Introduction
It is usually accepted that our atomic origins are extraterrestrial and that physics is universal. The chemical elements required for life were not created on Earth, but through nucleosynthesis during the Big Bang (H, He, Li), inside the cores of stars (He, C, N, O …) and within supernovae (Ca, P, S, Na, K, Cl …). The origin of terrestrial molecules required for life, notably water, is less certain, but comets and meteorites impacting the young Earth must have made a significant contribution and extraterrestrial origins are certainly not excluded. Water ice and organic material has recently been detected on a main belt asteroid (Rivkin & Emery Reference Rivkin and Emery2010) increasing their possible role in delivering molecules required for life. Chemistry is regarded as universal and our molecular origins are accepted as being both terrestrial and extraterrestrial. Biology is not generally regarded as universal and the question of whether our biological origins are terrestrial or extraterrestrial is highly controversial (Table 1).
Table 1. Extraterrestrial origins and transitions required for human life to emerge
RNA: ribonucleic acid; ISM: interstellar medium; DNA: deoxyribonucleic acid.
Standard evolutionary biology adopts a time on Earth between 3.5 and 4 Ga ago as its starting point with deep ocean hydrothermal vents as one possible location (Martin et al. Reference Martin2008) and recognizes that the rapid emergence of life is a puzzle. Maynard Smith & Szathmary (Reference Maynard Smith and Szathmary1995) have suggested eight steps on Earth leading from replicating molecules to mankind, of which seven are regarded as critical. Table 1 includes the critical transitions (1) to (7), but omits the faster transition expected from solitary individuals to colonies between (6) and (7).
A simple stochastic model, first proposed by Carter (Reference Carter1983) and discussed by Barrow & Tipler (Reference Barrow and Tipler1986), Hanson (Reference Hanson1998) and Flambaum (Reference Flambaum2003), assumes that evolution is governed by a series or critical transitions or bottlenecks, which must be passed to advance from basic molecules to simple, complex and then intelligent life. The anthropic model allowed the derivation of a probability density function and expectation time for the final step, based upon the habitable lifetime of the planet. Watson (Reference Watson2008) has further analysed the model to derive probability density functions and expectation times for every step. He identifies seven critical transitions in biological evolution from amongst the eight proposed by Maynard Smith & Szathmary (Reference Maynard Smith and Szathmary1995) and compares their probabilities with their estimated times of occurrence. He also discusses geochemical transitions relevant to biology, although they do not form part of the strictly biological evolutionary sequence based upon information.
Critical step model for evolution
The critical step model assumes that there is an ordered sequence of transitions that govern the pace of evolution. Any intermediate steps or stages are assumed to occur rapidly without increasing the time between steps. The critical steps are assumed to occur stochastically with uniform, small, but unequal probabilities, λ1 … λn, where λn<<1/t h, where t h is the habitable lifetime of the planet. One alternative would be a ‘long, slow fuse’ model, which allows for a much larger sequence of more likely events.
The probability density for the mth critical step in an n critical step model is
The expectation time for the mth critical step in an n critical step model is
i.e. the spacing of the steps will therefore tend to be even throughout the habitability period, although they will be subject to statistical variation.
Watson (Reference Watson2008) adopted 4 Ga ago as the start of habitability, corresponding roughly to the period of late, heavy bombardment. The end of habitability is taken as 1 Ga in the future, corresponding to the time when solar luminosity and atmospheric models predict an extreme temperature rise resulting from faster weathering of rocks to carbonates and subsequent CO2 loss. The probability density functions for the n-step models with n=1,2, …, 5 are the polynomials shown in Table 2.
The fit between the probability density distributions in the seven-step model and the estimated times at which the critical steps actually occurred is poor. The main cause of the discrepancy is that prokaryotic life emerged relatively soon after habitability. The first three steps are much more closely spaced than the subsequent steps, in disagreement with the expectation of closer spacing predicted by the model. Watson (Reference Watson2008) shows that the fit can be significantly improved by assuming that prokaryotic life only required a single step in a five-step model.
Considering the final transition alone, the emergence of humans after 4 Ga of a 5 Ga habitable lifetime on Earth implies that the nth out of n transitions occurred after 4 Ga. Table 3 shows the expectation times derived from Eq. (2) and indicates that this is most likely for n=4, since m=n=4 gives <t 4/4>=4 Ga. An alternative to a single step leading to prokaryotes is the suggestion that the timescale for evolution might be extended back by starting evolution earlier (Carter Reference Carter2008; Watson Reference Watson2008). Evidence of water on Earth 4.3 Ga (Valley et al. Reference Valley2002) ago could signify the start of habitability. Meteorites from Mars suggest that life might have originated there and migrated to Earth (Treeman et al. 2000). If the origin of life occurred elsewhere in the Solar System, it must have been within the past 4.6 Ga. This extension of 0.6 Ga to the time over which life evolved helps to resolve the discrepancy between the model and the estimated transition times but it does not alter the conclusion that the optimum number of critical transitions is less than seven. Carter (Reference Carter2008) suggests an optimum of six transitions if early evolution began on Mars, but stops short of proposing any earlier steps towards life.
Table 2. Probability density functions for one- to five-step models (habitability lifetime th=5 Ga)
Table 3. Expectation time for transitions, <tm/n> in Ga (habitability lifetime t h=5 Ga)
Origins within our Galaxy
Our Galaxy appears to be almost as old as the Universe itself, since the oldest known halo star is estimated at 13.2 Ga old (Frebel Reference Frebel2007). This ancient star is metal poor and lacking in the heavy elements needed for planetary formation. The oldest brown dwarfs, intermediates between stars and planets, are estimated to be 10 Ga old (Schilbach et al. Reference Schilbach, Roeser and Scholz2009). The Galactic thin disc, where conditions are more favourable for life, is estimated to be between 6.5 and 11.1 Ga old (Del Peloso Reference Del Peloso2005).
The concept of a Galactic Habitable Zone (GHZ), a region within the Galaxy favourable for the development of life, was first introduced by Gonzalez (Reference Gonzalez2001) and expanded upon in Gonzalez (Reference Gonzalez2005). Lineweaver et al. (Reference Lineweaver, Fenner and Gibson2004) identified the present GHZ as an annular region between 7 and 9 kpc, which has moved outwards from the Galactic centre and is composed of stars that formed between 4 and 8 Ga ago. Their model of Galactic evolution and habitability considered the need for adequate star formation, heavy elements for planets to form and time for life to evolve, together with an absence of supernovae. Prantzos (Reference Prantzos2008) concludes that that habitability is far less clear-cut, because the factors involved are poorly understood. In particular, the effect of heavy metals on planet formation, hot Jupiters on terrestrial planet survival and supernovae radiation on life are extremely uncertain. His own model predicts a narrow annulus for Galactic habitability starting at 3 kpc around 13 Ga ago, which then expands as it moves outwards, until it eventually encompasses the whole Galaxy within the lifetime of the Solar System and has a peak probability of Earth-like planets with life approaching 0.1 at 10 kpc from the Galactic centre today. More recent work (Mattson Reference Mattson2009) has modelled the build-up of carbon in the Galaxy, predicting a peak at ~5.5 kpc around 8 Ga ago and at the solar distance ~9 kpc around 5 Ga ago, close to the time when Earth formed.
Some of the necessary ingredients and conditions for life may have existed within the Galaxy, albeit at different locations, for many billions of years before the formation of Earth. Based upon current understanding, it is reasonable to consider the possibility of life originating elsewhere in the Galaxy before it began on Earth. Proponents of the Rare Earth Hypothesis (Ward & Brownlee Reference Ward and Brownlee2000) may place many further conditions upon the emergence of complex life, but we are concerned with the earliest, simple stages.
Table 4 summarizes some of the timings for key events and transitions through the history of the Universe and Earth. Although many may be regarded as controversial, they are used as best estimates in subsequent calculations. The origin of life in the Galaxy, or more specifically the start of habitability, is taken to have occurred 8.5±5 Ga ago, where the central value of 8.5 Ga reflects the work of Lineweaver et al. (Reference Lineweaver, Fenner and Gibson2004), Prantzos (Reference Prantzos2008) and Mattson (Reference Mattson2009) and the range of uncertainty allows for the most extreme conceivable values from the first stars in the Universe to the origin of life on Earth.
Table 4. Astrobiological timings
C: Cosmology; A: Astronomy/Galaxy; E: Earth Science/Geology; L: Lunar Science; B: Biological Information; (n) Critical Evolutionary Transitions [extreme estimates] best estimates; CMBR: cosmic microwave background radiation; RNA: ribonucleic acid. (1) to (7) represent the critical evolutionary transitions (Maynard Smith and Szathmary Reference Maynard Smith and Szathmary1995; Watson Reference Watson2008).
1Frebel (Reference Frebel2007) ; 2 See preceding text; 3Del Pelosa (Reference Melosh2005) ; 4Valley et al. (Reference Valley2002) ; 5Cohen et al. (Reference Cohen2000).
Extending the timescale in the critical transition model
Calculations of the critical transition model have been carried out using the Maple computer algebra system. Maple was used to plot and integrate the probability density distributions defined by Eq. (1) and hence determine the probability that a transition would occur before its estimated time. Since the distributions are polynomial functions, no numerical techniques have been required to perform the integrations. Figure 1 shows the probability density distributions for the seven-step and five-step models with the best estimates for the actual transition times marked on each curve by a cross. For the intermediate curves a cross towards the peak of the distribution suggests a good fit. The integrated area below the probability density curve to the left of the cross provides a more precise measure for establishing the goodness of fit. The adoption of the values in Table 4, which differ within reasonable limits from those adopted by Watson (Reference Watson2008), yields different probabilities that a step occurred at or before the observed time, but confirms his conclusions. A seven-step model fits poorly (probabilities of 25%, 10%, 3%, 33%, 23%, 11% and 21%, respectively), where values closer to 50% imply a more acceptable model. While a five-step model fits much better (probabilities of 41%, 70%, 50%, 27% and 33%, respectively). The essential distinguishing factor between the models is the rapid emergence of life, which is allowed for in the five-step model by combining the first three transitions of the seven-step into one.
Fig. 1. Critical transition models for (a) seven steps and (b) five steps compared with estimated transition times (start of habitability=4 Ga ago).
An alternative explanation is that the earlier transitions have occurred elsewhere in the Solar System or beyond. By considering the goodness of fit,
where P i is the probability of the ith step occurring before its actual estimated time (%) and n is the total number of steps, we have examined how the model performs when different numbers of steps and earlier transitions on extraterrestrial locations are allowed. If all the probabilities were 50%, giving F=0, the fit would be regarded as ideal. Figure 2 shows that F is minimized for n=5 and that the five-step model does indeed fit the data best for purely Earth-based evolution.
Fig. 2. Optimization of the number of transitions in the critical step model.
If these earlier transitions have taken place ‘off-site’ they can be re-incorporated into the model by extending the timescale. Given that this needs to be longer than the age of the Solar System to make any significant difference to the model, a time of 8 Ga ago, corresponding to the estimated age of the thin disc and start of Galactic habitability according to the Lineweaver et al. (Reference Lineweaver, Fenner and Gibson2004) model, is adopted. The probability density distributions and estimated transition times are shown in Figure 3, where the probabilities for the five terrestrial transitions become 77%, 84%, 70%, 46% and 44%. The first two extraterrestrial transitions need to be excluded from the goodness of fit, since there is no sensible estimate for their times.
Fig. 3. Critical transition models for seven steps compared with estimated transition times (start of habitability=8 Ga ago).
During the habitability period, the first two transitions would have taken place on an extraterrestrial location and the final five on Earth, where we assume that the migration to Earth is not a critical step. However, we can consider the consequences if the physical transfer to Earth is regarded as a critical step, resulting from an unlikely event over a long timescale. For example, a randomly occurring collision of a suitable comet or meteorite with Earth might be necessary. Alternatively, one collision or event might be required to initiate a transfer from one location and another to complete it by collision with Earth. Lithopanspermia, an idea first suggested by Lord Kelvin in 1871, has been well discussed in subsequent years. Some calculations have suggested that interstellar panspermia is unlikely (Melosh Reference Melosh2003), but viable mechanisms have subsequently been suggested (Napier Reference Napier2004; Wallis & Wickramasinghe Reference Wallis and Wickramasinghe2004). The effect of adding one or two critical transitions to the model is shown in Fig. 4.
Fig. 4. Critical transition models for (a) eight steps and (b) nine steps compared with estimated transition times (start of habitability=8 Ga ago).
The best fit is obtained with the nine-step model, i.e. by having two Earth migration transitions (Fig. 5(a)). By reducing the start of habitability to 6 Ga ago, a similar goodness of fit can be achieved without any Earth migration transitions (Fig. 5(b)). Any further reduction in the start of habitability towards the age of the Solar System (Mars) decreases the goodness of fit (Fig. 5(c)).
Fig. 5. Model dependence upon the number of earth migration transitions of habitability at (a) 8 Ga. (b) 6 Ga. and (c) 5 Ga.
Discussion
The equal spacing property of the critical transition model can be used to explain what is happening. If transitions 1–7 are equally spaced upon the x-axis, together with 0=start of Earth habitability and 8=end of Earth habitability, and the estimated times from Table 4 are plotted, then a best fit line through the origin can be used for comparison (Fig. 6). The fit is poor because of the rapid early transitions.
Fig. 6. The enforcement of critical spacing in a seven-step evolutionary model.
If the first two transitions are removed and the best fit line is no longer required to pass through the origin, the y-intercept of –1.6 Ga gives an estimate for the origin of life, i.e. around 5.6 Ga ago (Fig. 7). This corresponds to the value of 6 Ga identified for the start of habitability when there were no Earth migration transitions. If additional transitions are introduced for Earth migration, then the y-intercept will decrease and life emerges further back in the past.
Fig. 7. The enforcement of critical spacing in a five-step evolutionary model.
Lépine et al. (Reference Lépine, Acharova and Mishurov2003) have shown that resonance with the spiral gravitation field can cause stars to move radially through the Galaxy over distances of 2–3 kpc in significantly less than 1 Ga. Roškar et al. (Reference Roškar, Debattista, Quinn, Stinson and Wadsley2008) have modelled this stellar migration and considered its astrophysical implications. A serious possibility is that it could account for the migration of simple life from closer to the Galactic centre. Haywood (Reference Haywood2009) has analysed solar neighbourhood stars, showing that around 50% have come from elsewhere, primarily by migration from the inner disc, where Galactic habitability was greater at an earlier time. Not only does the GHZ move radially outwards from the Galactic centre according to most models (Lineweaver et al. Reference Lineweaver, Fenner and Gibson2004; Prantzos Reference Prantzos2008), but so do a significant number of stars. Thus from both a dynamic and chemical perspective, it may be possible for simple life to migrate from the inner disc of the Galaxy on realistic timescales and hence be included within the critical transition model. Wesson (Reference Wesson2010) argues that, despite viable mechanisms for distributing organic material throughout the Galaxy, life could not survive the UV and cosmic ray bombardment. He does though suggest that necropanspermia, the transfer of information via damaged biological molecules, is feasible.
Conclusions
A simple stochastic model for evolution, based upon the need to pass a sequence of n critical steps (Carter Reference Carter1983; Watson Reference Watson2008), has been applied to both terrestrial and extraterrestrial origins of life. In the former case, the time at which humans have emerged during the habitable period of Earth suggests a value of n=4. Progressively adding earlier evolutionary transitions (Maynard Smith & Szathmary Reference Maynard Smith and Szathmary1995) gives an optimum fit when n=5, implying either that the initial transitions are not critical or that habitability began around 6 Ga ago. The origin of life on Mars or elsewhere within the Solar System is excluded by the latter case. Carter (Reference Carter2008), in reviewing his original work, argues for a five-step model for terrestrial evolution and a six-step model if Mars evolution is included. If extra transitions are included to allow for Earth migration by simple life, the start of habitability needs to be at an even earlier time. Our present understanding of Galactic habitability and dynamics does not exclude this possibility. Each additional migration transition pushes back the start of habitability by around 1 Ga.
The Drake equation has long been used as a touchstone for astrobiology. Its mix of astrophysical, biological and social science, with an increasing level of uncertainty, continues to provoke discussion (Burchell Reference Burchell2006). The critical transition model addresses an issue for any Drake-type equation, e.g. the Rare Earth equation (Ward & Brownlee Reference Ward and Brownlee2000). If any one of the factors is zero, then the result is zero. The critical transition model breaks down the crucial biological steps, typically only represented by one or two factors, and introduces time dependence. In particular, it provides a reasonable fit to the timescales for the emergence of life on Earth. Furthermore, if the possibility of life originating beyond Earth is considered, it can provide useful clues as to the time that life might have emerged.
Whether the assumptions of the model and the identification of the transitions are reasonable is open to debate (e.g. Cirkovic et al. Reference Cirkovic, Vukotic and Dragicevic2009). For example, the likelihood of critical transitions could be governed by causal links between astrophysical and biological events.
Transitions might occur relatively quickly with a high probability if life emerges through stages of Galactic punctuated equilibrium separated by irregular catastrophic (catalytic?) events in the Galaxy such as gamma ray bursts or supernovae as suggested by Cirkovic et al. (Reference Cirkovic, Vukotic and Dragicevic2009). The Earth is certainly not a closed system, being exposed to electromagnetic radiation, neutrinos and cosmic rays from beyond the Solar System and material from within it. The extent to which the Earth is an open system and the degree of correlation between astrophysics and biology are key issues, which ‘grand’ astrobiological models can help to resolve. Critical transition models, incorporating both biological and astrophysical concepts, provide a standard against which other models can be judged.
