Editing Drake equation (section)

==Modifications==
As many observers have pointed out, the Drake equation is a very simple model that omits potentially relevant parameters,<ref>
{{cite journal
 |last1   = Hetesi
 |first1  = Z.
 |last2   = Regaly
 |first2  = Z.
 |year    = 2006
 |title   = A new interpretation of Drake-equation
 |url     = http://astro.elte.hu/~hetesizs/Hetesi%20Zsolt%20cikkei/new%20interpretation%20fo%20drake%20eq.pdf
 |archive-url = https://web.archive.org/web/20090205123935/http://astro.elte.hu/~hetesizs/Hetesi%20Zsolt%20cikkei/new%20interpretation%20fo%20drake%20eq.pdf
 |url-status = dead
 |archive-date = 2009-02-05
 |journal = [[Journal of the British Interplanetary Society]]
 |volume  = 59
 |pages   = 11–14
 |bibcode = 2006JBIS...59...11H
}}</ref> and many changes and modifications to the equation have been proposed. One line of modification, for example, attempts to account for the uncertainty inherent in many of the terms.<ref>
{{cite journal
 |last=Maccone |first=C.
 |year=2010
 |title=The Statistical Drake Equation
 |journal=[[Acta Astronautica]]
 |volume=67 |issue=11–12 |pages=1366–1383
 |bibcode= 2010AcAau..67.1366M
 |doi=10.1016/j.actaastro.2010.05.003
|s2cid=121239391
 }}</ref>
Combining the estimates of the original six factors by major researchers via a Monte Carlo procedure leads to a best value for the non-longevity factors of 0.85 1/years.<ref>{{Cite journal |last=Golden |first=Leslie M. |date=2021-08-01 |title=A joint mind consideration of the Drake equation in the search for extraterrestrial intelligence |url=https://www.sciencedirect.com/science/article/pii/S0094576521001338 |journal=Acta Astronautica |volume=185 |pages=333–336 |doi=10.1016/j.actaastro.2021.03.020 |bibcode=2021AcAau.185..333G |s2cid=233663920 |issn=0094-5765}}</ref> This result differs insignificantly from the estimate of unity given both by Drake and the Cyclops report.

Others note that the Drake equation ignores many concepts that might be relevant to the odds of contacting other civilizations. For example, [[David Brin]] states: "The Drake equation merely speaks of the number of sites at which ETIs spontaneously arise. The equation says nothing directly about the contact cross-section between an ETIS and contemporary human society".<ref name="GS">
{{cite journal
 |last=Brin |first=G. D.
 |year=1983
 |title=The Great Silence – The Controversy Concerning Extraterrestrial Intelligent Life
 |journal=[[Quarterly Journal of the Royal Astronomical Society]]
 |volume=24 |issue=3 |pages=283–309
 |bibcode=1983QJRAS..24..283B
}}</ref> Because it is the contact cross-section that is of interest to the SETI community, many additional factors and modifications of the Drake equation have been proposed.

;Colonization : It has been proposed to generalize the Drake equation to include additional effects of alien civilizations colonizing other [[star system]]s. Each original site expands with an expansion velocity {{mvar|v}}, and establishes additional sites that survive for a lifetime {{mvar|L}}. The result is a more complex set of 3 equations.<ref name="GS"/>

;Reappearance factor : The Drake equation may furthermore be multiplied by ''how many times'' an intelligent civilization may occur on planets where it has happened once. Even if an intelligent civilization reaches the end of its lifetime after, for example, 10,000 years, life may still prevail on the planet for billions of years, permitting the next [[Sociocultural evolution|civilization to evolve]]. Thus, several civilizations may come and go during the lifespan of one and the same planet. Thus, if {{math|''n''<sub>r</sub>}} is the average number of times a new civilization reappears on the same planet where a previous civilization once has appeared and ended, then the total number of civilizations on such a planet would be {{math|1 + ''n''<sub>r</sub>}}, which is the actual ''reappearance factor'' added to the equation.

:The factor depends on what generally is the cause of [[civilization extinction]]. If it is generally by temporary uninhabitability, for example a [[nuclear winter]], then {{math|''n''<sub>r</sub>}} may be relatively high. On the other hand, if it is generally by permanent uninhabitability, such as [[stellar evolution]], then {{math|''n''<sub>r</sub>}} may be almost zero. In the case of total life extinction, a similar factor may be applicable for {{math|''f''<sub>l</sub>}}, that is, ''how many times'' life may appear on a planet where it has appeared once.

;METI factor : [[Aleksandr Leonidovich Zaitsev|Alexander Zaitsev]] said that to be in a communicative phase and emit dedicated messages are not the same. For example, humans, although being in a communicative phase, are not a communicative civilization; we do not practise such activities as the purposeful and regular transmission of interstellar messages. For this reason, he suggested introducing the METI factor (messaging to extraterrestrial intelligence) to the classical Drake equation.<ref>
{{cite web
 |last=Zaitsev |first=A.
 |date=May 2005
 |title=The Drake Equation: Adding a METI Factor
 |url=http://www.cplire.ru/html/ra&sr/irm/Drake_equation.html
 |publisher=[[SETI League]]
 |access-date=2013-04-20
}}</ref> He defined the factor as "the fraction of communicative civilizations with clear and non-paranoid planetary consciousness", or alternatively expressed, the fraction of communicative civilizations that actually engage in deliberate interstellar transmission.

:The METI factor is somewhat misleading since active, purposeful transmission of messages by a civilization is not required for them to receive a broadcast sent by another that is seeking first contact. It is merely required they have capable and compatible receiver systems operational; however, this is a variable humans cannot accurately estimate.

;Biogenic gases : Astronomer [[Sara Seager]] proposed a revised equation that focuses on the search for planets with biosignature gases.<ref name="NYT-20161207">{{cite news |last=Jones |first=Chris |title='The World Sees Me as the One Who Will Find Another Earth' – The star-crossed life of Sara Seager, an astrophysicist obsessed with discovering distant planets. |url=https://www.nytimes.com/2016/12/07/magazine/the-world-sees-me-as-the-one-who-will-find-another-earth.html |date=7 December 2016 |work=[[The New York Times]] |access-date=8 December 2016 }}</ref> These gases are produced by living organisms that can accumulate in a planet atmosphere to levels that can be detected with remote space telescopes.<ref name="equation">{{Cite web |author1=Devin Powell |date=2013-09-04 |title=The Drake Equation Revisited: Interview with Planet Hunter Sara Seager |url=https://www.space.com/22648-drake-equation-alien-life-seager.html |access-date=2023-10-06 |website=Space.com |language=en}}</ref>

:The Seager equation looks like this:<ref name=equation />{{refn|group=lower-alpha|The rendering of the equation here is slightly modified for clarity of presentation from the rendering in the cited source.<ref name=equation />}}
::<math display=block>N = N_* \cdot F_\mathrm{Q} \cdot F_\mathrm{HZ} \cdot F_\mathrm{O} \cdot F_\mathrm{L} \cdot F_\mathrm{S}</math>
:where:
::{{math|''N''}} = the number of planets with detectable signs of life
::{{math|''N''<sub>∗</sub>}} = the number of stars observed
::{{math|''F''<sub>Q</sub>}} = the fraction of stars that are quiet
::{{math|''F''<sub>HZ</sub>}} = the fraction of stars with rocky planets in the habitable zone
::{{math|''F''<sub>O</sub>}} = the fraction of those planets that can be observed
::{{math|''F''<sub>L</sub>}} = the fraction that have life
::{{math|''F''<sub>S</sub>}} = the fraction on which life produces a detectable signature gas

:Seager stresses, "We're not throwing out the Drake Equation, which is really a different topic," explaining, "Since Drake came up with the equation, we have discovered thousands of exoplanets. We as a community have had our views revolutionized as to what could possibly be out there. And now we have a real question on our hands, one that's not related to intelligent life: Can we detect any signs of life in any way in the very near future?"<ref>{{cite web|url=http://io9.com/what-a-brand-new-equation-reveals-about-our-odds-of-fin-531575395|title=A New Equation Reveals Our Exact Odds of Finding Alien Life|date=21 June 2013 |publisher=[[io9]]}}</ref>

;Carl Sagan's version of the Drake equation:American astronomer [[Carl Sagan]] made some modifications<ref>{{cite web |title=The Drake Equation |url=https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Astronomy/Life_beyond_the_Earth/The_Drake_Equation#:~:text=Another%20version%20of%20the%20Drake,graced%20by%20a%20technological%20civilization. |website=phys.libretexts.org | date=13 August 2014 |access-date=4 February 2024}}</ref> in the Drake equation and presented it in the 1980 program ''[[Cosmos: A Personal Voyage]]''.<ref>{{cite web |title=Carl Sagan - Cosmos - Drake Equation | website=[[YouTube]] | date=24 March 2009 |url=https://www.youtube.com/watch?v=MlikCebQSlY}}</ref> The modified equation is shown below

<math display="block">N = N_\mathrm{*} \cdot f_\mathrm{p} \cdot n_\mathrm{e} \cdot f_\mathrm{l} \cdot f_\mathrm{i} \cdot f_\mathrm{c} \cdot f_\mathrm{L}</math><ref>{{cite web |title=Carl Sagan - Cosmos - Drake Equation | website=[[YouTube]] | date=24 March 2009 |url=https://www.youtube.com/watch?v=MlikCebQSlY |access-date=4 February 2024}}</ref>
where

* {{math|''N''}} = the number of [[civilization]]s in the Milky Way galaxy with which communication might be possible (i.e. which are on the current past [[light cone]]);

and

* {{math|''N''<sub>∗</sub>}} = Number of [[stars]] in the [[Milky Way Galaxy]]  
* {{math|''f''<sub>p</sub>}} = the fraction of those stars that have [[planet]]s.
* {{math|''n''<sub>e</sub>}} = the average number of planets that can potentially support [[life]] per star that has planets.
* {{math|''f''<sub>l</sub>}} = the fraction of planets that could support life that actually develop life at some point.
* {{math|''f''<sub>i</sub>}} = the fraction of planets with life that go on to develop [[intelligence|intelligent]] life (civilizations).
* {{math|''f''<sub>c</sub>}} = the fraction of civilizations that develop a technology that releases [[Technosignature|detectable signs of their existence into space]].
* {{math|''f''<sub>L</sub>}} = fraction of a planetary lifetime graced by a technological civilization