https://orcid.org/0000-0001-6517-2231
ABSTRACT
Recent detections of carbon-bearing molecules in the atmosphere of a candidate Hycean world, K2-18 b, with JWST are opening the prospects for characterizing potential biospheres on temperate exoplanets. Hycean worlds are a recently theorized class of habitable exoplanets with ocean-covered surfaces and hydrogen-rich atmospheres. Hycean planets are thought to be conducive to hosting microbial life under conditions similar to those in the Earth’s oceans. In this work, we investigate the potential for biological evolution on Hycean worlds and their dependence on the thermodynamic conditions. We find that a large range of evolutionary rates and origination times are possible for unicellular life in oceanic environments for a relatively marginal range of environmental conditions. For example, a relatively small (10 K) increase in the average ocean temperature can lead to over twice the evolutionary rates, with key unicellular groups originating as early as |${\sim} 1.3$| billion years from the origin of life. On the contrary, similar decreases in temperatures can also significantly delay the origination times by several billion years. This delay in turn could affect their observable biomarkers such as dimethyl sulphide, which is known to be produced predominantly by Eukaryotic marine phytoplankton in Earth’s oceans. Therefore, Hycean worlds that are significantly cooler than Earth may be expected to host simpler microbial life than Earth’s oceans and may show weaker biosignatures, unless they orbit significantly older stars than the Sun. Conversely, Hycean worlds with warmer surface temperatures than Earth are more likely to show stronger atmospheric biosignatures due to microbial life if present.
1 INTRODUCTION
The search for extraterrestrial life is one of the most fundamental quests in human history. It has the potential to both ascertain the uniqueness or ubiquity of terrestrial-like life in the Universe as well as provide insights into the conditions that led to the Origin of Life (OoL) here on Earth. Current advances in astronomical observations indicate a realistic possibility for detecting life beyond the Solar system in the foreseeable future. While an exact Earth-twin around a Sun-like star is yet to be discovered, a number of temperate Earth-size and sub-Neptune exoplanets have been discovered around M dwarf host stars which are smaller and cooler than the Sun and, hence, with habitable zones that are significantly closer to the stars (e.g. Montet et al. 2015; Dittmann et al. 2017; Gillon et al. 2017). Furthermore, the advent of new observational facilities, such as the JWST, and the upcoming extremely large telescopes on the ground promise the capability for detection of atmospheric signatures, including biomarkers, in such planets (Barstow & Irwin 2016; Wunderlich et al. 2019; Madhusudhan, Piette & Constantinou 2021).
An important recent development in this direction is the possibility of Hycean worlds, which increase both the numbers of potentially habitable planets and the ability to detect biosignatures in their atmospheres (Madhusudhan et al. 2021). Hycean worlds are a recently proposed class of planets with ocean-covered surfaces and hydrogen-rich atmospheres. Their volatile-rich interiors lead to larger sizes and extended atmospheres, compared to rocky planets of similar mass, and make them more conducive to atmospheric observations. Several candidate Hycean planets have been identified among the currently known temperate sub-Neptunes, as shown in Fig. 1, that are good targets for atmospheric observations with JWST (Madhusudhan et al. 2021). A major observational breakthrough came with the recent detection of carbon-bearing molecules, methane and carbon dioxide, in the candidate Hycean world K2-18 b using JWST (Madhusudhan et al. 2023b). Such observations and theoretical studies demonstrate the capability for the detection of biomarkers, if life is indeed present on such planets, using current observational facilities in the near future.
Bulk properties of temperate sub-Neptune exoplanets. The circles with uncertainties show a selected sample of temperate sub-Neptune exoplanets with confirmed measurements of radii and masses, with uncertainties below |$2 \, {\rm M}_{\oplus}$|, and zero-albedo equilibrium temperatures (|$T_{\rm eq}$|) below 600 K. The circles are colour-coded by |$T_{\rm eq}$| as denoted by the colour bar. The dashed lines show theoretical mass–radius curves of model planets of uniform interior compositions denoted in the legend and the cyan and crimson regions denote ranges of masses and radii allowed for Hycean and Dark Hycean planets, respectively, following Madhusudhan et al. (2021). A subset of these planets with |$T_{\rm eq}$| below |${\sim} 400$| K and lying in the cyan region, marked with grey outer circles, could be candidate Hycean planets (Madhusudhan et al. 2021). Adapted from Madhusudhan et al. (2021) with data updated based on the NASA Exoplanet Archive.
Hycean planets are expected to provide the chemical and thermodynamic conditions necessary for sustaining oceanic microbial life (Madhusudhan et al. 2023a; Glein 2024; Petraccone 2024). The |${\rm H}_2$|-rich atmospheres provide a rich source of organic prebiotic molecules in the early evolution of such planets, while the bioessential elemental requirements, including CHNOPS elements, can be met through a combination of external delivery and atmospheric precipitation (Madhusudhan et al. 2023a). The availability of abundant |${\rm H}_2$| and oxidized compounds such as |${\rm CO}_2$| can release significant metabolic energy through reductive reactions as well as the synthesis of complex hydrocarbons, including amino acids (Glein 2024). At the same time, the wide range of temperatures possible on such planets allows for diverse thermodynamic conditions to support life. In particular, most of the Hycean candidates currently known are expected to be warmer than average terrestrial conditions, leading to higher entropy and more conducive conditions for life (Petraccone 2024) than Earth-like rocky exoplanets in the habitable zone.
In this study, we investigate the prospects for biological evolution on Hycean worlds. Previous studies have shown that increased temperatures in habitable environments are generally more conducive to biological activity (Petraccone 2024) and lead to increased evolutionary rates and higher diversity (Lingam & Loeb 2018). We investigate the degree to which changes in the ocean surface temperature would affect the evolution of key groups of Earth-like unicellular life and their origination time-scales in a Hycean environment. This work, in turn, has observable consequences for prominent biosignatures on such planets, considering that unicellular phytoplankton is a major source of key biomarkers in the Earth’s atmosphere, such as dimethyl sulphide (DMS) which may be observable in Hycean atmospheres (Madhusudhan et al. 2021).
2 MODELLING BIOLOGICAL EVOLUTION ON HYCEAN PLANETS
We assess the nature of unicellular life one may expect, i.e. what makes up the composition of the biosphere, if life originated on a Hycean planet assuming Earth-like organisms, i.e. bacterial, archaea, and eukaryotic life. Biosphere composition depends on what organisms have evolved at a given point in time. For example, there were no animals 4 billion years ago, whereas today they dominate the biosphere. As such, the key aspect we wish to understand for a given Hycean exoplanet is what unicellular organisms could have evolved by a given time, i.e. what are the origination times for different major groups. However, the drivers that shape biological macroevolution are not always well resolved, especially for the origination of new groups, e.g. the origins of animals (Cavalier-Smith 2017; Hoffman et al. 2017; Sogabe et al. 2019; Liu et al. 2024; Stockey et al. 2024). This uncertainty behind evolutionary drivers makes predicting the evolutionary histories of life on exoplanets hard since there are not many direct causal relationships between biosphere conditions and origination of important clades (the group of species that includes the last common ancestor and all its living and extinct descendants). Yet often macroevolutionary patterns can be well modelled through neutral models of evolution, i.e. without incorporating causal biotic or environmental drivers into the models. Such models can capture large-scale patterns because without any environmental or biotic pressures, populations still change, and species evolve and go extinct through processes such as neutral molecular evolution (Kimura 1989; Ohta 1992).
Neutral evolution models provide a good empirical match to observed data on Earth across different temporal scales. On planetary time-scales, simple birth–death models of macroevolutionary patterns, whereby species evolve and go extinct with given probabilities, replicate the broad diversification patterns in large groups such as arthropods, tetrapod, and land plants (e.g. Budd & Mann 2020). Similarly, early animals appear to have neutral dynamics, in that they only have limited biotic interactions and interactions with their local environment (Mitchell et al. 2019). As such, the simplest models are these neutral models which not only give a good indicator of speciation rates without assuming any causal drivers, but also likely are the most conservative, i.e. likely to provide the slowest rate of evolution and speciation rates.
Evolutionary rates can be measured (and modelled) in different ways, including speciation rates through geological time or the number of nucleotide substitutions due to random mutations, i.e. neutral molecular evolution. One approach to modelling evolutionary rates is using the metabolic theory of ecology (MTE) to predict the evolutionary rates based on the metabolic rate of an organism (Allen et al. 2006). The MTE provides a framework for predicting biological traits, particularly metabolic rate, for a given organism (Brown et al. 2004). These predictions match empirical observations well (Brown et al. 2004), albeit the underlying mechanisms for this relationship are debated (e.g. West, Brown & Enquist 1997; O’Connor et al. 2007; Price et al. 2012; Maino et al. 2014). The MTE builds on metabolic scaling theory, which states that the metabolism of organisms is the fundamental biological rate that drives most observed patterns within biology and depends on the body size of the organism and the temperature of its environment (West et al. 1997; Gillooly et al. 2001; Brown et al. 2004). Body size changes metabolic rates due to surface–volume ratios because smaller organisms need more energy (per unit biomass) to transfer nutrients around their body than larger organisms. Metabolism is impacted by temperature because temperature will change the rate at which all biochemical/physiological reactions occur within an organism, thus speeding up rates of biochemical reactions. The MTE links the organism-level traits of metabolic scaling theory and metabolic rates to life history and ecological traits such as population growth, carrying capacity, and biodiversity (Brown et al. 2004; McCoy & Gillooly 2008) including large-scale patterns in current global diversity patterns such as the latitudinal diversity gradients (Righetti et al. 2019).
The key variables that predict the temperature-corrected metabolic rate for an organism are the environmental temperature, the mass of the organism, and the mass scaling component (Brown et al. 2004), as shown in equation (1) in Section 3. The mass scaling component is predicted by MTE and the metabolic scaling theory as |${-({1}/{4})}$| for the temperature-corrected metabolic rate, and has been repeatedly validated against empirical data (e.g. Raven & Geider 1988; Vetter 1995; McClain et al. 2012). There is a substantial amount of empirical evidence for the relationship between body size, temperature, and metabolic rates, consistently finding these relationships across all kingdoms of life, in different environments and across 50 orders of magnitude of body size, from bacteria to large whales (Brown et al. 2004; Munch & Salinas 2009; Gillooly, Gomez & Mavrodiev 2017). The largest deviations tend to include endothermic organisms, likely because they do not take on the ambient temperature of their environment such that birds, mammals, and some fish have greater deviations from the MTE predictions (Brown et al. 2004; Grady et al. 2014). Most of this work testing the MTE has focused on the 0–40°C range, but there is limited data for extremophiles such as hydrothermal vent organisms and deep-sea organisms (McClain et al. 2012), which also broadly fit the data. Empirical support for the life history, population, and ecosystem level traits predicted by Brown et al. (2004) are more variable, so for this study, we focus solely on evolutionary rates.
In terms of the use of MTE to make predictions about the evolution of life on exoplanets, Lingam & Loeb (2018) noted that because of the relationships predicted by MTE, once life has originated, the chance of complex life is greater on warmer planets because of increased evolutionary and speciation rates and also because of the greater biodiversity that comes with higher temperatures. In this study, we use the MTE to make quantitative inferences of the extent to which evolutionary rates change with temperature, and use these rates to infer how the time to the origination of clades will also change.
3 METHODS
The evolution rate of an organism is inversely proportional to the time to speciation and is proportional to metabolic rate (Allen et al. 2006). The relationship of metabolic rate with evolutionary and speciation rates has been verified using the model group foraminifera using speciation rates derived from fossil and extant foraminifera (Allen et al. 2006). Therefore, by calculating the predicted metabolic rate of an organism, the evolutionary rates and time to speciation can also be inferred.
In order to use the MTE to estimate how much time is required on different planets for the origination of major groups to evolve, we first need to estimate how much ‘evolution’ was required here on Earth. The amount of required evolution is taken to be (for a given sized organism) how many nucleotide substitutions (mutations) are needed here on Earth to go from the last common ancestor of all organisms to the origination of a new clade. These evolutionary relationships can be encapsulated by an evolutionary tree, or time-calibrated phylogeny where the patterns of the branches of the tree reflect the relationships between different species (or groups of species) and where the lengths of the branches depict time.
To generate these evolutionary trees for Hycean conditions, we make some minimal assumptions (see Appendix A for more details). (1) Life has originated (OoL). (2) Elements/resources are not limiting factors, as suggested in Madhusudhan et al. (2023a), so that the biosphere is stable and life is maintained. (3) Speciation leads to the origination of new clades similar to that in Earth’s oceans. (4) The planetary temperature is not significantly changed by the organisms considered. While the extent to which a Hycean world would satisfy these conditions is not yet known, these nevertheless provide a starting point to assess the prospects for the evolution of Earth-like unicellular life on such planets.
Evolutionary rates at a given point in time are calculated based on the temperature-corrected metabolic rate for the given organism:
where |$\bar{B}$| is the temperature-corrected metabolic rate, |$\beta$| is the mass scaling component, |$b_0$| is the taxa-dependant constant, and for unicellular organisms |$\ln(b_0)= 15.85$| (Brown et al. 2004). The activation energy E can vary between 0.2 and 1.2 eV, but consistently has an observed value in this MTE context of 0.65 eV (Raven & Geider 1988; Vetter 1995), 1 eV = |$1.602 \times 10^{-19}$| J. Here, k = |$8.62 \times 10^{-5}$| eV K−1 is the Boltzmann constant, M is mass in gram (g), and T is the absolute temperature in Kelvin (K). The mass scaling component |$\beta$| is predicted by MTE and the metabolic scaling theory as −1/4.
In this study, the input parameters in equation (1) were compiled from Brown et al. (2004) using values for unicellular organisms. The input masses for the different species are calculated from the volume, given in Table 1 which gives the median volume for the given organism as recorded in the literature. The masses were calculated as the volume times the density of phytoplankton of 1.1 g cm−3 (Padisák, Soróczki-Pintér & Rezner 2003).
Summary of the organisms and their properties considered for calculations of evolutionary rates. Node origination times are given by the median values of published works with the range of uncertainties given in parentheses.
| Clade | Example organism | Size (m3) | Reference | Node origination time from present (Myr) | Reference |
|---|---|---|---|---|---|
| Cyanobacteria | Prochlorococcus | |$9.06 \times 10^{-19}$| | Partensky, Hess & Vaulot (1999) | 2810 (2561–3306) | Kumar et al. (2022) |
| Aquificota | Aquifex | |$1.57 \times 10^{-18 }$| | Guiral et al. (2012) | 4101 (3644–4189) | Kumar et al. (2022) |
| Alphaproterobacteria | Alphaproterobacteria | |$1.77 \times 10^{-18 }$| | Brown et al. (2012) | 1900 (2423–1419) | Wang & Luo (2021) |
| Betaproterobacteria | Betaproterobacteria | |$4.91 \times 10^{-20}$| | Croué et al. (2013) | 1900 (2423–1419) | Wang & Luo (2021) |
| Gammaproteobacteria | Thiomargarita | |$3.35 \times 10^{-11}$| | Volland et al. (2022) | 1900 (2423–1419) | Wang & Luo (2021) |
| Thermoplasmatales | Thermoplasmatales | |$4.19 \times 10^{-18}$| | Paul et al. (2012) | 1704 (1132–2276) | Kumar et al. (2022) |
| Thermococcus | Thermococcaceae | |$1.72 \times 10^{-17}$| | Canganella et al. (1998) | 1576 (974–2410) | Kumar et al. (2022) |
| Methanococccea | Methanococcaceae | |$3.53 \times 10^{-18}$| | Jones et al. (1983) | 1576 (974–2410) | Kumar et al. (2022) |
| Archaeoglobus | Archaeoglobaceae | |$5.24 \times 10^{-19}$| | Slobodkina et al. (2021) | 1576 (974–2410) | Kumar et al. (2022) |
| Opisthokonta | Choanoflagellate | |$8.71 \times 10^{-17 }$| | Mah, Christensen-Dalsgaard & Leys (2014) | 1598 (1085–1671) | Kumar et al. (2022) |
| Excavata | Jakoba libera | |$3.14 \times 10^{-16}$| | Patterson et al. (1993) | 1598 (1085–1671) | Kumar et al. (2022) |
| Alveolata | ciliates | |$1.13 \times 10^{-13}$| | Nielsen & Kicrboe (1994) | 1040 (627–1344) | Kumar et al. (2022) |
| Stramenopiles | Sagenista | |$1.13 \times 10^{-16}$| | Cho et al. (2024) | 1106 (954–1234) | Kumar et al. (2022) |
| Rhizaria | Polycystinea | |$1.77 \times 10^{-12}$| | Smalley (1963) | 933 (812.4–1470) | Kumar et al. (2022) |
| Diatoms | Chaetoceros | |$2.68 \times 10^{-18}$| | Tomas (1997) | 206 (range unavailable) | Kumar et al. (2022) |
| Coccolithophores | Emiliania huxleyi | |$1.13 \times 10^{-16}$| | Hoffmann et al. (2015) | 280 (range unavailable) | Kumar et al. (2022) |
| Dinoflagellates | Pfiesteria piscicida | |$5.96 \times 10^{-12}$| | Burkholder & Glasgow (1997) | 239 (range unavailable) | Kumar et al. (2022) |
| Clade | Example organism | Size (m3) | Reference | Node origination time from present (Myr) | Reference |
|---|---|---|---|---|---|
| Cyanobacteria | Prochlorococcus | |$9.06 \times 10^{-19}$| | Partensky, Hess & Vaulot (1999) | 2810 (2561–3306) | Kumar et al. (2022) |
| Aquificota | Aquifex | |$1.57 \times 10^{-18 }$| | Guiral et al. (2012) | 4101 (3644–4189) | Kumar et al. (2022) |
| Alphaproterobacteria | Alphaproterobacteria | |$1.77 \times 10^{-18 }$| | Brown et al. (2012) | 1900 (2423–1419) | Wang & Luo (2021) |
| Betaproterobacteria | Betaproterobacteria | |$4.91 \times 10^{-20}$| | Croué et al. (2013) | 1900 (2423–1419) | Wang & Luo (2021) |
| Gammaproteobacteria | Thiomargarita | |$3.35 \times 10^{-11}$| | Volland et al. (2022) | 1900 (2423–1419) | Wang & Luo (2021) |
| Thermoplasmatales | Thermoplasmatales | |$4.19 \times 10^{-18}$| | Paul et al. (2012) | 1704 (1132–2276) | Kumar et al. (2022) |
| Thermococcus | Thermococcaceae | |$1.72 \times 10^{-17}$| | Canganella et al. (1998) | 1576 (974–2410) | Kumar et al. (2022) |
| Methanococccea | Methanococcaceae | |$3.53 \times 10^{-18}$| | Jones et al. (1983) | 1576 (974–2410) | Kumar et al. (2022) |
| Archaeoglobus | Archaeoglobaceae | |$5.24 \times 10^{-19}$| | Slobodkina et al. (2021) | 1576 (974–2410) | Kumar et al. (2022) |
| Opisthokonta | Choanoflagellate | |$8.71 \times 10^{-17 }$| | Mah, Christensen-Dalsgaard & Leys (2014) | 1598 (1085–1671) | Kumar et al. (2022) |
| Excavata | Jakoba libera | |$3.14 \times 10^{-16}$| | Patterson et al. (1993) | 1598 (1085–1671) | Kumar et al. (2022) |
| Alveolata | ciliates | |$1.13 \times 10^{-13}$| | Nielsen & Kicrboe (1994) | 1040 (627–1344) | Kumar et al. (2022) |
| Stramenopiles | Sagenista | |$1.13 \times 10^{-16}$| | Cho et al. (2024) | 1106 (954–1234) | Kumar et al. (2022) |
| Rhizaria | Polycystinea | |$1.77 \times 10^{-12}$| | Smalley (1963) | 933 (812.4–1470) | Kumar et al. (2022) |
| Diatoms | Chaetoceros | |$2.68 \times 10^{-18}$| | Tomas (1997) | 206 (range unavailable) | Kumar et al. (2022) |
| Coccolithophores | Emiliania huxleyi | |$1.13 \times 10^{-16}$| | Hoffmann et al. (2015) | 280 (range unavailable) | Kumar et al. (2022) |
| Dinoflagellates | Pfiesteria piscicida | |$5.96 \times 10^{-12}$| | Burkholder & Glasgow (1997) | 239 (range unavailable) | Kumar et al. (2022) |
Summary of the organisms and their properties considered for calculations of evolutionary rates. Node origination times are given by the median values of published works with the range of uncertainties given in parentheses.
| Clade | Example organism | Size (m3) | Reference | Node origination time from present (Myr) | Reference |
|---|---|---|---|---|---|
| Cyanobacteria | Prochlorococcus | |$9.06 \times 10^{-19}$| | Partensky, Hess & Vaulot (1999) | 2810 (2561–3306) | Kumar et al. (2022) |
| Aquificota | Aquifex | |$1.57 \times 10^{-18 }$| | Guiral et al. (2012) | 4101 (3644–4189) | Kumar et al. (2022) |
| Alphaproterobacteria | Alphaproterobacteria | |$1.77 \times 10^{-18 }$| | Brown et al. (2012) | 1900 (2423–1419) | Wang & Luo (2021) |
| Betaproterobacteria | Betaproterobacteria | |$4.91 \times 10^{-20}$| | Croué et al. (2013) | 1900 (2423–1419) | Wang & Luo (2021) |
| Gammaproteobacteria | Thiomargarita | |$3.35 \times 10^{-11}$| | Volland et al. (2022) | 1900 (2423–1419) | Wang & Luo (2021) |
| Thermoplasmatales | Thermoplasmatales | |$4.19 \times 10^{-18}$| | Paul et al. (2012) | 1704 (1132–2276) | Kumar et al. (2022) |
| Thermococcus | Thermococcaceae | |$1.72 \times 10^{-17}$| | Canganella et al. (1998) | 1576 (974–2410) | Kumar et al. (2022) |
| Methanococccea | Methanococcaceae | |$3.53 \times 10^{-18}$| | Jones et al. (1983) | 1576 (974–2410) | Kumar et al. (2022) |
| Archaeoglobus | Archaeoglobaceae | |$5.24 \times 10^{-19}$| | Slobodkina et al. (2021) | 1576 (974–2410) | Kumar et al. (2022) |
| Opisthokonta | Choanoflagellate | |$8.71 \times 10^{-17 }$| | Mah, Christensen-Dalsgaard & Leys (2014) | 1598 (1085–1671) | Kumar et al. (2022) |
| Excavata | Jakoba libera | |$3.14 \times 10^{-16}$| | Patterson et al. (1993) | 1598 (1085–1671) | Kumar et al. (2022) |
| Alveolata | ciliates | |$1.13 \times 10^{-13}$| | Nielsen & Kicrboe (1994) | 1040 (627–1344) | Kumar et al. (2022) |
| Stramenopiles | Sagenista | |$1.13 \times 10^{-16}$| | Cho et al. (2024) | 1106 (954–1234) | Kumar et al. (2022) |
| Rhizaria | Polycystinea | |$1.77 \times 10^{-12}$| | Smalley (1963) | 933 (812.4–1470) | Kumar et al. (2022) |
| Diatoms | Chaetoceros | |$2.68 \times 10^{-18}$| | Tomas (1997) | 206 (range unavailable) | Kumar et al. (2022) |
| Coccolithophores | Emiliania huxleyi | |$1.13 \times 10^{-16}$| | Hoffmann et al. (2015) | 280 (range unavailable) | Kumar et al. (2022) |
| Dinoflagellates | Pfiesteria piscicida | |$5.96 \times 10^{-12}$| | Burkholder & Glasgow (1997) | 239 (range unavailable) | Kumar et al. (2022) |
| Clade | Example organism | Size (m3) | Reference | Node origination time from present (Myr) | Reference |
|---|---|---|---|---|---|
| Cyanobacteria | Prochlorococcus | |$9.06 \times 10^{-19}$| | Partensky, Hess & Vaulot (1999) | 2810 (2561–3306) | Kumar et al. (2022) |
| Aquificota | Aquifex | |$1.57 \times 10^{-18 }$| | Guiral et al. (2012) | 4101 (3644–4189) | Kumar et al. (2022) |
| Alphaproterobacteria | Alphaproterobacteria | |$1.77 \times 10^{-18 }$| | Brown et al. (2012) | 1900 (2423–1419) | Wang & Luo (2021) |
| Betaproterobacteria | Betaproterobacteria | |$4.91 \times 10^{-20}$| | Croué et al. (2013) | 1900 (2423–1419) | Wang & Luo (2021) |
| Gammaproteobacteria | Thiomargarita | |$3.35 \times 10^{-11}$| | Volland et al. (2022) | 1900 (2423–1419) | Wang & Luo (2021) |
| Thermoplasmatales | Thermoplasmatales | |$4.19 \times 10^{-18}$| | Paul et al. (2012) | 1704 (1132–2276) | Kumar et al. (2022) |
| Thermococcus | Thermococcaceae | |$1.72 \times 10^{-17}$| | Canganella et al. (1998) | 1576 (974–2410) | Kumar et al. (2022) |
| Methanococccea | Methanococcaceae | |$3.53 \times 10^{-18}$| | Jones et al. (1983) | 1576 (974–2410) | Kumar et al. (2022) |
| Archaeoglobus | Archaeoglobaceae | |$5.24 \times 10^{-19}$| | Slobodkina et al. (2021) | 1576 (974–2410) | Kumar et al. (2022) |
| Opisthokonta | Choanoflagellate | |$8.71 \times 10^{-17 }$| | Mah, Christensen-Dalsgaard & Leys (2014) | 1598 (1085–1671) | Kumar et al. (2022) |
| Excavata | Jakoba libera | |$3.14 \times 10^{-16}$| | Patterson et al. (1993) | 1598 (1085–1671) | Kumar et al. (2022) |
| Alveolata | ciliates | |$1.13 \times 10^{-13}$| | Nielsen & Kicrboe (1994) | 1040 (627–1344) | Kumar et al. (2022) |
| Stramenopiles | Sagenista | |$1.13 \times 10^{-16}$| | Cho et al. (2024) | 1106 (954–1234) | Kumar et al. (2022) |
| Rhizaria | Polycystinea | |$1.77 \times 10^{-12}$| | Smalley (1963) | 933 (812.4–1470) | Kumar et al. (2022) |
| Diatoms | Chaetoceros | |$2.68 \times 10^{-18}$| | Tomas (1997) | 206 (range unavailable) | Kumar et al. (2022) |
| Coccolithophores | Emiliania huxleyi | |$1.13 \times 10^{-16}$| | Hoffmann et al. (2015) | 280 (range unavailable) | Kumar et al. (2022) |
| Dinoflagellates | Pfiesteria piscicida | |$5.96 \times 10^{-12}$| | Burkholder & Glasgow (1997) | 239 (range unavailable) | Kumar et al. (2022) |
Allen et al. (2006) derived how the evolutionary rates follow from equation (1), showing the mutation rate as the number of nucleotide substitutions per unit time (cf. neutral molecular evolution):
where the mutation rate |$\alpha$| can vary depending on the clade for given incident radiation, but can be assumed to be constant for a given clade. This equation can then be used to derive the time it takes for speciation to occur, |$t_\mathrm{ s}$|:
The origination times of different clades on Earth are dependent on the body size of the organism, planetary temperature, and the amount of neutral molecular evolution (the amount of background mutations). For the Earth’s temperature, we use the median temperature values as calculated by Krissansen-Totton, Arney & Catling (2018) at 0.01 Gyr intervals from the OoL at 4.3 billion years ago (Kumar et al. 2022) to the present. Required inputs for equation (1) are the body masses of the organisms (Table 1), with the other parameters adopted from the literature (Brown et al. 2004). Origination times are given using Time Tree (Kumar et al. 2022) which is a meta-analysis of published molecular clock studies that provides the origination times as the median values of published works (Table 1). Alphaproterobacteria, Betaproterobacteria, and Gammaproterobacteria origination times were not given by Kumar et al. (2022), so we used Wang & Luo (2021) for these three clades. We used Kumar et al. (2022) rather than multiple sources so as to enable a consistent treatment for as many clades as possible. The timings along with the calculated evolutionary rates were input into the phylogeny and plotted with the r package ggtree (Yu 2020).
In order to calculate the origination time of a group, the cumulative amount of substitutions needed for the origination of a group is calculated as the integral of equation (1) along all the ancestral branches. To calculate how the origination times for the clades change for different median temperatures (0, |${\pm} 5$|, and |${\pm} 10$| K), the total number of mutations needed |$\alpha _{\rm T}$| was calculated as the sums of the integrals of equation (2) for each ancestral branch of the phylogeny up to the origination times of the clade. At each new temperature, the number of mutations occurring up to each ancestral node was calculated in sequence up until the point that |$\alpha _{\rm T}$| was reached, and the corresponding time represented the origination time.
In this study, we model the evolutionary rates and origination times for the major clades across the tree of life, namely Terrabacteria and Pseudomondoata clades within Bacteria, Euryarchaea, and Thermoplasmatales within Archaea and SAR, Opisthokonta, and Excavata with the Eukaryotes. Within each of these clade, we use as a representative organism a unicellular, holoplanktonic species (organisms which live their entire life cycle in the water column) (Table 1). While our analyses are focused on the normal thermal tolerance range of 0–40°C because the majority of life lives within this range (Sunday, Bates & Dulvy 2012), the clades in our analyses include extremophiles, within Archaea, especially Euryarchaea containing numerous hyperthermophiles (|${\gt} 60^{\rm o}{\rm C}$|) and bacteria with thermophiles (|${\gt} 40^{\rm o}{\rm C}$|; Dalmaso, Ferreira & Vermelho 2015).
Other groups of interest include ones likely to produce biosignatures, such as DMS. DMS is produced biogenically, predominantly by marine phytoplankton as a breakdown of dimethylsulfoniopropionate (DMSP) which is an osmoregulator for phytoplankton (Andreae 1990; Yoch 2002). DMS (and DMSP) are released by phytoplankton through growth, as an excretion product and when they die (or are eaten) DMSP is released and converted to DMS (Kwint & Kramer 1995). DMS can be produced by a wide range of phytoplankton including bacteria such as Cyanobacteria and Gammaproterobacteria (Zheng et al. 2020; Teng et al. 2021) but the majority of DMS in today’s oceans are produced by dinoflagellates, diatoms, coccolithophores, and protists (Yoch 2002; Hopkins et al. 2023), i.e. Eukaryotes. In order to further explore the diversity of phytoplankton (photosynthetic autotrophs) on Hycean worlds, we also model the origination times of the major phytoplankton groups, Cyanobacteria, Gammaproterobacteria (within the group Pseudomonadota), Dinoflagellates, Coccolithophores, and Diatoms (Table 1). Animals such as corals can also produce DMS through their symbionts (Jackson et al. 2020), but due to their benthic nature are beyond the scope of this paper.
In order to assess how our results may change using the recent origination times of Moody et al. (2024), we used their origination times for the last universal ancestor for all (4.2 Ga) and common ancestors for Eukaryotes (2.3 Ga), Archaea (3.5 Ga), Bacteria (3.4 Ga), and oxyphotobacteria (3.0 Ga) using the divergence times for the ILN (independent lognormal), concatenated and cross-bracing A model.
4 RESULTS
We used the MTE model to assess the effect of temperature on the evolutionary rate and origination times of key unicellular and phytoplankton groups discussed above. To illustrate the impact of median surface temperature on evolutionary rates, we calculated the evolutionary rates for an example methanogen over 4.3 billion years for surface temperature changes of |${\pm} 5$|, |${\pm} 10$|, and |${\pm} 15$| K, relative to Earth. We then calculated the origination times for the key unicellular and phytoplankton groups for surface temperature changes of |${\pm} 10$| K relative to Earth.
4.1 Evolutionary rates
In order to illustrate how evolutionary rates change with temperature over planetary time-scales, we have calculated the evolutionary rates for an example organism (Aquifix) over the last 4.3 billion years. Aquifix is a suitable model organism because it is a good analogue to some of the first suggested life on Earth (Dodd et al. 2017) in that it has similar ecological and morphological properties such as size. In order to aid comparison of the relative speed of the evolutionary rates, we have normalized the rates so that the evolutionary rate at the Earth’s temperature OoL 4.3 billion years ago (i.e. at t = 0) is set to one.
Fig. 2 shows how the normalized evolutionary rate changes through time, with the fluctuations corresponding to the recorded median surface temperature through Earth’s history (Krissansen-Totton et al. 2018). The evolutionary rate decreases through time as the median surface temperature of the Earth decreases from 294 K at t = 0 to 286 K for the present time, with a present evolutionary rate of 52.2 per cent of the starting rate, i.e. that at t = 0. The mean normalized evolutionary rate over the last 4.3 Gyr is 60 per cent of the starting rate. When the median surface temperature of a planet increases, the evolutionary rate also increases. An increase of 5 K results in a faster evolutionary rate of 153 per cent at t = 0, higher present rates of 82 per cent, and a higher mean of 94 per cent over 4.3 Ga. An increase of 10 K corresponds to a faster evolutionary rate of 232 per cent at t = 0, 127 per cent in the present and a mean increase of 145 per cent over 4.3 Ga. An increase of 15 K corresponds to a faster evolutionary rate of 348 per cent at t = 0, 193 per cent in the present and a mean increase of 220 per cent over 4.3 Ga. Decreasing the median temperature decreases the evolutionary rates, with a 5 K decrease leading to rates of 64 per cent at t = 0, and 32 per cent in the present, with a mean of 38 per cent. A decrease of median temperature by 10 K further reduces rates to 40 per cen at t = 0, and 20 per cent in the present, with a mean of 24 per cent and a decrease of 15 K to 25 per cent at t = 0, and 12 per cent in the present, with a mean of 14 per cent.
Effect of temperature on normalized evolutionary rate for an analogue LUCA (last universal common ancestor) methanogen on Earth. Cases with increased temperatures of +5, +10, and +15 K, relative to Earth, are shown in different shades of red, and cases with decreased temperatures of −5, −10, and −15 K, relative to Earth, are shown in blue. t = 0 is set to when life is inferred to have originated, and the evolutionary rates normalized such that the evolutionary rate is 1 at t = 0 for Earth.
The relationship between surface temperature changes and evolutionary rates is non-linear, following an exponential relation as seen from equation (1). This non-linearity results in much larger and more variable impacts of high temperatures on evolutionary rates than for colder temperatures.
The range of surface temperatures that Fig. 2 covers is from 309 K (36°C) for the +15 K case at t = 0 to the coldest of 271 K (−2°C) at −15 K. The only scenario when the temperature is subzero is for the last 1.52 Gyr for the −15 K model run. The thermal tolerance for life without extremophile adaptations is 0–40°C (Sunday et al. 2012), thus it is only for the coldest run that caution is needed when considering canonical life.
4.2 Origination times of major groups
The dependence of the evolutionary rate on temperature has important consequences for the origination times of major unicellular groups across the tree of life. On Earth, the earliest domains to originate are the Bacteria and Archaea, within 0.31 Gyr after OoL, followed much later by the Eukaryotes at 2.7 Gyr. As shown in Fig. 3(a), the different groups within these domains originated over a wide range of times, with the Terrabacteria originating at |${\sim} 1.1$| Gyr while all the other groups originating beyond 3.2 Gyr. Overall, unicellular life in Earth’s oceans remained relatively simple for nearly 2 Gyr after OoL, until the emergence of Eukaryotes thereafter marking the onset of complex life. Fig. 3(a) also shows that the evolutionary rate across the different groups remained relatively uniform between |${\sim} 0.1$| and |$0.4 \times 10^{8}$| mutations−1 nucleotide−1 s−1, for our canonical case using an Earth-like temperature variation over time. We note that for a given temperature the evolutionary rates throughout the major unicellular groups are primarily driven by the body size (Fig. 3b), with larger species having lower metabolic rates and hence slower evolution.
Time-calibrated phylogenetic trees with calculated evolutionary rates at Earth’s median temperature (top) and at +10 K increase relative to Earth (bottom) with the colour indicating the evolutionary rates at the nodes.
A marginal increase in the median ocean surface temperature leads to significant changes in the origination times of different groups. Considering a median temperature of 10 K above that of Earth, the origination times of all the groups in the phylogeny happen significantly earlier, as shown in Fig. 3(b). In this case, all the major groups across all three domains now originate before 1.19 Gyr from OoL, with the Terrabacteria originating within 0.6 Gyr. The groups with the longest origination times in the canonical Earth-like case are affected more strongly than the others, because the effect of temperature change is cumulative. For example, the different Eukaryotic groups now originate within 1 Gyr compared to 3 Gyr in the canonical case, i.e. a 2 Gyr reduction in origination times. The changes in the origination times for the major groups for temperature differentials of |${\pm} 10 \, {\rm K}$| can be seen in Fig. 4. The earlier origination times for all the groups with a 10 K increase in temperature are evident as discussed above. On the contrary, a similarly marginal decrease in the ocean temperature significantly delays the evolutionary rates and origination times for most of the groups. For a 10 K decrease the earliest species, Archaea, originates as late as 0.7 Gyr from OoL, compared to 0.2 Gyr for Earth, and most of the other groups originate later than 4 Gyr from OoL.
Effect of temperature on origination times of major clades given in Fig. 3 (top) and of the key unicellular phytoplankton groups (bottom). The origination time on Earth of each group is marked with a forward arrow. Red indicates increased temperature by +10 K, and blue indicates decreased temperature by −10 K.
Overall, we find that for Hycean worlds with temperatures marginally higher than ocean temperatures on Earth, all the major groups in the phylogeny will have originated within 1.19 Gyr of OoL. These shorter origination times have important consequences for the prospects for biological evolution on such planets. Given the large planetary diversity in exoplanetary systems, and most with higher temperatures than on Earth, these findings indicate that at least microbial life could have evolved significantly earlier on such exoplanets than on Earth assuming such life formed in the first place. It also follows that for temperatures even higher than those considered here, i.e. |$\Delta T \gt 10 \, {\rm K}$|, the evolutionary rates could be even faster, until the temperatures become high enough to preclude survivability; on Earth, most life is unexpected to survive for steady-state ocean temperatures above 40°C (Sunday et al. 2012), albeit extremophiles are known to survive temperatures up to 120°C (Dalmaso et al. 2015).
4.3 Effect on key phytoplankton groups
We now focus on the evolutionary potential of several key phytoplankton groups, which are known to be abundant in the Earth’s oceans and are key producers of biosignature gases in the Earth’s atmosphere (Field et al. 1998). Such species are of particular interest for Hycean worlds whereby phytoplankton in the oceans could produce molecules such as DMS that could be observable in their atmospheres. As discussed above, we consider five major groups of phytoplankton which originated throughout Earth’s history: Cyanobacteria, Gammaproterobacteria (within the group Pseudomonadota), Dinoflagellates, Coccolithophores, and Diatoms; these latter three belonging to the Eukaryotic group. Within the Bacteria domain, Cyanobacteria are the earliest group, originating at 1.5 Gyr after OoL, followed by some Gammaproteobacteria at 2.4 Gyr. Within the Archaea domain, the three Eukaryotic phytoplankton groups originate relatively late with Dinoflagellates being the first at 3.6 Gyr, then Coccolithophores at 4.02 Gyr and Diatoms at 4.10 Gyr from OoL. For each of these groups, we investigate how their evolutionary rates and origination times depend on the surface temperature.
We find that the evolutionary behaviour of the phytoplankton groups follows a similar trend to other unicellular species considered above, i.e. that origination times are shorter with increased temperature. However, the key DMS phytoplankton groups are of consistently recent origin compared to other unicellular species in the Earth’s history. For example, three of the five groups considered here, with the exception of Cyanobacteria and Gammaproteobacteria, originated relatively recently, 3.9 Gyr after OoL (Kumar et al. 2022). In particular, these later three groups are also the key DMS-producing phytoplankton in the present-day oceans (Yoch 2002; Hopkins et al. 2023). We find that an increase in the surface temperature by 10 K results in all the phytoplankton groups originating within 1.3 Gyr of OoL, as shown in Fig. 4. In this case, Cyanobacteria have an origination time of only 0.25 Gyr post-OoL. The Gammaproteobacteria follows shortly afterward at 0.38 Gyr, and then the Eukaryotic phytoplankton groups all with origination times within 1.29 Gyr post-OoL.
On the contrary, a decrease in the surface temperature results in a significantly slower evolutionary rate. With a marginal decrease in temperature by 10 K none of the key phytoplankton groups would originate before 4.3 Gyr from OoL, i.e. by the present age on Earth. On Earth, DMS production would have started with cyanobacteria at 1.5 Gyr, but it is not until 3.9 Gyr that significant DMS is produced by Coccolithophores, followed Dinoflagellates by then Diatoms at 4.10 Gyr. However, on a planet with an increased surface temperature of 10 K relative to Earth, DMS could be started to be produced with cyanobacteria at 0.25 Gyr, with the major DMS producers by 1.28 Gyr. Therefore, the potential of a Hycean biosphere to produce large, detectable, amounts of DMS is present relatively early on in the planetary history for only a modest increase (+10 K) in temperature relative to Earth.
When the temperature change analyses were rerun using the Moody et al. (2024) dates, all key clades had evolved by 1.29 Gyr post-OoL versus 1.28 Gyr post-OoL with the time tree data and the key phytoplankton clade had evolved by 1.16 Gyr post-Ool versus 1.19 Gyr post-OoL. As such, our time tree data model represented a slightly more conservative estimate of these origination times.
5 SUMMARY AND DISCUSSION
In this study, we investigated the prospects for biological evolution of unicellular life in oceanic environments of Hycean worlds at different median surface temperatures compared to Earth. We find that relatively marginal changes in ocean surface temperatures compared to Earth’s surface temperature over planetary time-scales can lead to significant changes in the evolutionary rates and origination times of important species. For example, a 10 K increase relative to Earth leads to evolutionary rates which are over twice as fast, while a decrease of 10 K halves them. Faster evolutionary rates lead to faster speciation times meaning that the time it takes for new groups of species to form reduces. This increased rate has a significant impact on the origination times of unicellular groups such that for an increase of 10 K of surface temperature, all of the major groups will have originated by 1.19 Gyr post-OoL and all the key phytoplankton groups by 1.28 Gyr. In contrast, a decrease of 10 K of median surface temperature severely limits the origination rates, such that by 4 Gyr post-OoL only Bacteria and Archaea will have evolved, but not oxygenic photosynthesis or Eukaryotes.
5.1 Implications
A central finding of our study is that a large range of evolutionary rates and origination times are possible within our model framework for unicellular life in oceanic environments for a relatively marginal range of environmental conditions. First, given the wide range of possible atmospheric conditions in Hycean worlds, an equally wide diversity in microbial life could be expected. In particular, the origination of new clades in warm Hycean worlds can happen significantly faster than on Earth. This faster origination is of particular relevance for currently known candidate Hycean worlds, all of which are expected to host ocean temperatures significantly warmer than the Earth if at all they are habitable (Madhusudhan et al. 2021). Secondly, warm Hycean worlds that are significantly younger than Earth could also provide the conditions for originating and sustaining major unicellular groups. Within our model considerations, a marginal (10 K) increase in mean surface temperature relative to Earth can lead to the origination of major unicellular groups as early as |${\sim} 1$| Gyr from OoL. Therefore, candidate Hycean worlds orbiting stars significantly younger than the Sun, such as K2-18 b at 2.4 billion years old (Guinan & Engle 2019), could also provide important targets for biosignature searches.
Our results also indicate an optimal range of ocean surface conditions that may lead to significant atmospheric biosignatures. Planets with relatively colder surface temperatures can significantly inhibit evolutionary transitions and delay the origins of important microbial groups. In particular, we find that a lower median surface temperature that is 10 K below that of Earth value could cause a delay in the origination times of key phytoplankton groups by several Gyr. This delay in turn could affect their observable biomarkers such as DMS, which is known to be produced predominantly by Eukaryotic phytoplankton in Earth’s oceans which originated relatively late compared to other microbial species. Therefore, ocean worlds that are significantly cooler than Earth may be expected to host simpler microbial life (in terms of phyto-autotrophic systems) than Earth’s oceans and so may show weaker biosignatures, unless they orbit significantly older stars than the Sun. Conversely, habitable ocean worlds with warmer surface temperatures are more likely to show stronger atmospheric biosignatures due to microbial life if present.
5.2 Limitations
We have performed a conservative study on the evolutionary rate of well-studied unicellular organisms in the Earth’s oceanic environment over the history of life on Earth, with a single species representing each broad taxonomic group. There are some caveats to our study. First, the groups themselves are evolutionarily stable even though the species within them could speciate and go extinct, and so our results are limited to the behaviour of groups, rather than individual species. Secondly, the implications for our model should not be extended to multicellular complex organisms because we parametrized our model using empirically derived data for unicellular organisms, and so the dynamics of multicellular life are not necessarily represented by our model. Thirdly, the temperature range we considered was the normal thermal tolerance for life, and while there is evidence that the MTE holds for extremophiles (McClain et al. 2012), the variation/differences/constraints of the MTE relationships are not as well studied. Therefore, caution should be exercised when extending the results to temperatures above 313 K (|$40^{\circ} {\rm C}$|). Finally, we have used temperature as the key parameter influencing the origination times for the species we consider in this work. However, other factors such as the availability of bioessential chemicals may also need to be considered in future studies.
5.3 Future work
Within the framework of this study, we find the median ocean surface temperature and mass of the organism to be key determinants of the origination time for the predominant unicellular species considered. Our choices for the temperature and physical conditions considered were motivated by those of the Earth’s oceans. Therefore, our findings may only represent nominal estimates considering that a much broader environmental diversity is expected for extraterrestrial habitable planets. Future work in this direction could explore a range of other conditions, including the effect of gravity, pressure, larger temperature variations, and other environmental factors. Similarly, future studies could also investigate the implications for more complex life, beyond the unicellular life considered in this initial study, including multicellular/animal life in similar conditions as well as simpler life in more extreme conditions, i.e. extremophiles. Finally, while our focus in this work has been exoplanetary Hycean worlds, the results may also be extended to other habitable environments. Such habitats could include oceans on habitable rocky exoplanets, subsurface oceans on icy moons in the Solar system, as well as other ocean worlds with varied atmospheric compositions.
In conclusion, while our model makes some broad assumptions, the overarching patterns that emerge show that within our framework, for unicellular organisms, changes in median surface temperatures can have large impacts on the evolutionary rates and origination times of major groups. These changes mean that with different surface temperatures, the biosphere could be relatively complex at a young age for warmer planets, or relatively simple at an old age for cooler planets. Such biospheres with varied levels of complexity can impact the detectability of life on them, such that warmer planets have the potential to show strong atmospheric biosignatures.
ACKNOWLEDGEMENTS
EGM acknowledges support from a NERC IRF (2019–2024): NE/S014756/1. NM acknowledges support from UKRI Frontier Grant: EP/X025179/1. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.
Author contributions: EGM and NM conceived and planned the project. EGM performed the numerical calculations. EGM and NM discussed and synthesized the results and wrote the manuscript.
DATA AVAILABILITY
This is a theoretical work and no new data were generated as a result.
REFERENCES
APPENDIX A: MODEL ASSUMPTIONS
Robustly modelling the evolutionary history of life on a planet is a complex problem, and that is not fully understood on Earth. In order to understand the nature of life that may exist on other planets, we would need to fully understand the nature of both the origins of life and biological evolution over planetary time-scales. Yet, these are still very active areas of research, and fundamental questions, such as the extent to which evolution is deterministic, remain unanswered on Earth. As such, our approach involves working with neutral empirical models which capture macroevolutionary patterns well on Earth while minimizing assumptions and parametrization (e.g. Mitchell et al. 2019; Budd & Mann 2020). Therefore, we consider the simplest set of assumptions to provide a baseline of what the evolution of unicellular life on Hycean planets could look like. We consider only temperature as a free parameter and only the key unicellular groups that are well known from the evolutionary history of Earth.
The assumptions we need to make in order to make our theoretical predictions can be grouped into four categories: (1) assumption that life has originated; (2) conceptual assumptions about how evolution works; (3) input parameters for the MTE equations; and (4) differences that could occur on different planets.
First, because the conditions for life to have originated on Earth are very much debated (Yčas 1955; Rich 1962; Sasselov, Grotzinger & Sutherland 2020), we have made the assumption that it can and has started within our model. We also assume that once life has started, the environmental conditions are such that life can be maintained over the planetary time-scales. The biosphere today is a complex set of interactions and feedbacks such that perturbations to the biosphere are adjusted, helping to maintain long-term stability. Prior to the evolution of complex, multicellular life, i.e. animals, on Earth 600 Myr ago, such large-scale feedbacks were likely more limited, yet the biosphere was still stable. Life was maintained for billions of years before animals developed the capacity to adapt and change the environment for their own benefit. As such, assuming a stable biosphere for unicellular life, such as the one we have had on Earth, is a reasonable assumption.
Secondly, the assumptions with the most uncertainty are those that we need to make about how biological evolution works. It is currently unknown the extent to which, once life has started, the Earth’s patterns of evolution are deterministic or subject to some probabilistic pattern. There could also be certain bottlenecks that require a specific set of conditions in order for the next major evolutionary transitions to occur. Our model assumes the independence of different groups (i.e. no biotic or abiotic interactions). However, we know that key events such as the evolution of oxygenic photosynthesis led to diversification in bacteria (Davin et al. 2023) likely through abiotic selection pressures and/or the opening of niches and through biotic interactions. On the other hand, the |${\sim} 1.2$| billion years between the rise of oxygen and the origins of Eukaryotes (Olejarz et al. 2021) suggests that it is unlikely that oxygen directly drove the evolution of complex (i.e. Eukaryotic) life. Because oxygen is unlikely to be readily available in the |${\rm H}_2$|-rich atmospheres of Hycean worlds, it is unclear whether bacterial life would follow a similar evolutionary trajectory as on Earth but with different selection pressures or a different, possibly less diverse, trajectory altogether. Other key events also likely contributed to diversification, such as the origin of metazoan zooplankton resulting in predation pressure and leading to phytoplankton diversification (Butterfield 1997). If one of these key major evolutionary transitions did not happen, it is not clear what the impact is on the other groups. These are all major questions in evolutionary biology, and so to minimize assumptions of what key drivers are, and the likelihood that major evolutionary transitions occur, we take the simplest neutral model for this study, namely we only consider unicellular life and that evolution will proceed similarly to Earth's as a starting point for such exo-evolutionary studies.
Thirdly, we have to parametrize our MTE equations, which we know have variations within different taxonomic groups. We have limited the impact of such parametrization by focusing on unicellular organisms only, and discussing relative evolutionary rates, such that within a taxonomic group that has the same parameter set (e.g. within unicellular organisms), the absolute value will not change the results. This approach means that inferences for multicellular life should not be made based on our models. Our analyses also rely on observed (and calculated) values of the Earth's temperature, the origination times of groups, the body sizes of the model organisms for each group, and the topography for the phylogeny used.
Origination times for different groups vary depending on the methodology used, which is why we used a model averaging approach (Kumar et al. 2022) which enabled us to cover many different groups within the same approach. We also performed some sensitivity analyses using a more recent phylogeny (Moody et al. 2024), to assess how changing origination times impacted results. Broadly speaking the more recent the origination time, the smaller the confidence interval (e.g. Moody et al. 2024), while the earliest originating groups tend to have much larger confidence intervals, i.e. are not as precisely known. This pattern works in our favour because the longer a group takes to evolve, the greater the impact of a change of median temperature, but the smaller the origination time uncertainty, so that the groups with the largest uncertainty, i.e. the oldest ones will only have smaller changes to their origination times with different temperatures.
The topography of phylogenies can be highly variable with different methods and data (e.g. Williams et al. 2020; Moody et al. 2024), so we have worked with broad taxonomic groups which provide robustness to the variations in phylogeny topology that occur at a finer taxonomic scale. Sensitivity analyses on having three versus two domains showed only limited impact on the origination times of the groups, e.g. Eukaryotes changed origination time by 0.01 Gyr.
Organism body sizes vary, but because the metabolic rate scales with mass as |$\mathit{ M}^{-(1/4) }$| the impact of small uncertainties on our model is limited. However, because of the sensitivity of our model to temperature, the biggest source of practical (rather than conceptual) uncertainty comes from the resolution of the median Earth temperature. We used the median values from Krissansen-Totton et al. (2018), with their 95 per cent confidence intervals of |${\pm} 20$| K at 4 billion years ago but decreasing through time to a few degrees uncertainty for the last 500 Myr. Considering the full range of uncertainties at the beginning may have a significant impact on the results, which currently consider a maximum variation of |${\pm} 15$| K relative to Earth at any given time. However, using values at the limits of this confidence interval would also involve modelling outside the normal thermal tolerance of life, so would introduce more assumptions and uncertainty. As such, using the median surface temperature is a conservative approach.
Finally, we have assumed that the production of energy by unicellular life on Hycean worlds would operate similarly to life on Earth, namely carbon-based, nucleotide-based systems. Our model assumed such Earth-like life as the most conservative since other forms of life, such as silicon-based life, while possible are more challenging to occur than carbon-based life (Petkowski, Bains & Seager 2020). Yet different planets will have different gravities, different stellar flux, and potentially different types of dominant photosynthesis. Predicting how different gravity may change evolutionary rates and origination times is complex because the best proxy we have for gravity is the high pressures that we get in the deep sea. While deep-sea organisms can exhibit higher speciation rates (e.g. Martinez et al. 2021), these appear primarily driven by biotic not abiotic factors because the internal pressure of organisms is not dramatically reduced (1–2 per cent for 4 km deep). Therefore, the impact of increased pressure is likely much smaller than the biotic factors that likely drive the increased evolutionary rates, so is a more complex dynamics. Calculations of how different stellar spectra change input power have demonstrated that predicted variation is within an order of magnitude for cool stars (Duffy et al. 2023), suggesting limited influence compared to the impact of temperature, as considered in this work.
