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Co-evolution of primitive methane-cycling ecosystems and early Earth's atmosphere and climate
Carbon isotope evidence for large methane emissions to the Proterozoic atmosphere
Pierre Cadeau, Didier Jézéquel, … Magali Ader
Late Miocene cooling coupled to carbon dioxide with Pleistocene-like climate sensitivity
Rachel M. Brown, Thomas B. Chalk, … Gavin L. Foster
Redox-informed models of global biogeochemical cycles
Emily J. Zakem, Martin F. Polz & Michael J. Follows
Multiple carbon cycle mechanisms associated with the glaciation of Marine Isotope Stage 4
James A. Menking, Sarah A. Shackleton, … Vasilii V. Petrenko
Unique Neoproterozoic carbon isotope excursions sustained by coupled evaporite dissolution and pyrite burial
Graham A. Shields, Benjamin J. W. Mills, … Timothy M. Lenton
Materials and pathways of the organic carbon cycle through time
Matthieu E. Galvez, Woodward W. Fischer, … Timothy I. Eglinton
Methanogenesis sustained by sulfide weathering during the Great Oxidation Event
Shui-Jiong Wang, Roberta L. Rudnick, … Laura E. Wasylenki
A record of seafloor methane seepage across the last 150 million years
D. Oppo, L. De Siena & D. B. Kemp
End-Permian marine extinction due to temperature-driven nutrient recycling and euxinia
Dominik Hülse, Kimberly V. Lau, … Andy Ridgwell
Boris Sauterey ORCID: orcid.org/0000-0001-6164-756X1,2,3,
Benjamin Charnay4,
Antonin Affholder ORCID: orcid.org/0000-0003-3481-09521,2,3,
Stéphane Mazevet3 na1 &
Régis Ferrière ORCID: orcid.org/0000-0002-5806-55661,2,5 na1
Element cycles
Palaeoceanography
Palaeoecology
The history of the Earth has been marked by major ecological transitions, driven by metabolic innovation, that radically reshaped the composition of the oceans and atmosphere. The nature and magnitude of the earliest transitions, hundreds of million years before photosynthesis evolved, remain poorly understood. Using a novel ecosystem-planetary model, we find that pre-photosynthetic methane-cycling microbial ecosystems are much less productive than previously thought. In spite of their low productivity, the evolution of methanogenic metabolisms strongly modifies the atmospheric composition, leading to a warmer but less resilient climate. As the abiotic carbon cycle responds, further metabolic evolution (anaerobic methanotrophy) may feed back to the atmosphere and destabilize the climate, triggering a transient global glaciation. Although early metabolic evolution may cause strong climatic instability, a low CO:CH4 atmospheric ratio emerges as a robust signature of simple methane-cycling ecosystems on a globally reduced planet such as the late Hadean/early Archean Earth.
By 3.5 Ga, life had emerged on Earth1,2,3. Astrophysical and geophysical data concur in showing that the planet was habitable 400 My earlier at the very least, and possibly as early as ~4.5 Gya, depending on the occurrence, magnitude, and effect of large asteroid impacts during the Hadean3. Early on, Earth's carbon cycle likely established and maintained temperate climatic conditions4,5 in spite of a Sun being 20–25% dimmer than it is today6. The earliest microbial ecosystems evolving under these conditions, hundreds of million years before the first anoxygenic phototrophs7 became actors of the Archean climate8, most likely involved chemolithotrophs (i.e., unicellular organisms that use redox potential as energy source for biomass production) producing methane as a metabolic waste. Phylogenetic analyses2,7,9,10 combined with isotopic evidence11 and the then-time predominance12,13 of the electron donors H2 and CO lend weight to a very early origin of H2-based methanogens (MG), CO-based autotrophic acetogens (AG), and methanogenic acetotrophs (AT). As CH4 built up in the atmosphere, the evolution of anaerobic methanotrophy (MT) may have been favored. Contrary to the modern biosphere, the biomass productivity of such ecosystems was likely low and energy limited, i.e., limited by the availability of electron donors rather than nutrients such as nitrogen, phosphorus, or iron13,14. Whether and how the evolution of a primitive biosphere formed by these metabolisms influenced the planetary environment globally is unclear.
Previous studies8,12,13 have addressed the productivity of primitive, chemolithotrophic ecosystems and their influence on the young Earth's equilibrium atmospheric conditions. Such studies relied on equilibrium analyses of the planetary ecosystem; they made strongly simplifying assumptions on the function of chemolithotrophic microbial metabolisms, and did not close the feedback loop linking biological activity, atmospheric composition, and climate. Although these studies showed that primitive biospheres may have had a significant impact on the planet's early atmosphere and climate, their ability to quantify this impact and estimate the underlying biomass productivity was limited. Furthermore, earlier theory based on equilibrium analyses could not address the coupled dynamics of metabolic evolution and planetary surface conditions, whereby evolutionary changes might trigger significant atmospheric and climatic events and lead to novel steady states. Thus, advancing existing models is needed to generate hypotheses on the history of atmospheric and climatic conditions that metabolic evolutionary innovation may have driven on the early Earth.
Here we ask, how constrained was the habitability of late Hadean/early Archean Earth to methane-cycling ecosystems? How productive were these ecosystems and did they have a significant impact on the atmospheric composition and climate? How did their impact change as different metabolisms evolved? To answer these questions, we lay out a new probabilistic modeling framework for an evolving microbial community coupled to early Earth surface geochemistry and climate (Fig. 1, see "Methods" and Supplementary "Results and Discussion" for further details). The mean surface temperature and the composition of the atmosphere and oceans are parameterized using a 3D climate model4,15 and a 1D photochemical model16, combined with a simple temperature-dependent carbon cycle model5. Advancing the previous studies8,12,13, this planetary model is coupled dynamically to a biological model of cell population dynamics and evolutionary adaptation, constructed by scaling the intracellular processes of energy acquisition (i.e., catabolism), cell maintenance, and biomass production (i.e., anabolism) up to ecosystem function17,18. The biological model is grounded in thermodynamics and based on observations of cell size and temperature kinetic dependencies, widely and robustly shared among modern unicellular organisms19,20,21,22,23. Quantitative validation of similar models was obtained from laboratory experiments on anoxic ecosystems in bioreactors18.
Fig. 1: Primitive methanogenic ecosystems.
The ecosystem model resolves population abundance (total biomass, yellow arrows) of microbial H2-based methanogens (MG), CO-based acetogens (AG) and methanogenic acetotrophs (AT), along with CH4, CO, CO2, and H2 oceanic concentrations and atmospheric mixing ratios. Fluxes directly involved in the MG ecosystem function are indicated with black arrows. Fluxes additionally involved in the AG + AT ecosystem function are indicated in red. Key photochemical reactions are indicated with dotted arrows. The primary source of reducing power (H2) is volcanic outgassing. Fluxes across the ocean surface are governed by a stagnant boundary layer model. Rates of H2 escape to space and dead biomass burial in deep sediments are constant. Sulfate-based methanotrophs are not represented. See "Methods" for further details.
Ecosystems viability
First, we assess the viability of the methanogenic biospheres (MG, AG + AT, or MG + AG + AT) on an initially cool, lifeless Earth. The initial abiotic surface temperature TGeo is assumed to be 12 °C, corresponding to pCO2 = 2 × 105 ppm, negligible pCH4, and volcanic outgassing of H2, φvolc(H2), ranging from 5 × 109 to 2 × 1011 molecules cm−2 s−1. By performing a Monte-Carlo exploration of the space of biological parameters, we generate posterior distributions of possible life-atmosphere-climate outcomes (Supplementary Figs. 1 and 2), thus providing general insights that do not depend on specific parameterizations of chemolithotrophic metabolisms. We find that all three methanogenic ecosystems are viable (i.e., they can sustain a steady, positive biomass production) in more than 50% of the simulations, regardless of the intensity of H2 outgassing (further information on the region of viability in the space of biological parameters is provided in the Supplementary Results and Discussion). Among viable ecosystems, the posterior distributions of the planetary and ecological state variables are peaked and relatively narrow (Fig. 2). Hereafter we will focus on median values to describe model outputs.
Fig. 2: Short-term biological feedback to the atmosphere and climate.
Effects are computed as a function of the H2 volcanic outgassing, for each ecosystem composition. MG indicates H2-based methanogens (MG). AG+AT indicates CO-based acetogens and methanogenic acetotrophs consortia. MG+AG+AT indicates co-occurring methanogens, acetogens, and acetotrophs. a Global surface temperature at ecosystem-climate equilibrium. The dotted line indicates the initial abiotic surface temperature, TGeo = 12 °C. b Atmospheric composition at ecosystem-climate equilibrium. c Biogenic fluxes at ecosystem-climate equilibrium: CH4 production and carbon fixation in biomass (in molecules of C cm−2 s−1). Envelopes represent probability distributions from Monte-Carlo simulations across the biological parameter space, with each layer indicating output frequency ranging from 90 to 51%. Predictions from ref. 13 are also shown (dashed) for comparison. See "Methods" and Supplementary Tables 3 and 4 for parameter values.
Short-term effects of metabolic evolution
We first consider the direct effects on the early Earth's atmosphere and climate, on a relatively short timescale of ~106 years, of the transition from the initially cool, lifeless state to a planet populated by one of three methanogenic biospheres, MG, AG + AT, or MG + AG + AT. On such a short timescale, the carbon cycle has a negligible influence on the atmospheric CO2. H2 is both a metabolic substrate of MG and involved in the photochemical production of CO, the metabolic substrate of AG (Fig. 1). As a consequence, stronger H2 volcanic outgassing always enhances biomass production and CH4 emission (Fig. 2). The highest CH4 emission is achieved by MG ecosystems, with pCH4 ranging from 80 to 4000 ppm and equilibrium temperature, and TBioGeo, raised by +7° to +17° (Fig. 2). The environmental impact of AG + AT ecosystems is similar in magnitude, with pCH4 ranging from 50 to 1000 ppm, and temperature increases of +6° to +15° (Fig. 2).
The planet's abiotic surface temperature, TGeo, is likely to have a strong influence on methanogenic activity (see "Methods"). Temperature influences both cell kinetics (metabolisms are slower at lower temperature) and thermodynamics (strong negative effect of high temperatures on MG, less so on AG + AT). TGeo also correlates positively with pCO2 and pCO, which are both substrates of methanogenesis. We evaluate the influence of TGeo by examining bio-geo environmental feedbacks (i.e., how the change in metabolic activity due to variation in TGeo feeds back to climate) for TGeo ranging from −18 to 57 °C, which corresponds to pCO2 ranging from 5 × 10-4 to 1 bar (Fig. 3). We ran simulations using a default biological parameterization for which CH4 emissions are close to the median predictions described above. Note that we also considered TGeo as varying independently of pCO2, due to e.g. variation in stellar radiation; corresponding results are shown in Supplementary Fig. 3.
Fig. 3: Short-term biological feedback on the atmosphere and climate.
Effects are computed as a function of the H2 volcanic outgassing and abiotic surface temperature (TGeo), for each ecosystem composition. MG indicates H2-based methanogens. AG+AT indicates CO-based acetogens and methanogenic acetotrophs consortia. MG+AG+AT indicates co-occurring methanogens, acetogens, and acetotrophs. TGeo is varied by changing pCO2 in the climate model. a Atmospheric pCH4 at ecosystem-climate equilibrium. Shaded areas indicate conditions for organic haze formation. b Temperature differential between TGeo and the global surface temperature reached at ecosystem-climate equilibrium, TBioGeo. Shaded areas indicate conditions leading to organic haze formation (a) and glaciation (b). Other parameters are set at their default values (Supplementary Tables 2 and 3).
If the overall effect of TGeo on methanogenic activity is positive, the methanogenic ecosystem is expected to amplify temperature fluctuations driven by external events such as variation in CO2 outgassing. In this case, increasing TGeo should enhance the biogenic emission of CH4, further warming the planet through additional greenhouse effect; decreasing TGeo should have the opposite effect. In contrast, if the overall effect of TGeo on methanogenic activity is negative, methanogenic ecosystems will buffer temperature variation. For the MG ecosystem (Fig. 3), we find that there is a critical abiotic temperature TGeo ≈ 5 °C, almost insensitive to H2 outgassing, at which the warming effect of the ecosystem is maximum, from +5° to +17° across the range of H2 outgassing rates. The MG ecosystem buffers fluctuations of abiotic temperature above the critical value, whereas it amplifies abiotic temperature fluctuations below the critical value. In contrast, the AG + AT ecosystem always amplifies temperature variation at all abiotic temperatures, and its influence tends to dominate when MG and AG + AT metabolisms co-occur (Fig. 3). Such amplification or buffering of temperature variations can represent up to 33% of the abiotic fluctuations (Supplementary Fig. 4). Overall, the function and evolution of methanogenic ecosystems lead to a less resilient, more variable climate.
The formation of organic hazes when the pCH4-to-pCO2 ratio is greater than 0.2 (ref. 24) has been proposed as a general mechanism of climate regulation25. In the late Archean, pCO2 was low5, favoring organic haze formation that may have prevented hot runaway scenarios. In the Hadean/early Archean, however, our model predicts organic hazes to form in a limited range of conditions, at very high H2 volcanic outgassing rates, low pCO2, and low abiotic temperature close to or below the freezing point (Fig. 3). Under these specific conditions, the formation of organic hazes may overwhelm the warming effect of methanogenic ecosystems and leave the planet in a globally glaciated state. Under most conditions, however, it is the availability of electron donors (H2, CO) to methanogenesis, and not organic hazes, that is expected to limit Archean climate warming by biological activity.
In spite of their strong impact on the planet's atmosphere and climate, primitive methanogenic ecosystems are characterized by extremely low biomass productivity, AG + AT being the most productive pathway by far (Fig. 2). As microbial chemolithotrophs consume atmospheric electron donors, they drive the system closer to its thermodynamic equilibrium, thus gradually decreasing the thermodynamic efficiency of the metabolic coupling between energy acquisition (catabolism) and biomass production (anabolism; see "Methods equation (E2)"). As a consequence, for the highest value of abiotic H2 outgassing, our model predicts biomass production to range from 106 to 109 molecule C cm−2 s−1. This is 1–4 orders of magnitude below previous estimates13 (based on models that assumed a fixed biomass yield per electron donor consumed) and 4–7 orders of magnitude below modern values26.
Albeit extremely low, biomass production is very sensitive to the metabolic composition of the ecosystem and temperature, TGeo. Supplementary Fig. 5 shows how biomass production is influenced by these two factors. For the MG ecosystem, biomass production peaks for TGeo between −10 and 10 °C depending on the intensity of H2 volcanic outgassing (slightly above 109 molecules C cm−2 s−1 at high rates of H2 volcanic outgassing), and strongly decreases for higher TGeo. The maximum biomass production is of the same order in the AG + AT ecosystem and reached for similar conditions (intermediate TGeo, high H2 volcanic outgassing rate), but its dependence upon TGeo and the rate of H2 volcanic outgassing is much weaker. In the MG + AG + AT ecosystem the two methanogenic pathways interact synergistically, leading to a nonlinear, multiplicative increase in biomass production at low and high temperature. The synergy involves the combination of biogeochemical recycling loops, both locally and globally. Locally, while MG consumes CO2 to produce CH4, AT decomposes CH3COOH and produces CO2. The metabolic waste of AT is, therefore, the metabolic substrate of MG, and the combination of the two metabolic pathways pulls the system further away from its thermodynamic equilibrium, hence an increase in the efficiency of both pathways. Globally, as the MG metabolism releases additional CH4 in the atmosphere, the production of CO through photochemistry is accelerated; CO being the metabolic substrate of AG, its metabolic efficiency is enhanced. The synergistic effect is greatest at low abiotic temperature. In those very specific conditions and for the highest values of H2 outgassing, biomass production can reach about 1010 molecules C cm−2 s−1—about 1000 times less than estimates of modern primary production26.
Metabolic evolution and the carbon cycle
Next, we investigate how the evolutionary process of metabolic diversification of the primitive biosphere shaped the planet atmospheric and climatic history. We consider alternate scenarios of biosphere evolutionary complexification (Fig. 4a) consistent with phylogenetic and geological inferences2,7,9,10,11,27. Our evolutionary sequences culminate with the evolution of anaerobic methanotrophy, which uses the oxidation of CH4 as primary source of energy, based on the consumption of H2SO4, the main oxidative species of the globally reduced early Earth28. We, therefore, make the plausible assumption that a full methane-cycling biosphere may have evolved before the advent of photosynthesis.
Fig. 4: Equilibrium state of the planet as the biosphere diversifies.
a Plausible evolutionary sequences of metabolic innovation. Asterisks denote transitions that are very likely to cause a significant change in the atmospheric composition. b Scatterplot of the atmospheric compositions at equilibrium in CO, CH4, and H2, color-coded by the corresponding biosphere composition (1000 simulations for each ecosystem). c Corresponding distributions. d Distribution of the CO:CH4 ratio for each scenario. e Distribution of the surface temperature in each scenario. The white dots in d, e represent the median of the distributions, the thick gray lines the interquartile range, and thin gray lines the rest of the distribution.
This evolutionary process of diversification may have spanned several hundred million years (from the origin of life 3.9–4.5 Gya, to the origin of anoxygenic phototrophy, 3.5–3.7 Gya), thus unfolding on a timescale over which the geochemical cycles interacted dynamically and reciprocally with biological activity. In particular, it has been shown5 that on the timescale of 107 to 108 years, the carbon cycle tends to mitigate temperature variations through a negative feedback on the atmospheric CO2 concentration. We adapted the model from ref. 5 to add a full, temperature-dependent carbon cycle to our planetary ecosystem model. The abiotic equilibrium pCO2 is now determined by the balance between CO2 outgassing and sequestration in the oceanic floor; pCH4, by the balance between serpentinization and photodissociation rates; and pH2, by the balance between outgassing and photochemical reactions. Additionally, the H2SO4 oceanic concentration is determined by the balance between rainout and hydrothermal remineralization rates (taken from ref. 29). By drawing values for the abiotic supplies in CO2, CH4, H2, and H2SO4 from reasonable, log-uniform priors (Table 1), and starting from a lifeless primitive Earth, we evaluate the equilibrium state of the planetary system after each evolutionary metabolic transition in terms of atmospheric signatures (Fig. 4b–d) and mean surface temperature (Fig. 4e).
Table 1 Abiotic inputs of CO2, H2, CH4 and H2SO4.
First, we find that a lifeless Earth is characterized by a high CO:CH4 atmospheric ratio of 102–104 to 1, which differs markedly from the ratio predicted with a functional biosphere, regardless of its metabolic composition. As the biosphere complexifies, biological activity increases the atmospheric concentration in CH4, decreases the atmospheric CO, or both, causing the CO:CH4 ratio to fall. By comparing median values between the abiotic state and the most complex biosphere (MG + AG + AT + MT), the CO:CH4 ratio is predicted to be reduced by a factor of ~5000. The earliest evolutionary events, whereby the MG, AG, or AG + AT ecosystem emerges, all cause atmospheric shifts that can be distinguished in the pCO-pH2-pCH4 space (Fig. 4b and c). The atmospheric shifts caused by subsequent evolutionary complexification (leading to MG + AG, MG + AG + AT, or MG + AG + AT + MT ecosystems) are less pronounced and the corresponding atmospheric signatures are less distinctive among themselves. The evolution of anaerobic methanotrophy (MT) has for instance no effect on the equilibrium atmosphere of the planet because the influx of H2SO4 is sufficient for methanotrophs to survive and co-occur with methanogens, but not for them to consume a significant portion of the CH4 produced by methanogens.
Finally, although methanogenesis can have major effects on climate on relatively short time scales (Figs. 2 and 3), the carbon cycle buffers these effects at equilibrium on longer time scales: the average temperature difference between the planet with and without a methanogenic biosphere on its surface is only 4 °C (Fig. 4d). Biological effects on temperature may be further attenuated by the formation of cooling organic hazes favored by the enhanced sequestration of CO2 in response to methanogenesis25. However, the necessary conditions for organic hazes to form in this case are met in only 0.03% of the simulations including a methanogenic biosphere.
Transient climate destabilization by methanotrophy
How the planetary atmosphere-climate system responds to metabolic innovation may depend on the pace of evolution itself. The evolution of methanotrophy is a case in point. Slow evolution may delay methanotrophy after the response of the carbon cycle to methanogenesis. In this case, the oceanic stocks of H2SO4 are sufficient for methanotrophs to rapidly consume almost all of the atmospheric CH4 (Supplementary Fig. 6) and the planet is temporarily characterized by an atmospheric deficit in both CO2 and CH4. As a result, temperature plummets below the initial abiotic temperature. In contrast, if evolution is fast enough and methanotrophs evolve before equilibration of the methanogenic biosphere with the planetary atmosphere and climate, atmospheric CH4 may be consumed during or after the warming period (Fig. 3) but before the deficit in pCO2 builds up; temperature then returns close to its initial value (Supplementary Fig. 6).
Figure 5a illustrates the atmospheric and climatic consequences of slow evolution, when the wait time for methanotrophy is of the order of the carbon cycle timescale. In the two examples shown, the evolution of methanotrophs causes the sharp climatic response described above, and temperature falls respectively by 8 and 10 °C below TGeo = 2 °C, driving the planet into a global glaciation. Among 2000 simulated planetary conditions characterized by randomly drawn abiotic characteristics (i.e., the abiotic influxes of CO2, H2, CH4 and H2SO4, thereby setting the abiotic pCO2, pH2, pCH4, initial oceanic concentration of H2SO4 and surface temperature TGeo), and evolution time of methanotrophy (from 0 to 125 million years after methanogenesis), 50% experience a temperature drop larger than 8.3 °C below TGeo (Fig. 5b), and 40% actually end up in glaciation (Fig. 5b and Supplementary Fig. 7). As expected, delayed evolution of methanotrophy makes extreme cooling more likely (Fig. 5b). Because they lead to an enhanced abiotic response of the carbon cycle, conditions for which methanogenic ecosystems have the greatest warming effect (low abiotic TGeo, high H2 outgassing rate) are also the conditions under which the evolution of methanotrophy has the most dramatic effect on climate and habitability (Fig. 5a and c, Supplementary Fig. 8). Noticingly, this transient occurs irrespective of the metabolic composition of the methanogenic biosphere prior to the evolution of methanotrophy, as illustrated in Supplementary Fig. 7.
Fig. 5: Climate destabilization by evolutionary metabolic innovation.
a In this example, sulfur-based methanotrophy (MT) evolves 100 million years after MG + AG + AT, i.e. after equilibration of the methanogenic biosphere (MG + AG +AT) with the atmosphere and climate mediated by the carbon cycle, with TGeo = 2 °C, φvolc(H2) = 3 × 1011 (plain lines) and 1 × 1011 molecules s−1 cm−2 (dotted lines). Top, change in surface temperature. Bottom, change in atmospheric composition. b, d Distribution of outcomes across a range of abiotic temperature TGeo, H2 volcanic flux, and evolution time of MT (2000 randomly chosen combinations). b Amplitude of global cooling, ∆T, with respect to the evolution time of MT. c Frequency distribution of all temperature changes ∆T (blue) and of temperature changes conditional on glaciation outcome (yellow). d Estimated probability of glaciation as a consequence of MT evolution, given the abiotic temperature TGeo and H2 volcanic flux. Other parameters are set to their default values (Supplementary Tables 2 and 3).
For a methane-cycling ecosystem that triggers and eventually survives global glaciation, we expect the resulting equilibrium (co-occuring methanogens and methanotrophs with low pCH4) to be maintained only transitorily. We assume that during the early Archean, prior to the evolution of methanotrophy, the oceanic stock of H2SO4 builds up as volcanoes emit SO2 photochemically transformed into H2SO4, which then deposits on the ocean surface. With a deposition rate corresponding to our lowest value of 107 molecules cm−2 s−1 (ref. 30), and a hydrothermal removal rate of [H2SO4]oc. × 7.2 × 1012 L y−1 (ref. 29), we obtain an abiotic oceanic concentration of 0.4 mM. Such a stock is sufficient for methanotrophs to consume most of the atmospheric CH4, leading to the global cooling described above. Since the rate of CH4 reduction by methanotrophs is faster than the deposition rate, the H2SO4 stock will ultimately be depleted by methanotrophs, thereby driving a new abrupt environmental shift towards the equilibrium described in Fig. 4. At this new, stable equilibrium of coexisting methanogens and methanotrophs, the atmospheric pCH4 is high and the H2SO4 oceanic concentration is very low, below the micromolar, which aligns with the sulfur isotopic fractionation records30,31,32. This result suggests that anaerobic methanotrophy may have been the main sink of H2SO4 prior to the Neoarchean (2.5–2.7 Gya).
Our initial questions were: How constrained was the habitability of late Hadean/early Archean Earth to methane-cycling ecosystems? How productive were these ecosystems and did they have a significant impact on the atmospheric composition and climate? How did their impact change as different metabolisms evolved? To address these questions, we build on the previous theory8,12,13 by setting up a probabilistic modeling framework in which the evolution of a microbial biosphere is coupled to the dynamics of early Earth surface geochemistry and climate. We focus on four simple microbial metabolisms involved in methane cycling and likely to be some of the earliest players in Earth's ecology: hydrogenotrophic methanogenesis (MG), acetogenesis (AG), methanogenic acetotrophy (AT), and anaerobic oxidation of methane (MT). The biosphere evolves when a metabolism that was not present appears and adapts. By closing the global feedback loop between biological and planetary surface processes, the model predicts both ecosystem and atmosphere-climate states under the assumption that they reciprocally influence one another.
Our results confirm the contention that the late Hadean/early Archean planet was most likely habitable to methane-cycling chemolithotrophic biospheres and that under the assumption of high enough H2 supply, these biospheres were key factors of the climatic and atmospheric evolution of the planet8,12,13,33,34. On short time scales (105–106 years) the evolution of methanogenic biospheres may have considerably warmed the climate and influenced its resilience, in spite of a very low ecosystem productivity. On longer timescales, commensurate with the abiotic response of the carbon cycle to temperature variation, all ecosystems converge to new stable equilibria. Under these long-term equilibrium conditions, the mean surface temperature does not differ much from the lifeless state, and the carbon cycle is the predominant mechanism of climate regulation. However, all ecosystem equilibria share a robust atmospheric signature (low CO:CH4 ratio), distinctive from the lifeless state. In addition to influencing planetary characteristics at equilibrium, metabolic evolution generates atmospheric and climatic transients. The pace of evolution thus has a strong influence on the atmosphere and climate history. In particular, fast evolution of methanotrophs has limited or no effect on climate, whereas their delayed evolution may cause strong transients leading to global glaciation.
Although the influence of chemotrophic methane-cycling ecosystems on climate has been discussed in the previous work8,12,13,33,34, our model is the first to couple models of the Archean atmosphere, climate, and carbon cycle to an explicit eco-evolutionary model of cell population dynamics in order to quantify this effect. Our model differs from previous work primarily by addressing how climate change driven by ecological function feeds back to the biological activity of microbial populations, through the thermal dependence of the thermodynamics and kinetics of cell metabolism, and triggers an abiotic response of the carbon cycle. Closing the global feedback loop between ecological and planetary processes allows us to predict the ecosystem and climate states under the assumption that they reciprocally influence one another on multiple timescales.
A general result is that MG and AG + AT ecosystems are characterized by extremely low biomass production relative to their planetary impact on the atmosphere and climate. We predict biomass production to be 1–4 orders of magnitude smaller than previous estimates13 and 3–7 orders of magnitude below modern values26. Maximum global biomass production (reached for a very specific combination of biotic and abiotic conditions) is 1010 molecules C cm−2 s−1, or 3 × 107 ton C year−1. This is ~1000 times less than estimates of modern primary production. Both in terms of stock and fluxes, biomass has therefore very little effect on the biogeological coupling, which is a major difference with modern ecosystems.
A key assumption of our model is that nutrients N and P are not limiting; this assumption is backed up by the prediction of very low biomass production. As previously argued13,14, primitive ecosystems with such low productivity should have been limited by the availability in electron donors rather than by N and P nutrients. More specifically, ref. 14 evaluated the most likely limitation to biomass production prior to the evolution of oxygenic photosynthesis. By assuming a fixed yield for biomass production per molecules of electron donor consumed (as in ref. 13), they found that the N and P supplies were most likely sufficient during the Archean for electron donors to be limiting. This is even more likely given our finding of a biomass productivity far lower than the previous estimates13,14.
Our prediction of very low biomass productivity may help better constrain the timeline of the evolution of metabolic innovation on Earth. Even in our most productive scenario and under the (extreme) assumption that 100% of the dead organic matter is buried before remineralization, the estimated biomass production is still 4–5 times lower than the level consistent with the C isotopic fractionation estimated from rocks as old as 3.5 Gy1,35. This suggests that more productive, likely photosynthetic life forms must have evolved more than 3.5 Gya ago.
By performing equilibrium analyses of the planetary system on longer time-scales (107–108 years), on which the carbon cycle responds to ecosystem function and sequential metabolic diversification of the biosphere, we find that the climate regulation of the planet by the abiotic carbon cycle largely buffers the influence of early methanogenic activity on climate. However, depending on the pace of evolution, metabolic transitions such as the evolution of methanotrophy can interact with the abiotic carbon cycle and trigger strong transitory climatic events such as global glaciation over 107–108 years.
Even though the timing of the origin of anaerobic oxidation of methane (AOM), by reduction of nitrate, nitrite, or sulfate, is not well resolved, the fact that AOM proceeds enzymatically as a reversal of methanogenesis has been used to suggest that AOM may have evolved relatively soon after methanogens, i.e. before phototrophy36,37. Additionally, we find that the evolution of AOM prior to photosynthesis appears to be compatible with the sulfur isotopic fractionation record30,31,32. Our results thus highlight biological activity and the evolution of pre-photosynthetic methane-cycling ecosystems as a potential destabilizing factor of the early Earth climate system, alternatively or additionally to abiotic causes such as large impactors3,4,38.
The mechanism by which the evolution of early methane-cycling ecosystems may have exposed the Earth to high risks of global glaciation—fast removal of atmospheric methane, slow response of the carbon cycle—is general. It is, therefore, tantalizing to speculate about its potential involvement in the major climatic events that paralleled the evolution of oxygenic photosynthesis. By poisoning methanogens, removing the resource limitation (oxidizing species: O2, H2SO4, NO3, NO2) of methanotrophs, or by simply driving the abiotic oxidation of atmospheric CH4 by outgassed O2, oxygenic photosynthesis may have driven a dramatic decline in atmospheric CH4 which, coupled to a delayed response of the carbon cycle, could have caused global cooling, triggering the Proterozoic glaciation ~2.3 Gya39,40,41.
The substantial shifts in atmospheric composition driven by evolutionary metabolic innovation (Fig. 4) highlight the fact that simple methane-cycling ecosystems can have radically different atmospheric signatures. Thus, the atmosphere composition is shaped very early on by the course of biological evolution. We observe that the atmospheric signature of a specific metabolism is highly dependent on the ecological context set by the whole metabolic composition of the biosphere. As the biosphere evolves and complexifies, the atmospheric signature of each metabolic type becomes less identifiable, yet the state of the planet remains distinctive from the lifeless scenario. This backs up and quantifies the hypothesis that on a globally reduced planet such as the early Archean Earth, a low CO:CH4 atmospheric ratio is a highly discriminant indicator of inhabitation by a primitive CH4-based biosphere42.
In conclusion, our results suggest that life has had a dramatic impact on the anoxic Earth's surface environment, long before phototrophy evolved. They highlight the importance of the evolutionary process and its timeline in shaping up the planet's atmosphere and climate. In spite of extremely low productivity, metabolic evolutionary innovation in primitive methane-based biospheres is predicted to cause distinctive shifts in atmospheric composition, such as a decreasing CO:CH4 ratio as greater metabolic complexity evolves. The warming effect of methanogens and cooling effect of methanotrophs can be strong but they are only transient, on timescales that depend on the pace of evolution. We anticipate that the continued development of models that couple planetary processes with ecological and evolutionary dynamics of microbial biospheres will further advance our understanding of major events in the co-evolutionary history of life and Earth, and help identify detectable biosignatures for the search of life on Earth-like exoplanets.
Biological model
In the following section, we present the biological model. Parameters' definition, unit and default value are given in Supplementary Tables 1, 2, and 3.
The biological model describes the dynamics of one or several biological populations of chemotrophic organisms, driven by the growth, birth (division) and death of individual cells. The individual cell life cycle is controlled by catabolic and anabolic reactions occurring within cells17,18,43. Catabolism produces energy used by anabolism for biomass production, which determines cell growth and division; a fraction of energy produced by catabolism is used for cell maintenance. Energy thus flows from catabolism to maintenance and anabolism, and these processes can be described as follows:
$$\begin{array}{*{20}{l}} {{\mathrm{Catabolism}}} \hfill & : \hfill & {\mathop {\sum }\limits_{i = 1}^n \gamma _{S_i}^{cat}S_i \to \mathop {\sum }\limits_{i = 1}^m \gamma _{P_i}^{cat}P_i + {\mathrm{\Delta }}G_{cat}} \hfill \\ {{\mathrm{Maintenance}}} \hfill & : \hfill & {E_m} \hfill \\ {{\mathrm{Anabolism}}} \hfill & : \hfill & {\mathop {\sum }\limits_{i = 1}^{\dot n} \gamma _{S_i}^{cat}S_i + {\mathrm{\Delta }}G_{ana} \to \mathop {\sum }\limits_{i = 1}^{\dot m} \gamma _{P_i}^{cat}P_i + B} \hfill \end{array}$$
(E1)
where Si and Pi are the substrates and products of the metabolic reactions, and the \(\gamma\)'s are the corresponding stoichiometric coefficients. We follow ref. 17 and assume that the average organic compound \({\mathrm{C}}{\mathrm{H}}_{1.8}{\mathrm{O}}_{0.5}{\mathrm{N}}_{0.2}\) is a plausible approximation for the living biomass B. The energy Em (in kJ d−1) measures the cost of maintenance for a single cell per unit of time. The ∆G terms measure the oxidative power released or consumed by the catabolic and anabolic reactions; they are given by the Nernst relationship:
$${\mathrm{\Delta }}G(T) = {\mathrm{\Delta }}G_0(T) + {RTlog} \left(\mathop {\prod }\limits_{i = 1}^n S_i^{ \gamma _{S_i}}\mathop {\prod }\limits_{i = 1}^m P_i^{\gamma _{P_i}}\right)$$
where R is the ideal gas constant, T is the temperature (in K) and ∆G0(T) (in kJ) is the Gibbs energy of the reaction. ∆G0(T) is obtained from the Gibbs–Helmholtz relationship:
$${\mathrm{\Delta }}G(T) = {\mathrm{\Delta }}G_0(T_S)\frac{T}{{T_S}} + {\mathrm{\Delta }}H_0(T_S)\frac{{T_S - T}}{{T_S}}$$
where TS is the standard temperature of 298.15 K. Note that equations (E2) and (E3) describes how the thermodynamics of any given metabolism (i.e., the combination of catabolism and anabolism) vary with temperature.
Michaelis–Menten kinetics apply to catabolism:
$$q_{cat} = q_{max}\frac{{min(S_i^{cat}/\gamma _{S_i}^{cat})}}{{min(S_i^{cat}/\gamma _{S_i}^{cat}) + K_S}}$$
where KS is the half-saturation constant, qmax the maximum metabolic rate of the cell (d−1), and \(min(S_i^{cat}/\gamma _{S_i}^{cat})\) measures the concentration of the limiting substrate (taking stoichiometry into account). The energy produced is first directed toward maintenance. The cell energetic requirement for maintenance is:
$$q_m = \frac{{ - E_m}}{{{\mathrm{\Delta }}G_{cat}}}$$
The cell therefore meets its energy requirement only if qcat > qm. If the cell does not meet this requirement, the basal mortality rate of the cell, m, (in d−1), is augmented by a decay-related mortality term equal to \(k_d(q_m - q_{cat})\). Hence the actual mortality rate:
$$\begin{array}{*{20}{l}} {If\,q_{cat} \,<\, q_m} \hfill & : \hfill & {d = m + k_d(q_m - q_{cat})} \hfill \\ {If\,q_{cat} \,> \, q_m} \hfill & : \hfill & {d = m} \hfill \end{array}$$
When the energy requirements for maintenance are not met (qcat < qm) no energy is allocated to biomass production. Conversely, when those requirements are met (qcat < qm), then the energy remaining after allocation to cell maintenance can be directed to anabolism. A constant quantity of energy\({\mathrm{\Delta }}G_{diss}\) (in kJ) is then lost through dissipation. Following ref. 17 we consider the following empirical relationship:
$${\mathrm{\Delta }}G_{diss} = 200 + 18(6 - NoC)^{1.8} + e^{( - 0.2 - \alpha )^{2.16}(3.6 + 0.4NoC)}$$
where NoC is the number of carbons in the carbon source used by the anabolic reaction, and \(\alpha\) is its degree of oxidation. The efficiency of metabolic coupling (i.e., the number of occurrences of the catabolic reaction to fuel one occurrence of the anabolic reaction once the maintenance cost has been met) is then measured by
$$\lambda = \frac{{ - {\mathrm{\Delta }}G_{cat}}}{{{\mathrm{\Delta }}G_{ana} + {\mathrm{\Delta }}G_{diss}}}$$
The Michaelis–Menten kinetics of anabolism is given by
$$\begin{array}{*{20}{l}} {If\,q_{cat} \,> \, q_m} \hfill & : \hfill & {q_{ana} = \lambda (q_{cat} - q_{m})\frac{{min(S_i^{ana}/\gamma _{S_i}^{ana})}}{{min(S_i^{ana}/\gamma _{S_i}^{ana}) + K_S}}} \hfill \\ {If\,q_{cat} \,<\, q_m} \hfill & : \hfill & {q_{ana} = 0} \hfill \end{array}$$
where the half-saturation constant KS independent of the substrate, as was assumed in ref. 43. As biomass accumulates in the cell at rate qana, cell growth may lead to cell division. The cell division rate, r, is given by:
$$\begin{array}{*{20}{l}} {If\,B \,<\, 2B_{Struct}} \hfill & : \hfill & {r = 0} \hfill \\ {If\,B \,> \, 2B_{Struct}} \hfill & : \hfill & {r = r_{max}\frac{1}{{1 + e^{ - \theta log10((B - 2B_{Struct})/B_{Struct})}}}} \hfill \end{array}$$
(E10)
This means that a cell cannot divide if its internal biomass is not at least twice its cell structural biomass so that the two daughter cells meet this structural requirement. Above this threshold value of 2BStruct, r is of sigmoidal form so that the division rate first increases exponentially with the intracellular biomass content then saturates to rmax when biomass is largely available.
Using the rates of catabolic and anabolic cell activity and resulting cell division and mortality rates, we derive the following system of ordinary differential equations driving the cell population dynamics (dynamics of the number of cells and average cell biomass) and the feedback of the population on its environment (chemical composition of the ocean surface):
$$\begin{array}{*{20}{l}} {\frac{{dN_i}}{{dt}}} \hfill & = \hfill & {(r_i - d_i)N_i} \hfill \\ {\frac{{dB_i}}{{dt}}} \hfill & = \hfill & {q_{ana_i} - r_iB} \hfill \\ {\frac{{dX_j}}{{dt}}} \hfill & = \hfill & {F(X_j) + \mathop {\sum }\limits_{i = 1}^{MT} (q_{cat_i}\gamma _{i,X_j}^{cat} + q_{ana_i}\gamma _{i,X_j}^{ana})N_i} \hfill \end{array}$$
where MT denotes the ensemble of metabolic types considered, Ni is the number of individual cells in a population of a given metabolic type, Bi is the average cellular biomass of that type, and \(X_1,...,X_S\) are the concentrations of all relevant chemical species in the environment. The term \({\sum }_{i = 1}^{MT} (q_{cat_i}\,\gamma _{i,X_j}^{cat} + q_{ana_i}\gamma _{i,X_j}^{ana})N_i\) describes how concentrations vary according to the biological activity of each biological population i in the microbial community. The F(Xj) terms describe the environmental forcing resulting from ocean circulation and atmosphere-ocean exchanges as simulated by a stagnant boundary layer model as in ref. 13. The system of equations (E11) is solved numerically using a forward Euler method.
The flow of energy through the cell is driven by the maximum metabolic rate, qmax (in d−1), and the rate of energy consumption for maintenance, Em (in kJ d−1). They are both expressed as functions of temperature and cell size of the form ea+bTVc. Default values for parameters a, b and c entering qmax and Em are given in Supplementary Table 2.
The structural cell biomass BStruct increases with cell size according to BStruct = aVb. Both metabolic rate and maintenance cost increase with cell size, but not as fast as structural biomass. Consequently, the biomass specific rates of metabolism and energy consumption for maintenance decrease with cell size. Thus, small organisms are better at acquiring energy, but large organisms are more cost efficient due to lower maintenance requirements. A trade-off mediated by cell size thus exists between metabolic and maintenance rates, hence an optimal (intermediate) cell size, which is consistent with previous work conducted on unicellular marine organisms22. Both metabolic and maintenance rates increase with temperature, but the metabolic rate increases slightly faster19,20, shifting the trade-off toward larger sizes. As a consequence, the optimal cell size increases with temperature.
To compute the evolutionarily optimal cell size for a given metabolic type at a given temperature, we run simulations across a range of cell size and measure the level of resource use at equilibrium given by \(Q^ \ast = \mathop{\prod}\limits_{i = 1}^n {S_i^{ \gamma _{S_i}^{cat}}} \mathop{\prod}\limits_{i = 1}^m {P_i^{\gamma _{P_i}^{cat}}}\), the product of the metabolic substrates and wastes concentrations at equilibrium weighted by their stoichiometric coefficient. According to the classical principle of "pessimization" (maximization of resource use)44,45,46, populations that are better at exploiting their environment have lower Q* and evolution by natural selection will favor the cell size that minimizes Q*, thus leading to the evolutionarily optimal cell size. Supplementary Fig. 9 shows Q* as a function of cell size and temperature for the H2-based methanogenesis.
The optimal cell size, SC*, follows a positive relationship with temperature given by SC* = 10a+bT. We consider that over geological time scales, adaptive evolution acting on genetic variation among cells is fast enough so that SC is equal to SC*. As temperature changes, evolutionary adaptation by natural selection tracks the temperature-dependent optimal cell size.
In contemporary Earth oceans, most of the dead biomass is recycled by fermentors (>99%), and the rest is buried into the ocean floor. Although the most general version of our model includes populations of acetogenic biomass fermentors and acetotrophs, their inclusion considerably increases simulation time (results not shown). All the results presented in the main text have been obtained without fermentors, assuming that the dead biomass accumulates in the ocean's interior. It appears that biomass productivity is so low that the effect of biomass recycling (or lack thereof) on the atmospheric composition is negligible. We verified this by testing the effect of a recycling pathway in each ecosystem (MG, AG + AT, MG + AG + AT), for an intermediate value of H2 volcanic outgassing. Although biomass production is sufficient to sustain a population of fermentors, we found no significant effect of their biological activity on the atmospheric composition. Additionally, when we can compare the global atmospheric redox budget of the planet with and without biomass production (see Supplementary Results and Discussion, Supplementary Fig. 12), we find no significant differences. This further demonstrates that biomass production and the accumulation of dead biomass in the absence of remineralization represents a sink of C and H that is marginal compared to the other fluxes in the model. Note that the situation would be very different after the evolution of more productive, photosynthetic primary producers.
Because we do not model the fate of dead biomass explicitly, we evaluate the consistency of our predictions of biomass production with the geological record (carbon isotopic fractionation data) by taking biomass production as the upper bound for burial (in which case 100% of the produced biomass is ultimately buried) and using the modern value of burial (taken to be 0.2% as in e.g., ref. 13) as lower bound.
Planetary model
Our computation of climate state and mean surface temperature is based on 3D simulations with the Generic LMD GCM4,47,48. The model includes a 2-layer dynamic ocean computing heat transport and sea ice formation49. The radiative transfer is based on the correlated-k methods with k-coefficients calculated using the HITRAN 2008 molecular database. We used the simulations described in ref. 4 for the early Earth at 3.8 Ga, assuming no land, 1 bar of N2 and a 14 h rotation period. The simulation grid covers a range of pCO2 from 0.01 to 1 bar and pCH4 from 0 to 10 mbar. From this grid, we derived the following simple parametrization of the mean surface temperature as a function of pCO2 and pCH4 (expressed in bar):
$$T\left( {\! \deg {\mathrm{C}}} \right) = - 19.26 + 77.67 {\sqrt {p{\mathrm{C}}{{\mathrm{O}}_2}}} \,\,+\, 5{\mathrm{log}}10\left( {\frac{{1 + p{\mathrm{C}}{{\mathrm{H}}_4}{{10}^6}}}{3}} \right)$$
In the coupled biological-planetary model, we assume that the climate is always at equilibrium, meaning that the timescale of climate convergence is shorter than biological and geochemical timescales.
Photochemistry is computed with the 1D version of the Generic LMD GCM, which now includes a photochemistry core from ref. 50. The chemical network includes 30 species (mostly hydrocarbons) and 114 reactions. We use the reactions from ref. 50 for H2-H2O-CO2 and from ref. 51 for hydrocarbons. The photochemistry model also includes a pathway for the formation of hydrocarbon aerosol (C2H + C2H2 → HCAER + H)51,52.
We use the eddy diffusion vertical profile from ref. 53 and the solar UV spectrum at 3.8 Ga from ref. 54. Boundary conditions are set by the mixing ratios of CO2, CH4, and H2O at the first atmospheric layer. The atmospheric CO is either consumed biotically by acetogens when they are present in the biosphere, or abiotically by the formation of formate in the ocean (resulting in a deposition velocity of ~108 cm s−1) as in ref. 13,55. This eliminates the possibility of CO-runaway, which otherwise occurs in our simulations at high level of H2 or CO2. In addition, we assume that H2 undergoes diffusion-limited atmospheric escape (see for instance ref. 13).
We performed simulations across a range of pCO2 (104–105 ppm), pCH4 (1–104 ppm), H2 (100–104 ppm). For our range of atmospheric composition, photochemistry is dominated by the photolysis of CO2 and CH4, whose net reactions are:
$${\mathrm{CO}}_2 + {\mathrm{H}}_2 = {\mathrm{CO}} + {\mathrm{H}}_2{\mathrm{O}}$$
(R1)
$${\mathrm{CH}}_4 + {\mathrm{CO}}_2 = 2{\mathrm{CO}} + 2{\mathrm{H}}_2$$
From the simulation outputs we derived simple parametrizations for the production rates and loss rates of CH4, CO, H2 (see Supplementary Fig. 10). The reaction rates of (R1) and (R2) can be parameterized respectively as (in molecules cm−2 s−1):
$$F_1 = 1.8\,10^{10} \cdot \left( {\frac{{p{\mathrm{C}}{\mathrm{O}}_2}}{{10^{ - 1}}}} \right) \cdot \left( {\frac{{p{\mathrm{H}}_2}}{{10^{ - 4}}}} \right)^{0.4}$$
$$F_2 = 2\,10^{10}\left( {\frac{{p{\mathrm{C}}{\mathrm{O}}_2}}{{10^{ - 1}}}} \right)^{ - 0.2} \,\cdot\, \left( {\frac{{p{\mathrm{H}}_2}}{{10^{ - 4}}}} \right)^{ - 0.2} \,\cdot\, \left( {\frac{{p{\mathrm{C}}{\mathrm{H}}_4}}{{10^{ - 4}}}} \right)^u$$
where u (between 0.5 and 1) is given by
$$u = 0.6 + 0.1{\it{{\mathrm{log}}}}\left( {\frac{{p{\mathrm{H}}_2}}{{10^{ - 4}}}} \right) - \frac{{{\it{{\mathrm{log}}}}({\it{p{\mathrm{C}}{\mathrm{H}}}}_4) + 2}}{{15}} + 0.08\log \left(\frac{{p{\mathrm{C}}{\mathrm{O}}_2}}{{10^{ - 1}}}\right)$$
To simulate the evolution of pCO2 with time and feedbacks between the microbial community, climate, and the carbon cycle, we use a simple carbon cycle model based on ref. 5. The model computes the evolution of atmospheric CO2, dissolved inorganic carbon (CO2, HCO3− and CO32−) and pH in the ocean and in seafloor pores. The model takes into account outgassing (from volcanoes and mid-oceanic ridges), continental silicate weathering, dissolution of basalts in the seafloor, and oceanic chemistry, as sources and sinks of CO2. For all parameters in the carbon cycle model, we use the mean values given in ref. 5. For the temperature dependences of silicate weathering and oceanic chemistry, we use the mean surface temperature from our climate model. Even though this model only computes global mean quantities and does not take into account the organic matter in carbon sources and sinks of carbon, it is computationally very fast and well suited for studying the major feedbacks between biological populations and the atmosphere and climate.
Coupled biological-planetary model
The model resolves dynamics that take place on extremely different timescales—geological processes are extremely slow (103–106 years) compared to biological dynamics (days to years). We use a timescale separation approach and assume that the planetary environment is fixed on the biological time scale, and the biological system (population and local environment) is at ecological and evolutionary equilibrium on the geological time scale. This allows us to resolve the biological and geological dynamics separately and couple them at discrete points in time.
The biological dynamics are first resolved by the biological model for a fixed environmental forcing (equations (E11)), with microbial cells at their evolutionarily optimal size. The biological model is integrated over a sufficiently long time so that the local ecosystem reaches its equilibrium. Then we compute the biogenic fluxes between the surface ocean and the atmosphere, and between the surface ocean and the deep ocean, and feed them into the planetary model. The planetary model is then used to resolve the system's geochemical and climate dynamics, but only for a sufficiently small change in the planetary state (1% to 1‰ variation of the state variable that changes the most) so that this change would alter the biological equilibrium only marginally. The new biological equilibrium is then computed, and the process is re-iterated. This iterative process approximates a continuous coupling between the microbial community and its planetary environment.
Monte-Carlo simulations
We explore the parameter range by stochastically varying the parameters that determine the maximum metabolic rate, the rate of energy consumption for maintenance, the metabolic half-saturation constant, the decay and mortality rates, and the maximum division rate. We also vary the values of the parameters that shape the dependencies on size, temperature, and cellular biomass (see Supplementary Table 4). Parameter values are picked uniformly or log-uniformly (to avoid making prior assumptions on the likelihood of specific regions of the parameter space) within ranges constrained by empirical data from the literature, or large enough to cover plausible empirical variation. Three thousand simulations were run for the MG ecosystem, one thousand for the AG + AT ecosystem, and one thousand for the MG + AG + AT ecosystem, under four different values of volcanic outgassing: \(\phi _{{\mathrm{Volc}}}({\mathrm{H}}_2)\) = 2 × 109.5, 2 × 1010, 2 × 1010.5, and 2 × 1011 molecules cm−2 s−1, hence a total of 20,000 simulations. Each simulation was run to equilibrium.
The results can be divided into two subsets of roughly equivalent size, regardless of the ecosystems and volcanic activity considered: those with biological activity and those without (Supplementary Fig. 1A, B). We then verified that the number of simulations run for each of the considered scenarios was sufficient for the resulting distribution of equilibrium states to have converged. We evaluated convergence by subsampling, for each scenario, the subset of 'biologically viable' simulations with increasing sample size, and computing the average equilibrium biomass and CH4 biogenic emission of the subsamples. The results are shown in Supplementary Fig. 2 for the three scenarios and for \(\phi _{{\mathrm{Volc}}}({\mathrm{H}}_2)\) = 2 × 1010.5 molecules cm−2 s−1.
The data used to produce all the results presented in this study are available upon reasonable request to B.S.
The codes used in this study to produce the data analyzed are available on a git repository upon reasonable request to B.S.
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We thank Daniel Apai, Alex Bixel, Dillon Demo, Zach Grochau-Wright, François Guyot, Betul Kacar, James Kasting, Charles Lineweaver, Scot Rafkin and Alexander Sotto for discussion; and three anonymous reviewers for their insightful comments and helpful suggestions. This work was supported by Paris Sciences & Lettres University (IRIS OCAV and PSL-University of Arizona Mobility Program). B.S. acknowledges support from PSL IRIS Origins and conditions for the emergence of life (OCAV) program. R.F. acknowledges support from the United States National Science Foundation, Dimensions of Biodiversity program (DEB-1831493).
These authors contributed equally: Stéphane Mazevet, Régis Ferrière.
Institut de Biologie de l'Ecole Normale Supérieure (IBENS), Université Paris Sciences et Lettres, CNRS, INSERM, 75005, Paris, France
Boris Sauterey, Antonin Affholder & Régis Ferrière
International Center for Interdisciplinary Global Environmental Studies (iGLOBES), CNRS, ENS-PSL University, University of Arizona, Tucson, AZ, 85721, USA
Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE), Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Univ. Lille, F-75014, Paris, France
Boris Sauterey, Antonin Affholder & Stéphane Mazevet
LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, 92195, Meudon, France
Benjamin Charnay
Department of Ecology & Evolutionary Biology, University of Arizona, Tucson, AZ, 85721, USA
Régis Ferrière
Boris Sauterey
Antonin Affholder
Stéphane Mazevet
R.F. and S.M. conceived the study. R.F. designed the ecosystem model. A.A. and B.S. refined the model and developed the code. B.C. provided the climate and carbon cycle modules. B.S. and S.M. designed the Monte-Carlo approach and ran the simulations. B.S. analyzed the results and wrote the first version of the paper. All authors finalized the paper.
Correspondence to Boris Sauterey.
Peer review information Nature Communications thanks Janet Siefert and other, anonymous, reviewers for their contributions to the peer review of this work. Peer review reports are available.
Sauterey, B., Charnay, B., Affholder, A. et al. Co-evolution of primitive methane-cycling ecosystems and early Earth's atmosphere and climate. Nat Commun 11, 2705 (2020). https://doi.org/10.1038/s41467-020-16374-7
Early Mars habitability and global cooling by H2-based methanogens
Nature Astronomy (2022)
Understanding planetary context to enable life detection on exoplanets and test the Copernican principle
Joshua Krissansen-Totton
Maggie Thompson
Jonathan J. Fortney
Bayesian analysis of Enceladus's plume data to assess methanogenesis
The possible occurrence of iron-dependent anaerobic methane oxidation in an Archean Ocean analogue
Fleur A. E. Roland
Alberto V. Borges
Cédric Morana
Scientific Reports (2021)
Chance played a role in determining whether Earth stayed habitable
Toby Tyrrell
Communications Earth & Environment (2020)


Things have been very busy! I hope to have a nice full post to you soon. Until then here is a sample of what will be at Butcher, Baker, Candlestick-maker.
The past few days have been quite busy! During the week Jen visited and we did some sight seeing as well as enjoyed some time at the Kunstlerhaus. After she headed back home I had a studio visit on Friday which I found very refreshing. Later that night I went out to a few openings in Berlin such as Body/Controlled #4 - bio interfacing and an open studio night at the university.
Saturday I headed out to Stuttgart! The weather was not ideal for travel but all is safe and sound. Being in Stuttgart I went to visit the 72 Hour Urban Action even that took place here. There was a group of Cranbrook students which of course just made the will to go even stronger. It seems it was quite the experience for all with the limited time, language and sleep! Also, it rained for the whole 72 hours and everything was outdoors so you can only imagine.
After saying farewells and see you laters to the 72HUA group I was lucky enough to visit an artist at the Akademie Schloss Solitude residency. During my first week in Berlin I met Youki Hirakawa and his girlfriend, who are currently at Solitude. They gave a warm welcome and a lovely tour of their studios and the facilities at Schloss. We were also fortunate enough to visit the studio of Marianthi and Pe Lang. Being that it is a small world it turns out I saw Pe Lang's solo show in London when I visited in March. It was really great to talk to them both and see their process in the studio.
Well I have been here for about two weeks now and love it of course. During my time here I have met some of the other artists doing residencies here. They are great people to enjoy artist talks and dinners with I must say. If you would like to know some of my neighbors please check out www.bethanien.de .
Other than that I have done some walking about and exploring as well as visiting the Hause der Dinge. Hause der Dinge is basically a museum of objects and I really loved spending my rainy afternoon in their space. There was also an art opening at the Bethanien Gallery which included one of the residents here from Australia. It had a great layout and an even better turn out, so congrats!
Some of the images I have included are of the art chats, the show at Bethanien, Carson Grubaugh's work on this years Mercedes-Benz museum pass and package, some shots from around town as well as from the studio.
This week Jen Reich from Cranbrook is visiting me for a few days. After her visit I will be going to Stuttgart for the 72 hour Urban Action even as well as some other sight seeing opportunities. Upon my return I have another visitor! Alissa Lamarre, also a student from Cranbrook. She and I will be finishing up work for the exhibition in Brussels, Belgium as well as some running around the city here in Berlin!!


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text:
Dr Diana Fleischman
Qualifications: PhD
Role Title: Senior Lecturer
Address: King Henry Building, King Henry 1st Street, Portsmouth, Hampshire, PO1 2DY
Email: Diana.Fleischman@port.ac.uk
Department: Department of Psychology
Faculty: Faculty of Science
As an undergraduate I completed a year abroad at the London School of Economics with a heavy emphasis on evolutionary psychology which put me on track towards my PhD (2009) at the University of Texas at Austin (supervisor David Buss). My dissertation focused on hormonal influences on the psychology of disease avoidance and disgust. After my PhD I conducted research on behaviour change and hand washing at the London School of Hygiene and Tropical Medicine and worked at the Center for Women's Mood Disorders at the University of North Carolina at Chapel Hill. I joined the University of Portsmouth in September of 2011 and am a member of the Comparative and Evolutionary Psychology group.
Personal Webpage
Teaching Responsibilities
Currently I am unit coordinator for Exploring Psychology and design tutorials for first year students in psychology. I also coordinate the unit Introduction to Psychological Science for students studying psychology alongside another course. I give lectures for Issues in Clinical and Health Psychology, Key Ideas in Human and Animal Behaviour, The Psychology of Everyday Life and Comparative and Evolutionary Psychology.
My research focuses mostly on two broad themes: Hormonal influences on the behaviour of women and how humans adaptively avoid cues of contagion including how disgust is regulated.
Explore my research profile, publications and activities on the Portsmouth Research Portal
Community Collaboration

redpajama_set_name: RedPajamaCommonCrawl


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text:
The propensity theory of probability is a probability interpretation in which the probability is thought of as a physical propensity, disposition, or tendency of a given type of situation to yield an outcome of a certain kind, or to yield a long-run relative frequency of such an outcome.

Propensities are not relative frequencies, but purported causes of the observed stable relative frequencies.  Propensities are invoked to explain why repeating a certain kind of experiment will generate a given outcome type at a persistent rate.  A central aspect of this explanation is the law of large numbers.  This law, which is a consequence of the axioms of probability, says that if (for example) a coin is tossed repeatedly many times, in such a way that its probability of landing heads is the same on each toss, and the outcomes are probabilistically independent, then the relative frequency of heads will (with high probability) be close to the probability of heads on each single toss.  This law suggests that stable long-run frequencies are a manifestation of invariant single-case probabilities.  Frequentists are unable to take this approach, since relative frequencies do not exist for single tosses of a coin, but only for large ensembles or collectives. These single-case probabilities are known as propensities or chances. Hence, it can be thought of as "meta-probability".

In addition to explaining the emergence of stable relative frequencies, the idea of propensity is motivated by the desire to make sense of single-case probability attributions in quantum mechanics, such as the probability of decay of a particular atom at a particular moment.

The main challenge facing propensity theories is to say exactly what propensity means, and to show that propensity thus defined has the required properties.

History

A propensity theory of probability was given by Charles Sanders Peirce.

Karl Popper

A later propensity theory was proposed by philosopher Karl Popper, who had only slight acquaintance with the writings of Charles S. Peirce, however. Popper noted that the outcome of a physical experiment is produced by a certain set of "generating conditions".  When we repeat an experiment, as the saying goes, we really perform another experiment with a (more or less) similar set of generating conditions.  To say that a set of generating conditions has propensity p of producing the outcome E means that those exact conditions, if repeated indefinitely, would produce an outcome sequence in which E occurred with limiting relative frequency p.  For Popper then, a deterministic experiment would have propensity 0 or 1 for each outcome, since those generating conditions would have the same outcome on each trial.  In other words, non-trivial propensities (those that differ from 0 and 1) only exist for genuinely indeterministic experiments.

Popper's propensities, while they are not relative frequencies, are yet defined in terms of relative frequency.  As a result, they face many of the serious problems that plague frequency theories.  First, propensities cannot be empirically ascertained, on this account, since the limit of a sequence is a tail event, and is thus independent of its finite initial segments.  Seeing a coin land heads every time for the first million tosses, for example, tells one nothing about the limiting proportion of heads on Popper's view.  Moreover, the use of relative frequency to define propensity assumes  the existence of stable relative frequencies, so one cannot then use propensity to explain the existence of stable relative frequencies, via the Law of large numbers.

Recent work
A number of other philosophers, including David Miller and Donald A. Gillies, have proposed propensity theories somewhat similar to Popper's, in that propensities are defined in terms of either long-run or infinitely long-run relative frequencies.

Other propensity theorists (e.g. Ronald Giere) do not explicitly define propensities at all, but rather see propensity as defined by the theoretical role it plays in science.  They argue, for example, that physical magnitudes such as electrical charge cannot be explicitly defined either, in terms of more basic things, but only in terms of what they do (such as attracting and repelling other electrical charges).  In a similar way, propensity is whatever fills the various roles that physical probability plays in science.

Other theories have been offered by D. H. Mellor, and Ian Hacking

Principal principle of David Lewis
What roles does physical probability play in science?  What are its properties?  One central property of chance is that, when known, it constrains rational belief to take the same numerical value.  David Lewis called this the principal principle, a term that philosophers have mostly adopted.  The principle states:

 The Principal Principle. Let C be any reasonable initial credence function. Let t be any time. Let x be any real number in the unit interval. Let X be the proposition that the chance, at time t, of A's holding equals x. Let E be any proposition compatible with X that is admissible at time t. Then C(AIXE) = x.

Thus, for example, suppose you are certain that a particular biased coin has propensity 0.32 to land heads every time it is tossed.  What is then the correct credence? According to the Principal Principle, the correct credence is .32.

See also
 Bayesian probability
 Frequentism

References

Further reading

External links

Probability interpretations
Epistemology

redpajama_set_name: RedPajamaWikipedia


The abbreviation of the journal title "GPS solutions" is "GPS Solut.". It is the recommended abbreviation to be used for abstracting, indexing and referencing purposes and meets all criteria of the ISO 4 standard for abbreviating names of scientific journals.
GPS GPS Rule 4.4: Acronyms shall be retained in the abbreviated title.
solutions Solut. matches the word "solution"


text:
Lausanne Global Analysis · May 2019 · Volume 8 / Issue 3
The New Normal for Christianity in China
Adapting to a tighter political environment
A few years ago, Rob Gifford, author of China Road: A Journey into the Future of a Rising Power,[1] spoke at a ChinaSource conference in Hong Kong. He talked about the economic and social challenges that were likely to force China into drastic restructuring, noting that demographics alone would require it to move from being a labor-intensive, manufacturing-based economy to something else. 'One thing is certain', Gifford said, 'the next 30 years in China cannot look like the last 30 years.'
More recently, this sentiment was echoed by China watcher Bill Bishop, who wrote in November in the Axios[2] newsletter that 'we have to accept that China under General Secretary Xi Jinping is materially different from the China we knew under Hu Jintao and Jiang Zemin.'
One way that China is 'materially different' under Xi Jinping is a significantly tighter political environment.
One way that China is 'materially different' under Xi Jinping is a significantly tighter political environment. After three decades of loosening Communist Party control and expanding freedoms, Xi is systematically trying to reassert Party control over all sectors of society. This is behind so many of the reports we have seen of late of crackdowns and growing harassment/persecution of believers. However, the crackdowns are part of something much broader and it is a misinterpretation to assume that they are simply targeted at religion in general, or Christianity in particular.
This new political environment is impacting both local believers in China and foreign workers who have been serving the church in China.
End of the era of openness
The past few decades have seen an increased openness for churches and believers.[3] The urban house church movement came into its own. Unlike the rural house church movement that had grown up during the era of intense persecution and of necessity had been 'underground', these urban house churches are often public (complete with websites) and have adopted a less confrontational stance towards the government. The goal has been to show the authorities that they are not a threat.
The past few decades have seen an increased openness for churches and believers
Even though religious regulations were not changed, enforcement was relaxed, leading to an expanded gray zone that allowed for the growth of Christian publishing, media, and education. Local officials had leeway in overseeing religious affairs in their jurisdictions, and some even cultivated relationships with church leaders. This contributed to a more relaxed environment as Christians could offer assurances of not being a threat. As long as local churches and believers did not cause trouble, they were largely left alone.
For the foreign Christian community serving in China, the past few decades have been marked by increasing openness as well. While still not being allowed to engage officially in religious work, foreign Christians could live and work in China on a variety of legitimate visa platforms. These included teaching, studying, operating registered commercial enterprises, and establishing locally-registered NGOs. Some were working independently, while others were quietly part of sending organizations. So long as their visa and residence permission papers were in order, they were operating their businesses according to local laws and regulations and were considered to be providing legitimate services to the community, their presence was tolerated.
The 'New Normal'
The new environment, or 'New Normal'[4] as it is sometimes referred to, is making things more difficult for local believers. In 2018, the government issued a new set of religious regulations that make it significantly more difficult for unregistered churches (house churches) to function. Penalties can be levied against landlords who rent to unregistered groups, and local officials are under pressure to be stricter in their enforcement of these regulations. As a result, a few large, high-profile house churches have been closed and their leaders detained. Other larger house churches have made plans to divide (or have divided) into smaller churches should the need arise. In some ways this can be seen as Communist Party-led church multiplication.
The new environment, or 'New Normal' as it is sometimes referred to, is making things more difficult for local believers.
Registered churches ('Three-self' churches) are also feeling the pressure, with more political rhetoric and directives to 'Sinicize'.[5] Many registered church leaders now have to spend more time managing their relationships with government officials, leaving less time for shepherding the flock.
What does this new reality look like for foreign Christians serving in China?
1. Tolerance limits
We are being reminded of something that was perhaps forgotten, or at least overlooked—that China does not want, and never has wanted, foreigners engaged in religious activities. For a variety of reasons, however, their presence over the past 30 years has been tolerated. That tolerance is waning now, as the government moves to making sure those who enter China are engaged in activities that China deems valuable in light of its own goals and priorities. What is increasingly not tolerated is the presence of foreigners who are not obviously contributing to the achievement of China's strategic goals. In 2018 alone, hundreds of foreign Christian workers have left China, either by official decree or by choice, as it has become clear they cannot continue their work.
2. Security threats
Foreign Christians and foreign non-profit organizations are increasingly viewed by the Chinese government through a lens that sees them as potential national security threats. This is especially true for those individuals or organizations that work in minority areas, with work in Muslim minority areas being the most sensitive.
3. Surveillance state
China has become a surveillance state, and foreigners are not exempt. Once outside of a home or hotel room, a person is always in view of a camera. Much of the surveillance apparatus is used for everyday law enforcement enhancement (catching petty thieves or jaywalkers). However, it can (and has been) employed to track down people the government deems undesirable. How it can and will be used in the future is a matter of much speculation.
Implications for foreign Christians in China
What then are the implications for foreign Christian workers in China?
1. Serving China's goals
'Coloring outside the lines' is likely to become more difficult. This includes being on a student visa for years, setting up residence while on a tourist visa, or getting a work visa from a friend's business without any actual requirement to show up for work. Security officials who control access to visas and residence/work permits are under pressure to be more professional in managing immigration and visa issues, making sure that their decisions serve the broader goals of the Party and government.
In evaluating foreigner requests for visas, a key question is, 'What are you going to do for China?' This is an expression of Chinese pragmatism—balancing the pros and cons. Right now, the 'cons' of tolerating the presence of foreign Christian workers are given more weight. Unless they are seen to be contributing to China's goals, the incentives for approval are minimal.
2. 'Under the radar'
Foreign workers in China will need to re-think the meaning of 'under the radar'. It is sometimes thought that this means having little or no contact with government officials. This is short-sighted because relationships with local officials are often key in determining the success or failure of an endeavor.
It is also a mistake to think that it means simply avoiding certain religious language in correspondence or avoiding attendance at registered or international churches. However, what of the large family that rents a nice apartment, owns a car, travels abroad at least twice per year, and yet has no observable means of income? This is one criterion for identifying spies that is regularly seen on neighborhood 'anti-spying' posters.
Another common idea is that it is possible to remain under the radar by not using WeChat. Disconnecting from WeChat, however, in effect disconnects one from the Chinese community that we are seeking to serve. Using WeChat is almost a necessity of life in modern China. Using it wisely means having enough 'normal' chatter such that potentially problematic usage is relatively small and does not draw attention. How we present ourselves is important. In some ways, having a public Christian identity actually helps because then our Christian chatter is normal.
3. Contingency planning
Foreign Christian workers in China, no matter how 'safe' they think their situation is, need to engage in contingency planning. This should include a number of questions:
What do I need to have in place in case of a sudden departure?
How will I know if it is best to leave before the possibility of being deported?
What might trigger this decision to leave?
If I am interrogated, will confiscation of my cell phone and computer implicate Chinese or other foreign believers in a negative way?
It is possible, perhaps even likely, that the plans may never have to be implemented; however, having a plan may serve to lower anxiety and fear as well as minimizing the negative impact of actually having to leave.[6]
4. Indigenization
Foreign Christian workers in China need to be intentional about indigenization. A reading of the history of Christianity in China tells us that a day may come when foreigners are no longer welcome, especially in minority areas considered sensitive by the Chinese government. If this happens, will local leaders be prepared to carry on the work? If not, then we are in danger of repeating the mistakes of pre-1949 missionaries. The church in China is ultimately responsible for taking up its role in evangelism, discipleship, and reaching the unreached. Are we helping them to that end?
China under Xi Jinping is seeking to claim a leading role on the international stage by adopting a more activistic (some might say aggressive) foreign policy.
Mission to Chinese abroad
The nature and impact of the changes taking place are not limited to internal conditions or to foreigners working within China. China under Xi Jinping is seeking to claim a leading role on the international stage by adopting a more activistic (some might say aggressive) foreign policy. This is most keenly seen in the so-called 'Belt and Road Initiative', a Chinese government-policy to establish closer ties with countries in Asia, the Middle East, Eastern Europe, and Africa, by investing in economic development projects. As a result, more and more Chinese are traveling abroad.
Dark Red: Mainland China, Red: One belt economies; Pink: One road economies
This has two broad opportunities in terms of ministry:
Churches and believers in countries that are seeing an increase in their Chinese populations will have opportunities to reach them with the gospel. According to Asia News, in Africa alone, there are more than 1 million Chinese and 10,000 Chinese companies.[7] It also reports a growing movement of African churches and foreign mission groups engaging in evangelistic outreach among this Chinese diaspora.
These initiatives provide new opportunities for the growth of the Chinese church's nascent missions movement.[8] As the government encourages more of its people to go abroad, Christian entrepreneurs can establish their own modes of doing 'business as mission',[9] impacting their new communities for Christ.
As with anything in China, however, there are political risks. The death of Chinese missionaries in Pakistan in June 2017 heightened the Chinese government's awareness of, and sensitivity to, Chinese missionaries working in foreign countries. As a result, things have become more difficult for Chinese missionaries wanting to serve abroad.
While we do not know the specifics of what changes China will experience in the coming decades, we can be sure that, for local and foreign Christians, the next decades will not look like the past decades.
See https://www.amazon.com/China-Road-Journey-Future-Rising-ebook/dp/B000R38A48. ↑
See https://www.axios.com/china-communist-party-international-influence-307ad7e5-1b80-4578-a8f1-9b2333b4ecc3.html. ↑
Editor's Note: See article by David Ro, entitled, 'China's Conflicting Signals', in January 2016 issue of Lausanne Global Analysis https://www.lausanne.org/content/lga/2016-01/chinas-conflicting-signals. ↑
See https://www.chinasource.org/resource-library/chinasource-blog-posts/a-new-new-normal. ↑
See https://www.chinasource.org/resource-library/chinasource-blog-posts/sinicization-china-only-for-the-chinese. ↑
See https://www.chinasource.org/resource-library/chinasource-blog-posts/when-the-dream-comes-to-a-halt. ↑
See http://asianews.it/news-en/African-Evangelical-Christians-converting-China-46278.html. ↑
Editor's Note: See article by David Ro, entitled, 'The Rising Missions Movement in China (the World's New Number 1 Economy) and How To Support It', in May 2015 issue of Lausanne Global Analysis. https://www.lausanne.org/content/lga/2015-05/the-rising-missions-movement-in-china-the-worlds-new-number-1-economy-and-how-to-support-it. ↑
Editor's Note: See article by Mats Tunehag, entitled, 'Creating and Sharing Wealth', in May 2019 issue of Lausanne Global Analysis. https://www.lausanne.org/content/lga/2019-05/creating-and-sharing-wealth ↑
Feature image from 'People singing chant' (CC BY-SA 4.0).
Joann Pittman is the senior vice president of ChinaSource and editor of ZGBriefs. Prior to joining ChinaSource, Joann spent 28 years working in China as an English teacher, language student, program director, and cross-cultural trainer for organizations and businesses engaged in China. She has also taught Chinese at the University of Northwestern-St. Paul (MN), and Chinese Culture and Communication at Wheaton College (IL) and Taylor University (IN). She is the author of The Bells Are Not Silent: Stories of Church Bells in China
Date: 11 Apr 2019 · Grouping: Lausanne Global Analysis · Topics: Diasporas, East Asia, Religious Liberty
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