Estimating survival probability using the terrestrial extinction history for the search for extraterrestrial life

Several exoplanets have been discovered to date, and the next step is the search for extraterrestrial life. However, it is difficult to estimate the number of life-bearing exoplanets because our only template is based on life on Earth. In this paper, a new approach is introduced to estimate the probability that life on Earth has survived from birth to the present based on its terrestrial extinction history. A histogram of the extinction intensity during the Phanerozoic Eon is modeled effectively with a log-normal function, supporting the idea that terrestrial extinction is a random multiplicative process. Assuming that the fitted function is a probability density function of extinction intensity per unit time, the estimated survival probability of life on Earth is ~0.15 from the beginning of life to the present. This value can be a constraint on fi in the Drake equation, which contributes to estimating the number of life-bearing exoplanets.

FROM LOGNORMAL DISTRIBUTION TO POWER LAW: A NEW CLASSIFICATION OF THE SIZE DISTRIBUTIONS

We propose a new classification of the size distributions of entities based on an exponent α defined from the shape of the log–log Rank Size plot. From an inspection of a large number of cases in different fields, one finds three possibilities: α = 1 giving a power law, α > 1 (parabola like curve) and 0 < α < 1 (analogous to a log normal distribution). A fourth possibility that can be defined when α < 0 was never observed. We present a modified version of models based on a random multiplicative process and an introduction of new entities during the growth. We recover all three kinds of distributions and show that the type of a distribution is conditioned by the rate of the introduction of new entities.