On the Rate of Abiogenesis from a Bayesian Informatics Perspective

Life appears to have emerged relatively quickly on the Earth, a fact sometimes used to justify a high rate of spontaneous abiogenesis ($\lambda$) among Earth-like worlds. Conditioned upon a single datum - the time of earliest evidence for life ($t_{\mathrm{obs}}$) - previous Bayesian formalisms for the posterior distribution of $\lambda$ have demonstrated how inferences are highly sensitive to the priors. Rather than attempt to infer the true $\lambda$ posterior, we here compute the relative change to $\lambda$ when new experimental/observational evidence is introduced. By simulating posterior distributions and resulting entropic information gains, we compare three experimental pressures on $\lambda$: 1) evidence for an earlier start to life; $t_{\mathrm{obs}}$; 2) constraints on spontaneous abiogenesis from the lab; and 3) an exoplanet survey for biosignatures. First, we find that experiments 1 and 2 can only yield lower limits on $\lambda$, unlike 3. Second, evidence for an earlier start to life can yield negligible information on $\lambda$ if $t_{\mathrm{obs}} \ll \lambda_{\mathrm{max}}^{-1}$. Vice versa, experiment 2 is uninformative when $\lambda_{\mathrm{max}} \gg t_{\mathrm{obs}}^{-1}$. Whilst experiment 3 appears the most direct means of measuring $\lambda$, we highlight that early starts inform us of the conditions of abiogenesis, and that lab experiments could succeed in building new life. Together then, the three experiments are complimentary and we encourage activity in all to solve this grand challenge.