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Obviously around land masses or in shallow water where reefs and coral may grow, life is diverse and numerous. But how spread out is sea life in the open ocean (for example, half-way between Hawaii and California) where there is no land mass or shallow depths for hundreds or thousands of miles?

Does life exist in clusters with large swaths of oceanic desert in between or is it relatively homogenously spread?

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    $\begingroup$ You need to consider ocean currents. In a nutrient-rich current, density of life will be (much) higher than outside of it. $\endgroup$
    – Roland
    Commented Oct 26, 2020 at 12:29
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    $\begingroup$ Are you purely interested in distribution across the horizontal plain? If you consider depth in your equation, around 90% of marine life is concentrated in the upper palagic zones, as sunlight can't penetrate much deeper than around 600 meters. $\endgroup$
    – MikeyC
    Commented Oct 26, 2020 at 14:44

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This is sort of a partial answer, but here is a map using chloryphyl density to map the global distribution of marine life. As you would expect, most is clustered around costal regions, but you can also see some pretty distinct zones in open ocean, with more primary production apparently in the northern and southern latitudes. Not sure how much this map projection distorts apparent distances, but it should help give you an idea.

enter image description here

Here's where I found this map.

And here's one of the links they references, which looks to have some more resources to explore.

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