Main

Anthropogenic emissions of greenhouse gasses are pushing Earth’s climate towards a warmer state not seen for millions of years1, with repercussions for ecosystem resilience. Yet, it is unknown whether or when Earth’s dominant terrestrial animal species, mammals, will ever reach a climatic tipping point whereby their ascendancy is threatened. Sherwood and Huber2 have suggested that current global warming will raise temperatures above terrestrial mammalian physiological limits, rendering some parts of the world uninhabitable. Mid-to-late century International Panel on Climate Change Sixth Assessment Report3,4 high-emission scenarios suggest that some physiological thermal thresholds will be exceeded in small, mainly coastal, regions of Africa, Australia, Europe and South Asia5,6. Even with the combustion of all available fossil fuels (+12 °C by 2300), most of the land surface would still be habitable2. What is certain is that the Earth will leave the Sun’s habitable zone in several billion years7 when solar luminosity (F⨀; W m−2) reaches a point where radiative heating and moist processes initiate a runaway greenhouse. However, conditions that threaten mammalian predominance on Earth may naturally arise sooner.

Mammalian lineage (including endothermic vertebrates belonging to the class Mammalia of the phylum Chordata) first emerged ~310 million years ago (Ma)8 but only became the dominant species after the Cretaceous–Palaeogene (K–Pg) extinction9. Mammals’ success has seen habitation of nearly every terrestrial biome, encompassing periods of large climatic fluctuations and mass extinctions, showing resilience to climate change10,11. Mammalian physiology has evolved to remove excess heat through thermoregulatory mechanisms (sweat glands, locomotion and circulatory system) owing to an ancestral legacy having evolved under warmer, non-glaciated climates12. Although mammals are resilient to temperature fluctuations, thermal tolerances are invariant across latitudes, elevation and phylogeny12, showing that physiological constraints exist where survivability is limited. Sustained dry-bulb temperatures (Td) of >40 °C can lead to mortality12,13. Hyperthermia, a further upper limit, occurs when the ambient wet-bulb temperature (Tw) exceeds approximately 35 °C, because the transfer of metabolic heat through sweat-based latent cooling is insufficient2,13,14,15,16. Exposure above this threshold for >6 h leads to death13,17, but this threshold is rarely reached in our current climate14. Humidex, another heat stress measure, is a unitless indicator based on dry-bulb temperature and vapour pressure that is used by the Meteorological Service of Canada to represent human thermal comfort in hot, dry continental interiors18. Values of ≥30 indicate ‘some discomfort’, ≥45 is ‘dangerous’ and prolonged exposure will lead to heat stroke, while ≥54 indicates heat stroke and imminent mortality. There is a divergence between heat stress metrics where hyperthermia can be induced. Tw heat stress has a greater impact on tropical hot and humid regimes2,17, whereas Humidex better represents dry, hot climates like deserts18, such as those found in the continental interiors. Habitability is constrained not just by a warming climate but also by a cooling climate. Hypothermia can arise as a direct consequence of cold temperatures. Prolonged exposure to wind chill temperatures below −10 °C (Tfrost) causes ischaemic necrosis on exposed skin. However, a more relevant measure of habitability for mammals is temperatures below freezing (T0), which affects freshwater availability and induces plant dormancy (<5 °C; ref. 19). The planetary habitability index (PHI)20 also offers another measure to assess mammalian survivability on the basis of constructing indices from a star–planet distance, star temperature and the wavelengths of light absorbed by a planetary body21 to assess thermal tolerances.

The next supercontinent, Pangea Ultima (PU)22 (Fig. 1 and Supplementary Fig. 1), is predicted to form in the next ~250 Myr (ref. 23). By ~250 Myr our Sun will emit ~2.5% more energy compared with today (~1% per 110 Myr (ref. 24) in F⨀), a radiative forcing +5.55 W m−2 (more than double present-day \(p_{\mathrm{CO}_2}\) (3.7 W m−2)). Coupled with tectonic–geographic variations in atmospheric \(p_{\mathrm{CO}_2}\) and enhanced continentality effect for supercontinents25, Earth could reach a tipping point rendering it uninhabitable to mammalian life.

Fig. 1: PU temperature and habitability.
figure 1

a, Mammalian species diversity without the influence of humans (reproduced from ref. 41). b, Habitable regions (green area) in the Pre-industrial simulation. c–h, Cold month mean temperature (CMMT; °C) (c,f), warm month mean temperature (WMMT; °C) (d,g) and habitable regions (green area) (e,h) under two end members of our sensitivity analysis: low-\(p_{\mathrm{CO}_2}\) conditions (280 ppm) PU planetary configuration (+250 Ma) (c–e) and high-\(p_{\mathrm{CO}_2}\) conditions (1,120 ppm) PU configuration (+250 Ma) (f–h), with global land surface temperature (GLST) (grid-weighted) indicated.

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Predicting future \(p_{\mathrm{CO}_2}\) in ~250 Myr is challenging. The geologic record has shown large swings in \(p_{\mathrm{CO}_2}\) (ref. 26) over the past 3.5 billion years. However, there is an apparent cool–warm in-phase relationship (for example, the Rodinia and Gondwana supercontinents) as part of the natural cycle (~400–600 Myr) of assembly, tenure and break-up of supercontinents with \(p_{\mathrm{CO}_2}\). However, this is complicated and depends on mechanical and insulating effects of continents on mantle convection27 (for example, the Nuna Supercontinent stayed warm throughout the assembly–decay). This is a result of competing factors that modulate CO2 sources and sinks (volcanic outgassing versus silicate weathering) of the long-term carbon cycle27,28,29. There have been at least five periods of tectonic convergent cycles that have resulted in continental assembly30 coinciding with large variations in global temperature31. Relatively little is known about the \(p_{\mathrm{CO}_2}\) and climate conditions of the first four supercontinents (Vaalbara approximately 3,600–2,800 Ma, Kenorland approximately 2500 Ma, Nuna approximately 1,800–1,300 Ma and Rodinia approximately 1,100—600 Ma), although during the Snowball Earth events (approximately 720–650 Ma), \(p_{\mathrm{CO}_2}\) is believed to have built-up to two or three orders of magnitude greater than present-day values32,33. More is known about the most recent supercontinent, Gondwana, approximately 550—170 Ma (also including Pangea 330—170 Ma). During the time of the Gondwanan Supercontinent, atmospheric \(p_{\mathrm{CO}_2}\) varied from ~200 ppm (reconstructions vary between 96–435 ppm) at ~334 Ma to ~2,100 ppm (1,127–2,909 ppm) at ~255 Ma (ref. 34). This led to periods of extremes in temperature from panglacial climates during the Carboniferous (−5 °C compared with the present-day global mean35,36) to greenhouse climates of the Devonian (+10 °C compared with the present-day global mean37), all periods where F⨀ was weaker (<~3%; ref. 38) than today. It has been suggested that, once a supercontinent has assembled, the rate of Large Igneous Province (LIP) emplacement increases, raising \(p_{\mathrm{CO}_2}\). This process can initiate continental break-up39, leading to increased continental rifting and a further injection of \(p_{\mathrm{CO}_2}\) (ref. 40).

Will the formation and decay of the PU Supercontinent lead to Earth becoming uninhabitable for mammals by surpassing their thermal physiological limitations long before F⨀ becomes high enough to cause a runaway greenhouse? In this Article, we assess the impact of mammalian thermal tolerances resulting from numerical simulations at 0, 70, 140, 280, 560 and 1,120 ppm \(p_{\mathrm{CO}_2}\), under both modern and future F⨀ (1,364.95 and 1,399.07 W m−2). We employ a version of the United Kingdom Met Office Hadley Centre Coupled Model (HadCM3L) a dynamic fully coupled atmosphere-land-ocean general circulation model (GCM) with an interactive ozone scheme under a PU geography (see Methods for details). Further, we utilize the spatial-continuous integration (SCION) biogeochemistry model in conjunction with these simulations to quantitatively estimate background atmospheric carbon dioxide concentrations to predict how much of the land surface remains habitable by 250 Myr.

Results

PU mammalian thermal tolerance

PU grid-weighted global mean annual temperature (GMAT) ranges from 19.9 to 27.3 °C (land-only GMAT ranges from 24.5 to 35.1 °C) (0–1,120 ppm CO2; +2.5% Modern F⨀) (Fig. 1 and Table 1). The GMAT anomaly relative to the Pre-industrial control simulation (280 ppm \(p_{\mathrm{CO}_2}\); modern F⨀) for PU varies between +8.2 and +16.1 °C (land-only GMAT anomalies range between +12.2 and +29.8 °C). When changing only the global geography (280 ppm; Modern F⨀) from its Pre-industrial configuration to PU, GMAT warms by +3.5 °C, while land-only temperatures increase by +13.9 °C as a result of the continentality effect.

Table 1 Pre-industrial and PU climate simulations for a range of CO2 (ppm) and solar luminosities (Sol), both Modern and in 250 Myr (Sol + 2.5%); see Table 2 in Methods for details
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When the mammalian physiological metrics Td (Extended Data Fig. 1), Tw (Extended Data Fig. 2), Humidex (Extended Data Fig. 3), T0 and Tfrost are applied to all scenarios, they present varying amounts of mammalian habitation (Extended Data Fig. 4). Here, we define habitability (Table 1) by exceeding conditions where: (1) cold monthly mean temperature >0 °C (T0) for at least three consecutive months, (2) Tw < 34.5 °C and (3) THumidex < 45.

Hibernation is encoded in these metrics. Hibernation is an effective strategy for mammals in times of cold stress once sufficient fat stores have been built up. This is required as plants (food) enter dormancy once temperatures are <5 °C (ref. 19). Using a more conservative estimate of <0 °C also removes freshwater availability. Aestivation, that is, warm weather dormancy, cannot occur in regions where plants cannot grow, usually in hot, arid regions. Subsequently, we also rule out desert regions as habitable (low species diversity; Fig. 1a) owing to low water and food availability. To ensure that the model shows skill, we evaluated our Pre-industrial control simulation against Modern observed mammalian species distribution where the impact of humans has been removed41, showing good agreement (Fig. 1).

Only one scenario (280 ppm \(p_{\mathrm{CO}_2}\); Table 1) has comparable amounts of habitable land (54%) to the Pre-Industrial Earth (66%) under increased future F⨀. Under 560 or 1,120 ppm, habitability decreases to 16% and 8%, respectively. In all cases, increasing \(p_{\mathrm{CO}_2}\) pushes the majority of the land surface beyond thermal physiological tolerances for Td, Tw and Humidex (Fig. 1), and at 1,120 ppm the planet is practically uninhabitable (8% habitability). Even if the land surface height is doubled, habitability increases only marginally from 16% to 19% at 560 ppm (Table 1). Although silicate weathering feedbacks have the potential to draw down \(p_{\mathrm{CO}_2}\) to extremely low levels, leading to climates where cold thermal tolerances are exceeded and extinction occurs, such a scenario is less plausible under future F⨀ (ref. 42), As such, scenarios (Table 1) and analysis where \(p_{\mathrm{CO}_2}\) is low (140, 70 and 0 ppm) are only discussed in ‘Cold Stress Environments’ in Supplementary Information.

PU energy balance analysis

Energy balance analysis43 (Extended Data Figs. 5 and 6d) indicates that, changing from Pre-industrial geography to a PU geography (280 ppm CO2, Modern F⨀ kept constant to remove its influence) leads to an increase in GMAT of +3.7 °C (Extended Data Fig. 5a) driven by changes in surface albedo (+2.2 °C) and emissivity (+1.4 °C) at high latitudes owing to there being no polar ice (mainly though ice and cloud feedbacks). The addition of future F⨀ (+2.5% F⨀) increases GMAT by +8.2 °C (Extended Data Fig. 5d). A fraction (+1.8 °C) of this increase is directly attributable to increased F⨀ and indirectly through changes in albedo (+2.7 °C), emissivity (+3.7 °C) and heat transport (+0.1 °C) as a result of non-linear feedbacks that arise from increasing F⨀. This is driven by a reduction in seasonal sea ice at high latitudes (compare Extended Data Fig. 5a,d), whereas just increasing \(p_{\mathrm{CO}_2}\) impacts GMAT predominantly through emissivity-driven feedbacks (Extended Data Fig. 5a–c). Terrestrial albedo changes are primarily driven by vegetation feedbacks due to desertification under warming conditions (Table 1) that are already enhanced because of supercontinent formation with no \(p_{\mathrm{CO}_2}\) or F⨀ change (30–42%). When F⨀ is kept at Pre-industrial levels, deserts show a small decrease with increasing \(p_{\mathrm{CO}_2}\) owing to increased evaporation and moisture enrichment of the atmosphere, leading to an invigorated hydrological cycle in some regions (Table 1).

A stepwise doubling of \(p_{\mathrm{CO}_2}\) under F⨀ (+2.5%) from 280 to 1,120 ppm (Extended Data Fig. 6d–f) shows a general increase in equilibrium climate sensitivity (ΔTeq of 2.3–3.9 °C; Table 1). Interestingly, ΔTeq analysis of the same suite of \(p_{\mathrm{CO}_2}\) concentrations but with a modern F⨀ (Table 1) indicates more variable ΔTeq with \(p_{\mathrm{CO}_2}\) (ΔTeq of 2.4–4.8 °C), demonstrating non-linear climate feedbacks with changes in F⨀.

Finally, we consider an astrophysical classification of PHI in conjunction with an Earth Similarity Index (ESI) based on planetary mass, radius, temperature, stable substrate, available energy, chemistry and ability to host liquid water20. These are defined relative to the only known habitable planet, Earth, and habitability is defined as greater than 0.8 (see online methods for further details). Hence, by definition, the only parameter that changes in the future is GMAT, since all other factors remain constant. According to the ESI, no future scenario is predicted to remain habitable (Fig. 2).

Fig. 2: Astrophysical habitability index.
figure 2

ESI and PHI of all Solar System bodies and each PU \(p_{\mathrm{CO}_2}\) and solar luminosity (Modern (Sol) and solar luminosity in 250 Myr (Sol + 2.5%)) sensitivity study (orange symbols). Values within the green zone indicate habitability (see Methods for details). Values in the red zone indicate poor habitability due to having a rocky interior (high PHI) but not a temperate surface (low ESI) and vice versa. See ref. 20 for ESI and PHI for definitions and planetary body values for the Solar System.

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PU \(p_{\mathrm{CO}_2}\) modelling

Continent–continent collision during supercontinent formation, on average, is predicted to reduce, not increase, \(p_{\mathrm{CO}_2}\) drawdown because high topography (and more readily erodible material) is concentrated in the dry continental interiors, away from moisture sources27. Moisture pathways may be just as important as topography in influencing chemical weathering. This is corroborated in our model, which sees a reduction both in precipitation (Extended Data Fig. 7) and in runoff when only changing the continental configuration from a Pre-industrial world to a PU world. Increasing \(p_{\mathrm{CO}_2}\) reduces precipitation and runoff into the continental interior, theoretically further reducing chemical weathering and increasing \(p_{\mathrm{CO}_2}\).

To better constrain the likely \(p_{\mathrm{CO}_2}\) and understand the silicate weathering feedback in our PU reconstruction, we use the global climate–biogeochemical model SCION (see Methods for more information), which computes the long-term carbon cycle and uses a two-dimensional (2D) terrestrial weathering module informed by climate model simulations. Here, a data structure of climate model outputs at different CO2 levels is used to simulate spatial continental processes through variations in atmospheric CO2, and we update this with the climate model runs from this study both for the Pre-industrial (which determines the initial steady state) and for PU. To run the model, we must also prescribe the tectonic rate of CO2 degassing, which we estimate from a conservative set of plate boundaries (mid-ocean ridges and subduction zones) that might describe the gross tectonic fabric of the PU world (see Supplementary Information for more details). We find that PU is likely to have 1.3–1.9 times the degassing rate of the present-day Earth, which is roughly equivalent to the rates proposed for Pangea44. SCION ensemble simulations for PU predict a mean long-term background \(p_{\mathrm{CO}_2}\) of 621 ppm (range 410–816 ppm) when considering the range of uncertainty in the degassing rate as well as the potential for changing reactivity of global silicate rocks.

Discussion

The formation and decay of PU will limit and, given a much greater source-to-sink ratio of \(p_{\mathrm{CO}_2}\), ultimately end terrestrial mammalian habitability on Earth by exceeding their warm thermal tolerances, billions of years earlier than previously hypothesized. Inevitable changes in both plate tectonics and F⨀ create feedbacks in the climate, even in lieu of variable \(p_{\mathrm{CO}_2}\), that will raise GMAT.

Further, tectonic evolution of PU will lead to large variations in \(p_{\mathrm{CO}_2}\) (over 102 years (for example, hyperthermal events45) and 105 years (for example, volcanism46)), as observed through the geologic record and seen as a natural consequence of supercontinent assembly and decay27, enhancing GMAT (20.9–24.8 °C at 410–816 ppm \(p_{\mathrm{CO}_2}\)). Further, the tenure of PU possibly increases the likelihood of massive hyperthermal events akin to the Permian–Triassic event that saw up to 10 °C warming on 104 year time scales45.

Today, critical heat stress measures are rarely exceeded on land and, if so, only for short time scales14 (hours or days). If only the geography was to change, critical heat stress is not exceeded but does drive the climate towards critical thresholds (Fig. 1 and Extended Data Figs. 1–3). Combined with a future increase in F⨀, large regions of the supercontinent breach these critical thresholds for periods of >30 days (Table 1, Fig. 1 and Extended Data Fig. 4). At 280 ppm, most of the Tropics become uninhabitable, and by 1,120 ppm this extends through the mid to high latitudes. Although the high latitudes (>50°) at 1,120 ppm offer limited refugia from critical heat stress, cold stress metrics further reduce habitability (Extended Data Fig. 4). Only highly specialized migratory mammals would be able to compete. However, even a migratory strategy may be perilous for mammals owing to continent-wide deserts and aridity (Table 1) throughout PU acting as a biogeographic barrier (Extended Data Fig. 7). High Td and Tw as a function of increasing \(p_{\mathrm{CO}_2}\) require plentiful water availability for mammals to balance losses through evaporative cooling to stop hyperthermia. Rates of evaporative water loss will increase with hyperthermia as the rate of respiratory water loss increases in direct proportion to increases in the rate of gas exchange47, making traversing these near 50° N to 50° S continent-wide arid and desert regions impractical. A secondary impact of low moisture availability would be an increase in the vapour pressure deficit (VPD) and plant stress (not shown) and a reduction in the productivity and food availability of vegetated land for mammals. Under 1,120 ppm \(p_{\mathrm{CO}_2}\), the VPD between 50° N and 50° S is a factor of three or four greater than in the Gobi Desert today (with our Pre-industrial model showing similar values of approximately 10–12 hPa compared with observations48).

Hibernation (a seasonal adaptation to prolonged periods of food shortage and cold) and its hot weather equivalent, aestivation, have been effective strategies for mammals for millions of years to combat relative extremes in temperatures. Today, ~50% of mammals hibernate49, and of those, only a small fraction for more than 1 month50. With \(p_{\mathrm{CO}_2}\) predicted to be 410–816 ppm, cold stress will be less of a constraint on mammalian habitability (Extended Data Fig. 4). Burrows and cave systems, which are buffered from external air temperature, may allow some refugia for some mammal species if food and water are plentiful. Small burrowing rodents may show greater survivorship in regions above thermal thresholds if staying active at night rather than during the day. However, even if increasing the aestivation period is allowed from 1–3 months during the warmest months of the year, habitability is only marginally increased (Supplementary Table 2) at 280, 560 and 1,120 ppm from 25% 16% and 8% to 32%, 21% and 13%, respectively, as a result of adjoining months being above physiological thresholds.

Although we cannot discount evolutionary adaptation to heat and cold stress, recent studies have shown that mammalian thermotolerance upper limits are conserved through geologic time12,51 and have not increased during past rapid (for example, Palaeocene–Eocene Thermal Maximum) or slower warming events (Early-Eocene Climatic Optimum). Mammalian physiological limitations show that increasing their upper thermal tolerance is a slow process (0.6 °C per Myr) with an upper Td boundary of approximately 40 °C that is rarely crossed. At 40–60 °C, plant life and the basis of the terrestrial food chain begins to critically fail owing to damage to photosystem II, leading to decreased electron transport rates and photosynthetic failure12,52. At ≥560 ppm, daily Td > 40 °C are consistent throughout the supercontinent (at 1,120 ppm, this can often reach >50–60 °C). Although mammals are better at adapting to cold tolerance12,51, a more conservative ≤0 °C threshold whereby freshwater sources are rendered biologically unavailable offers a finite lower thermal tolerance limit. To adapt to more humid and warmer environments, endotherms would need to increase body temperature (Tb) above both the dry- and/or wet-bulb temperature (Ta) to maintain a negative Tb – Ta gradient. However, since most endotherms regulate Tb near lethal or physiological limits, there is probably only limited scope for thermal adaptation16. This is likely conservative given that juvenile mammals will be more susceptible to lower ranges53.

Over long-time scales (106 years), weathering feedbacks will regulate \(p_{\mathrm{CO}_2}\) owing to higher F⨀ increasing surface temperatures and enhancing the long-term hydrological cycle, thereby reducing \(p_{\mathrm{CO}_2}\). However, weathering feedbacks will have a lagged response28, operating on longer time scales than are important for mammalian habitability, meaning that any substantial \(p_{\mathrm{CO}_2}\) outgassing would lead to short-term (103–104 year) warming that would reduce habitability through heat stress, such as during supercontinent assembly that has consistently been shown to result in high \(p_{\mathrm{CO}_2}\) emissions (1,000–3,000 ppm)54 (see Methods for more details).

Reduced moisture advection (Extended Data Fig. 1) into continental interiors leads to large arid regions where surface runoff is reduced or non-existent (not shown). This reduces the carbon sink (via both chemical weathering and biotic factors), raising \(p_{\mathrm{CO}_2}\) through a reduction in terrestrial \(p_{\mathrm{CO}_2}\) sequestration, erosion and transport of carbon for oceanic sequestration55.

In PU, a Tropical east–west trending mountain range (Supplementary Fig. 1) is modelled, from which an invigorated hydrologic cycle is derived, driven from the mountain range proximity to oceanic moisture. Consequently, we speculate a moistened atmosphere from greenhouse conditions, and a strong land–sea contrast would progressively increase silicate weathering, drawing down \(p_{\mathrm{CO}_2}\). When the topography of PU is doubled in height, the hydrological cycle decreases over the higher mountains (Extended Data Fig. 7), suggesting that silicate weathering and \(p_{\mathrm{CO}_2}\) drawdown may slow. On the other hand, if the erodible material of these mountain ranges was made of sedimentary material with low silica content, it would instead release large amounts of \(p_{\mathrm{CO}_2}\) through the oxidation of rock-rich inorganic carbon and sulfide minerals56, increasing \(p_{\mathrm{CO}_2}\) further and expanding regions where mammals would experience critical heat stress.

Today critical cold stress (Tfrost or T0) environments are limited to the high to mid latitudes (>30°). Changing geography and increased F⨀ both shift this zone at least 10° towards the poles. Cold stress is still a factor limiting habitability regardless of changing geography and increased F⨀, which both act to warm the planet. Elevated \(p_{\mathrm{CO}_2}\) (>1,120 ppm) effectively removes all cold stress environments. Cool-adapted mammals that have lower thermal physiological limits will be particularly impacted by rising temperatures as well as increased competition from other species moving poleward as they migrate away from the Tropics.

Other future supercontinent configurations have been proposed (Novopangea, Aurica and Amasia23,57). All formations except Amasia suggest a supercontinent landmass centred in the Tropics and would likely lead to climates similar to PU. Amasia, however, would be centred over the North Pole (except for Antarctica, which remains in its present-day position). In such a scenario, under a range of \(p_{\mathrm{CO}_2}\) regimes, large regions would probably be less affected by critical heat stress and remain habitable. However, strong weathering feedbacks under such a scenario may present greater challenges from cold stress on mammalian physiology. Ice–albedo feedbacks may also present a situation where Amasia57 would glaciate more readily, even under higher \(p_{\mathrm{CO}_2}\) regimes and mass extinction.

Ultimately, it is supercontinent geography and increased F⨀ that drive the increased sensitivity to variable \(p_{\mathrm{CO}_2}\). Continued mammalian habitability will be contingent on no large, sustained, pulses of \(p_{\mathrm{CO}_2}\), either through processes in supercontinent assembly and decay or coincident outgassing events (for example, LIPs such as the Siberian or Deccan traps), both of which have precedent throughout the geologic record. Elevated \(p_{\mathrm{CO}_2}\) levels (>840 ppm), often associated with greenhouse climates, have been common over most of the Phanerozoic26,58. If \(p_{\mathrm{CO}_2}\) was to spike ≥560 ppm, even for a short period (102–103 years), Earth will become inhospitable for mammalian life, resulting in a mass extinction comparable to the ‘Big 5’ extinction events59. This may even be conservative. Song et al.60 suggest that warming of >5.2 °C from Pre-industrial levels led to previous mass extinctions in marine animals60, and their defined threshold is passed under scenarios below 280 ppm \(p_{\mathrm{CO}_2}\).

This analysis pinpoints the importance of tectonics, atmospheric constituents and solar energy for continued mammalian survivability. Under all scenarios of an ‘Earth-like’ planet, regions of habitability do exist (even for 1,120 ppm \(p_{\mathrm{CO}_2}\), F⨀ +2.5%, albeit small (Extended Data Fig. 4)). However, no future realization of PU where \(p_{\mathrm{CO}_2}\) is ≥280 ppm passes a well-used astrophysical assessment of habitability (Fig. 2), meaning that Earth will leave its astrophysical defined habitable zone (at least temporarily) well before a runaway greenhouse occurs. This suggests that the potential for human habitability of many exoplanets might be mistakenly discounted. This is illustrated by the recent discovery of KOI-456.04 (ref. 61), which has an Earth–Sun system similar to our own and an estimated GMAT of 5 °C. The habitability of KOI-456.04 may be more dependent on the position of its continental landmass and concentration of atmospheric constituents than an arbitrary habitable zone defined by planet–star distance.

Methods

Numerical modelling framework

An overview of the model setup, boundary conditions, sensitivity studies and carbon dioxide modelling is given below.

Model

Here, we utilize the HadCM3LB-M2.1aD63 GCM, a member of the UK Meteorological Office HadCM3 family of climate models64. The grid resolution is 3.75° × 2.5° in longitude × latitude in both the atmosphere (19 vertical levels) and ocean (20 vertical levels), employing the Arakawa B-grid scheme.

Ocean salinity is adjusted to an ice-free world global mean reference value of 34.23 practical salinity units and allowed to freely evolve globally. To prevent millennial-scale salinity drift during model spin-up, the total ocean volume integral is calculated and is re-adjusted to back to ice-free world global mean after each ocean time step. Sea-ice coverage is calculated from a zero-layer model overlaying the top-most layer of the ocean grid. Sea ice forms using a threshold value of −1.8 °C, with albedo set at 0.8 for temperatures below −10 °C and 0.5 for temperatures above 0 °C, with a linear variation between.

Parameterizations include the radiation scheme of Edwards and Slingo65, the convection scheme of Gregory et al.66 and the Met Office Surface Exchange Scheme (MOSES)-2.1 land-surface scheme, whose representation of evaporation includes the dependence of stomatal resistance on temperature, vapour pressure and CO2 concentration67. There are nine sub-grid-scale land surface types, four non-vegetated types (urban, lakes, bare soil, ice and inland water), and five plant functional types (broadleaf trees, needleleaf trees, shrubs, C3 (temperate) grasses and C4 (tropical) grasses), updated every 10 model days.

The Top-Down Representation of Interactive Foliage and Flora Including Dynamics (TRIFFID) dynamic vegetation model67 is employed, allowing two-way coupled interactions between the land surface and atmosphere. The MOSES 2.1 land surface scheme was employed, as opposed to MOSES 2.2, owing to the former producing a better representation of Pre-industrial climates in combination with the TRIFFID model68 as well as because the future distribution of vegetation needs to be predicted based on the simulated climate. Crucially, TRIFFID allows full interaction between climate and feedbacks associated with vegetation cover and complex land surface–atmosphere interactions.

Desert soil albedo is interactively updated on the basis of the soil carbon content, where low soil carbon concentrations result in a modified soil albedo of 0.32 (average modern-day Saharan albedo).

Typically, the ozone distribution is prescribed as a static latitude–pressure–time distribution in many climate models. However, in warmer climates of the past or future, the tropopause rises, meaning that stratospheric ozone penetrates into the troposphere69, which is unphysical if a Pre-industrial tropopause height is prescribed for warm time periods. Instead, the ozone distribution is prescribed using a dynamic approach70 in which ozone is dynamically coupled to the model tropopause height with constant values for the troposphere (0.02 ppm), tropopause (0.2 ppm) and stratosphere (5.5 ppm). This change makes a negligible difference to the global mean surface temperature but does have a small impact on the stratospheric temperature and winds.

HadCM3LB-M2.1aD, part of the United Kingdom Met Office HadCM3 family of climate models, has been extensively evaluated against modern-day observations as part of the International Panel on Climate Change Climate Model Intercomparison Project phase 5, showing good skill in reproducing a climate that is comparable to observations as well as other higher-fidelity climate models63. A full description of the individual sub-component models in HadCM3LB-M2.1aD is given in ref. 63.

Boundary conditions and initialization

The reconstruction of tectonics, structures and plate motion that underpin this study is based on a +250 Myr reconstruction of PU22. This reconstruction uses methods similar to those of Valdes and Markwick71, where land–sea mask, bathymetric, topographic and the sub-grid-scale orographic variables are required by the model and are interpolated onto the GCM resolution (Supplementary Fig. 1). There are no assumed terrestrial ice sheets in this reconstruction. Shorelines in this reconstruction represent the maximum transgression in sea level assuming that no terrestrial ice sheets are present. PU is only one of four potential configurations (three of which are similar in continental distribution with a supercontinent centred in the Tropics23) of supercontinent formation by 250 Myr.

All simulations are initialized from an equilibrated Pre-industrial state (atmosphere and ocean).

Modern F⨀ is set at 1,364.95 W m−2. F⨀ increases by ~1% per 110 Myr (ref. 38). We forecast an F⨀ of 1,399.07 W m−2 (+2.5% increase from Modern) by 250 Myr. Although modern solar luminosity has recently been revised to 1,361 W m−2, the model has been calibrated for the previous value of 1,364.95 W m−2. For all simulations conducted, we use a Modern orbital configuration. A set of sensitivity studies to constrain the impact of atmospheric carbon dioxide are conducted at 70, 140, 280, 560 and 1,120 ppm. Table 1 gives an overview of the sensitivity studies conducted in this study.

Simulations are run for 5,000 model years and reached equilibrium at both the surface (not strongly trending, less than 0.1 °C per century in the global mean) and deep ocean, with less than 0.3 W m−2 imbalance in the top-of-atmosphere net radiation. Long model integrations are required when running new configurations to ensure that ocean circulation is fully representative of the new model boundary conditions applied to the model. The exception was the 0 ppm \(p_{\mathrm{CO}_2}\) simulations at both 1,364.95 and 1,399.07 W m−2 solar luminosity. Each simulation ran for 550 and 700 model years, respectively. This is common where climate models using low \(p_{\mathrm{CO}_2}\) values become fully glaciated (complete sea-ice coverage).

Heat and cold stress indicators

Two heat stress indicators are used within this study: (1) the wet-bulb temperature and (2) Humidex, calculated as follows:

Wet-bulb temperature

Wet-bulb temperature (Tw) is derived from a more accurate computation from ref. 72 (their equation (3.8)) with equivalent potential temperature (θE) calculated from ref. 73 (their equation (38)). Wet-bulb approximations such as that of Stull74 are not desirable for use as it is calibrated for the modern day and does not apply to warmer time periods. The complete derivation can be found in appendix A of ref. 75. Tw values of ≥35 °C are assessed to be critically lethal and lead to mortality2,13,17.

Humidex index

Humidex is a measure of the combined effect of both temperature and humidity on human physiology. Although a more subjective metric and often equated to a simplified feels-like metric, it does have an upper limit of 54. Above this limit for 6 h, mortality will ensue through heat stroke as the body is unable to regulate its core body temperature (Tb) through evaporation at the skin surface. Humidex is calculated as

$${\mathrm{Humidex}}=T+0.5555\times \left(6.11\times {\mathrm{e}}^{5417.7530\times \left(\frac{1}{273.15}-\frac{1}{273.15-{T}_{\mathrm{dew}}}\right)}-10\right),$$
(2)

where T is air temperature (°C) and Tdew is the dew-point temperature (K)76. Here, we define a region as uninhabitable where the monthly mean Humidex value of ≥45 for acclimatized species, which is defined as dangerous by the Meteorological Service of Canada, where all activity should be stopped. Using mean monthly values is conservative given that daily maximum Humidex values will exceed this value consistently.

Warm stress: aestivation

Of mammals that hibernate, only a small proportion do so owing to warm weather conditions, and of those, only a small proportion aestivate (warm weather hibernation) for several hours to days15, of which an even smaller proportion do so on seasonal time scales. Hibernation helps cold climate survivorship more than warm weather. From an ecological point of view, aestivation results in different challenges and requirements compared with hibernation in winter; while heat can reduce access to food and water availability as well, it will also reduce access to refugia for low ambient temperature (Ta) for a substantial reduction of body temperature (Tb)50. High Ta prevents Tb from falling to low levels and will therefore limit the energy-conserving potential of aestivation as a viable solution50. This is compounded by mammals’ high metabolic rates that require an intake of large amounts of food, and when food supply is low or fluctuating, energy requirements may exceed energy availability. In response, here we take regions that are desert (as predicted by the dynamic interactive vegetation scheme TRIFFID) in the model and deem them uninhabitable owing to a lack of food (bare soil fraction >0.5 corresponds to uninhabitable).

Cold stress: hibernation

Today, approximately 50% of mammals hibernate49, and mainly for days or weeks50. Only a fraction can do so on seasonal time scales, with only one known mammal able to do so for 11 months of the year. Here, we take a very unlikely conservative approach with our simulations and allow all mammals to develop hibernation as a trait and to hibernate for 9 months to survive cold weather conditions. We define cold stress regions that inhibit mammal habitation where nine or more consecutive months fall below 0 °C. This threshold limits freshwater availability as well as placing plants into a state of dormancy (<5 °C; ref. 19).

Exoplanet similarity index

Exoplanet habitability assessments are commonly used quantitative measures of planetary habitability. Here, we use a weighted ESI20 that measures habitability in relation to present-day Earth. A value of between 1 (identical similarity) and 0 (no similarity) signifies the likelihood that a planet would have the same physical properties as Earth (for example, radius, mass and surface temperature). In this instance, the only changing parameter will be the global mean annual temperature, as the physical properties of Earth will not have changed in +250 Myr. Values of ≥0.8 indicate the potential to harbour life.

$${\mathrm{ESI}}\left(S,R\right)=1-\sqrt{\frac{1}{2}\left[{\left(\frac{S-{S}_{\oplus }}{S+{S}_{\oplus }}\right)}^{2}+{\left(\frac{R-{R}_{\oplus }}{R+{R}_{\oplus }}\right)}^{2}\right]},$$

where S is stellar flux, R is the radius, S⨁ is Earth’s solar flux and R⨁ is Earth’s radius.

ESI provides the physical properties of an exoplanet’s habitability but cannot explicitly measure the possibility of life. Here, we couple ESI with the PHI in a geometric mean of separate values that would constitute conditions applicable to life:

$${\mathrm{PHI}}={\left(S\times E\times C\times L\right)}^{1/4},$$

where S is the presence of a stable substrate (influenced by solid subsurface, atmosphere and magnetosphere), E is the availability of energy (influenced by light, heat, redox chemistry and tidal flexing), C is appropriate chemistry (influenced by polymetric chemistry) to support life and L is a liquid solvent (in either the atmosphere or the sub-surface). While values for S, E, C and L are difficult to exactly determine on exoplanets, for our purposes here these are known values with respect to Earth. See ref. 20 for further details.

$${\mathrm{PHI}}_{\mathrm{rel}}=\left({\mathrm{PHI}}/{\mathrm{PHI}}_{\max }\right).$$

Each parameter (S, E, C, L) is summed and divided by the maximum attainable value to normalize the score (PHIrel) to between 0 and 1. Here, we define values of ≥0.8 as giving a reasonable approximation of conditions that allow life. A value of 1.0 would constitute ‘maximum’ habitability. Today, Earth has a value of 0.96. See ref. 20 for further details.

Future \(p_{\mathrm{CO}_2}\) modelling

To quantitatively estimate the long-term stable atmospheric CO2 concentration during PU, we use the SCION earth evolution model77. SCION is a linked climate–biogeochemical model that estimates a self-consistent evolution of the major composition of Earth’s atmosphere and oceans over geological time. It is an extension of the popular Geologic Carbon-Cycle78,79 and Carbon, Oxygen, Phosphorus, Sulphur and Evolution80,81 box models that use a 2D continental surface and look-up tables of steady-state climate model outputs to approximate surface processes such as weathering. The model calculates atmospheric CO2 based on tectonic and weathering-related CO2 inputs, as well as carbon sequestration as organic carbon or carbonates. SCION has been tested over the Phanerozoic Eon and produces a reasonable fit to CO2 proxy data, particularly over the last 250 Myr (ref. 77).

Using HadCM3B runs for the present day and for PU, we update the climate and palaeogeographic data structure within SCION so that it can run from the Pre-industrial to 250 Myr in the future. SCION also requires an estimate of global tectonic CO2 degassing. This is derived from global tectonic fluxes (that is, the amount of new seafloor created at mid-ocean ridges and consumed at subduction zones) and the amount of carbon that is typically degassed from such environments. Estimates of both the flux and amount of carbon degassed are available for present day82,83, and we use the recent estimates of ref. 82 as our present-day benchmark for carbon degassing (13 and 18 Mt C per year at ridges and subduction zones, respectively).

To estimate the carbon degassing for PU, we first construct a hypothetical plate boundary network (that is, an interconnected set of subduction zones and mid-ocean ridges84; Supplementary Fig. 1). The configuration is based on that which is inferred to have existed while Pangea was active (and what is mostly still visible today): a ‘ring of fire’ acting as an (almost) complete girdle of subduction circumnavigating PU85,86,87. For mid-ocean ridges, we infer the simplest and most conservative of all configurations, a stable triple junction that can account for convergence at all subduction zones. (A similar approach is taken for plate tectonic models in deep time86,88.)

To determine the rate of crust being formed and consumed at ridges and subduction zones, we extracted the spreading rates of all oceanic tectonic plates that compose the Pacific Ocean since 154 Ma (the time at which we have preserved isochrons in the Pacific Ocean). We limit our analysis to just the Pacific Ocean, as it is most analogous to our PU world (that is, plates consisting just of oceanic crust that are being subducted; see the discussion in ref. 89). We find a mean spreading rate of 10.42 cm per year with a standard deviation of 1.76 cm per year (Supplementary Fig. 2). This range of 8.67–12.18 cm per year provides us with a possible estimate of mid-ocean ridge and subduction flux. We multiply and sum the fluxes by the expected carbon degassing for both present-day and PU and use the ratio of the two as the relative change in degassing. Our results suggest that PU is likely to have 1.3–1.9 times the degassing rate of present-day Earth (roughly equivalent to and in line with estimates for Pangea degassing relative to present day44).

Now that we have defined an assumed CO2 degassing rate and have built a data structure of climate model runs at different CO2 levels for 250 Myr+, we can run the SCION model forwards in time to simulate atmospheric CO2 evolution over geological time. We start the model run at 50 Myr with all forcings fixed at present-day values. Between 0 and 250 Myr+, we increase the degassing rate linearly between 1 (present day) and the 250 Myr+ value calculated above. To account for model uncertainty, we run the system 1,000 times subject to a random choice from the range of future degassing rates, as well as the parameter space tested in the standard Phanerozoic model ensembles77. Supplementary Fig. 3 shows the model spatial fields at Pre-industrial and 250 Myr+, and Supplementary Fig. 1 shows the predicted atmospheric CO2 concentration for each of these times, with the central marker showing the model ensemble mean and the bars showing the minimum and maximum. Like Pangaea, PU has a large arid interior zone in which silicate weathering is inhibited but also a large warm and wet climate zone in which weathering is enhanced. The overall combination of higher CO2 degassing and altered continental weatherability results in a prediction of 621 ppm (range 410–816 ppm) CO2, or a range of approximately 1.5–3 times Pre-industrial (Table 2).

Table 2 Description of sensitivity studies and model boundary conditions for a Pre-industrial climate (Modern geography) and PU geography
Full size table