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

David Kipping

TL;DR

This work uses Bayesian model comparison to test whether life's emergence on planets correlates with land fraction, comparing land-centric, ocean-centric, equi-centric, and indifferent observer models using Earth's $f=0.292$ as a single datum. With a noninformative prior on $f$, it derives analytical posteriors for each model and computes Bayes factors, finding no strong preference among models but a consistent tilt toward the equi-centric model and rejection of extreme heavy-tailed biases. The analysis also shows that adding a second datum (e.g., paleo-Mars) or a sample of exoplanets could dramatically alter model support, potentially favoring ocean-centric or equi-centric explanations if the additional data suggest different $f$ values. The results inform the Rare Earth debate and guide future observational strategies for testing how habitability relates to land-ocean partitioning, highlighting the need for more inhabited-world data to resolve which bias, if any, governs observer emergence.

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.

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

TL;DR

This work uses Bayesian model comparison to test whether life's emergence on planets correlates with land fraction, comparing land-centric, ocean-centric, equi-centric, and indifferent observer models using Earth's as a single datum. With a noninformative prior on , it derives analytical posteriors for each model and computes Bayes factors, finding no strong preference among models but a consistent tilt toward the equi-centric model and rejection of extreme heavy-tailed biases. The analysis also shows that adding a second datum (e.g., paleo-Mars) or a sample of exoplanets could dramatically alter model support, potentially favoring ocean-centric or equi-centric explanations if the additional data suggest different values. The results inform the Rare Earth debate and guide future observational strategies for testing how habitability relates to land-ocean partitioning, highlighting the need for more inhabited-world data to resolve which bias, if any, governs observer emergence.

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, , 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 (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 , 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.
Paper Structure (20 sections, 11 equations, 1 figure, 5 tables)

This paper contains 20 sections, 11 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. Comparing Simple Models
  3. Deriving Posterior Probabilities
  4. Prior on $f$
  5. Model L: The Land-Centric Likelihood
  6. Model O: The Ocean-Centric Likelihood
  7. Model E: The Equi-Centric Likelihood
  8. Model I: The Indifferent Likelihood
  9. Bayes Factors
  10. Critical $f$ Values
  11. Extreme Models Rejected by the Earth
  12. More Extreme Models
  13. Excluded Values of $n$
  14. Another Data Point
  15. Another Earth Example
  16. ...and 5 more sections

Figures (1)

  • Figure 1: Comparison of the posteriors (solid lines) from our four different fiducial models, labeled inset. The dashed-lines represent the likelihood functions of each, and the solid grey line is the prior - which is identical to the fourth model of indifference and thus not explicitly shown.