Aurélie Méjean
email: mejean@centre-cired.fr

Antonin Pottier

Marc Fleurbaey

Stéphane Zuber

A Pottier Cired

Ehess M Fleurbaey

Catastrophic climate change, population ethics and intergenerational equity

Keywords: Climate change, Catastrophic risk, Equity, Population, Climate-economy model

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Introduction

The risk of abrupt and irreversible changes to the climate is one of the five reasons for concern identified by the IPCC (McCarthy et al., 2001;Field et al., 2014). Such abrupt changes are generally associated with tipping points [START_REF] Lenton | Tipping elements in the Earth's climate system[END_REF], like the shutoff of the Atlantic thermohaline circulation, the collapse of the West Antarctic ice sheet or the dieback of the Amazon rainforest. They may have indirect impacts, for instance through increased migration and conflicts [START_REF] Reuveny | Climate change-induced migration and violent conflict[END_REF][START_REF] Hsiang | Quantifying the Influence of Climate on Human Conflict[END_REF]. Catastrophic outcomes can also arise from discontinuities in the response of socio-economic systems to climate change.

What is the impact of climate change catastrophes on climate policy making? In this paper, we study a specific instance of such a climate change catastrophe, namely human extinction. There is evidence that climate change may bring about a global catastrophe. One reason is that the level of warming itself is very uncertain and may be much larger than expected. [START_REF] Wagner | Climate Shock -The Economic Consequences of a Hotter Planet[END_REF] have produced estimates of possible extreme temperature rises in a medium-high emission pathway. They estimate the probability of eventual warming of 6 • C to be around 10%, and the probability of 10 • C to be around 3%. Such levels may threaten the Earth inhabitability for humans [START_REF] Sherwood | An adaptability limit to climate change due to heat stress[END_REF]. The climate tipping points could induce a runaway greenhouse effect where feedback loops reinforce the warming trends, creating overheating spirals well past survivability [START_REF] Steffen | Trajecto-ries of the earth system in the anthropocene[END_REF]. Last, climate change may trigger general warfare, the use of dangerous technology or other events that may entail human extinction.

Climate change is very unlikely to cause human extinction. However, even if human extinction is a very unlikely event, it is an event with large welfare consequences, which may be sufficient to justify a substantial policy response. Due to the speculative nature of the risk studied, our analysis should be taken mainly as a thought experiment, pointing to orders of magnitude and qualitative judgements instead of sharp, quantitative statements.

When climate change entails a risk of extinction of the human population, population ethics matters. Population ethics assesses the value of population size for social welfare. For example, the utilitarian social welfare function may be extended to "average utilitarianism" [START_REF] Hurka | Average utilitarianisms[END_REF], by looking at the average of people's well-being, or to "total utilitarianism" [START_REF] Sidgwick | The Methods of Ethics[END_REF], by looking at the sum of people's well-being. But other approaches are possible, for instance "critical-level utilitarianism" [START_REF] Blackorby | Critical-Level Utilitarianism and the Population-Ethics Dilemma[END_REF][START_REF] Broome | Weighing Lives[END_REF] or "number-dampened utilitarianism" [START_REF] Ng | What should we do about future generations? impossibility of parfit's theory x[END_REF]. Total utilitarianism is implicit in many Integrated Assessment Models (henceforth IAMs; see e.g., [START_REF] Nordhaus | Managing the global commons: the economics of climate change[END_REF]. Although it might seem obvious that human extinction would be a very bad thing, the issue is actually unclear [START_REF] Broome | The most important thing about climate change[END_REF]. There have been lots of debates in the population ethics literature as each of the existing ethical theories about the value of population has intuitively unattractive implications [START_REF] Parfit | Reasons and Persons[END_REF]. As climate change policies are expected to affect the size of the world's population, and different ethical theories may imply very different conclusions about the value of these policies, this raises a serious difficulty for evaluating policies aimed at mitigating climate change. This has largely been ignored in the literature [START_REF] Broome | Climate matters: ethics in a warming world[END_REF][START_REF] Millner | On welfare frameworks and catastrophic climate risks[END_REF][START_REF] Kolstad | Social, Economic, and Ethical Concepts and Methods[END_REF].

Another important ethical consideration for climate change is that of the distribution of well-being across individuals belonging to different generations. The utilitarian approach, discussed above in the context of population ethics, is insensitive to this distribution because it only looks at total well-being. On the contrary, prioritarian approaches look at the sum of transformed wellbeing, where the transformation through a concave function implies that an increase in well-being at low levels enhances social welfare more than a similar increase at high levels (see [START_REF] Adler | Well-Being and Fair Distribution: Beyond Cost-Benefit Analysis[END_REF], for a discussion of these issues and a presentation of prioritarianism). The degree of priority for worse-off individuals is measured by inequality aversion. In IAMs, priority is typically expressed with respect to consumption, and inequality aversion plays an important role in shaping optimal climate policy. When introducing extinction risk, inequality aversion will play an additional role: it may change the value of the population in the case where extinction does not happen (and thus the value of avoiding extinction). It is thus important to jointly study the role of population ethics and inequality aversion.

Using a broad class of ethical value functions -number-dampened utilitarian social welfare functions -we show that accounting for a risk of human extinction due to climate change alters the standard results of cost-benefit analysis carried out using IAMs. This is true even if the risk we consider is very small (up to four orders of magnitude below other exogenous causes of extinction). When assuming enduring technical progress and under high inequality aversion, these models usually recommend that we postpone climate change mitigation and let future, richer generations pay. We show that when accounting for a risk of extinction due to climate change, there are cases where a high inequality aversion favours the most ambitious climate policy.

Most of the climate economics literature about catastrophes has modelled them as large drop in consumption: either as the certainty-equivalent loss of risky catastrophic damages [START_REF] Nordhaus | Warming the world: economic models of global warming[END_REF], or as a sudden jump in climate damages when the temperature rises above a given temperature threshold [START_REF] Ambrosi | Optimal Control Models and Elicitation of Attitudes towards Climate Damages[END_REF][START_REF] Pottier | The Comparative Impact of Integrated Assessment Models' Structures on Optimal Mitigation Policies[END_REF], or through a power law damage function with a large exponent [START_REF] Hope | The marginal impact of CO2 from PAGE2002: An integrated assessment model incorporating the IPCC's five reasons for concern[END_REF][START_REF] Ackerman | Fat tails, exponents, extreme uncertainty: Simulating catastrophe in DICE[END_REF][START_REF] Weitzman | GHG Targets as Insurance Against Catastrophic Climate Damages[END_REF]. 1 The case of human extinction is different, as it is an irreversible regime shift in the sense that post-catastrophe welfare is independent from pre-catastrophe actions. In this paper, we thus choose a simplified representation of human extinction so that (i) once started, the extinction process is irreversible; (ii) it happens within a time step in our analysis. 2 In this paper, we explicitly account for the risk of extinction of future generations. We use the IAM RESPONSE [START_REF] Ambrosi | Optimal Control Models and Elicitation of Attitudes towards Climate Damages[END_REF][START_REF] Pottier | The Comparative Impact of Integrated Assessment Models' Structures on Optimal Mitigation Policies[END_REF], representing the interaction between climate and the economy, to assess the impacts of three scenarios (a business-as-usual case, a 2 • C and a 3 • C stabilisation policy) in terms of future consumption paths and extinction risk associated to climate change. We analyse the role of inequality aversion and population ethics for policy evaluation within the class of number-dampened utilitarian social welfare functions. This paper is thus at the crossroads of the literature on catastrophic climate change and the nascent literature on population ethics applied to climate change. Although the importance of population growth for future greenhouse gas emissions has long been recognised [START_REF] Gaffin | Population and global warming with and without co2 targets[END_REF][START_REF] Kelly | Malthus and Climate Change: Betting on a Stable Population[END_REF], and thus population control has been mentioned as a possible way to mitigate climate change (see [START_REF] Cafaro | Climate ethics and population policy[END_REF], for an advocacy), it is only very recently that the role of population ethics for climate policy analysis has started to be discussed. [START_REF] Adler | Prioritarianism and Climate Change[END_REF] propose a prioritarian framework to evaluate scenarios with variable population in the case of climate change. [START_REF] Scovronick | Impact of population growth and population ethics on climate change mitigation policy[END_REF] show that putting a larger weight on population size warrants tighter climate policy whereas Lawson and Spears (2018) discuss how the preference for large populations can be overturned when environmental constraints are accounted for. This paper is the first to examine the role of population ethics in the context of catastrophic climate change.

The paper is structured as follows. Section 2 presents the framework used to evaluate climate policies. The numerical analysis presented in section 3 shows that the preferred climate policy depends on the relative impact of ethical parameters on the welfare gain due to a lower hazard rate (risk effect) and the welfare loss due to a lower consumption stream (consumption effect). In particular, we find cases where increasing inequality aversion favours the most ambitious climate policy. This new result is explained by the differentiated impact of inequality aversion on the risk and consumption effects. Section 4 concludes.

Evaluating the effects of climate policies

Evaluating climate policies involves two steps: first, each climate policy is translated into a social prospect using a climate-economy model; second, social prospects are evaluated using a social welfare function, policies are then ordered in terms of social welfare. We present the social welfare function to value social prospects in section 2.1 and the climate-economy model that computes social prospects from policies in section 2.2.

how human extinction might come about (it may take several years). But this simplification can be justified by saying that the extinction process is predetermined and rapidly yields a situation that is equivalent to extinction in terms of welfare (for instance because the extinction may involve a lot of suffering for many years where people live very bad lives).

Number-dampened utilitarianism with a risk of extinction

Policy choices may impact consumption, population size and the probability of stochastic events. This paper focuses on the risk of extinction and therefore the only uncertain variable is the date at which extinction occurs. For a given policy, consumption and population are deterministic but conditional on existence. Key data of social outcomes from a policy are the sequence n = (n 0 , n 1 , • • • , n t , • • • ) which gives each generation's population size conditional on existence, and the sequence c = (c 0 , c 1 , • • • , c t , • • • ) which gives each generation's consumption per capita conditional on existence. Indeed, we do not consider intra-generational inequalities, and we assume that consumption is equally distributed among individuals of the same generation, so that we can refer either to a generation or to a (representative) individual of that generation. Generation t, if it exists, is thus of size n t and enjoys consumption per capita c t . We now introduce the social welfare function used throughout the paper in two steps, starting with sure social outcomes.

In this paper, we use a social welfare approach to rank policies according to the prospects they induce. Relying on a value function (the social welfare function), our approach is concerned with the goodness of the outcomes or consequences of actions, and thus belongs to a broad class of consequentialist theories (see [START_REF] Adler | Well-Being and Fair Distribution: Beyond Cost-Benefit Analysis[END_REF], for a presentation of the social welfare approach and its ethical underpinnings). It however means that we ignore some important justice issues such as those related to the notions of harm, virtues or duties. 3 We think that even people who do not think that consequentialism is the only relevant ethical view may still think that consequences are part of the ethical considerations we should rely on. Using a social welfare approach is at least a way to discuss some relevant justice issues.

Sure social outcomes and main parameters

First, consider a social outcome for which the date of extinction is known for sure. If the time horizon is H, only the first H generations exist and social welfare is generated by the size of generations n = (n 0 , n 1 , • • • , n H ) and their consumption per capita c = (c 0 , c 1 , • • • , c H ). We thus write the social outcome (n, c, H), as this triplet fully describes it. To value this social outcome, we follow most of the existing literature and assume that aggregate welfare V from outcome (n, c, H) has the following generalised utilitarian form 4 .

3 See for instance [START_REF] Jamieson | When utilitarians should be virtue theorists[END_REF] or [START_REF] Shue | Climate Justice. Vulnerability and Protection[END_REF] for examples of such approaches to climate justice. 4 The economic literature usually uses the term 'generalised utilitarian' rather than prioritarian as we did in the introduction. The formula here is prioritarian with respect to consumption; it may be viewed as utilitarian if function u(c) = c 1-η 1-η is the true utility function. There exists a limited literature in population ethics proposing alternatives to this generalised utilitarian formula, for instance equally-distributed equivalent criteria [START_REF] Fleurbaey | Discounting, beyond Utilitarianism. Economics: The Open-Access[END_REF], egalitarian criteria [START_REF] Blackorby | Leximin population ethics[END_REF] or rank-dependent criteria (Asheim andZuber, 2014, 2016).

Definition 1 (Number-dampened utilitarian social welfare functions) A social welfare function is a number-dampened utilitarian social welfare function (NDU SWF) if there exist real numbers β ∈ [0, 1], c ∈ R ++ and η ∈ R + such that:

V (n, c, H) = N β H H t=0 n t N H c 1-η t 1 -η - c 1-η 1 -η , (1)
where N H = H t=0 n t is the total (cumulated) population that comes into existence in social outcome (n, c, H). The utility enjoyed by an individual of generation t is

c 1-η t 1-η - c 1-η
1-η . The utility averaged across individuals and generations is:

AU H (n, c) = H t=0 n t N H c 1-η t 1 -η - c 1-η 1 -η ,
so that social welfare (1) is the product of average utility and a population weight N β H . Note that if we consider social outcomes with the same total population, the terms N β H and c 1-η 1-η do not play any role: our social welfare function then gives the same ranking as the usual utilitarian social welfare function H t=0 n t c 1-η t 1-η . However, this is not true anymore when population varies and can endogenously change with the policy, as in the case of the extinction risk we consider afterwards.

The NDU SWF is a variant of number-dampened utilitarianism proposed by [START_REF] Ng | Social criteria for evaluating population change: An alternative to the Blackorby-Donaldson criterion[END_REF], where welfare is the product of average utility and a concave function of total population size. The slight difference is that Ng's concave function has a finite limit at infinity to avoid Parfit's Repugnant conclusion, whereas ours has not. However, [START_REF] Blackorby | Population Issues in Social Choice Theory, Welfare Economics, and Ethics[END_REF] use the term numberdampened (general) utilitarianism for a generalisation of our specification. Several other authors have used the same variant of NDU as we do, but averaging utility over periods, not over the entire history, and computing the weight accordingly, see for instance [START_REF] Boucekkine | Egalitarianism under population size: age-structure does matter[END_REF] or [START_REF] Lawson | Optimal population and exhaustible resource constraints[END_REF].

A key property of our NDU SWF is that it does not exhibit pure time discounting: contrary to most approaches in climate economics, it treats generations in a symmetric way. 5 This also implies that only the total number of individuals at a given consumption welfare matters, irrespective of their distribution across time. We describe the main axiomatic properties of our NDU SWF in the Electronic supplementary material (section S.A).

The NDU SWF embodies the preferences of an evaluator through three important ethical parameters.

5 See [START_REF] Ramsey | A mathematical theory of saving[END_REF] and [START_REF] Stern | The economics of climate change: the Stern review[END_REF] for arguments on why we should treat generations in a symmetric way. Observe that one reason for discounting, namely the possibility that future generations may not exist, is not yet accounted for, given that the existence (or nonexistence) of generations is for the moment known for sure. The next section will show that the extinction risk creates endogenous discounting.

1. Parameter η is the (intergenerational) inequality aversion coefficient. It determines the marginal utility of individual consumption. A high value of η implies that the utility function of individuals is strongly concave in consumption, so that marginal utility at high consumption levels is much lower than at low consumption levels. A more inequality averse social welfare function means that we are willing to sacrifice more to equalise consumption levels across generations. 2. Parameter β is the population ethics coefficient and determines the value of large populations. Indeed, Eq. ( 1) embeds well-known views of utilitarianism when population size varies. Total or classical utilitarianism values the total sum of utilities, which corresponds to β = 1. Average utilitarianism, on the contrary, values the average utility, which corresponds to β = 0.

Varying β between 0 and 1 spans cases between the total and the average utilitarian views. 3. Parameter c is a consumption per capita threshold. The interpretation of this threshold is that it corresponds to the neutral level of utility, i.e. the level above which a life is worth living (life is assumed to be not worth living below that level of consumption). 6 In the case of total utilitarianism (β = 1), it is also the critical level of consumption, i.e. the level of consumption such that, if enjoyed by an additional individual, total welfare is left unchanged when that individual is added to the population. This parameter plays a key role in critical-level generalised utilitarianism [START_REF] Broome | Weighing Lives[END_REF][START_REF] Blackorby | Population Issues in Social Choice Theory, Welfare Economics, and Ethics[END_REF]. When β = 1 however, the critical level is not constant and depends on population size and average utility. Parameter c still influences aggregate welfare and the value of changing population size.

Risky social prospects

Consider now a risky social prospect. As explained before, the only risk considered here is a risk on the existence of future generations. Hence, a social prospect is still partly described by a deterministic population stream n and a deterministic consumption stream c, i.e. population size is n t and consumption per capita is c t , conditional on existence at period t. Due to the risk of extinction, the time horizon is unknown. The risk of extinction is specified as an infinite stream of hazard rates p. The hazard rate p t is the probability of extinction at the end of period t, conditional on existence at the beginning of period t. The survival probability at t is P ≥t = t-1 τ =0 (1 -p τ ) (probability that the time horizon is greater than or equal to t). The probability that humanity becomes extinct right after generation t is P t = p t P ≥t , which we name the horizon probability, i.e. the probability that the time horizon is t. The risky 6 The notion of the neutral level of utility is important in the literature on population axiologies, as many paradoxes or principles (for instance "avoiding a repugnant conclusion", or the "mere addition principle"), rely on the notion (see Arrhenius, forth.). The notion has been defended for instance by [START_REF] Holtug | On the value of coming into existence[END_REF]. Still, there are discussions about the exact meaning of "a life is worth living" and the level of c.

social prospect is fully represented by a triplet (n, c, p). To extend the NDU SWF to social prospects with unknown time horizons, we simply assume that aggregate welfare W is the expected value of the NDU welfare of each possible outcome.

Definition 2 (Expected number-dampened utilitarian social welfare functions) A social welfare function is an expected number-dampened utilitarian social welfare function (ENDU SWF) if there exist real numbers β ∈ [0, 1], c ∈ R ++ and η ∈ R + such that:

W (n, c, p) = ∞ H=0 P H N β H H t=0 n t N H c 1-η t 1 -η - c 1-η 1 -η = ∞ t=0 ∞ H=t P H N β-1 H θt n t c 1-η t 1 -η - c 1-η 1 -η . (2) By definition W (n, c, p) = ∞ H=0 P H V (n, c, H), so that V (n, c, H) = W (n, c, 1 H ) (
where 1 H is the prospect assigning probability 1 to extinction at date H and 0 otherwise). So there are two ways by which population size may vary in our model. First, the deterministic path n of population size conditional on existence may vary. Second, the probability p of the extinction risk may vary, making expected population size and the distribution of population sizes endogenous. For instance, comparing prospects (n, c, 1 H ) and (n, c, 1 H+1 ) requires to be able to compare populations with different sizes. In the rest of the paper, we will assume that policy does not affect n, i.e. that it does not affect a generation's population size, conditional on its existence.7 However, given that policy will affect the hazard rates p, the existence of future generations and the distribution of population size will be endogenous. Population ethics considerations will therefore matter for policy assessment.

In Eq.( 2), the scalar θ t is tantamount to a time discount factor on the utility of generation t. This discount factor is not related to pure time discounting but stems from the uncertainty about the horizon, a rationale for discounting already discussed in the Stern Review (2007). It is actually an endogenous discount factor that depends on the stream of hazard rate p. It also depends on the attitudes towards population size as embodied in the population ethics coefficient β. This role of views about population ethics on discounting has been discussed before by [START_REF] Fleurbaey | Discounting, beyond Utilitarianism. Economics: The Open-Access[END_REF] and [START_REF] Scovronick | Impact of population growth and population ethics on climate change mitigation policy[END_REF]. When β = 1, the discount factor θ t on the utility of generation t is exactly its probability of existence. When β < 1, this discount factor is the probability of existence multiplied by a factor which is decreasing with time, so that future generations' utility is discounted beyond what follows from their probability of existence.8

Modelling the social outcomes of climate policies

We present the climate-economy model (section 2.2.1) and the way the risk of extinction is modelled (section 2.2.2).

The climate-economy model

To translate climate policies into social prospects to be evaluated by the ENDU SWF, we use the IAM RESPONSE [START_REF] Ambrosi | Optimal Control Models and Elicitation of Attitudes towards Climate Damages[END_REF], which belongs to the tradition of compact IAMs [START_REF] Nordhaus | Managing the global commons: the economics of climate change[END_REF][START_REF] Hope | Policy analysis of the greenhouse effect -An application of the PAGE model[END_REF][START_REF] Tol | On the optimal control of carbon dioxide emissions: an application of FUND[END_REF]. It combines a simple representation of the economy and a climate module. The economic module is a Solow-like growth model with capital accumulation and exogenous population. It includes climate mitigation costs and a climate damage function, that is chosen here to be equivalent to that of DICE. A key parameter is exogenous technical progress (Total Factor Productivity growth), which decreases over time.9 A thorough description of the model and its equations can be found in [START_REF] Dumas | Comprehensive Description of RESPONSE[END_REF] and [START_REF] Pottier | The Comparative Impact of Integrated Assessment Models' Structures on Optimal Mitigation Policies[END_REF].

A policy (or scenario) i is specified as the decision variables of the model, which consists of a saving rate stream and an abatement stream. The model computes outputs from these decision variables. Model outputs include the stream of consumption per capita c i . Because population (conditional on existence) is exogenous, the generation size stream n does not depend on policy i (it will thus be common to all social prospects that will be evaluated). To complete the description of the social prospect (n, c i , p i ) of policy i, we only need to specify how the hazard rate p is computed.

The risk of extinction

Before describing how the hazard rate is modelled, let us motivate the introduction of a risk of extinction due to climate change. In our model (which follows standard specifications), climate damages on consumption are not sufficient per se to trigger the extinction of the human population. We consider that the risk of extinction does not stem from dwindling consumption, but from a societal regime shift induced by climate change. Such a regime shift can be initiated by extreme climate events, climate tipping points, or for instance an epidemic outbreak due to global warming. Such initiating events would provoke a chain reaction, e.g. through inappropriate policy responses, large migration waves, general warfare, which would challenge the physical, political and social infrastructures of global society, leading to its collapse. This is the type of event described under the label "risk of extinction": a catastrophe that destroys society and its institutions.

We model extinction as an abrupt event that occurs over the course of one period (a decade). This is of course a harsh simplification of actual processes, which would be gradual and involve feedbacks between institutions, consumption, mortality and fertility. In reality, the ultimate consequences of such a catastrophe would probably take decades to unfold. Following the work by [START_REF] Cropper | Regulating activities with catastrophic environmental effects[END_REF] and [START_REF] Clarke | Consumption/pollution tradeoffs in an environment vulnerable to pollution-related catastrophic collapse[END_REF] in modelling environmental catastrophes, we consider that what is crucial for our analysis is that postcatastrophe variables do not depend on pre-catastrophe variables, so that a transfer of wealth (or population, which is more important for population ethics) cannot occur across the time of the catastrophe, i.e., the course of post-catastrophe events is inevitably set and cannot be acted upon. Since post-catastrophe welfare cannot be changed, we abstract from the details of the extinction process and adopt the simplifying assumption that what triggers the catastrophe also represents the end of time.

Whether such a catastrophic chain of events would actually lead to the extinction of all human beings is controversial and may be considered as highly unlikely. An important point of this paper is that even a remote possibility of human extinction may be sufficient to justify a policy response (see Section 3.2). The probability of the extinction risk is however difficult to determine as its calibration cannot rely on the frequentist approach (no similar event has ever happened). Given the large uncertainty surrounding the probability of such events, we decided to remain neutral on the issue and to explore many possibilities. We thus attempt to cover a wide range of possible values.

To further simplify this first inquiry into the role of the risk of extinction, we assume that the hazard rate p depends on the temperature increase T only, and not, for example, on wealth or on a proxy of adaptive capacity. We therefore disregard any factor, social or natural, that may mitigate the effect of climate change on the risk of extinction. More precisely, we model the hazard rate p as a linear function of temperature increase T (in • C above the preindustrial level), above a temperature threshold T 0 (set at 1 • C). The hazard rate at date t, p t , is thus p(T t ), a function of temperature increase T t at date t. We assume that this function is valid in a range of temperature increase spanning from 1 • C to 10 • C, which includes the values of temperature increase presented in the numerical analysis (cf. section 3).

p(T ) =      p 0 , if T ≤ T 0 p 0 + b • (T -T 0 ), if T 0 ≤ T ≤ T 0 + 1-p0 b 1, if T 0 + 1-p0 b ≤ T, (3)
where p 0 is the exogenous minimum hazard rate (set at 10 -3 per annum), and b is the marginal hazard rate per • C above T 0 . As argued above, there is no available data about its realisation from which the parameters of the hazard rate function could be inferred. The calibration can thus only be illustrative and tentative. We retain a range of b between 10 -1 and 10 -7 per • C per annum (see the Electronic supplementary material, section S.B.1, for a detailed description).

Decomposition of the welfare impacts of policy change

Climate policies affect social prospects, as they alter both the consumption path and the probability of catastrophic outcomes yielding an early extinction. For example, a stringent mitigation policy that reduces greenhouse gas emissions compared to a business-as-usual case will reduce consumption now and in the short run, but increase consumption in the long run by avoiding climate damages; the hazard rate in all future periods will be also reduced, as temperature increase is lower.

We want to better understand how the preferred policy varies with the ethical parameters of the social welfare function, namely the inequality aversion parameter η and the population ethics parameter β. We may think that these parameters actually have different effects depending on whether we look at the impact of policy on consumption or at its impact on the extinction risk. We use a welfare decomposition method (described in Electronic supplementary material, section S.C.1 in particular Table S.3) in the numerical analysis below to determine which effect (the risk effect or the consumption effect) is larger depending on the value of ethical parameters η and β.

Numerical evaluation of three climate policies

A numerical analysis is necessary to understand the role of ethical parameters on the preferred policy. We set out three climate policies (section 3.1) and rank them using the ENDU SWF. We examine specifically the role of the risk of extinction (section 3.2) and the role of ethical parameters (section 3.3) in determining the preferred climate policy among the set of policies considered.

The numerical experiment: climate policies and their social outcomes

We introduce the climate policies and parameter ranges used in the numerical experiment. We consider three climate policies: one business-as-usual scenario, i.e., continuing past trends of emissions, calibrated on the middle of the range of business-as-usual scenarios from the database used for the fifth assessment report of the IPCC, see (IIASA, 2014); and two abatement scenarios which are expected to limit the increase of the global temperature above the preindustrial level to 3 • C and 2 • C. We provide a detailed description of the policies considered in the Electronic supplementary material, section S.B.2.

In terms of ethical parameters used for the evaluation, we choose 0 ≤ β ≤ 1, which means there is at least a weak preference for large populations. The case β = 0 corresponds to average utilitarianism, while the case β = 1 corresponds to total utilitarianism. We test a wide range of values for the inequality aversion coefficient η, spanning from 0.5 to 5. The threshold per capita consumption parameter is calibrated on an extreme poverty consumption level, as in [START_REF] Bommier | Models-as-usual for unusual risks? On the value of catastrophic climate change[END_REF]. The parameter value ranges are summarised in Table S.2 in the Electronic supplementary material.

We do not formally consider other sources of uncertainty than the risk of extinction in this paper. Our aim is to illustrate and give broad orders of magnitude about the trade-off between present consumption and the existence of future generations. We keep the rest of the analysis as simple as possible, and use central values for uncertain parameters such as the climate sensitivity, the convexity of the damage function or the rate of technical progress in the numerical assessment.

Results: The role of the risk of extinction and climate damages

This section examines the effect of the risk of extinction on the preferred policy between a business-as-usual scenario (BAU) and a 3 • C scenario10 , with and without accounting for climate damages. When not accounting for climate damages on consumption, we primarily focus on the trade-off between consumption and the risk of extinction. In doing so, we do not consider the intertemporal consumption trade-off determined by the balance between abatement costs and climate damages. Abatement reduces both the stream of consumption c and the stream of hazard rate p over the whole period11 . The most ambitious climate policy would therefore be favoured because of a reduction in the risk of extinction, while the least ambitious policy would be favoured because of an increase in consumption in early periods.

We examine the preferred policy option between BAU and 3 • C as a function of the marginal hazard rate b for a given degree of inequality aversion (η = 2.0) and for a given value of the population ethics coefficient (β = 1.0, i.e. the case of total utilitarianism). hazard rate streams are then identical in the 3 • C scenario and the BAU scenario. This means that when the 3 • C scenario is preferred to the BAU, this is due to its effect on reducing the hazard rate.

The role of damages

So far, the analysis has not accounted for the intertemporal consumption trade-off between abatement costs and climate damages. We now test the sensitivity of the results to the inclusion of climate damages in the model. Climate damages occur due to temperature increase, and are subtracted from production, thus reducing consumption. As before, they can be mitigated thanks to abatement, which comes at a cost. The results in table ?? show that the preferred policies are unchanged whether or not climate damages are accounted for, with the exception of b = 0 per The first row of table 1 shows the case without climate change damages. The results show that in that case, only a zero marginal hazard rate b (i.e., the case of a purely exogenous hazard rate) leads to favour the BAU scenario (i.e., no abatement). With a marginal hazard rate equal to zero, mitigation has no impact on extinction and only reduces consumption. So, climate policy necessarily reduces welfare if we exclude climate damages. With a marginal hazard rate b greater than zero, there is a chance that climate action may avoid extinction, and the 3 • C scenario is favoured over the BAU. The first row of table 1 shows that the difference in the hazard rate always explains the preference for the 3 • C scenario, while the difference in consumption counteracts (dark grey cells). Conversely, the difference in consumption explains the preference for the BAU scenario when the hazard rate is purely exogenous (i.e., for a marginal hazard rate b = 0 per • C per annum), as hazard rate streams are then identical in the 3 • C scenario and the BAU scenario. This means that when the 3 • C scenario is preferred to the BAU, this is due to its effect on reducing the hazard rate.

The second row of table 1 shows the case with climate damages. Climate damages occur due to temperature increase, and are subtracted from production, thus reducing consumption. As before, they can be mitigated thanks to abatement, which comes at a cost. The results in table 1 show that the preferred policies are unchanged whether or not climate damages are accounted for, with the exception of b = 0 per • C per annum, i.e. for a purely exogenous hazard rate. The second row of table 1 shows that when damages are accounted for, the 3 • C scenario is preferred due to both the risk and the consumption effects (black cells, again with the exception of b = 0 per • C per annum). This contrasts with the case without climate damages, where the 3 • C scenario was preferred due to the risk effect alone (dark grey cells), while the consumption effect played in favour of the BAU (light grey cells). The effect on consumption is indeed expected to favour the 3 • C scenario, as the reduced consumption of future generations due to climate damages can impact total welfare in a significant way. The results also show that when damages are accounted for and when there is no risk of extinction (b = 0 per • C per annum), the 3 • C scenario is preferred to the BAU scenario. This result is in accordance with the results of the Stern Review (2007), which, assuming a pure time preference of 10 -3 per annum, concludes that the avoided damages of a 3 • C scenario outweigh its abatement costs, and that such a policy should be pursued. It is interesting to note that, with climate damages, the 3 • C scenario is no longer preferred due to higher consumption when b increases from 10 -3 to 10 -2 per • C per annum. Indeed, the 3 • C scenario is then preferred due to the risk of extinction only, as the intertemporal consumption trade-off no longer plays in favour of the 3 • C scenario for higher values of b. This is due to the fact that with a higher marginal hazard rate b, the benefits of abatement on future consumption through avoided climate damages have less weight in total welfare, as future generations are less likely to exist. This is an example of how the hazard rate and climate damages interact in the intertemporal consumption trade-off.

Results: The role of ethical parameters

We now examine the role of ethical parameters in determining the preferred policy in a case with climate damages in addition to the catastrophic risk of extinction due to climate change. We consider in turn the role of the population ethics coefficient (β), and the role of inequality aversion (η).

The role of population ethics

In table 2, we examine preferred policy options (between the BAU, 3 • C and 2 • C scenarios)12 as a function of the marginal hazard rate b for various population ethics coefficients (β) and for given values of the inequality aversion coefficient (η = 1.5 and η = 2.5). The contributions of the difference in hazard rate and of the difference in consumption to the difference in welfare is calculated when comparing the preferred policy and the next best policy (see section 2.3).

For a given marginal hazard rate b, a higher population ethics coefficient favours the most ambitious climate policy. This result is consistent with intuition, as ambitious climate policies allow for larger cumulative population. Above a certain value of the marginal hazard rate b, the value of β plays no role on the preferred policy. We show that the difference in hazard rate always explains the preference for the most ambitious climate scenario (dark grey cells).

Conversely, the difference in consumption always explains the preference for the least ambitious climate scenario (light grey cells), except when the hazard rate is purely exogenous (i.e. for a marginal hazard rate b = 0 per • C per annum). Note that the results in table ?? show that for the values of η considered, the BAU scenario is never preferred when climate damages are accounted for.

β b (per • C) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [10 -5 ; 10 -1 ] 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [4.10 -6 ; 9.10 -6 ] 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [2.10 -6 ; 3.10 -6 ] 3°C 3°C 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 10 -6 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 2°C 2°C 10 -7 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 0 (a) η = 1.5 β b (per • C) 0.0 0.

22

(a) η = 1.5

For a given marginal hazard rate b, a higher population ethics coefficient favours the most ambitious climate policy. This result is consistent with intuition, as ambitious climate policies allow for larger cumulative population. Above a certain value of the marginal hazard rate b, the value of β plays no role on the preferred policy. We show that the difference in hazard rate always explains the preference for the most ambitious climate scenario (dark grey cells).

Conversely, the difference in consumption always explains the preference for the least ambitious climate scenario (light grey cells), except when the hazard rate is purely exogenous (i.e. for a marginal hazard rate b = 0 per • C per annum). Note that the results in table ?? show that for the values of η considered, the BAU scenario is never preferred when climate damages are accounted for. For a given marginal hazard rate b, a higher population ethics coefficient favours the most ambitious climate policy. This result is consistent with intuition, as ambitious climate policies allow for larger cumulative population. Above a certain value of the marginal hazard rate b, the value of β plays no role on the preferred policy. We show that the difference in hazard rate always explains the preference for the most ambitious climate scenario (dark grey cells).

β b (per • C) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [10 -5 ; 10 -1 ] 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [4.10 -6 ; 9.10 -6 ] 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [2.10 -6 ; 3.10 -6 ] 3°C 3°C 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 10 -6 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 2°C 2°C 10 -7 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 0 (a) η = 1.5 β b (per • C) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [10 -4 ; 10 -1 ] 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [3.10 -6 ; 10 -5 ] 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [10 -6 ; 2.10 -6 ] 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 2°C 2°C 10 -7 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C
Conversely, the difference in consumption always explains the preference for the least ambitious climate scenario (light grey cells), except when the hazard rate is purely exogenous (i.e. for a marginal hazard rate b = 0 per • C per annum). Note that the results in table ?? show that for the values of η considered, the BAU scenario is never preferred when climate damages are accounted for.

β b (per • C) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [10 -5 ; 10 -1 ] 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [4.10 -6 ; 9.10 -6 ] 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [2.10 -6 ; 3.10 -6 ] 3°C 3°C 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 10 -6 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 2°C 2°C 10 -7 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 0 (a) η = 1.5 β b (per • C) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [10 -4 ; 10 -1 ] 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [3.10 -6 ; 10 -5 ] 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [10 -6 ; 2.10 -6 ] 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 2°C 2°C 10 -7 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 3°C 0 (b) η = 2.5
social outcome preferred due to higher consumption social outcome preferred due to lower risk For a given marginal hazard rate b, a higher population ethics coefficient favours the most ambitious climate policy. This result is consistent with intuition, as ambitious climate policies allow for larger cumulative population. Above a certain value of the marginal hazard rate b, the value of β plays no role on the preferred policy. We show that the difference in hazard rate always explains the preference for the most ambitious climate scenario (dark grey cells). Conversely, the difference in consumption always explains the preference for the least ambitious climate scenario (light grey cells), except when the hazard rate is purely exogenous (i.e. for a marginal hazard rate b = 0 per • C per annum). Note that the results in table 2 show that for the values of η considered, the BAU scenario is never preferred when climate damages are accounted for.

The role of inequality aversion

We here examine preferred policy options as a function of the risk of extinction (i.e. as a function of the marginal hazard rate b) for various degrees of inequality aversion (η) and for given values of the population ethics coefficient (β = 0, 0.1, 1). We examine the preferred policy between the BAU, 3 • C and 2 • C scenarios13 in table 3.

In the case of average utilitarianism (β = 0, table 3a), at a given level of risk (i.e., at a given b), a higher inequality aversion favours the least ambitious climate policy. As the risk of extinction is reduced (i.e., as the marginal hazard rate b decreases), the minimum level of inequality aversion that justifies the least ambitious scenario is reduced: with a lower risk of extinction the catastrophe is postponed and richer generations are added, which enhances inequalities between generations because the present generation is still assumed to be relatively poorer. For a high extinction risk (i.e., for large values of the marginal hazard rate b), the most ambitious climate scenario is favoured for all values of inequality aversion.

As climate damages are accounted for, the 2 • C scenario is preferred due to both lower risk and higher consumption (black cells) for relatively low values of inequality aversion (η ≤ 1.0). contrasts with the case without climate damages, where the most ambitious scenario is preferred due to the difference in hazard rate alone, while the consumption effect plays in favour of the least ambitious policy (see section S.E.1. of the Electronic supplementary material). The difference in consumption is indeed expected to favour the most ambitious climate policy for low inequality aversion only, as climate damages reduce the consumption of future generations more than that of present ones. As future generations are richer than present ones in the BAU scenario due to technical change, this effect only occurs for low inequality aversion.

Note that, as before, the contributions of the difference in extinction risk and the contribution of the difference in consumption in determining the preferred policy are calculated when comparing the preferred policy and the next η b (per best policy. When the 3 • C policy is preferred, the next best policy is either the BAU or the 2 • C. When the 3 • C scenario is preferred (see for instance table 3a), and when the next best policy is the 2 • C, the corresponding cell is light grey (i.e., the 3 • C scenario is preferred to the 2 • C due to higher consumption); when the next best policy is the BAU, the corresponding cell is dark grey (i.e., the 3 • C scenario is preferred to the BAU due to the difference in hazard rate). More results comparing policies in pairs, with and without accounting for climate damages, are presented in the Electronic supplementary material (section S.E.). The pattern is different for β = 0.1 (table 3b). In this case, increasing the inequality aversion η still favours the least ambitious climate policy for low values of η, but the effect is reversed for η > 2.0. There are two opposite effects of increasing the inequality aversion coefficient: it decreases the value of reducing the risk of extinction but it also decreases the cost of implementing the policy by making the first (relatively poorer) generations pay. These intuitions are formalised in Propositions S.1 and S.2 in the Electronic supplementary material (section S.C.2). Both effects are also at play in the case β = 0, as shown in the analytical results presented in the section S.C.2 Electronic supplementary material. However, in the numerical results, we find instances where the decrease in the costs of implementing the policy dominates only for β > 0.

2°C 2°C 3°C 3°C 3°C 3 • C 3 • C 3°C 2°C 2°C 10 -7 2°C 2°C 3°C 3°C 3°C BAU BAU BAU BAU BAU 0 (b) β = 0.1 η b (per • C) 0.
(a) β = 0 η b (per • C) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [10 -2 ; 10 -1 ] 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [4.10 -6 ; 10 -3 ] 2°C 2°C 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2°C 3.10 -6 2°C 2°C 3°C 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2.10 -6 2°C 2°C 3°C 3°C 3°C 2°C 2°C 2°C 2°C 2°C 10 -6 2°C 2°C 3°C 3°C 3°C 3 • C 3 • C 3°C 2°C 2°C 10 -7 2°C 2°C 3°C 3°C 3°C BAU BAU BAU BAU BAU 0 (b) β = 0.1 η b (per • C) 0.
(a) β = 0 η b (per • C) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [10 -2 ; 10 -1 ] 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C 2°C [4.10 -6 ; 10 -3 ] 2°C 2°C 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2°C 3.10 -6 2°C 2°C 3°C 3°C 3°C 2°C 2°C 2°C 2°C 2°C 2.10 -6 2°C 2°C 3°C 3°C 3°C 2°C 2°C 2°C 2°C 2°C 10 -6 2°C 2°C 3°C 3°C 3°C 3 • C 3 • C 3°C 2°C 2°C 10 -7 2°C 2°C 3°C 3°C 3°C BAU BAU BAU BAU BAU 0 (b) β = 0.1 η b (per • C) 0.5 1.0 1.
The choice of β significantly changes the preferred policy option for low values of the marginal hazard rate (b), but plays no role for higher values of b (top lines of the tables). In the case of average utilitarianism (β = 0, table 3a), inequality aversion plays a role on the preferred policy option for a wider range of b values than in the case of total utilitarianism (β = 1, table 3c). The choice of β does not influence the preferred policy when the extinction risk is exogenous (i.e for a marginal hazard rate b equal to zero).

Conclusion

With a probability of extinction that depends on temperature increase compared to pre-industrial levels, two effects are competing. On the one hand, future generations are assumed to be richer, and a high inequality aversion thus gives preference to present consumption. This plays in favour of the least ambitious climate policy which preserves the consumption of the present, poorer generation. On the other hand, abatement can prevent extinction, which can favour ambitious climate policies. Our main results are summarised below.

The preferred policy depends on the relative effects of inequality aversion and of the preference for large populations on the welfare gain due to a lower risk of extinction, and on the welfare loss due to lower consumption. A high inequality aversion reduces the welfare gain due to higher consumption. It also reduces the value of postponing extinction. A preference for large populations increases both the welfare loss due to lower consumption, and the welfare gain as the size of the cumulative population increases due to a lower risk of extinction.

A preference for large populations always favours the most ambitious climate scenario. This result is consistent with our first intuition: a preference for large populations gives a larger weight to the welfare of future generations. Low inequality aversion also usually favours the most ambitious scenario, as future generations are assumed to be richer. This is consistent with results from the literature. More precisely, the results confirm that total utilitarians who are little inequality averse would tend to favour ambitious climate policies.

However, we find cases where a higher inequality aversion favours the most ambitious climate policy. This new result is explained by the relative effect of inequality aversion on the risk and consumption components of the difference in welfare between policies. This analysis may thus help identifying new spaces of compromise between various ethical stances to set the ambition of climate policies. Indeed, a coalition could be formed between opposite sides of the ethical spectrum regarding inequality aversion.

The effect of ethical choices on the preferred policy should be further explored. One may for instance want to consider more general welfare functions that disentangle risk aversion and inequality aversion, to explore whether one of these parameters has more influence on the results. One could also include the possibility of partial extinction, i.e. allow for a variable population size as a function of the severity of climate change instead of the 'all-or-nothing' set-up used in this paper.

As mentioned before, our work makes several simplifying assumptions and future work could explore whether those can be relaxed to provide more realistic assessments. First, the probability of extinction depends only on global temperature. One could think that the adaptive capacities of human may depend to some extent on income or wealth. If costly adaptation measures can be taken to survive (for instance we can get protection from heat through air conditioning), humanity would not face extinction even if temperature increase is very large. Also, we could study the consequence of a global catastrophe that is not extinction but a large civilisation collapse. The problem here would be to choose a precise scenario for such a collapse (followed perhaps by a recovery).

  due to higher consumption social outcome preferred due to lower risk Note that the preferred policy is written inside each cell, while the color of the cell indicates what determines the welfare difference Table 4: Preferred policy (BAU vs. 3 • C) for (β = 1.0, η = 2.0)

  0 (b) η = 2.5 social outcome preferred due to higher consumption social outcome preferred due to lower risk Table 6: Preferred policy (BAU vs. 3 • C vs. 2 • C) as a function of β and b (with climate damages) 22 (b) η = 2.5

Table 5 :

 5 Preferred policy (BAU vs. 3 • C) with and without damages (β = 1.0, η = 2.0)

Table ? ?

 ? shows that the 3 • C scenario is preferred due to both the risk and the consumption effects (black cells, again with the exception of b = 0 per • C per annum). This contrasts 20

Table 1 :

 1 Preferred policy(BAU vs. 3

• C) with and without damages (β = 1.0, η = 2.0)

Table 6 :

 6 Preferred policy (BAU vs. 3 • C vs. 2 • C) as a function of β and b (with climate damages)

Table 6 :

 6 Preferred policy (BAU vs. 3 • C vs. 2 • C) as a function of β and b (with climate damages) 22

Table 2 :

 2 Preferred policy (BAU vs. 3 • C vs. 2 • C) as a function of β and b (with climate damages)

Table 7 :

 7 Preferred policy (BAU vs. 3 • C vs. 2 • C) as a function of η and b (with climate damages)

					η						b (per • C)
	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0	4.5	5.0
	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	[10 -2 ; 10 -1 ]
	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	10 -3
	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	10 -4
	2°C	2°C	2°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	10 -5
	2°C	2°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	[8.10 -6 ; 9.10 -6 ]
	2°C	2°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	[4.10 -6 ; 7.10 -6 ]
	2°C	2°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	3.10 -6
	2°C	2°C	3°C	3°C	3°C	3°C	3°C	BAU	BAU	BAU	2.10 -6
	2°C	2°C	3°C	3°C	3°C	BAU	BAU	BAU	BAU	BAU	10 -6
	2°C	2°C	3°C	3°C	3°C	BAU	BAU	BAU	BAU	BAU	10 -7
	2°C	2°C	3°C	3°C	3°C	BAU	BAU	BAU	BAU	BAU	0
						(a) β = 0 (a) β = 0
					η						b (per • C)
	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0	4.5	5.0
	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	[10 -2 ; 10 -1 ]
	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	[4.10 -6 ; 10 -3 ]
	2°C	2°C	3°C	3°C	2°C	2°C	2°C	2°C	2°C	2°C	3.10 -6
	2°C	2°C	3°C	3°C	3°C	2°C	2°C	2°C	2°C	2°C	2.10 -6
	2°C	2°C	3°C	3°C	3°C	2°C	2°C	2°C	2°C	2°C	10 -6
						25

Table 7 :

 7 Preferred policy (BAU vs. 3 • C vs. 2 • C) as a function of η and b (with climate damages)

	(b) β = 0.1
	25

Table 7 :

 7 Preferred policy (BAU vs. 3 • C vs. 2 • C) as a function of η and b (with climate damages)

					η						b (per • C)
	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0	4.5	5.0
	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	[10 -2 ; 10 -1 ]
	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	10 -3
	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	2°C	10 -4
	2°C	2°C	2°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	10 -5
	2°C	2°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	[8.10 -6 ; 9.10 -6 ]
	2°C	2°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	[4.10 -6 ; 7.10 -6 ]
	2°C	2°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	3°C	3.10 -6
	2°C	2°C	3°C	3°C	3°C	3°C	3°C	BAU	BAU	BAU	2.10 -6
	2°C	2°C	3°C	3°C	3°C	BAU	BAU	BAU	BAU	BAU	10 -6
	2°C	2°C	3°C	3°C	3°C	BAU	BAU	BAU	BAU	BAU	10 -7
	2°C	2°C	3°C	3°C	3°C	BAU	BAU	BAU	BAU	BAU	0
							(c) β = 1.0
							25

Table 7 :

 7 Preferred policy (BAU vs. 3 • C vs. 2 • C) as a function of η and b (with climate damages) 25

Table

  Preferred policy (BAU vs. 3 • vs. 2 • C) as a function of η and b (with climate damages)

The stochastic nature of catastrophes is also sometimes explicitly accounted for[START_REF] Peck | Optimal CO2 control policy with stochastic losses from temperature rise[END_REF][START_REF] Lontzek | Stochastic integrated assessment of climate tipping points indicates the need for strict climate policy[END_REF]

2015;[START_REF] Lemoine | Economics of tipping the climate dominoes[END_REF]). 2 This modelling strategy follows a strand of literature[START_REF] Cropper | Regulating activities with catastrophic environmental effects[END_REF][START_REF] Clarke | Consumption/pollution tradeoffs in an environment vulnerable to pollution-related catastrophic collapse[END_REF][START_REF] Gjerde | Optimal climate policy under the possibility of a catastrophe[END_REF][START_REF] Tsur | Endogenous Discounting and Climate Policy[END_REF] that considers that abrupt climate change introduces an irreversible regime shift. Characteristic (ii) is not an accurate description of

Section S.A. in the Electronic supplementary material considers the possibility that policy choices affect population size from a theoretical point of view.

See also section S.A.2. of the Electronic Supplementary Material for a clarification of the discount rate and the underlying Ramsey formula in our framework.

In this paper, we assume a decreasing Total Factor Productivity (TFP) growth due to the very long time horizon considered (of the order of

10,000 years). Indeed, assuming constant TFP growth would bring unrealistically high levels of consumption per capita at the time scales considered. This issue is usually not discussed in the literature due to the shorter time horizon used in models (typically a few hundred years).

We do not include the • C scenario in this section for the sake of clarity.

The stream of consumption is lower over the whole period due to the fact that we do not account for climate damages. This is not the case if climate damages are accounted for, cf. Figure S.3 in the Electronic supplementary material.

See section S.E.2. of the Electronic supplementary material for the comparison between the 3 • C and BAU scenarios, and between the 3 • C and 2 • C scenarios.

See section S.E.2 of the Electronic supplementary material for the comparison between the 3 • C and BAU scenarios, and between the 3 • C and 2 • C scenarios.

Acknowledgements The authors would like to thank those who provided valuable feedbacks, in particular three anonymous reviewers.

Funding

This research has been supported by the Agence nationale de la recherche through the Fair-ClimPop project (ANR-16-CE03-0001-01) and Investissements d'Avenir program (ANR-10-LABX-93). Financial support from the Swedish foundation for humanities and social sciences is also gratefully acknowledged (Anslag har erhallits från Stiftelsen Riksbankens Jubileumsfond).

Conflict of interest

The authors declare that they have no conflict of interest.

Author attribution

A.M., A.P., M.F., and S.Z. jointly wrote the paper, designed the research, and analysed the results. A.M. and A.P. conducted model simulations. A.M. generated figures and tables. A.P. developed the original model.


Patryk Filipiak
email: patryk.filipiak@inria.fr

Fabien Almairac

Théodore Papadopoulo

Denys Fontaine

Lydiane Mondot

Stéphane Chanalet

Maxime Descoteaux

Rachid Deriche

Maureen Clerc

Demian Wassermann

Towards Validating Structural Connectivity in the Human Language System: An Intraoperative Cortico-Cortical Stimulation Experiment

We aimed to validate structural connectivity measures based on diffusion MRI with Direct Electrical Stimulation (DES) of the human brain cortex. For this, we combined white matter fiber tractography with propagation of Cortico-Cortical Evoked Potentials (CCEPs) induced by intrasurgical DES in the language system of brain tumor patients. Our results showed high correlation (Pearson's coefficient 0.5-0.9) between delays of CCEPs and pathways connecting stimulation sites with recording electrodes. Our approach outperformed earlier study based on Diffusion Tensor Imaging. This potentially indicates that probabilistic tractography is an effective tool to quantify cortico-cortical communication noninvasively.

Introduction

We aimed to validate structural connectivity measures based on diffusion Magnetic Resonance Imaging (dMRI) with Direct Electrical Stimulation (DES) of the human brain cortex. For this, we combined probabilistic tractography with propagation of Cortico-Cortical Evoked Potentials (CCEPs) induced by intrasurgical DES in the language system of brain tumor patients. Our results showed high correlation (Pearson's coefficient 0.5-0.9) between delays of CCEPs and pathways connecting stimulation sites with recording electrodes. Despite the use of low-current 2.0-3.5 mA DES and a small-sized stimulating electrode, our findings were in accordance with the studies performed in different schemes [START_REF] Matsumoto | Functional connectivity in the human language system: a corticocortical evoked potential study[END_REF][START_REF] Conner | Anatomic and electro-physiologic connectivity of the language system: a combined dti-ccep study[END_REF][START_REF] Keller | Mapping human brain networks with cortico-cortical evoked potentials[END_REF][START_REF] Yamao | Intraoperative dorsal language network mapping by using single-pulse electrical stimulation[END_REF], where higher current intensities and larger electrodes ensured better signal-tonoise ratio.

Methods

We acquired pre-surgical multishell dMRI (b ∈ {400, 800, 1550, 3100} [s/mm 2 ] with {6, 13, 29, 51} directions, respectively), from which we obtained probabilistic tractography. We dissected Arcuate Fasciculus (AF) and Superior Longitudinal Fasciculus III (SLF3) with MI-Brain [5] to plan the positioning of recording electrocorticographic (ECoG) electrodes. Next, following the awake craniotomy procedure, a neurosurgeon performed brain cartography with high-frequency 50 Hz DES to identify functional cortical sites related to AF and SLF3. Then, we placed the ECoG electrodes on the cortical terminations of those tracts determined with structural information from the dMRI-based tractography and functional information from the DES-based cartography, as illustrated in Figure 1.

In this work, we considered two patients with written consent to participate in our study: 46-year old male (Patient 1) and 25-year old female (Patient 2). For both of them, we performed the ECoG recording under general anesthesia, right after the tumor resection. We used biphasic, bipolar 3.5 mA DES with the frequency 5 Hz for Patient 1 and 2.0 mA DES with the frequency 2 Hz for Patient 2. We recorded the signal, referenced to the average of all the electrodes, using the sampling frequency 2 kHz. The stimulation sites were located in the proximity of the reachable recording electrodes as illustrated in Figures 1 and2. Each stimulation was repeated about 20 times.

In the post-processing, we averaged the ECoG signal of each DES trial in order to decrease the noise. Next, we computed the delays of the observed CCEPs and correlated them with the probability that a white matter bundle connects the stimulation and electrode sites. For that, we considered seeds located in the points of interest identified with the clinical neuronavigation system, surrounded by spheres of the 5 mm in diameter to account for a brain shift.

Results

Typically, an evoked potential consists of three consecutive voltage peaks named N1, P1, and N2 [START_REF] Vincent | Electrophysiological brain mapping: Basics of recording evoked potentials induced by electrical stimulation and its physiological spreading in the human brain[END_REF]. In most of our ECoG signals, we could identify the downward N1 peak propagating from the stimulation site, as illustrated in Figure 2. Figure 3b summarizes the number of fibers linking the examined pairs of points aggregated by the lengths. As expected, the majority of fibers connect neighboring sites located 10-20 mm away from each other.

Figures 4 and5 illustrate the correlation that we observed between delays of N1 and numbers of pathways connecting stimulation sites with recording electrodes. In most of the cases the Pearson's correlation coefficient laid between 0.5 and 0.9.

Discussion

Elucidating the relationship between structure and function of the brain is one of the main challenges in neuroscience [START_REF] Jbabdi | Measuring macroscopic brain connections in vivo[END_REF]. In this work, we addressed an open question, whether tractography provides an index of cortico-cortical communication. We assesed the relationship between structural connectivity, measured through probabilistic tractography, and cortico-cortical communication as measured by injected DES. Despite being criticized, the correspondance between probabilistic tractography and the probability of an axonal connection has been accumulating positive evidence (e.g. in animal models [START_REF] Donahue | Using diffusion tractography to predict cortical connection strength and distance: a quantitative comparison with tracers in the monkey[END_REF]). In our case, the observed high correlation provides initial evidence that our tested hypothesis is correct. Our results outperform the previous streamline tractography study [START_REF] Conner | Anatomic and electro-physiologic connectivity of the language system: a combined dti-ccep study[END_REF], where the Pearson's correlation coefficient 0.4 was reported for the pathways obtained from Diffusion Tensor Imaging. This potentially indicates that probabilistic tractography is an effective tool to quantify cortico-cortical communication non-invasively.

Conclusion

Our study validates the structural connectivity measures based on white matter tractography with the propagation of CCEPs. We believe that combining those two modalities will help understand the organization of cognitive functions and support neurosurgical planning.

Fig. 1 :

 1 Fig. 1: Tractography-based Arcuate Fasciculus and Superior Longitudinal Fasciculus III (marked as blue streamlines), ECoG electrode placements (red circles), and stimulation points (green crosses).

Fig. 2 :

 2 Fig. 2: Placement of ECoG electrodes and sample recordings of the CCEP propagation. The signals from the electrodes nearest the stimulation site are printed in red. The N1s are visible as downward peaks recorded by the electrodes located up to 4cm away from the stimulation site.

Fig. 3 :

 3 Fig. 3: Means and standard deviations of (a) CCEP delays, (b) number of fibers originating from a stimulation site. The measurements are aggregated by the fiber lengths. Our delays are in accordance with the literature.

Figure

  Figure3aillustrates the means and standard deviations of delays of the N1 peaks aggregated by the lengths of the shortest fibers connecting a given stimulation-recording pair. The results for Patient 1 are less dispersed, reaching 23.6±13.0 ms delay on the fibers between 30-and 40-millimeter long, while for the Patient 2 we observed 43.7±23.2 ms delay for the same distance length. Figure3bsummarizes the number of fibers linking the examined pairs of points aggregated by the lengths. As expected, the majority of fibers connect neighboring sites located 10-20 mm away from each other.Figures4 and 5illustrate the correlation that we observed between delays of N1 and numbers of pathways connecting stimulation sites with recording electrodes. In most of the cases the Pearson's correlation coefficient laid between 0.5 and 0.9.

Fig. 4 :

 4 Fig. 4: Correlation between the probability that there is an axonal connection linking stimulation sites and recording electrodes, and the latencies of corresponding N1 peaks of the induced CCEPs for Patient 1. The Pearson's correlation coefficients and p-values are given for each stimulation site. Statistically significant results are printed in bold. The squares on white are the reference stimulation points.

Fig. 5 :

 5 Fig. 5: Correlation between the probability that there is an axonal connection linking stimulation sites and recording electrodes, and the latencies of corresponding N1 peaks of the induced CCEPs for Patient 2. The Pearson's correlation coefficients and p-values are given for each stimulation site. Statistically significant results are printed in bold. The squares on white are the reference stimulation points.

Acknowledgements

This work has received funding from the ANR/NSF award NeuroRef; the MAX-IMS grant funded by ICM's The Big Brain Theory Program and ANR-10-IAIHU-06.


Liping Wang

Qiliang Lai

Mohamed Jebbar

Zongze Shao
email: shaozz@163.com

Karine Alain
email: karine.alain@univ-brest.fr

Complete genome sequence of Methanofervidicoccus sp. A16, a thermophilic methanogen isolated from Mid Cayman Rise hydrothermal vent

Keywords: Thermophilic Methanogenesis Methanofervidicoccus sp. Hydrothermal vent ANI, average nucleotide identity, CDS, coding DNA sequences, COG, clusters of orthologous groups, GO, gene ontology, KEGG, Kyoto encyclopedia of genes and genomes, ORFs, open

Methanofervidicoccus sp. A16 is a novel thermophilic and obligate hydrogenotrophic methanogen isolated from a deep-sea hydrothermal vent chimney sample at the Mid Cayman spreading center, Caribbean Sea. Here we report the complete genome of strain A16, which has one circular chromosome of 1,485,358 bp with a mean G+C content of 35.01 mol%. The complete genome harbors 1442 predicted protein-encoding genes. Genes involved in hydrogenotrophic methane production and N 2 fixation were identified in this genome. This study expands our knowledge of methanogenesis at high temperatures and the involvement of these microorganisms in the carbon and nitrogen cycles of deep-sea hydrothermal environments.

Introduction

Methanogenic archaea are strictly anaerobic prokaryotes that are widely distributed in anoxic environments such as wetlands, paddy fields, sediments and digestive tracts [START_REF] Thauer | Methanogenic archaea: ecologically relevant differences in energy conservation[END_REF]. They produce methane as the terminal step of organic matter fermentation. Of the 500-600 million tons of methane released into the atmosphere each year, 69% originate from microbial metabolism [START_REF] Conrad | The global methane cycle: recent advances in understanding the microbial processes involved[END_REF]. Methanogens can use carbon dioxide and H 2 , simple carbon compounds (acetate, formate, etc) or methylated compounds (methylamine, dimethylsulfide, choline, etc) as energy and carbon sources, and produce methane as a metabolic waste product. Nowadays, a number of hyperthermophilic or thermophilic methanogenic archaea belonging to the order Methanococcales have been isolated from a variety of marine hydrothermal environments, including Methanococcus igneus Kol 5 T , Methanotorris formicicus Mc-S-70 T , Methanothermococcus okinawensis IH1 T , Methanococcus jannaschii DSM 2661 T , Methanocaldococcus infernus ME T , Methanocaldococcus indicus SL43 T , Methanocaldococcus villosus KIN24-T80 T , Methanocaldococcus bathoardescens JH146 T and further species [START_REF] Jones | Methanococcus jannaschii sp. nov., an extremely thermophilic methanogen from a submarine hydrothermal vent[END_REF][START_REF] Burggraf | Methanococcus igneus sp. nov., a novel hyperthermophilic methanogen from a shallow submarine hydrothermal system[END_REF][START_REF] Jeanthon | Methanococcus infernus sp. nov., a novel hyperthermophilic lithotrophic methanogen isolated from a deep-sea hydrothermal vent[END_REF][START_REF] Takai | Methanothermococcus okinawensis sp. nov., a thermophilic, methane-producing archaeon isolated from a Western Pacific deep-sea hydrothermal vent system[END_REF][START_REF] L'haridon | Methanocaldococcus indicus sp. nov., a novel hyperthermophilic methanogen isolated from the Central Indian Ridge[END_REF][START_REF] Takai | Methanotorris formicicus sp. nov., a novel extremely thermophilic, methane-producing archaeon isolated from a black smoker chimney in the Central Indian Ridge[END_REF][START_REF] Bellack | Methanocaldococcus villosus sp. nov., a heavily flagellated archaeon that adheres to surfaces and forms cell-cell contacts[END_REF][START_REF] Stewart | Methanocaldococcus bathoardescens sp. nov., a hyperthermophilic methanogen isolated from a volcanically active deep-sea hydrothermal vent[END_REF].

The A16 genome sequence and its annotation is reported in the study. Strain A16 was isolated from a deep-sea hydrothermal vent chimney sample collected in a depth of 2295 m from Von Damm vent field (Hole to Hell site) (18°22.6007′ N, 81°47.8909′ W) at the Mid Cayman spreading center, Caribbean Sea. It was enriched and purified in DSM 141 medium, at 70 °C, under an atmosphere of H 2 /CO 2 (80/20, 0.2 MPa). Strain A16 was identified as a potential novel species of the genus Methanofervidicoccus, with highest 16S rRNA sequence similarity of 98.6% to Methanofervidicoccus abyssi HHB T , which was reported recently as a novel methanogen belonging to the order Methanococcales [START_REF] Sakai | Methanofervidicoccus abyssi gen. nov., sp. nov., a hydrogenotrophic methanogen, isolated from a hydrothermal vent chimney in the Mid Cayman spreading center, the Caribbean Sea[END_REF]. Strain A16 is an obligate anaerobic archaeon that can use CO 2 and H 2 as the sole carbon and energy sources to produce CH 4 .

Data description

Genomic DNA of strain A16 was extracted with the QIAGEN Genomic-tip 20/G (QIAGEN, Düsseldorf, Germany) kit following the manufacturer's standard protocol. The complete genome sequence of strain A16 was determined by Shanghai Majorbio Bio-pharm Technology Co., Ltd. (Shanghai, China), using the PacBio RSII platform (Table 1). For whole genome sequencing, a 10 kb DNA fragment library was constructed and sequenced on the PacBio RSII sequencing platform, with one SMRT cell (MajorBio Co., Shanghai, China). After quality control, reads were assembled by HGAP 3.0 [START_REF] Chin | Nonhybrid, finished microbial genome assemblies from long-read SMRT sequencing data[END_REF]. Gene prediction was performed using Glimmer version 3.02 (http:// cbcb.umd.edu/software/glimmer/). In addition, rRNA and tRNA genes were identified using Barrnap 0.4.2 and tRNA scan-SE v1.3.1 softwares. Functional annotation was performed using NCBI prokaryotic genome annotation pipeline [START_REF] Tatusova | NCBI prokaryotic genome annotation pipeline[END_REF], the Rapid Annotation using Subsystem Technology (RAST) pipeline (http://rast.nmpdr.org/) [START_REF] Overbeek | The SEED and the Rapid Annotation of microbial genomes using Subsystems Technology (RAST)[END_REF], and the the MicroScope Microbial Genome Annotation and Analysis Platform (MaGe) [START_REF] Vallenet | MicroScope: a platform for microbial genome annotation and comparative genomics[END_REF]. Deduced gene products were blasted against KEGG, COG, String and GO databases.

The complete genome of the strain A16 consists of a single circular chromosome with a total length of 1,485,358 bp and an average G+C content of 35.01 mol% (Fig. 1). A total of 1442 protein-coding sequences (CDSs) were predicted, with a summed up gene length of 1,178,139 bp, giving a coding intensity of 78.71%. Majority of the CDSs (1206/1422, 84.81%) could be assigned to a putative function according to COG categories, while the rest were annotated as hypothetical proteins. 34 tRNA genes for 21 amino acids, two 5S rRNAs, two 16S rRNA, two 23S rRNA, 2 miscellaneous RNAs (misc RNA) and 2 pseudogenes were also identified in the genome.

Strain A16 can use H 2 as electron donor and CO 2 as carbon source for growth and produce CH 4 . Genes coding for the full pathway of hydrogenotrophic methanogenesis were identified in the genome, S1). At the time of writing, twenty-three genomes belonging to the order Methanococcales were available in the NCBI and JGI databases. Based on core genome analysis, strain A16 featured the closest phylogenetic relationship to Methanofervidicoccus abyssi HHB T (Fig. S1). The average nucleotide identity (ANI) value between strain A16 and HHB T were 85.2%, which was below standard ANI criteria for species identity (95-96%) [START_REF] Richter | Shifting the genomic gold standard for the prokaryotic species definition[END_REF]. Further genome sequence analysis of strain A16 revealed 116 unique genes mainly involved in Energy production and conversion, Amino acid transport and metabolism, Replication, recombination and repair, Cell wall, membrane and envelope biogenesis and Inorganic ion transport and metabolism, when compared with HHB T (Table S2). A minimum set of six genes, nifH (CFE53_01675), nifD (CFE53_01660), nifK (CFE53_01655), nifE (CFE53_01645), nifN (CFE53_01640) and nifB (CFE53_05660), coding for structural and biosynthetic components of nitrogenase [START_REF] Santos | Distribution of nitrogen fixation and nitrogenase-like sequences amongst microbial genomes[END_REF] are present in the A16 genome, while these are absent in strain HHB T . In additon, two genes (CFE53_01665 and CFE53_01670) coding for nitrogen-fixation associated regulatory protein P-II are also located in this gene cluster. Comparative genome analyses further showed that the gene cluster for nitrogen fixation also exists in other sixteen strains of the order Methanococcales, although they show some differences in gene synteny, as shown in Fig. 2 and Fig. S1. Among these strains, Methanothermococcus thermolithotrophicus DSM 2095 T [START_REF] Belay | Dinitrogen fixation by a thermophilic methanogenic bacterium[END_REF][START_REF] Leigh | Nitrogen fixation in methanogens: the archaeal perspective[END_REF], Methanococcus maripaludis DSM 2067 T [START_REF] Blank | Genetics in methanogens: transposon insertion mutagenesis of a Methanococcus maripaludis nifH gene[END_REF], M. maripaludis S2 [START_REF] Kessler | The nif gene operon of the methanogenic archaeon Methanococcus maripaludis[END_REF][START_REF] Santos | Distribution of nitrogen fixation and nitrogenase-like sequences amongst microbial genomes[END_REF], Methanococcus aeolicus Nankai-3 T [START_REF] Kendall | Methanococcus aeolicus sp. nov., a mesophilic, methanogenic archaeon from shallow and deep marine sediments[END_REF], Methanotorris formicicus Mc-S-70 T [START_REF] Takai | Methanotorris formicicus sp. nov., a novel extremely thermophilic, methane-producing archaeon isolated from a black smoker chimney in the Central Indian Ridge[END_REF] and Methanocaldococcus sp. FS406-22 [START_REF] Mehta | Nitrogen fixation at 92 degrees C by a hydrothermal vent archaeon[END_REF], have been reported as diazotrophic methanogens. In this study, the genome analysis of strain A16 will help to understand the ecological role of this species in carbon and nitrogen cycle in submarine hydrothermal environments.

Nucleotide sequence accession number

The complete genome sequence of Methanofervidicoccus sp. A16 has been deposited in the GenBank database under number CP022242. The strain is available from the Université de Bretagne Occidentale Culture Collection under number UBOCC-M-3304.

  , CFE53_06105, and CFE53_06110), formylmethanofuran-tetrahydromethanopterin N-formyltransferase (Ftr, CFE53_06700), N5, N10-methenyltetrahydromethanopterin cyclohydrolase (Mch, CFE53_06735), F 420 -dependent methylenetetrahydromethanopterin dehydrogenase (Mtd, CFE53_05635), F 420 -dependent N5, N10-methylenetetrahydromethanopterin reductase (Mer, CFE53_02485), N5-methyltetrahydromethanopterin: coenzyme M methyltransferase (Mtr, CFE53_01150, CFE53_01155, CFE53_01160, CFE53_01170, CFE53_01175, CFE53_01180, CFE53_01185), Methyl coenzyme M reductase (Mcr, CFE53_01190, CFE53_01195, CFE53_01200, CFE53_01205 and CFE53_01210), and heterodisulfide reductase

Fig. 1 .

 1 Fig. 1. Circular map of the chromosome in the genome of Methanofervidicoccus sp. A16. From the outside to the center: label of genome size, CDSs on forward strand (colored by COG categories), CDSs on reverse strand (colored by COG categories), RNA genes (tRNAs and rRNA operons), DNA G+C content and GC skew. CDSs are depicted in different colors according to COG categories.

Fig. 2 .

 2 Fig. 2. Comparison analysis of the nitrogen fixation gene arrangement based on the genomes of Methanofervidicoccus sp. A16 and other sixteen methanogens within the order Methanococcales.

Table 1

 1 General features of Methanofervidicoccus sp. A16.

	Items	Description
	General features
	Superkingdom	Archaea
	Strain	Methanofervidicoccus sp. A16
	Geographic location	Atlantic Ocean: Caribbean Sea, Von Damm vent field
		(Hole to Hell site) at the Mid Cayman spreading center
	Sample type	deep-sea hydrothermal vent chimney sample
	Latitude and longitude	18°22.6007′ N, 81°47.8909′ W
	Depth	-2295 m
	Collection date	June 2013
	Biotic relationship	Free-living
	Genome characteristics
	Sequencing platform	PacBio RSII
	Assembly method	HGAP 3.0
	Genome coverage	650×
	Finishing quality	Complete genome
	NCBI accession number	CP022242
	BioProject	PRJNA391986
	BioSample	SAMN07281457
	Size (bp)	1,485,358
	DNA G+C content (%)	35.01
	CDSs	1422
	tRNAs	34
	16S-23S-5S rRNAs	2-2-2

Acknowledgments

We are very grateful to the YK13-05 cruise operation teams for helping us to collect the hydrothermal samples and to the chief scientist Ken Takai. We thank Stéphane L'Haridon for the isolation of the strain. This work was supported by the PHC Cai Yuanpei Provirvent (N° 34634WE), the program MERLIN Abyss, the LIA 1211 MicrobSea and the "Laboratoire d'Excellence" LabexMER (ANR-10-LABX-1), National Key R&D Program of China (No. 2018YFC0310701), National Natural Science Foundation of China (No. 41506152).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.margen.2020.100768.


domain: chim spi

text:
Jessy Elias

Xavier Mercier

Alessandro Faccinetto

Nicolas Nuns

S Godey

D Deresmes

Thierry Melin

T Mélin

Coupling of ToF-SIMS and AFM for the identification of the chemical species involved in the nucleation process of soot particles in flame combustion

Introduction Sampling

ToF-SIMS AFM

Perspectives

The soot nucleation process, corresponding to the transformation of gaseous molecular precursors into condensed phase soot particles, is the less understood step of the soot formation process in flame combustion. The hypothesis of a nucleation process driven by the dimerization of small polycyclic aromatic hydrocarbons (PAHs), has been used in models but experimental evidences are still lacking.

In this work, ToF-SIMS and AFM are coupled with the aim of characterizing the species involved in the soot nucleation process.

Reaction axis

• Laminar methane diffusion flame stabilized at atmospheric pressure. • Samples extracted from the centreline of the flame at different heights above the burner (HAB) using a quartz microprobe and deposited on titanium wafers.

Results

Sample

Mass defect plot Δ = m/z -m Assignement of a molecular formula to the selected m/z.

Principal Component Analysis:

PCA is used to classify the data and explain the variance of the database.

Atomic Force Microscopy delivers direct molecular imaging of the surface at the atomic scale and gives access to the electronic properties of the molecular species.

Preliminary results

Soft spherical structures on a 55 mm HAB sample having a 2-4 nm diameter and a 0.3 Å height, consistent with the size of nascent soot nanoparticles.

In future work, we will use a functionalized CO tip, which probes the molecules with a sub-Å oscillation amplitude at low temperature, to resolve isomeric structures that are detected at the same m/z, for a complete characterization of the species involved in the soot nucleation process.