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A stochastic process approach of the drake equation parameters

  • Nicolas Glade (a1), Pascal Ballet (a2) and Olivier Bastien (a3)


The number N of detectable (i.e. communicating) extraterrestrial civilizations in the Milky Way galaxy is usually calculated by using the Drake equation. This equation was established in 1961 by Frank Drake and was the first step to quantifying the Search for ExtraTerrestrial Intelligence (SETI) field. Practically, this equation is rather a simple algebraic expression and its simplistic nature leaves it open to frequent re-expression. An additional problem of the Drake equation is the time-independence of its terms, which for example excludes the effects of the physico-chemical history of the galaxy. Recently, it has been demonstrated that the main shortcoming of the Drake equation is its lack of temporal structure, i.e., it fails to take into account various evolutionary processes. In particular, the Drake equation does not provides any error estimation about the measured quantity. Here, we propose a first treatment of these evolutionary aspects by constructing a simple stochastic process that will be able to provide both a temporal structure to the Drake equation (i.e. introduce time in the Drake formula in order to obtain something like N(t)) and a first standard error measure.


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Annis, J. (1999). An astrophysical explanation for the great silence. J. Br. Interplanet. Soc. 52, 1922.
Bastien, O. (2008). A simple derivation of the distribution of pairwise local protein sequence alignment scores. Evol. Bioinf. 4, 4145.
Bromm, V. & Loeb, A. (2002). The expected redshift distribution of gamma-ray bursts. Astrophys. J. 575, 111.
Burchell, M.J. (2006). W(h)ither the drake equation? Int. J. Astrobiol. 5(3), 243250.
Capiński, M. & Kopp, E. (2002). Measure, Integral and Probability. Springer-Verlag, Berlin.
Cirkovic, M.M. (2004a). Earths: rare in time, not space? J. Br. Interplanet. Soc. 57, 53.
Cirkovic, M.M. (2004b). The temporal aspect of the drake equation and SETI. Astrobiology 4(2), 225231.
Cirkovic, M.M. & Bradbury, R.J. (2006). Galactic gradients, postbiological evolution and the apparent failure of SETI. New Astron. 11, 628639.
Dick, S.J. (2003). Cultural evolution, the postbiological universe and SETI. Int. J. Astrobiol. 2, 6574.
Diehl, R., Halloin, H., Kretschmer, K., Lichti, G.G., Schönfelder, V., Strong, A.W., von Kienlin, A., Wang, W., Jean, P., Knödlseder, J. et al. (2006). Radioactive 26Al from massive stars in the Galaxy. Nature 439, 4547.
Drake, F. (1965). The radio search for intelligent extraterrestrial life. In Current Aspects of Exobiology, ed. Mamikunian, G. & Briggs, M.H., pp. 323345. Pergamon, New York.
Drake, F. & Sobel, D. (1991). Is anyone out there? Simon and Schuster, London.
Foata, D. & Fuchs, A. (2002). Processus Stochastiques. Processus de Poisson, chaînes de Markov et martingales. Dunod, Paris.
Forgan, D.H. (2009). A numerical testbed for hypotheses of extraterrestrial life and intelligence. Int. J. Astrobiol. 8(2), 121131.
Forgan, D.H. (2011). Spatio-temporal constraints on the zoo hypothesis, and the breakdown of total hegemony. Int. J. Astrobiol. 10, 341347.
Glade, N., Ben Amor, H.M. & Bastien, O. (2009). Trail systems as fault tolerant wires and their use in bio-processors. In Modeling Complex Biological Systems in the Context of Genomics, Proceedings of the Spring School, Nice 2009, ed. Amar, P. et al. , pp. 85119.
Gonzalez, G., Brownlee, D. & Ward, P. (2001). The galactic habitable zone: galactic chemical evolution. Icarus 152(1), 185200.
Gowanlock, M.G., Patton, D.R. & McConnell, S.M. (2011). A model of habitability within the milky way galaxy. Astrobiology 11(9), 855873.
Hair, T.W. (2011). Temporal dispersion of the emergence of intelligence: an inter-arrival time analysis. Int. J. Astrobiol. 10, 131135.
Heavens, A., Panter, B., Jimenez, R. & Dunlop, J. (2004). The star-formation history of the Universe from the stellar populations of nearby galaxies. Nature 428, 625627.
Itô, K. (2004). Stochastic Processes. Springer-Verlag, Berlin.
Juneau, S., Glazebrook, K., Crampton, D., McCarthy, P.J., Savaglio, S., Abraham, R., Carlberg, R.G., Chen, H.W., Borgne, D.L., Marzke, R.O et al. (2005). Cosmic star formation history and its dependence on galaxy stellar mass. Astrophys. J. Lett. 619(2), L135.
Koroliouk, V. (1978). Aide-Mémoire de théorie des probabilités et de statistique mathématique. Edition de Moscou, Moscou. pp. 51.
Lineweaver, C.H., Fenner, Y. & Gibson, B.K. (2004). The galactic habitable zone and the age distribution of complex life in the Milky way. Science 303(5654), 59.
Maccone, C. (2010). The statistical drake equation. Acta Astronaut. 67(11–12), 13661383.
Ortet, P. & Bastien, O. (2010). Where does the alignment score distribution shape come from? Evol. Bioinf. 6, 159187.
Prantzos, N. (2008). On the “galactic habitable zone”. Space Sci. Rev. 135, 313322.
Reber, G. & Conklin, E.H. (1938). UHF receivers. Radio 225, 112.
Shermer, M. (2002). Why ET Hasn't Called. Scientific American 8, 21.
Shklovsky, I.S. & Sagan, C. (1966). Intelligent Life in the Universe. Holden-Day, San Francisco.
Skorokhod, A.V. & Prokhorov, I.U.V. (2004). Basic Principles and Applications of Probability Theory. Springer-Verlag, Berlin.
Vukotic, B. & Cirkovic, M.M. (2007). On the timescale forcing in astrobiology. Serb. Astron. J. 175, 4550.
Vukotic, B. & Cirkovic, M.M. (2008). Neocatastrophism and the Milky way astrobiological landscape. Serb. Astron. J. 176, 7179.
Walters, C., Hoover, R.A. & Kotra, R.K. (1980). Inter- stellar colonization: A new parameter for the Drake. Equation? Icarus 41, 193197.
Wilson, T.L. (1984). Bayes’ theorem and the real SETI equation. Q. J. R. Astron. Soc. 25, 435448.


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A stochastic process approach of the drake equation parameters

  • Nicolas Glade (a1), Pascal Ballet (a2) and Olivier Bastien (a3)


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