What to make of the Earth's curiously intermediate land fraction?

Abstract

Approximately two-thirds of the Earth, the only known inhabited planet, is covered in ocean. Why not 0.01% or 99.99%? It has been previously suggested that this may represent a certain degree of fine-tuning, and thus perhaps observers are a-priori more likely to develop on those rare worlds with nearly equal land-ocean ratios, such as our own. In this work, we take the single datum of the Earth and then use Bayesian inference to compare four models for the probability distribution of a planet becoming inhabited by observers as a function of land-fraction, $f$, which we classify as i) land-centric ii) ocean-centric iii) equi-centric and iv) indifference. We find that no model is strongly favoured over the others, but that 1) the land-centric model is disfavoured over all others, and, 2) the equi-centric model is favoured over all competitors. Further, we show that more extreme models with heavy tail-weighting are strongly disfavoured even when conditioned upon the Earth alone. For example, a land-centric model where the median planet has $f=0.82$ (or greater) is in strong tension with our existence. Finally, we consider the potential addition of more data via Mars or exoplanets. Should paleo-Mars have once harboured life and had $f<0.20$, then this would strongly favour the ocean-centric model for life, over a land-centric hypothesis. We show that strong evidence for/against the equi-centric model versus its competitors would likely require at least a dozen inhabited exoplanets, offering a well-motivated sample size for future experiments.