Ludicrous Theoretical Diverspace of the Marine Biosphere: Could Oceans Hide a Mole of Species?

In unraveling the geological history of biodiversity, paleontologists have focused on empirical approaches aimed at quantifying the fossil record of diversity. While process-oriented hypotheses have been proposed, they typically represent inductive, a posteriori explanations of empirically-derived diversity curves. But can we infer from first principles what the upper and lower bounds of global biodiversity ("Theoretical Diverspace") should be? Although such exercises require empirical parameterization, they can estimate theoretical biodiversity and offer a comparative baseline for assessing diversity levels actually experienced by our planet through time. Here, we present a first step toward estimating the maximum Theoretical Diverspace of the Earth's marine biosphere.

The largest possible diversity can be achieved by assuming (1) the smallest possible species body-size (3.3*10^-23 m³); (2) population size of one individual per species; and (3) 0% apartment vacancy rate in oceans (i.e., ocean water is packed with taxonomically unique specimens representing bacteria-size species). These estimates yield an absurdly high upper bound for the marine biosphere of 2.9*10⁴⁰ species, which exceeds by 32 orders of magnitude the highest guesstimates for global biodiversity today. This scenario is also grossly incompatible with the stratigraphic record in a number of obvious ways.

If more reasonable estimates are used for the minimum size of preservable (biomineralized) organisms (7.2*10^-15 m³), minimum viable population size (10⁶ individuals) and the fraction of ocean volume occupied (0.5%), the resulting Theoretical Diverspace (6.6*10²³ species) approximates Avogadro's number and still exceeds the highest biodiversity estimates by 15 orders of magnitude. This discrepancy may mean that the neontological and paleontological diversity levels have been both severely underestimated or that the global biosphere is extremely undersaturated in terms of diversity. Alternatively, it is conceivable that our approach brutally overestimates the upper bound of Theoretical Diverspace and that more sophisticated parameterizations are required.