“…where B(α, β ) denotes the beta function with two free parameters of α and β , and Γ(k) denotes the gamma function with two free parameters of k and λ . These functions were previously used to estimate the factors in the Drake equation 20 . Figure 2 also shows the best-fitting curves of these distribution functions.…”
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.
“…where B(α, β ) denotes the beta function with two free parameters of α and β , and Γ(k) denotes the gamma function with two free parameters of k and λ . These functions were previously used to estimate the factors in the Drake equation 20 . Figure 2 also shows the best-fitting curves of these distribution functions.…”
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.
“…Since the terrestrial extinctions are caused by random events, such as volcanic activities 27 – 29 , asteroid impacts 30 , superflares of the Sun 31 , 32 , gamma-ray bursts 33 , and so on, it is justified that the terrestrial extinction intensity can be expressed by a log-normal probability distribution as a result of these random multiplicative processes. The ultimate use of a log-normal distribution has precedence in the context of the Drake equation 18 , 20 , 34 . Figure 2 Histogram of extinction intensity.…”
Section: Histogram Of the Terrestrial Extinction Historymentioning
confidence: 99%
“…The same fitting procedures were applied to the histogram data using two additional distribution functions: the beta prime distribution function and the gamma distribution function : where denotes the beta function with two free parameters of and , and denotes the gamma function with two free parameters of k and . These functions were previously used to estimate the factors in the Drake equation 20 . Figure 2 also shows the best-fitting curves of these distribution functions.…”
Section: Histogram Of the Terrestrial Extinction Historymentioning
We discuss f i among these conjectural factors in the Drake equation in this paper. Previous estimates of f i range from pessimistic (f i ∼ 0) to optimistic (f i ∼ 1). In general, while many physicists and astronomers prefer the optimistic value, many biologists prefer a value several orders of magnitude smaller 8,9. Table 1 shows the various estimated values of f i and f l • f i • f c to date. This paper introduces a new approach to estimating the probability that life on Earth has not gone extinct since the birth of life, f i,⊕. Since its birth, life on Earth has gone through many extinction events due to various random external factors, such as changes in the environment or impacts of meteorites. Extinction events of high intensity (where a significant fraction of species disappear) occur much less frequently than events of low intensity. The fossil record in the Phanerozoic Eon, which covers 540 Myr to the present 22,23 , indicates that a histogram of extinction intensity can be well modeled by a log-normal distribution. This log-normal distribution of extinction was converted into a cumulative probability that life on Earth survives up to the present, f i,⊕ , by "continuing to win the lottery of extinction" since its birth. The obtained survival probability, f i,⊕ , can be a template for estimating f i in the Drake equation, or other factors for estimating the number of life-bearing exoplanets, assuming that life on any other exoplanets essentially always becomes complex if it does not become extinct first.
“…Hart 1975; Brin 1983; Barlow 2013; Anchordoqui et al 2017; Forgan 2017; Carroll-Nellenback et al 2019; Sotos 2019). There are many propositions aimed at solving this paradox, which make use of statistical (Horvat 2006; Maccone 2015; Solomonides et al 2016) or stochastic approaches (Forgan 2009; Forgan and Rice 2010; Glade et al 2012; Bloetscher 2019). Regarding the Drake equation, analytical interpretations (Prantzos 2013; Smith 2009) or reformulations (Burchell 2006, and references therein) have also been proposed.…”
Section: Introductionmentioning
confidence: 99%
“…The quest for a formal statistical theory has also lead to important progress in the mathematical foundations of SETI. Recently, Bloetscher (2019) considers a Bayesian approach, still motivated by the Drake equation, to estimate the number of civilizations in the Galaxy. To that end, the authors employ Monte Carlo Markov Chains over each factor of the Drake equation, and combine the mean values to reach a probabilistic result.…”
In this work we address the problem of estimating the probabilities of causal contacts between civilizations in the Galaxy. We make no assumptions regarding the origin and evolution of intelligent life. We simply assume a network of causally connected nodes. These nodes refer somehow to intelligent agents with the capacity of receiving and emitting electromagnetic signals. Here we present a three-parametric statistical Monte Carlo model of the network in a simplified sketch of the Galaxy. Our goal, using Monte Carlo simulations, is to explore the parameter space and analyse the probabilities of causal contacts. We find that the odds to make a contact over decades of monitoring are low for most models, except for those of a galaxy densely populated with long-standing civilizations. We also find that the probability of causal contacts increases with the lifetime of civilizations more significantly than with the number of active civilizations. We show that the maximum probability of making a contact occurs when a civilization discovers the required communication technology.
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