4.1. Astronomical Terms
The three first terms in Equation (1
) are representative of astronomical parameters. They can be estimated with a relatively good accuracy based on our knowledge of the Universe and data coming from various telescopes.
is the proportion of stellar systems having a star compatible with the occurrence of the considered stage of life. The essential requirements of prokaryote-like unicellular life are relatively simple; this kind of life form does not require as much energy or nutrients as macroscopic multicellular organisms in order to flourish. While being broadly globally distributed on Earth, certain strains of microbes can also develop patchily, for instance in ecological niches at the sub-millimetre scale [33
]. Therefore, it is expected that prokaryote-like life could develop at the surface or subsurface of planets or satellites. Most stars are thought to have at least one planet [40
], and many planets are thought to have satellite(s) [41
]. Even if the presence of extraterrestrial life is not probable around massive blue giants due to their very short lifetime, exoplanets have been found around them [42
] and these systems can thus potentially host habitable niches without requiring that life had the time to appear. Thus, we can consider that more or less all stellar systems have bodies compatible with prokaryote-like unicellular life and
can be approximated to 100%.
In contrast to this, multicellular macroscopic organisms only appeared on Earth after several billion years of evolution, and only after the rise of atmospheric oxygen in the Great Oxygenation Event [43
], implying that photosynthetic organisms played a key role in the rise of multicellularity. Using a restrictive approach, it is thus possible to consider that multicellular macroscopic organisms may only develop under the influence of a star small enough to be stable for several billions of years, but large enough to produce the energy required, i.e., ‘Sun-like stars’ [45
]. This is ever truer for extraterrestrial civilisations. In the Milky Way, with the proportion of ‘Sun-like stars’ being around 10%, it is possible to set
is the proportion of previous stellar systems having at least a rocky body located at a distance from the star compatible with the considered stage of life.
To be habitable at the global scale, a planet must be located in the habitable zone of its star, i.e., where the liquid water can be stable at the surface [46
]. Petigura et al., howed that about 22% of Sun-like stars would have a planet located in the habitable zone [45
]. The term
for macroscopic life and intelligent civilisations can thus be set
. In contrast, for unicellular prokaryote-like organisms that can develop in ecological niches in subsurface of any rocky body (planets or icy moons) where there is liquid water, the concept of a habitable zone around a star being restricted to bodies with stable liquid water at the surface is no longer valid. The habitable zone becomes so vastly extended that
can be set at
is the proportion of the previous bodies compatible with the emergence of life. In the Solar System, the smallest body upon which life may have appeared is Enceladus, a moon of Saturn [36
]. There are 8 planets and 19 moons larger than or equal in size to Enceladus in the Solar System and six of them (the Earth, Mars, Enceladus, Europa, Ganymede, and Titan) have, or had, environmental conditions compatible with the emergence of life, i.e., 22% of them. Using the Solar System as an example, we can set
The planets located in the habitable zone of their star are not necessarily compatible with complex life. In particular, atmospheric evolution would play a key role in the habitability of a planet through time. For instance, a planet could lose its atmosphere with the consequence that liquid water would no longer be stable at its surface (similar to Mars), or a planet may have environmental conditions that are incompatible with the emergence of life (Venus, for instance). The observation of exoplanets located in the habitable zone of their star is still relatively limited and the proportion of planets located in the habitable zone of Sun-like stars that are truly habitable is difficult to determine. However, of the confirmed exoplanets located in the habitable zone of their star, only ‘mesoplanets’, i.e., planets where the temperature at the surface is potentially between 0 and 50 °C, are compatible with complex life. Our knowledge about surface properties of exoplanets is very limited, however, following https://fr.wikipedia.org/wiki/Liste_d’exoplanètes_potentiellement_habitables
, we can roughly estimate this proportion to be 75%. The terms
can thus be set to 75%. This term appears to be higher for macroscopic multicellular life and extraterrestrial civilisations than for prokaryote-like organisms but this can be explained by the fact that it applies to planets located in the habitable zone in the case of complex and intelligent life, while for it applies to any rocky bodies in the case of prokaryotic life.
4.2. Empirical Terms
The main problem of astrobiology is the fact that the only known life is life on Earth. This unique example engenders the biggest challenge of our approach, which is to estimate the order of magnitude of the probabilistic terms related to life itself corresponding to the last three terms in Equation (1
). What is the probability for life to appear on a habitable planet? What is the probability that life evolves into macroscopic multicellular organisms? And into intelligent organisms? C. Maccone described Darwinian Evolution as an exponential growth of evolution with time, leading to an increase in the probability of extraterrestrial civilisations with time [26
]. In the present model, less mathematically developed than that of C. Maccone, we also based our approach on the fact that, with increasing time, there is more possibility for life to evolve. Using life on Earth as a reference, we thus considered that the probability to reach each of the three considered stages of evolution is inversely proportional to the ratio of the time they spent to appear on Earth over the time in which they could have appeared. This approach, which consists in considering that the time span between when conditions are required for an event to occur and the moment when it effectively occurs provides a metric of the probability of this event, has been used before to evaluate the probability of abiogenesis based on the history of life on Earth and has been discussed by Spiegel and Turner (2012) [48
]. Similarly, we also considered that the probability of coexistence of a given stage of evolution corresponds to the ratio of the time it would have been present on the Earth over the total existing time of the Earth. This approach is illustrated in Figure 1
. In order to estimate probability using this method, several examples would normally be required. Indeed, our approach amounts to saying that life on Earth is the paragon of life in the Universe, which is extremely hypothetical, and even optimistic. Furthermore, if the chemical processes leading to abiogenesis can be considered as relatively ‘simple’, evolution of life is very sensitive to the environment and the different stages of evolution considered in this study are the consequences of very specific properties and events that occurred during the history of the Earth such as the formation of the Moon, plate tectonics, major extinction events, etc. Our approach thus demands more speculation as the stage of evolution increases. In any case, it is an easy way to obtain orders of magnitudes that can be discussed later.
is the probability that life appeared on the bodies where the considered stage of life could appear. For habitable planets, if we look at the Earth, we could be tempted to set the probability of appearance of life to 100%. However, as explained by C.S. Cockell, a habitable planet does not necessarily mean an inhabited planet [49
]. The proportion
of habitable planets where life indeed appeared is thus not necessarily equal to 100%. If we look at the Solar System, there is presently only one planet in the habitable zone and it was inhabited about 300 million years after its formation 4.543 Ga ago. It is also well established that there was surface liquid water 4.3 Ga ago [51
]. Moreover, it was showed that the Earth will remain in the habitable zone of the Sun for a further 1 billion years [52
]. Ergo, life appeared after 300 million years during the total 5.3 billion years of Earth habitability, i.e., approximately at 6% of that duration. Using our approach, since the probability of occurrence of that event is considered to be inversely proportional to the time it took to occur, we consider that the probability of appearance of life of any type on a habitable planet is
. Due to our approach itself, the rapid appearance of life on Earth leads to this very high value of
for habitable planets. However, and as stated previously by [48
], the rapid appearance of life on Earth does not necessarily mean that the same process of abiogenesis occurred with equal rapidity elsewhere.
For prokaryote-like life potentially inhabiting ecological niches, life on Earth cannot be used as a model since, even it is chemically plausible, we do not know if life actually appeared, for example in the deep sea of Europa. It is thus preferable to advocate a conservative view saying that out of the six bodies of the Solar System where life could have appeared, it only appeared on the Earth; we thus set 17%.
is the probability that life reached the considered stage on the considered bodies. For prokaryote-like life it is thus 100% (if life emerged, it emerged as prokaryotic life, as per our model) and
. On Earth, the first occurrence of proposed macroscopic multicellular life has been described from 2.1 Ga old black shales in Gabon [53
]. This is debated but we can consider that multicellular life began to undeniably proliferate during the Ediacaran, 600 Ma ago, i.e., after 3.8 billion years out of the 5.3 billion years of Earth’s habitability, i.e., approximately after 72% of that duration. Following the same reasoning as above, we can thus set
. Finally, Homo sapiens, which developed the first intelligent civilisation on Earth, appeared 200 000 years ago, i.e., after 4.3 billion years out of the 5.3 billion years of Earth’s habitability, i.e., approximately at 81% of that duration. Following the same reasoning as above, we can thus set
is the probability that the considered life is still presently active on the bodies in question. As stated previously, it is equivalent to the probability of life having reached a given stage of evolution on two bodies simultaneously. Prokaryotes are known to be very resistant and to have a very great capacity for adaptation to environmental stresses at both the local and regional scale. Only a global change affecting the whole considered body, both at the surface and in the subsurface, would lead to the disappearance of prokaryote-like unicellular life. We can thus consider that microbial life could survive until the end of the life of the stellar system in which they developed. On Earth they would then have been present during about 9 billion years over the estimated 10 billion years of life time of the Solar System, before the Sun becomes a Red Giant. We can thus set .
Similarly, since it appeared on Earth, macroscopic multicellular life never completely disappears despite catastrophic events, but rather changes its distribution, mode and faunal hierarchy [54
]. If we consider that macroscopic life will remain on the Earth until it remains habitable at its surface, for another further 1 billion years, the Earth’s surface would have been inhabited by macroscopic multicellular life during about 1.6 billion years out of the 10 billion year lifetime of the Solar System. We can thus set
The duration of a civilisation is difficult to evaluate. If we decide to be very conservative (or even pessimistic) and state that humanity might disappear today, from the emergence of Homo sapiens, it would have existed during 2 × % of the life time of the Solar System. We can thus set .