Matthew Fontaine Maury compiled a definitive set of wind and current charts based largely on information provided by whalemen. In his chart of the Pacific is a vast oval-shaped area, stretching from the lower portion of the Offshore Ground to the southern tip of Chile, called the “Desolate Region.” Here, Maury indicates, “[m]ariners report few signs of life in sea or air.” The three Essex whaleboats were now in the heart of the Desolate Region.
Maury describes it in similar terms in his book The Physical Geography of the Sea, and Its Meteorology:
Between Humboldt's Current and the great equatorial flow, there is an area marked as the "desolate region." It was observed that this part of the ocean was rarely visited by the whale, either sperm or right; why, it did not appear; but observations asserted the fact. Formerly, this part of the ocean was seldom whitened by the sails of a ship, or enlivened by the presence of man. Neither the industrial pursuits of the sea nor the highways of commerce called him into it. Now and then a roving cruiser or an enterprising whale-man passed that way; but to all else it was an unfrequented part of the ocean, and so remained until the gold-fields of Australia and the guano islands of Peru made it a thoroughfare. All vessels bound from Australia to South America now pass through it, and in the journals of some of them it is described as a region almost void of the signs of life in both sea and air. In the South Pacific Ocean especially, where there is such a wide expanse of water, sea-birds often exhibit a companionship with a vessel, and will follow and keep company with it through storm and calm for weeks together. Even those kinds, as the albatross and Cape pigeon, that delight in the stormy regions of Cape Horn and the inhospitable climates of the Antarctic regions, not unfrequently accompany vessels into the perpetual summer of the tropics. The sea-birds that join the ship as she clears Australia will, it is said, follow her to this region, and then disappear. Even the chirp of the stormy-petrel ceases to be heard here, and the sea itself is said to be singularly barren of life.
The crew did eventually run into Henderson Island, where they found birds to eat and fresh water to drink for a time. But they quickly ran through the island's supply and most of them – realizing that the island couldn't sustain them for much longer – set off again. (Three men stayed and were rescued after nearly a year). But Henderson was an anomaly in the area, where the food chain was such that its peculiar ecosystem, or lack thereof, was devoid of nutrients for the phytoplankton, no phytoplankton for the fish, and no fish for the birds.
References:
Maury, M. F. (1855). The physical geography of the sea. Sampson, Low, Son & Co.
Conerly, J. (2019, March 8). This disastrous shipwreck forced survivors into cannibalism and inspired the tale of moby dick. Historycollection.Com. https://historycollection.com/this-disastrous-shipwreck-forced-survivors-into-cannibalism-and-inspired-the-tale-of-moby-dick/
Philbrick, N. (2000). In the heart of the sea: The tragedy of the whaleship Essex. Penguin.