Bayesian analysis of the astrobiological implications of life's early emergence on Earth

Abstract

Life arose on Earth sometime in the first few hundred million years after the young planet had cooled to the point that it could support water-based organisms on its surface. The early emergence of life on Earth has been taken as evidence that the probability of abiogenesis is high, if starting from young Earth-like conditions. We revisit this argument quantitatively in a bayesian statistical framework. By constructing a simple model of the probability of abiogenesis, we calculate a bayesian estimate of its posterior probability, given the data that life emerged fairly early in Earth's history and that, billions of years later, curious creatures noted this fact and considered its implications. We find that, given only this very limited empirical information, the choice of bayesian prior for the abiogenesis probability parameter has a dominant influence on the computed posterior probability. Although terrestrial life's early emergence provides evidence that life might be abundant in the universe if early-Earth-like conditions are common, the evidence is inconclusive and indeed is consistent with an arbitrarily low intrinsic probability of abiogenesis for plausible uninformative priors. Finding a single case of life arising independently of our lineage (on Earth, elsewhere in the solar system, or on an extrasolar planet) would provide much stronger evidence that abiogenesis is not extremely rare in the universe.

Fig. 1.

PDF and CDF of λ for uniform, logarithmic, and inverse-uniform priors, for model optimistic, with λ_min = 10^-3 Gyr^-1 and λ_max = 10³ Gyr^-1. (Left) The dashed and solid curves represent, respectively, the prior and posterior PDFs of λ under three different assumptions about the nature of the prior. The green curves are for a prior that is uniform on the range 0 Gyr^-1 ≤ λ ≤ λ_max (uniform); the blue are for a prior that is uniform in the log of λ on the range -3 ≤ log λ ≤ 3 [Log (-3)]; and the red are for a prior that is uniform in λ^-1 on the interval 10^-3 Gyr ≤ λ^-1 ≤ 10³ Gyr [InvUnif (-3)]. (Right) The curves represent the CDFs of λ. The ordinate on each curve represents the integrated probability from 0 to the abscissa (color and line-style schemes are the same as in Left). For a uniform prior, the posterior CDF traces the prior almost exactly. In this case, the posterior judgment that λ is probably large simply reflects the prior judgment of the distribution of λ. For the prior that is uniform in λ^-1 (InvUnif), the posterior judgment is quite opposite—namely, that λ is probably quite small—but this judgment is also foretold by the prior, which is traced nearly exactly by the posterior. For the logarithmic prior, the datum (that life on Earth arose within a certain time window) does influence the posterior assessment of λ, shifting it in the direction of making greater values of λ more probable. Nevertheless, the posterior probability is approximately 12% that λ < 1 Gyr^-1. Lower λ_min and/or lower λ_max would further increase the posterior probability of very low λ, for any of the priors.

Fig. 2.

Lower bound on λ for logarithmic prior, hypothetical model. The three curves depict median (50%), 1-σ (68.3%), and 2-σ (95.4%) lower bounds on λ, as a function of λ_min.

Fig. 3.

CDF of λ for abiogenesis with independent lineage, for logarithmic prior: λ_min = 10^-3 Gyr^-1, λ_max = 10³ Gyr^-1. A discovery that life arose independently on Mars and Earth, on an exoplanet and Earth, or that it arose a second, independent, time on Earth would significantly reduce the posterior probability of low λ.