arxiv:1803.08063v2 [astro-ph.ep] 23 mar 2018 · ing us to isolate purely biotic phenomena emerging...

Gaian bottlenecks and planetary habitability maintained by evolving

model biospheres: The ExoGaia model

Arwen E. Nicholson,1∗David M. Wilkinson,2 Hywel T. P. Williams,1

and Timothy M. Lenton1

1Earth System Science, University of Exeter, UK2School of Life Sciences, University of Lincoln, UK

Accepted for publication by MNRAS 12th March 2018

Abstract

The search for habitable exoplanets inspires the question - how do habitable planets form? Planet habitabilitymodels traditionally focus on abiotic processes and neglect a biotic response to changing conditions on aninhabited planet. The Gaia hypothesis postulates that life influences the Earth’s feedback mechanisms to forma self-regulating system, and hence that life can maintain habitable conditions on its host planet. If life has astrong influence, it will have a role in determining a planet’s habitability over time. We present the ExoGaiamodel - a model of simple ‘planets’ host to evolving microbial biospheres. Microbes interact with their host planetvia consumption and excretion of atmospheric chemicals. Model planets orbit a ‘star’ which provides incomingradiation, and atmospheric chemicals have either an albedo, or a heat-trapping property. Planetary temperaturescan therefore be altered by microbes via their metabolisms. We seed multiple model planets with life while theiratmospheres are still forming and find that the microbial biospheres are, under suitable conditions, generallyable to prevent the host planets from reaching inhospitable temperatures, as would happen on a lifeless planet.We find that the underlying geochemistry plays a strong role in determining long-term habitability prospectsof a planet. We find five distinct classes of model planets, including clear examples of ‘Gaian bottlenecks’ -a phenomenon whereby life either rapidly goes extinct leaving an inhospitable planet, or survives indefinitelymaintaining planetary habitability. These results suggest that life might play a crucial role in determining thelong-term habitability of planets.

∗ [email protected]

1 Introduction

Most models of habitable planets and the boundaries ofthe habitable zone focus on the physical processes hap-pening on planets to determine the limits of habitabil-ity (for example [Cockell, 2007] and [Kopparapu et al.,2013]). These models neglect a biotic response to chang-ing conditions on an inhabited planet. The Gaia hypoth-esis postulates that life influences the Earth’s feedbackmechanisms to form a self regulating system [Lovelockand Margulis, 1974, Lenton, 1998, Lovelock, 2000]. Wesee the signature of life on our planet in the chemicalcomposition of our atmosphere, oceans, and soil. If lifehas a large effect on its host planet, this has implica-tions for habitable exoplanet research. One area wherethe Gaia hypothesis has relevance for exoplanet researchis around the establishment of life on a previously unin-habited planet. The idea of Gaian bottlenecks [Chopraand Lineweaver, 2016] suggests that early in a planet’shistory, assuming initially habitable conditions, life mustquickly establish self regulating feedback loops in orderto maintain habitable conditions. If it fails, life goesextinct and leaves the planet in a lifeless state. Gaianbottlenecks could be linked to recent models of bifurca-tions in early planet formation [Lenardic et al., 2016].

[Lenardic et al., 2016] suggest that the end state ofa planet is not entirely deterministic. Plate tectonics,key to climate regulation, are affected by the tempera-ture of the planet. To demonstrate this, Lenardic et. al.simulate a planet with plate tectonics, heat the planetuntil the tectonics disintegrate and then cool the planetback to its original temperature. After cooling, the platetectonics are not reformed, suggesting that there are twostable states for the same temperature. Venus and Earthare traditionally thought to be different classes of planet- although similar in size, mass and chemical composi-tion, Venus’s closer orbit to the Sun is thought to havedoomed it to its current state. However, evidence sug-gests that Venus once hosted large bodies of water [Don-ahue et al., 1982, Jones and Pickering, 2003], which sinceboiled away in a runaway greenhouse effect ([Kasting,1988]), leading to present day surface temperatures ofover 400oC. Lenardic et. al. suggest that Earth andVenus could represent two different stable states for thesame system. They predict that small fluctuations earlyin a planet’s history could determine the end state ofthat planet, with life possibly providing such a pertur-bation. Earth is very different from what it would beif it were uninhabited. Our atmosphere would be domi-nated by CO2 as is the case on Venus and Mars and this

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would affect the Earth’s surface temperature. If Venusonce had life back when it had water, could we be onthe lucky side of a Gaian bottleneck? While most modelsplace Venus outside the habitable zone as Venus receivesalmost twice the amount of solar radiation as Earth, afew allow the potential for a habitable Venus today (e.g.[Zsom et al., 2013] and [Yang et al., 2014]). Recent mod-els ([Yang et al., 2014, Way et al., 2016]) demonstratethe important role planetary rotation and topographyplay in understanding a planet’s climatic history, andsuggest that rocky planets that retain significant waterafter formation can experience habitable conditions wellwithin the traditionally defined inner edge of the habit-able zone (e.g [Kopparapu et al., 2013]).

Inspired by these important questions, we present anew abstract model of environmental regulation per-formed by evolving biospheres - the ExoGaia model. Wemodel simple ‘planets’ with atmospheres whose chemicalcomposition influences planetary temperatures. Modelmicrobes consume and excrete atmospheric chemicals,via temperature dependant metabolisms. Thus microbescan impact planetary temperatures by altering the chem-ical composition of their host planet’s atmosphere. Weinvestigate whether a simple biosphere can regulate itshost planet’s temperature within habitable bounds. Wefocus on a biotic response to planetary conditions, incontrast to most habitability models. We do not at-tempt to model the complexities of real planets, allow-ing us to isolate purely biotic phenomena emerging fromthe model. As most models of planetary habitabilityfocus on abiotic phenomena alone, future work shouldcombine these abiotic models, with a biotic model suchas ExoGaia to investigate the impact of adding bioticfeedback.

We will use real world language such as ‘planet’ and‘temperature’ when discussing ExoGaia as the model isinspired by real world questions. However, ExoGaia isnot intended to be a realistic model of planetary for-mation or dynamics; ExoGaia is an abstract model of athought experiment, in line with e.g. Daisyworld ([Wat-son and Lovelock, 1983]) that can be used to generatehypotheses about real planets - can a biosphere performplanetary regulation? Do Gaian bottlenecks occur?

This work builds on previous Gaian model research.There is a large body of literature on the Gaia hypoth-esis and on the many models used to investigate thishypothesis and so an in-depth review of Gaia will notbe given here but the reader is pointed to [Boston andSchneider, 1993, Lovelock, 2000, Schneider et al., 2013]for background on the Gaia hypothesis, and [Down-ing and Zvirinsky, 1999, Wood et al., 2008, McDonald-Gibson et al., 2008, Williams and Lenton, 2010, Dykeand Weaver, 2013, Nicholson et al., 2017, Arthur andNicholson, 2017] for an overview of some key Gaian mod-els investigated to date.

2 The ExoGaia Model

ExoGaia is heavily based on the ‘Flask’ models [Williamsand Lenton, 2007, Williams and Lenton, 2008, Williamsand Lenton, 2010, Nicholson et al., 2017], and shares

similarities with the ‘Greenhouse world’ model [Worden,2010, Worden and Levin, 2011]. We will first describethe model, then point out the key similarities and differ-ences between these models and ExoGaia. An in depthmodel description is given in Appendix A.

2.1 Model outline

We model simple ‘planets’ with well-mixed planetary at-mospheres, the composition of which influences plane-tary temperatures. These planets are host to microbiallife that consume and excrete atmospheric chemicals. Allplanets orbit a ‘star’ that provides incoming radiation.We use the following terminology to describe ExoGaia:

• Chemical - a particular chemical species. Eachchemical has either a cooling (e.g. reflective, highalbedo) or warming (e.g. insulating) effect on theatmosphere.

• Chemical Set - as the set of chemical species presentin the system.

• Geochemistry - the static network of geochemicallinks between chemical species, i.e. the abiotic pro-cesses.

• Connectivity - the probability of any two chemi-cal species in a chemical set being connected by ageochemical process (also referred to as a link orconnection).

• Planet - a system with a unique chemical set andgeochemistry combination.

• Biochemistry - the biological links created by mi-crobe metabolisms forming the biochemical net-work. Unlike the geochemistry of a planet, the bio-chemistry is not fixed; it evolves as a function ofmicrobial evolutionary and ecological dynamics.

• Abiotic Temperature (Tabiotic) - the temperature ofa planet without life when its atmosphere is in equi-librium. Most of our simulated planets have abiotictemperatures that are inhospitable to life. (For theresults presented in this paper the majority of sim-ulated planets (over 70%) have inhospitably highabiotic temperatures. Appendix B explores alter-native scenarios).

Figure 1 shows a schematic for the ExoGaia modelillustrating how each part of the planet - the chem-istry, geochemistry and biochemistry are connected. Weuse agent based dynamics to model our ExoGaia ex-periments and therefore time is represented in model‘timesteps’.

2.2 Microbes

Model microbes consume and excrete atmospheric chem-icals. Microbe metabolisms are genetically encoded andassume an external energy source, i.e. a star. Thetemperature of the host planet, Tplanet , affects microbemetabolisms, and for simplicity all microbes share thesame temperature preference, Tpre f . At Tplanet = Tpre f

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Figure 1: The ExoGaia model schematic. Circles repre-sent chemical species and arrows represent the geochem-ical or biochemical links between them.

microbial growth rates will be at the maximum. AsTplanet moves away from Tpre f the microbes’ consump-tion rate decreases and the growth rate drops. If thedifference between Tpre f and Tplanet is too large, mi-crobes will be unable to metabolise and will not con-sume/excrete any chemicals. Microbes die if theirbiomass drops below a certain threshold and there isalso a constant probability of random death. If a mi-crobe’s biomass reaches the reproduction threshold itreproduces asexually, with a constant probability of mu-tation for each gene, allowing new species to evolve onplanets.

2.3 Chemicals

Model planet atmospheres are composed of various‘chemical species’. There is a large body of literatureon chemical reaction network theory [Feinberg, 1987]which models the behaviour of real world systems andhas been applied to planetary atmospheres, e.g. [Soleand Munteanu, 2004]. We use a very simple chemicalreaction network in ExoGaia.

Each chemical species has an insulating or a reflectiveproperty. We simplify real chemistry and limit a chem-ical species to being either insulating or reflecting, butnot both. We can also take this simplification to be theoverall impact a chemical has on the atmosphere. Thecollection of chemical species (and their greenhouse /albedo properties) possible on an ExoGaia planet is re-ferred to as a ‘chemical set’. Not all chemical species ina chemical set might be present on a model planet. For achemical species to be present it must be created by someprocess. The processes by which a chemical species canbe created (or destroyed) are covered in later Sectionson “Atmosphere”, “Geochemistry” and “Biochemistry”.

All model atmospheric chemicals are assumed to begaseous. Realistic atmospheric gases have both in-sulating and reflecting properties (via absorption andRayleigh scattering) with the net effect depending onthe abundance of the gas, the overall atmospheric mass[Wordsworth and Pierrehumbert, 2013], and the spec-tral energy of the host star [Kaltenegger and Sasselov,2011]. In the ExoGaia model only the abundance of thegas determines it’s overall impact on the host planet.In realistic scenarios, the outer edge of the Habitablezone depends on the limit where the condensation and

scattering caused by adding more CO2 to an atmosphereoutweighs its greenhouse effect [Kopparapu et al., 2013].

2.4 Temperature

We use a linear approximation of the Stefan-Boltzmannlaw when calculating Tplanet . This simplification hasbeen shown to not greatly change the overall behaviourof the Daisyworld model [Watson and Lovelock, 1983][Saunders, 1994] [De Gregorio et al., 1992] [Weber, 2001][Wood et al., 2006]. The Stefan-Boltzmann equation isclose to linear at real world habitable temperatures, i.e.near 22oC. In ExoGaia, we are only interested in plane-tary dynamics when there is life on a planet, so while the‘temperature’ in the ExoGaia model is not constrained,we are only interested in a narrow range of habitabletemperatures. The temperature behaviour outside thisrange is not important to the results. We will be usingan unrealistic Tpre f for our model microbes to highlightthe abstract nature of the model, however as a near lin-ear relationship exists at habitable conditions on Earth,and we are striving to simplify the model abiotic envi-ronment as much as possible, we use a linearised Stefan-Boltzmann law in our model and take β ∝ T , where β isthe energy provided to the planet by the host star pertimestep and T is temperature. We then make a fur-ther simplification and take the value of β to be equalto the value of T . Appendix B4 further explores thistemperature simplification.

2.5 Atmosphere

Many real planets have (or had), for example, volcanoesthat spew forth aerosols and gases which come from thecrust and the mantle. Gases can be lost from the planet’satmosphere by processes such as sublimation or somegases (e.g. hydrogen) can be lost to space. We abstractthese processes in the ExoGaia model.

All model planets start with an ‘empty’ atmosphere,and a constant inflow of chemicals from an externalsource begins at the start of each experiment. The‘source chemicals’ are the subset of chemical species inthe chemical set that experience this inflow. Non-sourcechemicals do not exist on a planet unless created viaa geochemical or biochemical process. There is a con-stant rate of atmospheric chemical outflow, performedby removing a fixed percentage of the well-mixed atmo-sphere each timestep. There is no spatial structure inthe model.

A planet’s atmospheric composition influences Tplanet .We define AI as the fraction of the planet’s current ther-mal energy retained by the atmosphere via insulation,and AR as the fraction of incoming radiation reflectedby the atmosphere. Using the simplification describedin Section 2.4, the value of βplanet is the value of Tplanet .Therefore (1− AI )βplanet is equivalent to a planet’s tem-perature decrease due to energy radiation into space,where βplanet is the thermal energy of the planet. Simi-larly, (1 − AR)βstar is equivalent to the increase in tem-perature due to incoming solar radiation, where βstar isthe incoming solar radiation to a planet per timestep.

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Therefore a stable temperature is achieved if:

(1 − AI )βplanet = (1 − AR)βstar (1)

The values of AI and AR depend on the chemical com-position of the atmosphere, and exist in the range [0, 1].This relation is described in an equation in AppendixA. We calculate βupdate, the updated thermal energy ofa planet including the insulating and reflecting effect ofthe atmosphere, in the following way:

βupdate = AI βplanet + (1 − AR)βstar (2)

We neglect to model the complexities of atmosphericabsorption in ExoGaia as that level of realism is unnec-essary given the abstract simplified nature of the model.We also see that each timestep:

βlost = (1 − AI )βplanet + ARβstar (3)

of energy is lost to space either as radiation from theplanet or as reflected solar radiation. Although real starsage and change in luminosity, we keep our model simpleand keep βstar constant, to investigate the habitability ofplanets without external perturbation. This also makessense biologically when considering the generation lengthof a microbe. It would take very, very many generationsof microbes for a star to alter its solar radiation in asignificant way.

If AI = 1, a planet will perfectly insulate, and ifAR = 1 a planet will perfectly reflect all incoming radia-tion. Neither of these extremes is physically realistic; noatmosphere can perfectly insulate, nor reflect all incom-ing radiation, however this approach was favoured overchoosing an arbitrary cut-off value. We are interestedin regulation on habitable planets and in our experi-ments, the probability of Tplanet equalling Tstable, thetemperature required for a stable microbe population,at these limits is extremely unlikely. Taking Equation1, if AI = 1, then AR = 1 must also be true for a con-stant Tplanet . For long-term habitability, AR = AI = 1must occur when Tplanet = Tstable. This is highly un-likely and this scenario was not found to have happenedin the results presented in this paper. Therefore thissimplification does not impact on the conclusions drawnfrom our model.

2.6 Geochemistry

Geological links, or reactions, represent geological activ-ity and take the form of A → B, where A and B aredifferent chemical species. This is a simplification ofreal chemistry where multiple reactants come togetherto form multiple products. Keeping the geological re-actions simple allows us to more easily track chemicalsthrough the system as they are converted via geologicalprocesses.

Geochemical links are generated based on a connec-tivity parameter C, which has a value between [0, 1].C = 0.2 would determine a 20% probability for any pair

of chemical species to be connected by a geochemicalprocess. The direction of the link connection determineswhich direction a process take place, i.e. A → B orB → A. We limit geological processes to acting in onlyone direction, i.e. if A → B then B → A is not al-lowed. We therefore describe only the net movementof chemicals linked by a geological process. The direc-tion of a process has equal probability of acting in eitherdirection. The link ‘strength’ determines how strong ageological process / reaction is, and is taken from therange [0, 1]. A link strength of L = 0.3 in the directionA→ B would mean that per timestep, 30% of the parti-cles of chemical A would be converted into chemical B.Figure 2 depicts two different geochemistries. As chem-ical abundances change, the rate of a geological processwill change. E.g. a geological process of the type A→ Bwill happen at a faster rate when chemical A is abundantcompared to when it is scarce.

Geochemical links are not temperature dependant andremain constant throughout each experiment, thereforethere are no geochemical temperature feedback loops inExoGaia. Although many real world processes, e.g. sil-icate weathering, are temperature dependant, to isolateregulating effects caused by the microbes we remove thisaspect from our model. This allows us to be confidentthat any regulation emerging in ExoGaia is due to theactions of the biosphere. This simplification does how-ever limit the realism of the model and thus limit itsapplicability to real planets.

2.7 Biochemistry

Model microbes form temperature dependant biochemi-cal links via their metabolisms, e.g. a species that con-sumes chemical A and excretes chemical B forms thebiochemical link: A → B. The strength of a biochem-ical link depends on the number of microbe with thecorresponding metabolism. Unlike the geochemical net-work, the biochemical network is not static; Biochemi-cal links can change in strength, appear, and disappear,over time as the microbe community changes. Biochem-ical links can act in both directions, e.g. the biochemicallinks A → B and B → A are allowed to exist simulta-neously. An example biochemistry is depicted in Figure2. These microbe metabolisms are highly simplified hav-ing only a single chemical reactant and single chemicalproduct. Real microbe metabolism are more complexwith multiple reactants and products. Using simplifiedmicrobe metabolisms allows for easier tracking of chem-icals around ExoGaia systems, and makes the networkdiagrams presented later in this paper easier to produceand interpretable. Versions of the Flask model, on whichExoGaia is heavily based, have explored more complexmicrobe metabolisms with abiotic environmental regula-tion remaining a feature of these models [Williams andLenton, 2008] [Nicholson et al., 2017].

The outflow of chemicals from the atmosphere is keptlow, such that the timescale for a chemical to completelyleave the atmosphere once produced by microbial activ-ity is far longer than the typical lifespan of a microbe.This decouples the selection on individuals from theirenvironmental effects and allows for long-term conse-

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(a) Chemical set A (b) Weakly connectedgeochemistry

(c) Highly connectedgeochemistry

(d) Example biochem-istry

Figure 2: Geochemical and biochemical networks. Cir-cles represent chemical species. The number inside eachchemical species is its greenhouse (positive) or albedo(negative) property. Red circles are source chemicals;they have an influx from outside the system. Black solidarrows represent the geochemical links between chemicalspecies. Green dashed lines represent biochemical linkscaused by microbes’ metabolisms. The size of the circledoes not represent the abundance of a chemical species;if a chemical species is not a source chemical nor hasany geochemical or biochemical processes producing it,it has an abundance of zero.

quences (when compared to the average lifespan of amicrobe) to occur from microbe activity. One real worldexample of this is the time it would take for our at-mosphere on Earth to lose most of its O2 if photosyn-thesis suddenly ‘switched off’. If a species evolves witha metabolism that produces a chemical not currentlyabundant in the atmosphere - Cnew, a different speciesthat consumes Cnew needs to emerge quickly before itbuilds up enough to disrupt the temperature regulation,or the species producing Cnew must die out, otherwisethe whole community is susceptible to extinction.

2.8 Planets

We define a planet as a system with a particular chem-ical set and geochemistry. We can therefore run manyexperiments on a single planet to determine whether aplanet has differing end states depending on early con-ditions.

No external forcing is present on our planets. Eachplanet’s geochemistry remains fixed throughout an ex-periment and the incoming radiation βstar remains con-stant. Real planets are subjected to changing host starluminosities and changing rates of geological processesover time, however to understand how the biota are ableto adapt their host planet, we keep the environmentfixed. It is then clearer when emerging phenomena aredue to the biota.

An in-depth description of the model can be found inAppendix A.

2.9 New Features

ExoGaia is based on the Flask model [Williams andLenton, 2007, Williams and Lenton, 2008, Williams andLenton, 2010, Nicholson et al., 2017], which featuresmodel ‘flasks’ containing microbe communities. Theseflasks experience an inflow and outflow of ‘nutrients’,with the inflow medium at a constant ‘temperature’.Microbes change the temperature directly as a byprod-uct of their metabolism - increasing or decreasing it bya set amount. Differing from previous models such asDaisyworld [Watson and Lovelock, 1983], microbe’s donot have localised space, however temperature regula-tion still robustly emerges. In the ExoGaia model, in-stead of microbes directly affecting a temperature, theyimpact Tplanet via consuming and excreting atmosphericchemicals. Also differing from the Flask model, the mi-crobes are introduced to an ExoGaia planet, in mostcases, before the atmosphere has reached equilibrium.

‘Greenhouse World’ [Worden, 2010, Worden andLevin, 2011] is a model of microbe communities inter-acting with insulating chemicals via their metabolismto regulate their environmental temperature. Althoughsimilar, ExoGaia has some key differences. Firstly, mu-tation only takes place in Greenhouse world when thesystem is in a stable state. Second, Greenhouse systemsare seeded with a diverse community of microbes. Thesecommunities then reorganise via species dying off until astable configuration is reached. Greenhouse world there-fore demonstrates how diverse communities can scaledown to a stable state, whereas in ExoGaia we seed witha single species, and the microbe community must evolvesuitable metabolisms to regulate their environment, thusbuilding up a regulating community where Greenhouseworld reduces down. All life on Earth shares a commonancestor [Sapp, 2009], and so while it may theoreticallybe possible for life to form independently multiple times,that does not seem to be the case on Earth, and so wemirror this behaviour in our model.

A slow outflow of chemicals from a planet’s atmo-sphere means that the consequences of microbial actionspersist longer than their average lifespan - an impor-tant feature not present in previous models - allowingus to see how communities of microbes react to thelong-term effects, especially the negative effects, of theirmetabolism.

3 Method

Using this model, we investigate how the geochemicalnetwork of a planet affects the planet’s colonisation suc-cess and the long-term habitability.

We set the incoming radiation from the ‘star’ pertimestep βstar = 500 and set all microbes to share apreferred temperature Tpre f = 1000. As this Tpre f cor-responds, in our model, to a thermal energy of βpre f =1000, we see that for a planet to reach habitable con-ditions, it must have an insulating atmosphere. Recall

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Table 1: The greenhouse and albedo properties of chemi-cal set A. The bold chemicals represent the source chem-icals. The values in the table represent each chemical’simpact on the atmosphere - insulating if positive, andreflective if negative.

Chemical Greenhouse / albedo properly1 -0.402 -0.473 0.404 0.945 -0.436 0.427 0.478 0.98

Mean 0.23

that all temperatures and energy values in the ExoGaiamodel are abstract. We generate the insulating / re-flective properties of each chemical in our Chemical setby drawing a random number from the range [−1,+1].A negative value means a chemical species is reflective,and a positive means it is insulating. We have 8 chemi-cal species in our chemical set. We choose a chemical setsuch that the average effect of each chemical species isinsulating. As βstar < βpre f , choosing an overall insulat-ing chemical set insures many planets in our experimentswill reach habitable planetary temperatures. This allowsus to investigate how the microbe community interactswith it’s host planet. Choosing an insulating chemicalset does bias us to see more potentially habitable planetsand thus increase the number of experiments where long-term habitability may be possible, but it does not helpmicrobe communities, once seeded, in regulating theirplanet. The quantitative values produced by the Exo-Gaia model cannot be translated into real world valuesfor an abstract model such as this. The qualitative be-haviour of the model is the key point of interest. Chem-ical set A is used for the results presented in this paper,see Table 1.

Despite sharing the same chemical set, planets varyhugely from one another due to their geochemical net-works. These networks will determine how fast temper-atures change, and the value of Tabiotic, for each planet.As we will see, sharing a chemical set does not result inidentical planetary behaviours. The huge number of geo-chemical network configurations allows for many uniqueplanets. In Appendix B, we present results from ex-periments with alternative chemical sets, but the sameβstar = 500 value, exhibiting the same model behaviourspresented with chemical set A, thus showing that chem-ical set A is not a unique case.

We investigate a range of geological connectivity, C,for our planets: C = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9].As our model is abstract, we do not know what connec-tivities might be represented in the real world and so wecover almost the full range of possible values excludingC = 0, as we certainly live in a world of chemical reac-tions, and C = 1 as not every chemical can react withevery other in real world chemistry. By exploring thislarge range we can investigate the effect connectivity has

on the habitability of a planet and see how importantthis parameter is to the system dynamics.

We perform the following steps for each connectivityin list C:

1. Set up the planet’s geological network

(a) Begin the geological processes on the planet,allowing atmospheric chemicals to build up

(b) Seed planet with a single species whenTplanet = Tpre f

(c) if Tpre f is never reached, seed after 5 × 104

timesteps

(d) The experiment ends 5 × 105 timesteps afterseeding

2. Repeat step b) 100 times with different randomseeds initialising the microbes

3. Repeat steps (a) to (c) 100 times with different ran-dom seeds initialising the planet’s geological net-work

There is evidence suggesting that life appeared onEarth as soon as conditions allowed [Nisbet and Sleep,2001]. We treat our simple ExoGaia planets in a simi-lar manner, seeding the planet when Tplanet = Tpre f (ifthis happens at all, some planets will never reach Tpre f ).Because of the way temperature is determined in themodel, planet temperatures might never exactly matchTpre f , so to ensure seeding happens we determine a suit-able ‘seeding window’ Sw = [Tpre f ,Tpre f + 50]. Seedingcan occur when planet matches any temperature in Swbut seeding can only occur once. If a seed window hasnot been passed after 5 × 104 timesteps then an seedingattempt is made once, and the model then continues asusual for 50 × 104 timesteps.

This means that we will often be seeding the planetsbefore the atmosphere is at equilibrium, and the Tabiotic

of a planet will often be far too hot for our microbe lifeto survive - effectively undergoing a highly simplifiedgeologically induced greenhouse runaway. We thereforewant to investigate whether the model microbes, withtheir simplified metabolisms, can take control of theirhost planet once they appear and keep the planet’s tem-perature within habitable bounds.

When we seed our planet with a single species, we seedwith a species that consumes chemicals currently avail-able on the planet. Any life with an unviable metabolismwould very quickly die out. We could continually seedrandomly until a species took hold on the planet, butpredetermining that species we are seeding with couldpotentially survive (it has a food source) saves time.

3.1 Habitability

There are two types of habitability of interest to us:

• Colonisation success - what percentage of the timea planet is able to support life for tsurvive > 103

timesteps.

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• Long-term habitability / survivability - what per-centage of the time a planet is able to support lifefor the entire experiment duration: tsurvive = 5×105

timesteps.

The colonisation success indicates whether planetaryconditions were suitable to support a self sustaining pop-ulation for some time. 103 timesteps is twice as long asthe timescale for microbe death; therefore if the bio-sphere survives longer than 103 timesteps, conditionsmust have allowed microbes to consume enough food toreproduce at a high enough rate to support a stable pop-ulation. Long-term habitability measures the microbesability, once they have successfully colonised a planet, tomaintain habitable conditions for long time spans.

Over a number of experiments, if a planet has highcolonisation success but low late term habitability, it isa planet where life is usually able to colonise the planetand become established, but often fails to survive to theend of the experiment. If a planet has equal colonisationsuccess and long-term habitability, it means that oncelife is established on a planet, it always survives the fullexperiment.

4 Results

In a highly abstract model such as ExoGaia, quanti-tative results cannot be applied directly to real worlddata, however exploring the qualitative behaviour of themodel demonstrates how biosphere-environment coupledsystems, such as the Earth and other inhabited planets,might emerge and under what circumstances. We findthat on a diverse array of planets, life is able to ‘catch’the planetary atmospheric evolution of it’s host planetand maintain habitable conditions. For the majority ofExoGaia planets, the Tabiotic of the planet is highly in-hospitable, yet we find many model planets hosting bio-spheres for long time spans. This demonstrates thatmodel biospheres are capable of preventing planetarytemperatures from reaching uninhabitable levels, andthus in principle, of regulating planetary temperatures.

We find that colonisation success and long-term hab-itability success rates differ between model planets. Aswe performed 100 experiments on each planet, we cancreate a survival curve for each planet. Figure 3 showsthe survival curves - the number of experiments (out of100) with surviving life - for each planet against time(note the log x-axis).

For low C, Figures 3a and 3b, there is no strong trendfor when systems become extinct. Life is often able tosuccessfully colonise a planet, but the planet is unlikelyto experience long-term habitability. For higher C westart to see planets with two distinct experiment out-comes: either life fails to colonise the planet and quicklygoes extinct, or life successfully colonises the planet andsurvives the full experiment. For these planets, thecolonisation success and the long-term habitability suc-cess of the planet are equal, meaning that if life is able toestablish itself, it will survive for an indefinite period oftime. This behaviour is explained in Section 4.3.3. Wesee for C = 0.9, Figure 3f, that all experiments either

(a) C = 0.1 (b) C = 0.2

(c) C = 0.4 (d) C = 0.6

(e) C = 0.8 (f) C = 0.9

Figure 3: Each line represents the survival curve of aplanet. These survival curves tell us out of 100 exper-iments, how many are alive for each timestep. Criticalplanets show extinctions at random times, while Bot-tleneck planets show an early abrupt dying out and nodeaths at longer timescales. Abiding planets have all100 experiments alive for the whole experiment, and Ex-treme and Doomed planets always quickly die off earlyon in the experiment with non surviving to mid or longtimescales. The first extinctions seen in each plot showthe minimum time it takes for a microbe to starve todeath. Note the log x-axis.

survive for the full duration, or become extinct early on,with no mid or late time extinctions taking place.

Table 2 shows the number of planets that fail colonisa-tion for all 100 experiments, and planets that had long-term habitability for all 100 experiments. In Figure 3the number of planets that always immediately becameextinct is difficult to determine, and it is not possibleto see the number of planets that always survived thefull experiment, so taking Figure 3 and Table 2 togetherwe get a more complete picture of the different planets’behaviour with changing connectivity.

Based on our results we can determine 5 differentclasses of planet:

• Extreme - Planets that never reach habitable tem-peratures

• Doomed - Planets that do reach habitable temper-atures but are unable to support life

• Critical - Planets that can be successfully colonisedby life, but go extinct at random times

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Table 2: The number of planets that failed colonisationfor 100% of experiments, and the number of planets thathad long-term habitability (l.t.h.) success for 100% ofexperiments. The total number of planets simulated foreach C was 100.

C 100% failed colonisation 100% l.t.h success0.1 18 10.2 35 00.3 38 70.4 36 130.5 39 310.6 32 420.7 15 640.8 12 700.9 12 77

• Bottleneck - Life either fails to colonise these plan-ets, or successfully colonises and enjoys long-termhabitability - a bottleneck effect

• Abiding - Life successfully colonises and experi-ences long-term habitability for all experiments

These planet class definitions are based only on twotimescales: the colonisation success timescale which de-pends on the microbe death timescale; and the experi-ment length.

We will now explain the regulation mechanism emer-gent in the ExoGaia model, and then show how aplanet’s geochemical network affects planetary habit-ability. We will then present example model planets todemonstrate various model behaviours, and finally showhow planetary habitability is affected by connectivity.

4.1 Regulation Mechanism

The regulation mechanism takes the form of a negativefeedback loop. All microbes share the same Tpre f andthe same well-mixed environment, therefore any envi-ronmental change impacts all microbe species equally.There is no mechanism by which microbes can evolveonly heating or cooling metabolisms, if abundant chem-icals of any type are present on a system, microbes can,and will, evolve to consume those chemicals. There-fore it is the collective behaviour of the whole biospherethat leads to regulation rather than any specific mi-crobe species. When Tplanet = Tpre f , assuming abundantchemicals, microbe populations will increase. The con-sumption rate of the microbes, K, drops as temperaturesdiverge from Tpre f , therefore there are two temperatureswhere the value of K will lead to a stable population:T+s > Tpre f and T−s < Tpre f . For a stable Tplanet microbepopulations must be stable.

When βstar < βpre f , where βpre f is the thermal en-ergy of a planet at Tpre f , an insulating atmosphere isrequired for habitable temperatures. This is the case forthe results presented in the main body of this paper (al-ternative scenarios are explored in Appendix B). In thisscenario, when Tplanet < Tpre f , the effects of increasing(+) Tplanet are:

1. + Tplanet → + Population

2. + Population → - Tplanet

Flipping the signs, we also see that a decrease inTplanet leads to an increase in Tplanet . This forms a neg-ative feedback loop. Increasing Tplanet improves habit-ability, which increases K, and thus increases microbepopulations. This causes planetary cooling as the insu-lating power of the atmosphere is reduced via increasedmicrobe consumption. Cooling degrades the environ-ment, reducing microbe populations, and thus causeschemicals to build up in the atmosphere, increasingTplanet and bringing us back to the start of the loop.This behaviour is known as ‘single rein-control’ wherethe biota collectively form a single ‘rein’ which ‘pulls’ thesystem in one direction, while the abiotic processes onthe planet ‘pull’ the system in the other direction. Rein-control feedback mechanisms have been demonstratedin previous Gaian models, namely in Daisyworld [Woodet al., 2008], and the Flask model [Nicholson et al., 2017].

If instead Tplanet > Tpre f , the effects of increasing thetemperature are now:

1. + Tplanet → - Population

2. - Population → + Tplanet

Now an increase in Tplanet degrades the environmentfor life and leads to further rises in Tplanet in a desta-bilising positive feedback loop. This results in microbeextinction. Temperature regulation therefore takes placeat T−s but not at T+s . The behaviour seen in both feed-back loops is known as feedback on growth [Lenton,1998].

(a) Negative feedback loop forTplanet < Tpre f

(b) Positive feedback loop forTplanet > Tpre f

Figure 4: The regulating negative feedback loop (a), andthe destabilising positive feedback loop (b). Arrows in-dicate the effect of an increase in the source on the tar-get. The sign indicates whether an increase in the sourceleads to an increase or decrease the target. In (a) an in-crease in temperature causes an increase in population,whereas an increase in population causes a decrease intemperature. This forms a negative feedback loop. In(b) an increase in temperature decreases the population,and a decrease in population further increases the tem-perature. This forms a positive feedback loop.

When Tplanet > Tpre f a positive feedback loop in theopposite direction is possible, with runaway planetarycooling occurring until Tplanet < Tpre f , where the neg-ative feedback loop takes over. However as Tabiotic >Tpre f for a habitable planet, when Tplanet > Tpre f a re-duction in temperature is unlikely; when habitability islow the abiotic processes on the planet dominate. IfTplanet rises to above Tpre f , extinction is the expected

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outcome. Figure 4 shows the positive and negative feed-back loops for Tplanet < Tpre f and Tplanet > Tpre f .

4.2 Geochemistry and Habitability

We investigated the underlying geochemical networks forplanets of each class to determine what lead to the dif-ferent planetary behaviours, and found that a planet’sgeochemical network strongly determines its chance forlong-term habitability success. We found two key prop-erties:

• The geochemical network must be such that plane-tary temperatures recover faster from any microbeinduced cooling than the time it would take for thepopulation to go extinct due to starvation.

• For long-term habitability success, the geochemi-cal network must provide many recycling chemicalloops.

Different geochemical networks will lead to tempera-ture changes taking place at different rates on differentplanets. As seen in Section 4.1, for potentially habit-able planets, microbe populations cause planetary cool-ing. For a planet to be habitable, the geochemical net-work must be such that Tplanet increases after microbeinduced cooling fast enough to avoid microbe extinction.The rate of temperature change due to abiotic processesalone plays a strong role in determining the colonisationsuccess of a planet.

This is not enough to guarantee long-term habitabil-ity however. As seen in Figure 3, many planets thatwere successfully colonised later went extinct. Planetsthat experienced long-term habitability all shared thefeature of having a geochemical network that providedmany chemical recycling loops. For an example, assumethat there are only four chemicals in the chemical setand take the geochemical network 1→ 2→ 3→ 4→ 1,where numbers represent chemical species and arrowsare geological processes. In this example, for any mi-crobe metabolism, the geochemistry recycles the wasteproduct back to the food source. This allows a microbecommunity to ‘control’ the entire atmosphere with only asingle metabolism. By influencing the abundance of onechemical species in the loop, all other chemical speciesare impacted. Temperature regulation takes place in Ex-oGaia via the collective actions of the biosphere consum-ing the atmospherical chemicals without bias, thereforeif there are many geochemical recycling networks, andmicrobes can influence the abundance of many chemi-cal species with fewer metabolisms, achieving planetaryregulation is likelier.

Now consider the geochemical network 2→ 3→ 4→1. Chemicals now accumulate as chemical species 1, andthe geochemical network does not recycle waste backto food for many metabolisms e.g. 2 → 3 or 3 → 1.These scenarios are depicted in Figure 5. Biologicallinks are temperature dependant and change as plan-etary conditions change. This makes them less stablethan the temperature independent geochemical links.Therefore if a geochemical network does not have many

Figure 5: Circles represent chemical species and arrowsrepresent the geochemical links between them.

recycling loops, and biology must ‘complete’ many miss-ing links, the system will be more sensitive to tempera-ture changes. Biological links can amplify perturbationsthroughout the system as Tplanet impacts the biosphere,which impacts the biochemical network, which furtherimpacts Tplanet . Therefore these systems are highly sus-ceptible to perturbation, and as any large-scale changesin temperature carry a risk of extinction, these systemsare less likely to experience long-term habitability.

4.3 Example planets

We now present an example planet for each planet class(each example planet has connectivity C = 0.4) todemonstrate how the underlying geochemical networkimpacts a planet’s colonisation success and long-termhabitability.

4.3.1 Uninhabitable planets

The majority of model planets that fail in every experi-ment to support life have a Tabiotic that’s too cold for lifeto survive. Once seeded, life either cannot metabolise atall, or can only metabolise at levels too low for a sta-ble population, leading to extinction. The underlyinggeochemistry doesn’t have much effect here other thanto convert the heating chemical species to cooling onesthus rendering the planet uninhabitable. We will referto this type of uninhabitable planet as ‘Extreme’ planets- planets with temperatures that never reach habitablelevels.

A small number of uninhabitable planets have aTabiotic such that Tabiotic ≥ Tpre f . These planets typi-cally have only weakly insulating atmospheres, and tem-peratures rise very slowly. On these planets when lifeis seeded, it consumes this insulating atmosphere andcauses planetary cooling pushing the planet to unin-habitable temperatures. This in turn causes the mi-crobe population to decline. With a smaller population,the abiotic processes on the planet dominate, howeverTplanet does not rise to the bounds of habitability fastenough and life on the planet goes extinct. We referto these planets as ‘Doomed’ planets; although temper-atures on these planets do reach habitable levels andmicrobes can initially metabolise, life always fails tocolonise the planet.

Figure 6 shows snapshots of the geochemistry andbiochemistry of an example Doomed planet that hadan Tabiotic such that Tabiotic > Tpre f . The static geo-chemistry is represented by black solid lines (with the

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(a) tseed (b) tseed + 100

(c) Temperature and totalpopulation for early time

Figure 6: Example Doomed Planet: Snapshots oftwo experiments for the same planet showing the geo-chemical network in black solid lines, and the biochemi-cal network in green dashed lines. Red circles representsource chemicals. tseed is the time the planet was seededwith life. Plot c) shows temperature (red) and total pop-ulation (black) against time. C = 0.4. The thick end ofthe geochemical links indicates positive direction.

thick end indicating a positive direction of chemical flow)and the non-static biochemistry is represented by greendashed lines and changes as the microbe communitychanges. Circles indicate chemical species with sourcechemicals as red circles. We see the microbe seeding oc-cur when Tplanet = Tpre f . Microbes are able to establishbiochemical links beyond the seed species (Figure 6b),however the planet becomes extinct soon after. Figure6c shows that the planet’s temperature was increasingvery slowly before microbe seeding, and that planetarytemperatures do not recover fast enough from microbeinduced cooling to avoid microbial extinction. For thisplanet, the geochemical network was arranged such thatabiotic temperature changes happen too slowly to coun-teract microbial cooling making the planet unsuitable forlife. This behaviour, where life reduces the habitabilityof its environment, is often called ‘anti-Gaian’ behaviourin contrast to ‘Gaian’ behaviour where life enhances itsenvironment’s habitability.

This behaviour highlights an important feature of themodel - a habitable temperature is not enough for hab-itability. All life interacts with its environment, remov-ing and producing chemicals during metabolisation. Assuch, life requires an environment where interacting withthe environment does not destroy habitability. On these‘Doomed’ planets, the atmosphere is only weakly insulat-ing, and atmospheric depletion by the seeded microbes’consumption quickly results in inhospitably cold tem-peratures. As all life in this model experiences the sameenvironment, it is not possible for microbes to evolveonly metabolisms that consume cooling chemicals. If life

cannot interact with its environment without pushing itpast the bounds of habitability, then despite reachinghabitable temperatures, such planets are not good can-didates for hosting life. The behaviour of these planetswhen ‘reseeding’ - life is reintroduced after going extinct- is included in the experiments is explored in AppendixB.

4.3.2 Critical planets

Critical planets often have high colonisation success how-ever long-term habitability is unlikely. There is no obvi-ous trend in when a Critical planet will become extinct.Critical planets tend to have geochemical networks thatcause Tplanet to rise faster than seen in Doomed planets,meaning that Critical planet temperatures can recoverfrom microbe induced cooling fast enough to prevent ex-tinction. This provides a good environment for colonisa-tion success, however, Critical planet geochemical net-works do not provide a large number of chemical re-cycling networks, therefore certain chemical species canquickly accumulate in abundance and require microbeintervention to prevent large temperature changes.

Figure 7 shows snapshots of the geochemistry and bio-chemistry on a Critical planet, with the temperature andpopulation curves against time. We see that the bio-chemistry acts erratically; biochemical links quickly infil-trate the geochemical network but later disappear. Fig-ure 7e shows a large population spike after seeding whichthen dies down. Differing from the Doomed planet (Fig-ure 6), the temperature recovers fast enough from mi-crobe induced cooling to avoid extinction, and the plan-etary temperature is then regulated by the microbes forapproximately 55,000 timesteps, Figure 7f. For Doomedplanets, cooling by microbes results in extinction, how-ever for this Critical planet, cooling prevents Tplanet

from rising to inhospitable levels, and thus avoids mi-crobial extinction. In Figure 7f we can see the purelyabiotic temperature behaviour of this planet when lifegoes extinct; we see that the planet’s temperature im-mediately and rapidly climbs after microbial extinction.This demonstrates how the same behaviour by life couldbe classed as ‘Gaian’ or ‘anti-Gaian’ depending on theexternal environment.

Figure 7f shows the total population fluctuates arounda value of ≈ 120 with extreme population spikes hap-pening a few times - the last of these causing the ex-tinction of the system. These extreme population spikesoccur due to the disconnected nature of the geochemicalnetwork; chemical species 2 is entirely unconnected toother chemical species geochemically. Figure 7c show abiochemical link from 8 → 2, however no biochemicallink converting chemical species 2 to any other chemicaland thus the abundance of chemical species 2 increasesrapidly. If a microbe evolves that consumes chemical2, it will have an abundant source of food. As chemi-cal 2 is a cooling chemical (see Table 2), depleting thischemical species will heat the system, pushing Tplanet

closer to Tpre f and increasing all microbes’ reproductionrates, causing an explosion in population. This popula-tion explosion will cause overall depletion of the atmo-spheric chemicals, and thus, as on average the chemicals

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(c) tseed + 500 (d) tseed + 1000

(e) Temperature and totalpopulation for early time

(f) Temperature and totalpopulation for the inhabitedperiod of the experiment

Figure 7: Example Critical Planet: Snapshots of asingle experiment showing the geochemical network inblack solid lines, and the biochemical network in greendashed lines. Red circles represent source chemicals.tseed is the time the planet was seeded with life. Plotse) and f) show temperature (red) and total population(black) against time. C = 0.4. The thick end of thegeochemical links indicates positive direction.

in Chemistry A are greenhouse chemicals, the temper-ature will cool and the population will die back down.This scenario is the cause of the first extreme spike seenin Figure 7f. Not all Critical planets have completelyunconnected chemical species as in Figure 7 but theyshare the common characteristic of a more disconnectedgeochemical network with fewer purely geochemical re-cycling loops. Biochemical links are more susceptible tooscillation as changes in one link can have knock on ef-fect to others amplifying the perturbation, thus the morebiochemical links required to close recycling loops, theless stable the system is. This is what makes Criticalplanets susceptible to total extinction.

4.3.3 Bottleneck planets

Bottleneck planets either fail to be successfullycolonised, or are successfully colonised and life survivesthe full experiment. Bottleneck planets once successfullycolonised are not susceptible to extinction.

Figure 8 shows snapshots of the biochemistry overlaid


(c) tseed + 500 (d) tseed + 1000


(f) Temperature and totalpopulation for fullexperiment

Figure 8: Example Bottleneck Planet: Snapshots ofa single experiment showing the geochemical network inblack solid lines, and the biochemical network in greendashed lines. Red circles represent source chemicals.tseed is the time the planet was seeded with life. Plotse) and f) show temperature (red) and total population(black) against time. C = 0.4. The thick end of thegeochemical links indicates positive direction.

on the geochemistry for a Bottleneck planet. Examin-ing the geochemistry we see that there are two chemicalspecies, 8 and 4, with no geochemical process convert-ing them to another chemical species. The initial seedspecies consumes chemical 4. After seeding, there is apopulation explosion and many new biochemical linksare formed including metabolisms consuming 8. Thesystem now has metabolisms controlling both these im-portant chemical species. The population explosion andsubsequent consumption of the atmospheric chemicalshas caused Tplanet to cool, causing a sharp decline in thetotal population, allowing the abiotic processes to takeover, warming the planet once more. This improves con-ditions for life allowing the population to rise again, thistime to a more sustainable level, and Tplanet stabilisesunder the microbes’ regulation. We see that there aremany recycling loops already provided by the geochem-istry, any waste (barring waste of chemical species 8 or4) produced by a microbe can be recycled back into itsfood source, although some loops take more geochemicalreactions than others. This makes it easier for the mi-

11

crobes to retain control over their planet’s atmosphereas geochemical links, unlike biochemical links, are notprone to temperature dependant fluctuations.


(c) tseed + 500 (d) Temperature and totalpopulation for early time

Figure 9: Example Bottleneck Planet: Snapshots ofa single experiment showing the geochemical network inblack solid lines, and the biochemical network in greendashed lines. Red circles represent source chemicals.tseed is the time the planet was seeded with life. Plotc) shows temperature (red) and total population (black)against time. C = 0.4. The thick end of the geochemicallinks indicates positive direction.

Figure 9 shows an experiment for the same planet as inFigure 8. This time life failed to survive the bottleneck.We see a very similar pattern as in Figure 8 however im-portantly the microbes in this experiment fail to evolve ametabolism to consume the chemical species 8. The sys-tem can survive a while, compensating for the buildupof chemical 8 by depleting other atmospheric chemicals,however without full control over the atmospheric chem-ical make-up, the microbes are unable to prevent Tplanet

from rising, and life goes extinct.

Bottleneck planets share the characteristic of havingtwo places where chemicals can accumulate. They oth-erwise feature many purely geochemical recycling loops.The bottleneck effect occurs early on when life must gaincontrol over the two chemical species with accumulatingchemicals; if successful, the recycling loops in the geo-chemistry prevent the system from fluctuating as wildlyas seen in Critical planets. After seeding, Bottleneckplanets typically experience a population burst followedby a rapid population decline, before stabilising to a rel-atively constant total population. The temperature fluc-tuates the most during this early seeding period. Bot-tleneck planets can experience population spikes at latertimes but they are not as severe as seen for Critical plan-ets (Figure 7) and do not carry the same risk of extinc-tion. Bottleneck planets must also have a geochemistrythat allows the temperature to rise fast enough followingthe cooling caused by the early population burst to pre-

vent inevitable extinction, as seen on Doomed planets(Figure 6).

4.3.4 Abiding planets

Abiding planets are always successfully colonised bylife which then goes on to enjoy long-term habitabil-ity for every experiment. Abiding planets provide manypurely geochemical recycling loops making the systemless prone to perturbation than Critical planets for ex-ample, however microbe intervention is still required forcontinued habitability. One simplification of ExoGaiais that geochemical reactions are temperature indepen-dent which prevents abiotic temperature feedback loops.Without the influence of life, the vast majority of Abid-ing planets will quickly reach inhospitable temperaturesduring their atmospheric evolution. Therefore, while thepresence of many geochemical recycling loop can greatlyimprove the long-term habitability chances of an inhab-ited planet, on an uninhabited planet there is no temper-ature feedback process, and thus nothing to prevent tem-peratures rising to inhospitable abiotic temperatures.

Figure 10 shows snapshots of the biochemistry on anexample Abiding planet. The geochemical network ofthe planet does not provide recycling loops for chem-ical species 4, but otherwise the geochemistry is wellconnected with recycling loops present for all possiblemicrobe metabolisms barring those that excrete chemi-cal 4. Figure 10a shows the first species seeded on theplanet with metabolism 4→ 2. As time progresses, thebiochemistry infiltrates more and more of the geochem-ical network. Figure 10e does not show the populationexplosion and fall back seen for the Bottleneck planet;instead the population rises and reaches a steady valueand stays there. Figure 10f shows very little fluctuationin the total population or temperature over time.

Abiding planets all share the characteristics of hav-ing abundant, purely geochemical, recycling loops. Fornearly all microbe metabolisms there are geochemicalloops recycling the waste back to food. Abiding plan-ets also typically either have the chemicals well spreadbetween chemical species, or have only a single chemicalspecies that accumulates at high levels. These propertiescombined make it very easy for life to gain control of itshost planet’s atmosphere and retain that control. Withmany geochemical recycling loops that are not subject tofluctuation as biochemical links are, the system is highlystable and thus life is able to successfully colonise andenjoy long-term habitability on Abiding planets.

4.4 Planet Class Frequency by Connec-tivity

Figure 11 shows the frequency of each class of planetagainst connectivity, C. We see a general trend of Abid-ing planets dominating at high connectivity, Bottleneckplanets present mainly at mid and high connectivity, andCritical planets dominating for low connectivity. Thenumber of Extreme planets increases for mid connectiv-ity and then decreases again. Doomed planets make upa small fraction of the planets for all C.

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(c) tseed + 500 (d) tseed + 1000


(f) Temperature and totalpopulation for fullexperiment

Figure 10: Example Abiding Planet: Snapshots ofa single experiment showing the geochemical network inblack solid lines, and the biochemical network in greendashed lines. Red circles represent source chemicals.tseed is the time the planet was seeded with life. Plotse) and f) show temperature (red) and total population(black) against time. C = 0.4. The thick end of thegeochemical links indicates positive direction.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9C

0

20

40

60

80

100

plan

et fr

eque

ncy

A B C D E

Figure 11: The frequency of Abiding, Bottleneck,Critical, Doomed, and Extreme planets against connec-tivity for chemical set A

As an abundance of geochemical recycling loops, cou-pled with biotic temperature feedback loops, leads tohigher rates of long-term habitability, it is clear whyplanets with higher C are more likely to be Abidingplanets. With more geochemical links there is a greaterchance of geochemical recycling loops. Decreasing Cmeans fewer geochemical links, therefore Bottleneck andCritical planets become more likely with Critical planetsdominating for very low C. For low C, biology will haveto create more recycling loops itself to successfully reg-ulate the planet’s atmosphere, making the system moreprone to large scale fluctuations that carry a risk of ex-tinction.

As the source chemicals on average insulate, with fewgeochemical links most planets for low C will be hotenough for successful colonisation, leading to few Ex-treme planets. As C increases, the probability of in-sulating chemicals being converted to reflective chemi-cals increases and thus so does the frequency of Extremeplanets. Increasing C further, the chemicals will becomemore evenly spread between all chemical species in thechemical set. The average abiotic effect of all the chem-ical species in chemical set A is insulating, and so thefrequency of Extreme planets falls. The exact shape ofthe planet frequency against C curves in Figure 11 arean artefact of the chemical set used. However, as theyare the result of an abstract model, they cannot corre-spond to any real world data, and we have only one datapoint to compare to in any case - Earth. The importantfeature of ExoGaia is that these planet classes emerge,not the relative frequencies of each. The supplementarydata for this paper explores alternative chemical sets todemonstrate that chemical set A is not a special case.

4.5 Planets with habitable Tabiotic

A small number of modelled planets have habitableTabiotic values. We can compare how the habitabilityof these planets compares to those planets with Tabiotic

values that are too hot for life - ‘hot’ planets. Hot planetswill have passed through Tpre f in their past allowing forseeding; in order to survive, life will have to take controlof its planet’s atmosphere to maintain habitable condi-tions and prevent the temperature from rising to theinhabitable Tabiotic. Table 3 lists the number of plan-ets that have a habitable Tabiotic for each connectivity,and compares this number to the number of ‘hot’ plan-ets. Table 3 shows that the habitable Tabiotic planetsonly make up a small percent of the potentially habit-able planets.

Comparing to Figure 11 we see that the frequencyof Critical, Bottleneck, and Abiding planets is far higherthan the number of planets with habitable Tabiotic valuesfor each C, demonstrating that microbes are frequentlysuccessful in colonising planets during a short time pe-riod of habitability and then acting to prevent tempera-tures from rising to inhospitable Tabiotic values. For midand high connectivities where we see large numbers ofBottleneck and Abiding planets we see that life can notonly colonise planets with inhospitable Tabiotic, but canmaintain long-term habitability. This demonstrates thatthe microbes can be very successful in regulating their

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Table 3: The number of planets with habitable Tabiotic

and number of hot planets for all C

C No habitable Tabiotic No hot planets0.1 1 800.2 4 620.3 3 590.4 6 610.5 7 590.6 13 600.7 5 840.8 3 870.9 2 88

planet’s atmosphere.Of the planets with habitable Tabiotic values listed in

Table 3, only one, for C = 0.4 was an Abiding planet.None were Bottleneck planets; the majority were foundto be Critical and Doomed planets. This shows thatplanets where Tabiotic is habitable are in fact not gen-erally planets that support life long-term. The reasonfor this is as outlined in Section 4.3.1 for the exampleDoomed planet - life must be able to remove chemicalsfrom the atmosphere to metabolise and survive, and do-ing so must not push the planet beyond the bounds ofhabitability. If a planet has a Tabiotic ≈ Tpre f then re-moving chemicals is highly likely to decrease habitabil-ity, rather than maintain it (as is the case on many ‘hot’planets) thus making such planets, somewhat counter-intuitively, mostly poor candidates for long-term habit-ability.

5 Discussion

The ExoGaia model demonstrates planetary tempera-ture regulation, performed by a simple biosphere. Thereare two extinction mechanisms in ExoGaia - planetaryover cooling caused by microbe activity, or over heat-ing due to abiotic processes following the loss of bioticatmospheric control. Under favourable conditions, lifeon an ExoGaia planet can enjoy long-term habitabil-ity and can prevent temperatures from rising to inhos-pitable levels as would happen on a planet devoid oflife. For colonisation success, microbes require the hostplanet’s temperature to reach a preferred temperature,Tpre f , during its atmospheric evolution, and require ageochemical network that allows temperatures to recoverfast enough after microbe induced cooling to avoid mi-crobe extinction. For long-term habitability, microbesrequire a planet with a geochemical network that pro-vides many chemical recycling loops. By seeding plan-ets at Tpre f we have investigated the microbes’ abilityto maintain the planetary temperature within habitablebounds. The ExoGaia model demonstrates that appar-ently complex global phenomena such as regulation canarise from the simple interaction of the small parts mak-ing up a system. Five distinct planet classes emerge fromthe ExoGaia model:

• Extreme - Planets that never reach habitable tem-peratures

• Doomed - Planets that reach habitable tempera-tures but are unable to support life.

• Critical - Planets that have a higher colonisationsuccess than long-term habitability success.

• Bottleneck - Planets that if successfully colonisedenjoy long-term habitability.

• Abiding - Planets that are always successfullycolonised and always have long-term habitability.

We can consider what these results might imply forreal planets. Our model predicts that more geologicallyactive planets may be more suitable hosts for life. Moregeochemical processes provide more potential chemicalrecycling networks for life to exploit and our model bio-spheres are more adept at dampening or acceleratingpre-exiting geochemical reactions than at forming stablestand alone chemical links. There are clear real worldexamples however where biological processes are domi-nant, i.e. the concentration of oxygen in our atmosphere,highlighting the limits of our model for application to thereal world.

Which model planet class might Earth belong to?Clearly we do not live on an Doomed or an Extremeplanet. We also do not see frequent rapid very large-scale changes in the total population of the biosphere ofEarth, perhaps making it unlikely that Earth is a Criti-cal planet. The mass extinctions during the Phanerozoic[Raup and Sepkoski, 1982], were not the regular large-scale stochastic fluctuations typical of our model Criticalplanets, but rather more akin to regime shifts betweenperiods of quasi-stability. Many of the suspected trig-gers for these mass extinctions are abiotic phenomenaexcluded from the ExoGaia model, such as meteor im-pacts, volcanic events, and changing sea levels [Whiteand Saunders, 2005]. These extinctions were also mainly- but not exclusively - of macroscopic organisms, whichare a tiny percentage of the biodiversity on Earth eventoday; from the point of view of microbes, making up themajority of Earth’s biomass, these events would proba-bly not be classed as mass extinctions [Nee, 2004]. IfVenus and Earth are alternate states of the same system[Lenardic et al., 2016] perhaps we are on the lucky sideof a Gaian bottleneck? We know that certain biologicalinnovations, e.g. the evolution of oxygenic photosynthe-sis [Hoffman, 2013], and later on the evolution of landplants [Lenton et al., 2012], likely triggered ice ages, theformer as oxidation of the atmosphere mediated collapseof a CH4 greenhouse effect, and the latter as land plantsincreased weathering thus increasing the rate of CO2 re-moval from the atmosphere. This is perhaps similar tothe cooling some Bottleneck planets experience when lifeis first established. Models of the habitable zone underpurely abiotic control, e.g. carbonate-silicate weather-ing, predict that Earth would be habitable without life(e.g. [Kopparapu et al., 2013]). When examining plan-ets with habitable Tabiotic values in Section 4.5 we sawCritical and one Abiding planet represented. This couldsuggest that Earth might be an Abiding planet.

Venus’ current inhospitable state could indicate it be-ing on the ‘losing’ side of a Gaian bottleneck as pre-viously speculated, or could indicate a break down of

14

regulation being performed by a hypothetical Venusianbiosphere, making Venus a Critical planet. There isno data on how a life-environment coupled Venus sys-tem would behave over long time periods, preventingthe sort of analysis possible for Earth. If the runawaygreenhouse that occurred on Venus was unavoidable, asmany models suggest (e.g. [Kopparapu et al., 2013]),then Venus would perhaps most closely correspond to aDoomed planet due to the evidence that it once hostedliquid water ([Donahue et al., 1982, Jones and Picker-ing, 2003]) and thus may have once been potentiallyhabitable. Changes in solar luminosity were not con-sidered within the ExoGaia model, and so planets thatmight have hosted a biosphere, and then lost habitabil-ity through unavoidable external factors, do not fit wellinto the model planet classification system.

We can also consider Mars as observational evidencepoints to it once having had large bodies of liquid water,e.g. [Milton, 1973]. It is not known what the earlyenvironment of Mars was like, whether it was warmand wet [Craddock and Howard, 2002], or cold withvolcanism and impacts causing transient warm condi-tions [Wordsworth et al., 2013]. If the latter, poten-tial habitats for Martian life might have been heteroge-nous throughout time and space, possibly preventingany early life from spreading across the planet [Cock-ell et al., 2012]. If this were the case, Mars might mostclosely correspond to a Doomed planet - a window ofhabitability existed, however life was unable to flourish.If Mars did at one point host a substantial biosphere,it has clearly lost it. Mars once had a far thicker at-mosphere which it has since lost [Pepin, 1994], causingthe dry cold conditions on Mars today. Atmosphericloss was not taken into account in the ExoGaia model,however this could perhaps be very loosely comparedto an uncontrolled build-up of a cooling chemical on amodel planet that a biosphere might mitigate for a while,potentially making Mars a Critical planet. However,Critical planets are theoretically habitable indefinitely,while any planet undergoing significant atmospheric losswill experience drastic changes in its surface environ-ment, making this comparison far from ideal. Thereis ongoing speculation that life might yet be found onMars in sparse pockets [Wilkinson, 2006]. ExoGaia ismainly concerned with large-scale planetary regulation,and therefore small refuges of life with little to no impacton global parameters are predicted to impact model re-sults only if conditions improved to allow this life anotherchance of becoming globally established (see AppendixB for experiments along this theme).

With a highly simplified and abstract model like Ex-oGaia, no strong predictions can be made for individ-ual planets, and comparisons between real planets andmodel planet classifications highlight the many limita-tions of the model. More complex future versions ofExoGaia could begin to address some of the questionsraised by considering specific planets within the Exo-Gaia framework and future space missions to Venus andMars might provide more data to compare with modelplanet classifications. It is difficult to determine whichclass a planet might fall into based on a single time point;the planet classes in ExoGaia are best identified by look-

ing at the whole planet history. Therefore, any methodsthat can provide long timescale observations of planetswould provide the best data for comparison with modelpredictions.

The ExoGaia model adds to the narrative that fora planet to remain habitable, it must be inhabited[Lenardic et al., 2016]. It suggests that geologicallyactive planets still early in their atmospheric evolutionwould be the most suitable candidates for colonisationby life and agrees with the idea that when searchingfor inhabited exoplanets we should look for planets withatmospheres in disequilibrium [Lovelock, 1965]. Ourmodel suggests that many planets that have had life willhave lost it, however that some, with the right geologicalconditions, can enjoy long-term uninterrupted habitabil-ity. Currently with only one data point - the Earth, wecannot draw any conclusions. As more exoplanets arefound, their macro properties determined, and their at-mospheres analysed, we will have more data available tocompare with model predictions.

Further work should explore how the ExoGaia modelbehaviour is impacted by adding temperature dependantabiotic processes, and the effects of changes in solar lu-minosity or other abiotic perturbations. Our model mi-crobes could also be made more complex, as microbescan be found in almost any part of our globe, fromthe Mars-like conditions of the Antarctic dry valleys[Siebert et al., 1996] to hydrothermal vents at around122oC [Clarke, 2014], a fact not reflected in our modelwhere microbes have a universal temperature preference.Adding spatial structure to models has been shown tobe very important in work in theoretical ecology overrecent decades [Nee, 2007] and therefore is an obviousnext step in developing this model. Introducing spa-tial heterogeneity into the model would also allow life toseek refuges during periods of extreme climate change,similar to how life is thought to have survived in smalloases during the snowball earth events, or speculated topossibly persist on Mars today. The change in modeldynamics in response to adding spatial structure wouldbe an important next step in improving the applicabilityof the ExoGaia to real planets.

Acknowledgements

We thank the Gaia Charity and the University of Exeterfor their support of this work.

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17

A ExoGaia Model Description

Code made available upon reasonable request to corre-sponding author.

The ExoGaia model uses agent based dynamics to de-scribe a biosphere consisting of simple microbes interact-ing with a host planet via consumption and excretion ofatmospheric chemicals. These chemicals determine thesurface temperature of the planet. In this appendix eachpart of the model will be described in detail and then theexperiment method will be presented at the end.

A.1 Microbes

The microbes consume chemicals as food and excretechemicals as waste products. A particular microbe’sfood and waste product are encoded in the genome ofeach microbe species. All microbes share the same idealtemperature (i.e. the temperature which results in themaximum growth rate). Microbes grow by consumingchemicals and converting them to biomass. They repro-duce asexually by splitting once their biomass reachesa threshold. Biomass is decreased by a fixed amountper timestep to represent the cost of staying alive. Mi-crobes die if their biomass drops below a fixed threshold,which can happen due to food limitation or temperaturelimitation leaving the microbes unable to consume thechemicals present.

In the code we do not record microbes of the samespecies individually as doing so would slow the sim-ulations considerably. Instead we group microbes ofthe same species together and record the species’ totalbiomass. Thus each species can be thought of as a listM:

M = (g, N, B, F,W,Tpre f ) (4)

where g is the species’ genome (represented as a deci-mal number), N is the population of the species, B is thetotal biomass of the species, F is total number of con-sumed food chemicals not yet converted into biomass, Wis the total number of waste chemicals not yet excretedby members of the species, and Tpre f is the tempera-ture that maximises the growth rate for species M. Allspecies share the same Tpre f .

A.1.1 Genotype

The genotype of a microbe is recorded as the decimalrepresentation of an 8 bit binary string, and this is usedto group microbes into species. Microbes that sharethe same genome are of the same species. We createtables for microbe chemical consumption and excretionrules, and this genome is used as the reference to lookup the particular metabolism for a microbe. These ta-bles are generated in the following way: for each possiblegenome, a chemical species is selected at random to bethe food source for microbes of that genome. Anotherchemical species is then selected at random to be thewaste for microbes of that genome. The food source andwaste of a microbe must not be the same, so if the waste

Table 4: Example microbe metabolism look up table

Index Food Chemical Waste Chemical0 2 61 4 12 1 2

chemical species selected is the same as the food, an-other chemical species is chosen at random until theseare not the same. All microbes consume only one typeof chemical and excrete only one type of chemical. Theindex of a microbe’s metabolism in the table is the dec-imal value of the microbe’s genome. With an 8 bit longbinary genome there are 256 possible species (as eachgene in a genome can have the value 0 or 1).

Table 4 shows an example look up table. To use Table4, for a microbe with genome 000000010, we convertto its decimal value, 2, and find that this microbe hasmetabolism 1 → 2 i.e. it consumes chemical species 1and excretes chemical species 2.

A.1.2 Chemical Consumption

When a microbe is selected to consume, it will attemptto eat Kj units of its chemical food source (the value ofKj depends on how closely the planetary temperaturematches the microbes’ preferred temperature, and themicrobes’ sensitivity to the environment), and will besuccessful if the chemicals are available.

For simplicity we limit our microbes to single chemicalmetabolisms, meaning that a microbe only consumes onetype of chemical, and only excretes one type of chemical,with the limitation that no microbe may consume whatit excretes.

A.1.3 Metabolism

The microbes convert their food into biomass in an in-efficient process that produces waste product. The effi-ciency of this conversion is given by θ, and the amountof biomass produced is given by:

Bj = θFj (5)

where Bj is the number of biomass units produced andFj is the number of food units currently ‘contained’ witha microbe j. The waste excreted in this process is givenby:

Wj = (1 − θ)Fj (6)

where Wj is the number of waste units produced,which are released into the environment after thebiomass has been created, in the form of the chemicalsdetermined by microbe j’s specific metabolism (e.g. seethe look up table example in the previous section).

A.1.4 Effect of temperature on metabolic rate

The state of the abiotic environment affects the rate atwhich microbes can consume chemicals which in turn af-fects the rate of biomass production and thus the growth

18

of the microbes. A microbe will attempt to consume anamount of chemicals Kj each timestep with the demandbeing met depending on chemical availability. Kj is cal-culated for each microbe j as a function of the differencebetween the microbes’ ideal temperature and the currentplanetary temperature. This function is has a Gaussianform and falls away smoothly from its maximum as thedistance between the optimum and the current environ-ment increases. This is a widely used assumption whenmodelling an organism’s response to the temperate of itsenvironment. Mathematically we write this as:

Kj = ψjKmax (7)

ψj = e−(τp j )2 (8)

pj =

√(Tplanet − Tpre f )2 (9)

where Kmax is a constant determining the maximumrate of consumption for any microbe, ψj is a microbespecific measure of the microbe’s satisfaction with thecurrent abiotic environment, τ is a universal constantparameter that determines how sensitive the microbesare to their environment (τ = 0 means the microbes arenot affected by the abiotic environment at all, and ahigher τ means the microbes become more sensitive tothe abiotic conditions). The effects of changing this τparameter has on system dynamics has been explored inthe Flask model (e.g. [Nicholson et al., 2017]) on whichthis model is heavily based on. pj is a measure of the(positive) distance between the current environmentaltemperature, Tplanet , and the microbe’s preferred tem-perature, Tpre f .

A.1.5 Maintenance Cost

There is a fixed biomass cost λ of staying alive for eachmicrobe. This reduces a microbe’s biomass by a constantrate. This cost represents the energy costs of maintain-ing cellular machinery and metabolic inefficiency. Thiscost is assumed to be lost as unrecoverable heat radia-tion. This ensures that the chemicals cannot be infinitelyrecycled and it sets the carrying capacity of the sys-tem. This carry capacity is reached when the total heatdissipation matches the energy supplied in the form ofchemicals, i.e. the food the microbes consume. As anyheat dissipation of the microbes in the real world dueto metabolic inefficiency is many orders of magnitudesmaller than the effects of the atmospheric compositionon planetary temperatures, we neglect this heat dissipa-tion when calculating planetary temperatures.

A.1.6 Reproduction and Mutation

If the microbe is able to consume enough chemicals toreach the reproduction threshold TR, it will reproduceasexually, splitting in half. Half of the biomass with go tothe new microbe and the parent microbe will be left withhalf its biomass. The new microbe will have the same

genome as the parent unless a mutation occurred duringthe reproduction. There is a small constant probabilityof mutation, Pmut , for each locus. During a reproductionevent, the code iterates through the genome of the newmicrobe and if a mutation occurs at a locus then thegene at that point will be ‘flipped’, turning it to 0 if itwere previously 1, or to 1 if it were previously 0. Thisnew mutant genome will then dictate the new microbe’smetabolism.

A.1.7 Death

If a microbe’s biomass falls to a starvation thresholdTD the microbe will starve to death. There is anothersmall probability of death PD that represents death byhazardous mutation or damaging local environmentalchanges etc. When a microbe dies its biomass is removedfrom the system, as if the dead microbe, for example,fell to the bottom of the ocean. During a death event,we first check to see if the selected microbe has enoughbiomass to avoid death by starvation. If the microbe hasnot starved to death it will be killed with probability PD.

A.2 Selecting a microbe

We use agent based dynamics in our model. This meanswithin a timestep, a microbe is chosen randomly for anevent and time is effectively frozen while the microbeperforms that event. Time is then restarted and anothermicrobe is chosen at random for an event.

As we record microbes grouped together in a species(Equation 4), for any particular species we have the pop-ulation of the species, the total species biomass, and thetotal consumed food not yet converted into biomass. Toselect a single individual of a particular species we there-fore need to determine how much biomass and uncon-verted food this individual has. If a microbe is selectedfor a reproduction event, we need to know how muchbiomass it has to know if it has reached the reproduc-tion threshold for example.

There will be variation between individuals of aspecies and so we assume a normal distribution ofbiomass and unconverted food between individuals ofa species. The biomass normal distribution is centredaround the average amount of biomass Bav per microbe(i.e. the total species biomass divided by the speciespopulation), with standard deviation of the distributionis Bav×0.1. The normal distribution for the unconvertedfood is the same but with Fav, the average amount of un-converted food per microbe, instead. The standard devi-ation for both distributions is small, resulting in a smalllevel of variation in the population. Therefore most in-dividuals of the same species will have the same biomassand food levels.

Once we have selected a microbe and calculated itsbiomass and food level, the microbe can then attemptto perform the event it was selected for.

A.3 Planet setup

Each planet has a well mixed atmosphere with no spatialelement. The atmosphere is characterised by chemicals.

19

There are 8 possible chemicals in ExoGaia, althoughnot all chemicals have to be present in the atmosphereat the same time. The chemicals present in the atmo-sphere may be consumed by microbes and converted intobiomass, and the atmospheric chemical composition de-termines the temperature of a planet.

A.3.1 ‘Temperature’ in ExoGaia

When calculating temperatures in the ExoGaia modelwe make a simplification of the Stefan-Boltzmann law.Instead of β ∝ T4 , where β is the incoming energy to theplanet from the ‘star’ and T is planetary temperature,we simplify to β ∝ T . This approximation has been usedbefore in Daisyworld to make determining the under-lying regulation mechanisms easier. It has been noted([Watson and Lovelock, 1983] [Saunders, 1994] [De Gre-gorio et al., 1992] [Weber, 2001] [Wood et al., 2006])that this simplification does not greatly change the over-all behaviour of the Daisyworld model. The Stefan-Boltzmann equation is close to linear at real world hab-itable temperatures, i.e. near 22oC. In ExoGaia, we areonly interested in planetary dynamics when there is lifeon a planet, so while the ‘temperature’ in the ExoGaiamodel is not constrained, we are only interested in anarrow range of temperatures where life is possible. Thetemperature behaviour outside this range is not impor-tant to the model results. We use an unrealistic Tpre f

for our model microbes to highlight the abstract natureof the model, however as a near linear relationship existsat habitable conditions on Earth, and we are striving tosimplify the model abiotic environment as much as pos-sible, we take β ∝ T , where β is the energy provided tothe planet by the host star per timestep, T is temper-ature. We then make a further simplification and takethe value of β to be equal to the value of T .

A.3.2 Chemical Species

In ExoGaia we have different ‘chemical species’ as anabstract representation of real-world atmospheric gasese.g. CO2, CH4, or O2. These abstract chemical speciesare not meant to mimic any specific real world chemistry.Each chemical species insulates or reflects by a particularamount. The maximum reflective or insulating propertyof a chemical species i is represented by ai. These aivalues are taken from the range [ -1, +1]. A negativeai corresponds to a reflective chemical species, and apositive ai means it is insulating. A positive ai mightrepresent for example the maximum insulating effect ofan atmosphere saturated with CO2. The strength of theeffect exhibited by any chemical species, Si, depends onthe number of particles of that chemical in the system,e.g. the abundance of CH4 say in the atmosphere:

Si = ai tanh(ni

D

)(10)

where ni is the abundance of chemical species i, i.e.the number of particles of chemical i present in the at-mosphere, and D is a large number to make the effectsof a single ‘particle’ of each chemical species small. This

enables large populations to be supported where the in-dividual effect of a single microbe’s consumption andexcretion of chemicals is small. We use tanh as it isa function that smoothly varies between 0 and 1. Themaximum effect any chemical species, i, can have is de-termined by its ai value and by using tanh we can capthe reflective or insulating effects of a chemical species toits ai value. This does not prevent runaway temperaturechanges in the model, as seen when planetary tempera-tures rise to above the microbe’s ideal temperature.

A subset of chemical species are chosen as ‘sourcechemicals’. These are chemical species with an inflowfrom what we could think of as the ‘mantle’ of the planet,e.g. CO2 from volcanoes. Each source chemical has aconstant inflow rate IN , and there are NS source chemi-cals. This inflow is kept at a constant rate per timestepfor the full experiment. Any chemical species that isnot a source chemical does not exist in the atmosphereunless it is produced by a geochemical or biochemicalprocess.

A.3.3 Atmospheric properties and planetarytemperatures

The state of the atmosphere is given by a vector V:

V = (n1, ..., nN ) (11)

where ni is the abundance of chemical species i, andN is the number of chemical species. As each chemicalspecies in the model has an insulating or a reflectiveproperty, the planet atmosphere’s insulating or reflectiveeffect will depend on the chemical composition of theatmosphere.

We define AI as the fraction of the planet’s currentthermal energy retained by the atmosphere via insula-tion, and AR as the fraction of incoming solar radiationreflected by the atmosphere. The total reflective andinsulating properties of the atmosphere depends on theamount of each type of chemical present. We calculateAR, and AI in the following way:

AR =∑i∈R−ai tanh

(niD

)(12)

AI =∑i∈I

ai tanh(ni

D

)(13)

R is the set reflective chemical species and I is the setof insulating chemical species. ni and D are the sameas for Equation 10. AR and AI are constrained to bebetween 0 and 1, as the maximum amount of thermalenergy a planet can retain is the energy it currently has,and the maximum amount of incoming radiation thatcan be reflected is the amount incoming from the hoststar, so we also have:

if AR > 1→ AR = 1 (14)

if AI > 1→ AI = 1 (15)

20

We define βplanet as the planetary thermal energy andβstar as the incoming solar radiation per timestep. Wethen calculate βupdate, the updated thermal energy ofthe planet including the insulating effect of the atmo-sphere in the following way:

βupdate = AI βplanet + (1 − AR)βstar (16)

Using the simplification in Section A.3.1, the β valuescorrespond to temperature values, so that if the thermalenergy of a planet was βplanet , then the value of βplanetwill be the same as the value of Tplanet - the temperatureof the planet.

A.3.4 Chemical inflow and outflow

There is a constant rate of inflow of source chemicals.Each timestep, IN particles of each source chemical willbe added to the system. There is a rate of outflowfrom every chemical species that is abundance depen-dant. Each timestep every chemical species will experi-ence an outflow of ni ×ON where ni is the abundance ofchemical species i, and ON is a constant rate of outflow.Therefore more abundant chemical species will experi-ence a higher rate of outflow than less abundant ones.

A.3.5 Geochemistry setup

Each planet has geochemical reactions taking placethroughout the experiment. For our geochemistry,we have links between chemical species converting onechemical type to another. The process is assumed tobe 100% efficient, so one particle of chemical A wouldbe converted to one particle of chemical B. Links be-tween chemical species can only flow in one direction,so if we have a process converting chemical A → B,we cannot then have another geochemical process con-verting B → A. Other routes are allowed though, i.e.B → C → A for example. This simplification makes itsimpler to track chemicals as they move through the sys-tem. Real world systems have chemical reactions thatcan be reversed, however we could also consider this sim-plification to be the net movement of chemicals once eachdirection of the reaction has been taken into account. IfA → B and B → A, we can still describe the overallmovement of chemicals between A and B with a link ofeither A→ B or B→ A.

Geochemical reactions take place at a rate that de-pends on the abundance of the reactant chemical species.Each geochemical link is randomly assigned a valuetaken from the uniform range [0, 1) which we call the‘link strength’. This number determines what percent-age of the reactant chemical species is converted to theproduct chemical species due to the geological process,per timestep. E.g. if we have a geological link: A→ B,with strength 0.2, this means every timestep 20% ofchemicals type A are converted into chemicals of typeB.

If we have a matrix G that represents a planet’s geo-chemical reactions, Gi j would be the flow from chemicalspecies i, to chemical species j due to a geochemical re-action. If Gi j > 0, then G ji = 0 as we don’t allow for

links flowing between the same two chemical species inopposites directions. For a particular connectivity, sayC = 0.1, each chemical species has 10% chance of beingconnected to another. We then determine the strengthof the connection, i.e. how fast the process is that con-verts A to B. We set up our geochemical processes in thefollowing way.

To populate the geochemical reaction matrix G, weconsider each pair of chemical species in turn. The con-nectivity C tells us the probability that these two chem-ical species will be connected by a geological reaction,or link. We generate a random number r1 taken fromthe uniform range [0, 1), and if r1 < C then our chemi-cal species are connected by a link. If r1 ≥ C the twochemical species are not connected.

If the chemical species are connected we then gener-ate another random number, r2, also from the uniformrange [0, 1) to determine which direction the link flowsin, e.g. A → B or B → A with each direction havingequal probability.

Once the direction of the link is determined, thestrength of the link is then found by generating a thirdrandom number, r3, (from the uniform range [0, 1) ) andthe link strength Ls = r3. We repeat this process foreach pair of chemical species.

Thus we end up with a matrix G of the following form:

G =

0 0 a2,0 0 0

a0,1 0 0 a3,1 00 a1,2 0 a3,2 00 0 0 0 a4,30 a1,4 0 0 0

(17)

G contains all the geological processes happening ona planet, with their strength and direction. All the Gii

indices are 0, and where Gi j > 0 it is always true thatG ji = 0. If G1,2 = 0.7 for example, it means that everytimestep 70% of chemical species 1, will be convertedinto chemical species 2.

Each timestep we can therefore loop though G to de-termine where chemicals are moving due to geochemicalprocesses. For a non zero Gi j value, chemical speciesi will be depleted by niGi j and chemical species j willbe incremented by the same amount due to the geolog-ical process. We do this for each geochemical processand add up the total amount of chemicals added to orremoved from each chemical species for each timestep.

A.4 Seeding a planet

A planet is seeded with microbial life when the tem-perature of the planet Tplanet equals the microbes’ pre-ferred temperature Tpre f . Because of the way temper-ature is determined in the model, planet temperaturesmight never exactly match Tpre f , so to ensure that seed-ing still occurs we determine a suitable ‘seeding window’Sw - a small temperature range close to Tpre f . Seedingcan occur when planet matches any temperature in Swbut seeding only occurs once. These Tpre f and Tplanet

temperatures correspond to thermal energies, and usingthe simplification in Section A.3.1 we can take the val-

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ues of Tpre f and Tplanet to be same as the values of thecorresponding thermal energies βpre f and βplanet .

For the case where βstar < βpre f we require an insulat-ing atmosphere for habitability. Therefore we determineour seed window, Sw, as the range [Tpre f ,Tpre f +50]. Aswe know for βstar < βpre f we must have an insulatingatmosphere for potential habitability, the Sw range goeshigher than the ideal temperatures, so that if temper-atures never exactly match Tpre f as the temperaturescontinue to rise, seeding still takes place, and life willstill be seeded at a hospitable temperature.

For the case where βstar > βpre f , we need a cool-ing atmosphere for habitability therefore we set Sw =[Tpre f − 50,Tpre f ]. The logic is the same, however here,as the atmosphere on a potentially habitable planet inthis setup will be a cooling atmosphere, the temperaturewill be falling when it passes through Tpre f so we allowfor slightly cooler temperatures in case βplanet = βpre fin the simulation never takes place exactly.

When βstar = βpre f , we have an extra requirementthat is automatically fulfilled in the previous two sce-narios. When we seed with life, we require there to befood for the life to consume. When βstar is far fromβpre f , we know that when the planet’s temperature be-comes habitable, it is because an atmosphere has builtup. When βstar = βpre f , seeding could occur when nofood was present. To deal with this we add an extra re-quirement for seeding when βstar = βpre f . Sw is now inthe range [Tpre f − 50,Tpre f + 50] as a potentially habit-able planet could have either a cooling or insulating at-mosphere, and now we require that at least one chemicalspecies in the system must have an abundance greaterthan 1000. This means that although conditions willstart with Tplanet = Tpre f seeding is delayed until thereare some atmospheric chemicals present for the microbesto consume. These chemicals will likely alter planetarytemperatures and thus degrade the environment, how-ever provided an abundant food becomes available be-fore the seed window is missed, seeding will take place.

For all scenarios, when seeding a planet, we seed withone species and we seed with MN individuals of thatspecies. We choose the seed species at random, howeverwe ensure that the species chosen has an abundant foodsource available to it. If species A consumes chemicalCA, if there are greater than 1000 units of chemical CA

in the atmosphere at the time of seeding, species A is asuitable seed species. If there are fewer than 1000 unitsof CA present in the atmosphere at the time of seedingthen species A is not a suitable seed species and anotherspecies is chosen at random until a suitable species, thatconsumes a presently abundant chemical, is found. Thismakes biological sense as a species will not evolve toconsume a nonexistent food source.

If a seed window has not been passed after 5 × 104

timesteps then an seeding attempt is made once, andthe model then continues as usual for 50×104 timesteps.

It seems sensible that life on Earth will have emergedto initially consume something plentiful which is whywe take this approach in our model. If life initiallyemerged to consume something not plentiful then ex-tinction will have quickly followed. As life did indeedemerge on Earth, either it initially had a stable food

source, or it emerged many times and went extinct un-til a life-form that consumed a food source abundantlypresent emerged and avoided extinction via starvation.

A.5 Model Timesteps

We use agent based dynamics to run the simulation anda timestep is broken down into ‘iterations’. The numberof iterations per timestep depends on the the number ofmicrobes alive in the system at the start of the timestep.In reality, microbes eat food, create biomass, excretewaste, reproduce, and die all in parallel with one an-other. The model steps performed within a timestep inthe ExoGaia model would also ideally all be computedin parallel but computational limitations prevent this,and so for agent based dynamics we effectively freezethe system while a selected microbe performs an action.Therefore timesteps are broken down into iterations. Aniteration consists of the following steps:

• A microbe is randomly selected for a chemical con-sumption event

• A microbe is randomly selected for a biomass cre-ation event

• A microbe is randomly selected for a reproductionevent

• A microbe is randomly selected for a death event

These events are repeated NM times each where NM

is the microbe population at the start of a timestep. Amicrobe selected for an event will not necessarily performthat event. For example, the microbe might not haveenough biomass to reproduce, or the temperature mightbe too hot or cold for a microbe to consume chemicals.Being selected for an event means that a microbe willperform that event only if conditions allow, and dependson the probability of the event successfully occurring.

We also break down the inflow and outflow of chem-icals and to prevent sudden changes at the the start ofeach timestep. If we simply added and deducted thechemical flow amounts at the start of each timestep, mi-crobes selected at the beginning of a timestep could seea very different world to those selected at the end of atimestep and large sudden changes could occur betweentimesteps. Although these effects would largely aver-age out due to the random selection of microbes duringeach timestep, a single large influx per timestep couldbe thought of as a periodic perturbation on the systemwhich could affect the results seen. To counter this,we calculate the total inflow (from external sources ifa source chemical, and from inflows due to geologicalprocesses) and outflow of each chemical species at thestart of each timestep and divide this by the number ofiterations in the timestep, i.e. the microbe populationat the start of the timestep, NM :

Nchangei = IN −ON Nab

i /NM (18)

IN is the number of units of chemical inflow pertimestep, ON is the percentage outflow, and Nchange

i

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is amount we increment chemical species i’s abundanceeach iteration. This results in the same quantity ofchemicals being added / removed from the system asif there was just one update at the start of the timestep,but it results in a much smoother transition and meansthat microbes selected at the start and end of a timestepwill see much more similar worlds. Of the life eventsof a microbe, only chemical consumption depends onthe external environment which means only one eventwithin an iteration is dependant on environmental con-ditions. The other events: biomass production, repro-duction, and death, depend only on internal parametersof a microbe (amount of biomass etc.) and PD which isnot affected by environmental conditions. Therefore itis not necessary break chemical inflow / outflow furtherdown to increment between each iteration step.

In this process, we treat chemical levels as continuousbut the microbes always treat the chemicals as units. Sofor a timestep, each iteration we might add 10.7 chemicalunits per iteration, but microbes in the system can onlyact on the integer amounts of chemicals present.

A.6 Method

We perform the following steps for each connectivity inlist C:

1. Set up the planet’s geological network

(a) Begin the geological processes on the planet,allowing chemicals to build up

(b) Seed planet with a single species whenTplanet = Tpre f

(c) if Tpre f is never reached, seed after 5 × 104

(d) The experiment ends after 5 × 105 timestepsafter seeding

2. Repeat step b) 100 times with different randomseeds initialising the microbes

3. Repeat steps (a) to (c) 100 times with different ran-dom seeds initialising the planet’s geological net-work

A.7 Parameters

Tables 5, 6, and 7 show the parameter values used togenerate the data presented in this paper.

Table 5: Planet parameters

Parameter Value DescriptionN 8 Number of chemical

speciesNS 2 Number of source chem-

istryIN 75 Rate of chemical influx

(units / timestep) persource chemical

ON 0.0001 Rate of chemical outflux(percentage / timestep)

Pabiotic 1 Probability of a chemicalspecies having an insulat-ing or reflecting effect

ai [-1, +1] A chemical species’s re-flective (if -ve) or insu-lating (if +ve) effect onthe planet generated fromrange [-1, +1]

βstar [500,1000,1500]

Solar radiation providedby host star / timestep

D 75,000 A constant to dampen theeffects of a single ‘particle’in the atmosphere

C [0.1, 0.2,0.3, 0.4,0.5, 0.6,0.7, 0.8,0.9]

Planet connectivity, i.e.the proportion of chemicalspecies connected by geo-chemical processes

Table 6: Microbe parameters

Parameter Value DescriptionBR 120 Reproduction threshold

(biomass units)BD 50 Starvation threshold

(biomass units)Pmut 0.01 Probability of mutation at

each locus during repro-duction

PD 0.002 Probability of death bynatural causes (otherthan starvation) at eachtimestep

Kmax 10 The maximum number ofchemicals a microbe caneat per timestep whenconditions are ideal

Ngene 8 Microbe genome lengthλ 1 Maintenance cost

(biomass units / timestep)θ 0.6 Chemical conversion effi-

ciencyτ 0.015 Level of influence of

abiotic environment onmetabolism

Tpre f 1000 Microbes’ temperaturepreference

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Table 7: Setup parameters

Parameter Value DescriptionMN 100 Number of individuals in

planet inoculumBinit 80 Biomass of each seed indi-

vidualtrun 5 × 105 Duration of run

(timesteps)SW 0.002 Probability of death by

natural causes (otherthan starvation) at eachtimestep

SF 1000 Available food requiredfor a seed species to be vi-able (units)

B Supplementary material

Here we present some results further exploring the Ex-oGaia model. These results do not change the mainresults of the paper but reinforce that ExoGaia exhibitsself-regulation of planetary atmospheres by a microbialbiosphere for a range of initial conditions.

B.1 Reseeding with life

We investigated the difference that reseeding with lifehad on the results. For the results presented thus far,once a system goes extinct, it remains so. We per-formed reseeding experiments where, after extinction, ifthe planet’s temperature reached Tpre f again, the planetwas reseeded with a single microbe species. We did notlimit the number of times a system could be reseeded.As the origins of life remain largely a mystery we don’tknow whether life emerged once and took off straightaway, or whether it required a few starts, so investigat-ing each scenario is of interest. Another way to thinkabout this reseeding is that some microbial ‘spores’ maybe so robust that they survive the crash of the system for‘geological’ lengths of time [Nicholson et al., 2000] [Wellset al., 2003] [Wilkinson, 2006], however with numbers solow that they do not have any influence on the evolutionof their planet. Therefore if conditions improve, life isready to take advantage immediately. For example itis speculated that, assuming Mars once had abundantlife back when it had large quantities of liquid water,life could still exist on Mars in sparse pockets ‘waiting’for conditions to improve [Wilkinson, 2006]. We foundthat the qualitative results are largely the same as fornon-reseeding experiments, however survivability for allplanets is improved. See Figure 12 for a comparison be-tween non-reseeding and reseeding experiments.

Figure 12 shows the number of each Class of plan-ets for Chemistry A both with and without reseeding.We see the most difference in the number of Bottleneckplanets. For higher connectivity, we see the numberof Bottleneck planets is lower for the reseeding exper-iment. These planets having now multiple chances forlife to take hold have multiple attempts to overcome thebottleneck. This means some planets where bottlenecks

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Figure 12: The frequency of Abiding, Bottleneck,Critical, Doomed, and Extreme planets against connec-tivity for Chemistry A.

were previously seen now become Abiding planets withall simulations surviving the experiment.

Some previously Doomed planets became Criticalplanet class under the reseeding experiment, howevermost remained in the Doomed classification and thosethat transitioned to being critical planets were still poorlong-term hosts for life, with the planet experiencingmultiple reseeding events over the course of the exper-iment. Therefore, while some Doomed planets might,under reseeding, support life for overall longer times-pans, if we consider the implications for real planets, wecan infer that these planets would be unlikely to sup-port complex life due to the frequent extinction eventsoccurring.

B.2 Chemical Set B and C

We repeated the non-reseeding experiments with two dif-ferent chemical sets, to check that the results presentedin the main body of the paper were not just a specialcase. We found that different chemical sets affect thequantitative results, but not the qualitative results ofhigher C correlating with higher survival rates, and Ga-ian bottlenecks as an emergent feature of the model. Thefive planet classes emerge for all three chemical sets, withthe number of Abiding planets increasing with increas-ing C, and the number of Critical planets decreasing withincreasing C. The exact number of each planet class dif-fers between chemical sets, however the key result is thatchemical set A, used for the results in the main body of

24

Table 8: The greenhouse and albedo properties for chem-ical sets B and Chemistry C. The bold chemicals repre-sent the influx chemical.

Chemical index Chemical set B chemical set C1 -0.56 -0.732 0.67 0.883 0.79 -0.824 -0.40 0.275 0.04 0.526 0.26 0.117 0.04 -0.388 -0.31 0.39

Mean 0.07 0.03

the paper, is not a special case.

Table 8 shows the chemical species ai values for bothchemical set B and C. We can see that we would expect aplanet with chemical set B to be on average warmer thana planet with chemical set C, as the chemical speciesare on average more insulating. Both chemical sets aresignificantly cooler than chemical set A. We put thesetwo different chemical sets though the same experimentsas before, investigating only the non-reseeding case. Wewould predict that chemical set C, being colder thanchemical set B, would result in fewer habitable planets.

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Figure 13: The frequency of Abiding, Bottleneck,Critical, Doomed, and Extreme planets against connec-tivity

Figure 13 shows the number of each class of planets forchemical set B and C. We see that these quantitativelydiffer from one another and from chemical set A, but

Table 9: The greenhouse and albedo properties for chem-ical sets D and Chemistry E. The bold chemicals repre-sent the influx chemicals

Chemical index Chemical set D chemical set E1 0.95 -0.882 -0.70 -0.913 -0.05 -0.434 -0.39 0.945 -0.54 0.996 -0.20 -0.047 0.78 -0.808 -0.19 -0.90

Mean -0.34 -2.03

general trends are similar. The number of Abiding plan-ets is highest for high C. Critical and Extreme planetsdecrease with increasing C, and Bottleneck planets aremore common for middling and high C values. Doomedplanets make up a very small percentage of the simu-lated planets for both chemical sets We find overall thecolder chemical set C results in more Extreme planets,as expected. We see see that our original chemical set A,presented in the main body of the paper, is not a spe-cial case, and that viable biospheres are possible withdifferent chemical sets.

B.3 Changing βstar

The results presented so far have βstar < βpre f . Thismeans that model planets need to have insulating at-mospheres to reach habitable conditions. We now in-vestigate how changing βstar affects the results. Weexplore two cases: Chemical set D with βstar = 1500,therefore with βstar > βpre f (instead of βstar < βpre f asfor chemical set A, B, and C), and chemical set E withβstar = βpre f = 1000. See Table 9 for the ai values forthe chemical species of chemical sets D and E.

We find for βstar > βpre f , 5 planet classes againemerge and temperature regulation can still take place.For a planet to be habitable when βstar > βpre f the at-mosphere must now have an overall cooling effect on theplanet. In this scenario, rather than temperature regu-lation taking place below Tpre f with the microbes collec-tively reducing the insulating power of the atmosphere tomaintain habitable conditions, regulation instead takesplace above Tpre f with the microbes collectively reduc-ing the reflective effect the atmosphere. The negativefeedback loop, and the positive feedback loop are thesame as outlined in Section 4.1 in the main paper butwith the signs flipped such that when Tplanet < Tpre f ,effects of increasing (+) the temperature are:

1. + Temperature → + Population

2. + Population → + Temperature

resulting in a runaway positive feedback loop. Thisalso means decrease in Tplanet will result in a decreasein the microbe population, further decreasing Tplanet asabiotic processes dominate, leading to total extinction.A positive feedback loop where Tplanet is increasing will

25

result in Tplanet > Tpre f where the negative feedbackloop occurs, as for Tplanet > Tpre f :

1. + Temperature → -Population

2. + Population → + Temperature

resulting in a stabilising negative feedback loop. Fig-ure 14 shows the frequency of each planet class for chem-ical set D with βstar > βpre f and for chemical set E withβstar = βpre f . The βstar > βpre f case qualitativelylooks the same as the βstar < βpre f scenarios for chemi-cal set A, B, and C. All 5 planet classes are seen and as Cincreases the long term habitability of planets increases.

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Figure 14: The frequency of Abiding, Bottleneck,Critical, Doomed, and Extreme planets against connec-tivity

Figure 14b shows planet class frequency for βstar =βpre f . The behaviour of the model changes slightly un-der these conditions. As a planet with no atmospherewill now have Tplanet = Tpre f , the microbes, once seeded,experience a positive feedback where an increase in pop-ulation leads to an increase in habitability (as the at-mospheric chemicals are reduced). Thus after seeding,if habitability prevails long enough, the microbes willquickly consume all of the atmosphere. With no at-mosphere the population becomes nutrient limited andtemperature regulation via a negative feedback loop doesnot take place. Microbes maintain habitable conditionssimply by preventing any atmosphere building up. Thisphenomena is known as biotic-plunder [Tyrrell, 2004]where the biota exhaust resources and so achieve sta-bility, while the resources remain at very low levels.

If microbe populations decrease due to stochastic fluc-tuations, atmospheric chemicals can build up, movingTplanet away from Tpre f and leading to a positive feed-back loop, resulting in extinction. For high C the tem-perature change is small enough that microbe numberscan recover in time to consume the excess chemicalsand remain nutrient limited. For low C, where chem-ical species can accumulate more rapidly, microbes aresometimes unable to prevent the positive feedback loop.Therefore we see far more Critical planets occurring forlow C than for high.

There are no Extreme planets when βstar = βpre f .As conditions at the start of each experiment haveTplanet = Tpre f , all planets spend time in a habitabletemperature range and thus all planets are potentiallyhabitable. Doomed planets are those where Tplanet di-verges from Tpre f too quickly before a food source hasbuilt up for microbes, preventing successful colonisationof the planet. For higher C where the chemicals are moreevenly distributed between each chemical species, tem-peratures change at a slower rate, and thus the numberof Doomed planets decreases.

Bottlenecks are rare for βstar = βpre f . Previous re-sults, Figures 6 - 10 in the main paper, showed that whenmicrobes were seeded on a planet when βstar < βpre fthey caused a reduction in habitability (the same is truefor βstar > βpre f ). For βstar = βpre f the sudden decreasein atmospheric chemicals due to seeding will instead leadto an increase in habitability. This prevents much of thethe bottleneck behaviour seen when βstar is far fromβpre f , as in Figures 7 and 8, i.e. the decrease in hab-itability followed by a rapid population reduction, withthe population sometimes recovering and sometimes go-ing extinct. Bottleneck behaviour can still emerge how-ever when microbes do not evolve metabolisms fastenough to consume all chemical species building up inthe atmosphere. However, with the increase in habitabil-ity after seeding, reproduction rates and thus mutationrates are higher than when βstar is far from βpre f andso varied metabolisms appear more rapidly making Bot-tleneck planets less likely for βstar = βpre f .

It seems unlikely that the biosphere on a real planetwould consume the entire atmosphere, perhaps makingthe model results for βstar = βpre f less realistic thanfor βstar < βpre f or βstar > βpre f , however nutrientlimitation is a well-known phenomena in ocean systems[Moore et al., 2013]. The ExoGaia model demonstratesthat habitable conditions can be maintained by a bio-sphere under a range of conditions, and we see that foreach scenario tested the underlying geochemical networkplays a key role in determining a planet’s suitability forlong term habitability.

B.4 Changing the β and T relation

The results presented throughout the main paper andthis Appendix thus far have used a linear relationshipbetween β and temperature. Figure 15a shows a plotof the Stefan-Boltzmann law: β = σT4 (where σ is theStefan-Boltzmann constant), for temperatures between0−100oC, and a linear approximation (dashed). We cansee that the linear approximation is a close fit to the T4

26

curve. Figure 15b shows β = T4 for the range of habit-able abstract temperatures in ExoGaia: 916− 1084, alsowith a linear approximation (dashed). The T4 relationin Figure 15b is slightly less curved than in Figure 15ahowever they are not vastly different. Therefore a linearapproximation of β ∼ T in these temperature ranges is aclose approximation.

(a) Real world habitabletemperature range

(b) ExoGaia habitable tem-perature range

Figure 15: β ∼ T4 (solid) and linear approximations(dashed) for the habitable temperature ranges for thereal world (a) and ExoGaia worlds (b)

We can investigate the behaviour of the ExoGaiamodel with the more realistic β = T4 instead of β = T .Multiplying T4 by a constant, e.g. σ, is not importantas this constant cancels out in the equation updating thethermal energy in a planet’s atmosphere (Equation 16)and so can be safely ignored. Omitting σ also serves as areminder that all temperatures in ExoGaia are abstract.

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Figure 16: The frequency of Abiding, Bottleneck,Critical, Doomed, and Extreme planets against connec-tivity for simulations where β = T4.

Figure 16 shows the frequency of each planet classagainst connectivity. These results use the same param-eters as those used for results in the main paper, theonly change being β = T → β = T4. We see that theoverall behaviour of the model is unchanged, 5 planetclasses emerge, with increasing connectivity correlatedwith increased long-term habitability success for plan-ets. The planet class frequencies between Figure 16 and12a (the results from the main body of the paper) differsignificantly however.

The reason for this is not due to the curved β and Trelation, but due to the fact that when β = T4, doublingβ no longer corresponds to doubling T . The β = T4 re-lation results in far more planets being too cold for life,

hence the large number of Extreme planets seen in Fig-ure 16. As temperature in the ExoGaia model is uncon-strained, fitting β = A×T4 + B to approximate β = T (tocapture the curvature of a T4 relation but maintain sim-ilarity with the original data), results in imaginary tem-peratures being possible - which is of course unphysical.Therefore, no fitting was performed and thus the rela-tive planet class frequencies are quite different. HoweverFigure 16 demonstrates that using a T4 relation insteadof a linear one does not impact the important resultsof the model, and that the model results are robust tosignificant changes to the β and T relationship.

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arxiv:1803.08063v2 [astro-ph.ep] 23 mar 2018 · ing us to isolate purely biotic phenomena emerging...

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