Metabolic trait diversity shapes marine biogeography

Abstract

Climate and physiology shape biogeography, yet the range limits of species can rarely be ascribed to the quantitative traits of organisms^1,2,3. Here we evaluate whether the geographical range boundaries of species coincide with ecophysiological limits to acquisition of aerobic energy⁴ for a global cross-section of the biodiversity of marine animals. We observe a tight correlation between the metabolic rate and the efficacy of oxygen supply, and between the temperature sensitivities of these traits, which suggests that marine animals are under strong selection for the tolerance of low O₂ (hypoxia)⁵. The breadth of the resulting physiological tolerances of marine animals predicts a variety of geographical niches—from the tropics to high latitudes and from shallow to deep water—which better align with species distributions than do models based on either temperature or oxygen alone. For all studied species, thermal and hypoxic limits are substantially reduced by the energetic demands of ecological activity, a trait that varies similarly among marine and terrestrial taxa. Active temperature-dependent hypoxia thus links the biogeography of diverse marine species to fundamental energetic requirements that are shared across the animal kingdom.

Main

The provisioning of energy to organisms in their natural environment is a key determinant of fitness. The energetic demands of ectothermic organisms increase with temperature and activity, and must be met by an adequate supply of oxygen (O₂) and food. At a minimum, physiological survival requires that the supply of energy matches the maintenance costs of an organism in a resting state; these energy demands vary by body size, temperature and species^6,7. Additional energetic costs are incurred by the growth and activity required for ecological survival, which depend on lifestyle and ecological niche and typically increase energy expenditure several-fold above resting rates^8,9.

Energy provision can be limited by O₂ if its availability falls short of the metabolic demands of the organism, inducing a hypoxic condition^10,11,12. This is more common in aquatic environments due to the slower diffusion of O₂ in water than in air¹³. The effects of an acute reduction in O₂ on population fitness can induce considerable die-offs^14,15; however, the presence of metabolic barriers in habitats under stable conditions are difficult to observe. Recent analyses suggest that the current latitude and depth limits of several marine ectothermic species coincide with an O₂ pressure that is just adequate to fuel the energy demand for physiological maintenance and sustained ecological activity^4,16,17. Here we evaluate the metabolic causes and biogeographical consequences of the constraints to aerobic energy by combining a mathematical model of temperature-dependent hypoxia with laboratory and field data from the broadest-available diversity of marine animal species.

Temperature-dependent O₂ tolerance

The aerobic energy balance of an organism can be represented by a Metabolic Index⁴ (Φ), which is defined as the ratio of O₂ supply to resting demand (Fig. 1a and Methods):

$$\Phi =\frac{{\alpha }_{{\rm{S}}}}{{\alpha }_{{\rm{D}}}}{B}^{\varepsilon }{p}_{{{\rm{O}}}_{2}}\exp \,\left\{\frac{{E}_{{\rm{o}}}}{{k}_{{\rm{B}}}}\left[\frac{1}{T}-\frac{1}{{T}_{{\rm{ref}}}}\right]\right\}$$

(1)

where α_D is the resting metabolic rate per unit body mass (B) at a reference temperature (T_ref), and α_S is the efficacy of O₂ supply per unit body mass and the O₂ pressure $({p}_{{{\rm{O}}}_{2}})$ of the ambient medium (units are described in Fig. 1 and the Methods). The ratio of α_D/α_S defines a first key physiological trait of an organism: its resting vulnerability to hypoxia at the reference temperature, V_h = α_D/α_S, which is measurable as the lowest O₂ pressure (P_crit) that can sustain resting metabolic demand (Φ = 1) (Fig. 1a). The inverse of hypoxia vulnerability is hypoxia tolerance, which is denoted A_o = 1/V_h, as defined previously⁴. A second key trait, E_o, is the sensitivity of hypoxia vulnerability to temperature (T), which is described by the exponential Arrhenius function (Fig. 1a) (Boltzmann constant, k_B) and is equal to the difference between the temperature variation in the metaboli4c rate (E_d) and the O₂ supply (E_s), such that E_o = E_d − E_s (Methods). The exponent ε is the allometric scaling of the supply-to-demand ratio, which is typically near zero¹⁸.

Fig. 1: Relationships among species traits that govern the temperature-dependent vulnerability to hypoxia of marine animals.

a, Curves of constant  Metabolic Index (Φ) trace the ${p}_{{{\rm{O}}}_{2}}$ required to satisfy the O₂ demand of species for resting (blue) or active (red) metabolic rates. b–e, The resting curve of each species is defined by a hypoxia vulnerability (V_h) and its temperature sensitivity (E_o), each of which reflect separate traits for O₂ supply and demand (b, d) and their covariation (c, e). Active curves, which are increased from the resting curve by sustained activity (SMS), require a correspondingly higher Φ (Φ_crit) (Fig. 4). The intersection of Φ curves with atmospheric ${p}_{{{\rm{O}}}_{2}}$ define the upper thermal limits of aerobic metabolism (AT_max) (Fig. 5). b, c, Hypoxia vulnerability (V_h; atm) and O₂ demand at rest (b; α_D; μmol O₂ h⁻¹ g^−3/4, log₁₀ scale) vary widely among species but are uncorrelated because the metabolic rate and the efficacy of the O₂ supply (c; α_S; μmol O₂ h⁻¹ g^−3/4 atm⁻¹) are strongly correlated (Extended Data Table 1). d, The temperature dependence of the hypoxia vulnerability (E_o; eV) is shifted to lower values than that of resting metabolic rate (E_d; eV) because the O₂ supply accelerates with temperature (that is, E_s = E_d − E_o > 0), partially compensating the thermal rise in metabolic demand. e, The relationship between E_o and E_d (dotted line; slope < 1) (Extended Data Table 1) suggests that species with a stronger metabolic response to temperature also exhibit stronger compensatory O₂ supply mechanisms (Extended Data Fig. 2b). Values of E_s are within the range predicted for diffusion (yellow shading) and empirically estimated from rates of the ventilation and circulation of animals in cool waters (blue shading; 0.55 ± 0.15 eV (mean ± s.d.) and warm waters (red shading; 0.04 ± 0.18 eV (mean ± s.d.)) (Extended Data Fig. 3). c, e, Data (points and error bars, or centred dot, if the error bars are shorter than marker) are mean ± s.e.m. for species with n > 2 temperature values. See Supplementary Table 1 for the number of independent experiments for each species, and Extended Data Table 1 for statistics on the two-sided t-tests of the trait correlations.

A third component of the energetic balance of an organism is the O₂ needed to fuel growth and essential ecological activities. In terrestrial animals, sustained metabolic rates range from 1.5 to 7 times those at rest, a ratio termed the sustained metabolic scope (SMS)^8,9. For aquatic aerobic organisms, such levels of activity would increase the resting vulnerability to hypoxia from V_h to a higher value, V_h × SMS, which requires that the minimum Φ of a given species in its environment increases above its resting minimum (which is set to 1, see above) by the same factor, denoted Φ_crit. The ratio SMS will depend on the ecology and life history of each species. This ecological trait is not directly measured in marine species, but it can be estimated from the maximum metabolic rates, while Φ_crit can be inferred as the lowest value of Φ that bounds the geographical distribution of a species⁴. If values of Φ_crit match those of SMS, this strongly indicates that there is an energetic limit on marine species habitats.

To characterize the variation in these traits across diverse marine animal species, we analysed published physiological rates and thresholds (Methods), and the global geographical distributions of the species (OBIS; https://obis.org/). The dataset of 199 species includes 145 species with temperature-dependent metabolic rates and associated parameters (E_d and α_D; hereafter called ‘metabolic traits’) (Extended Data Fig. 1a) and 72 species with temperature-dependent hypoxia thresholds and corresponding parameters (E_o and V_h; hereafter called ‘hypoxic traits’) (Extended Data Fig. 1b and Supplementary Table 1). The species span more than eight orders of magnitude in body size, inhabit all ocean basins and biomes (Extended Data Fig. 1c), belong to five phyla (Annelida, Arthropoda, Chordata, Cnidaria and Mollusca) and broadly but incompletely sample the metabolic, geographical and taxonomic diversity of the ocean.

Physiological trait diversity

Resting metabolic rates normalized by temperature and body mass vary by orders of magnitude among all 145 species (Fig. 1b), but remain within the range found across the tree of life¹⁹. The critical O₂ pressures also show a well-defined distribution of resting hypoxia vulnerability across species (Fig. 1b). Although metabolic rates are a direct driver of hypoxia vulnerability, the two traits are uncorrelated across species, and α_D exhibits greater interspecies variation than does V_h. These observations suggest that animals with a high metabolism also have a high efficacy of O₂ delivery. Indeed, the absolute metabolic rates and coefficients of O₂ supply are highly correlated among species (Fig. 1c and Extended Data Table 1), which indicates that there is a strong selective pressure for tolerance to low O₂ , even for species that live outside relatively small ocean regions commonly termed hypoxic zones²⁰.

The temperature sensitivity of metabolic rates within species exhibits substantial variation across species (Fig. 1d). The mean value, standard deviation and range of E_d (0.69 ± 0.36 eV, 0.1–2.0 eV) are similar to the thermal acceleration of the metabolic rates of organisms that are observed across the tree of life²¹. The temperature sensitivity of hypoxia vulnerability also varies widely across species (Fig. 1d), but E_o has a smaller mean, standard deviation and range (0.4 ± 0.28, −0.2–1.3 eV) that includes negative values. The differences in E_o relative to E_d reflect the effect of temperature on O₂ supply (E_S), the positive mean value (0.29 ± 0.23 eV) of which suggests that the supply of O₂ also accelerates with temperature²². The temperature effect on the supply of O₂ therefore counteracts, and for species with E_o < 0, even exceeds the thermal increase in metabolic rates.

To confirm the role of the O₂ supply in moderating the temperature sensitivity of the vulnerability to hypoxia, we estimated the thermal response of three processes that transport O₂ from ambient fluid to body tissue: the ventilation of water past the organism, the diffusion of O₂ through the boundary layer at the water–body interface and the internal transport of O₂ by animals that have circulatory systems. Diffusive O₂ fluxes increase with temperature in proportion to gas diffusivity (κ) and increase inversely to the decrease in kinematic viscosity (υ). The ratio of gas diffusivity to kinematic viscosity—the Schmidt number (Sc = υ/κ)—predicts a diffusive O₂ flux²³ for which the temperature dependence, E_s, lies between 0.21 and 0.42 eV (Extended Data Fig. 3a). This range encompasses the mean value of E_s that was inferred from all species for which E_o and E_d can both be estimated (Fig. 1e), but cannot account for its full interspecies range.

The ventilation of O₂ to and circulation in the body may also modify the temperature sensitivity of hypoxia tolerance^24,25,26,27 (Extended Data Fig. 3b). Both ventilation and circulation rates increase with temperature in cooler waters (E_s = 0.55 ± 0.15 eV (mean ± s.d.)) (Fig. 1e and Extended Data Fig. 3c), but the response decreases or even reverses in warmer conditions (E_s = 0.04 ± 0.18 eV (mean ± s.d.)) (Fig. 1e and Extended Data Fig. 3c). These thermal responses of the O₂ supply combined with those of metabolic demand (E_d) can account for nearly the entire range of the temperature-dependence of hypoxia vulnerability (E_o). Moreover, the stronger thermal response of the ventilation and circulation rates in cool compared with warm waters is consistent with the weaker temperature sensitivity of species vulnerability to hypoxia (lower E_o) that is observed under cold relative to warm conditions (Extended Data Fig. 3d). Thus, both biological and physical responses of the O₂ supply to temperature reduce the temperature sensitivity of hypoxia vulnerability, relative to that of the metabolic demand alone. The compensation of faster metabolic rates at higher temperatures by a more rapid O₂ supply indicates that there is a strong selective pressure for oxygen supply to meet demand across the range of inhabited temperatures.

Linking physiology to biogeography

The variation in temperature-dependent hypoxia traits suggests that species experience distinct geographical patterns of hypoxia risk (Fig. 2). In the upper ocean, both temperature and ${p}_{{{\rm{O}}}_{2}}$ decrease with depth, but often have opposing gradients with latitude; temperature decreases as subsurface ${p}_{{{\rm{O}}}_{2}}$ increases away from the Equator. The resulting spatial variation in Φ depends on the strength of these gradients, and on the temperature sensitivity parameter, E_o. For species with strongly positive values of E_o, Φ decreases towards the warm low-O₂ waters of the shallow tropics (Fig. 2a). However, positive E_o also weakens any vertical decrease in Φ, because the decline in ambient O₂ is compensated by a slower metabolic rate, which extends the potential habitat of species into deeper waters. By contrast, for species with E_o < 0, the highest Φ is found in tropical waters, but declines rapidly with depth below the surface due to both lower O₂ levels and cooler temperatures (Fig. 2c). The diversity in temperature-dependent hypoxia traits suggests that species that are limited by low Φ conditions may occupy distinct ocean habitats with global coverage, from shallow tropical waters to high-latitude and deep water, with a continuum of patterns in between (Fig. 2b).

Fig. 2: Spatial distributions of the Metabolic Index and species with distinct temperature sensitivities.

a, Northern shrimp (Pandalus borealis) from the north Atlantic, Pacific and Arctic Oceans. b, Small-spotted catshark (Scyliorhinus canicula) from the eastern Atlantic Ocean and Mediterranean Sea. c, Sea squirt (S. plicata), a cosmopolitan tunicate. The Metabolic Index is computed from monthly climatological measurements using the traits of each species, and averaged annually and over its longitudinal range in OBIS (http://iobis.org) for mapping (northern shrimp, 180°–45° E; catshark, 20° W–15° E; sea squirt, all longitudes). The species have similar hypoxia vulnerability (V_h, around 0.10–0.16 atm), but their temperature sensitivities (E_o) vary widely (northern shrimp, E_o ≈ 0.9; catshark, E_o ≈ 0.2; sea squirt, E_o ≈ −0.2) yielding different Φ gradients across latitude and depth. A single lower limit of Φ bounding each species range is contoured (Φ_crit; black lines), along with climatological isotherms (grey lines, in °C) and observed species occurrences (blue dots) (Methods).

To test whether the range of the predicted geographical habitat niches corresponds to the actual distributions of marine species, we extracted global occurrence data¹⁴ for all species in the physiological database. For the 72 species with Metabolic Index parameters (E_o, V_h), distribution data were available for most species (n = 68), and the sampling resolution of many species was sufficient to reveal clear range boundaries in depth and latitude (Fig. 2 and Extended Data Figs. 4, 5). These data include three species that have similar V_h but span the full range of E_o, from strongly positive (E_o = 0.9, northern shrimp) to slightly negative (E_o = −0.2, sea squirt) and an intermediate value (E_o = 0.2, small-spotted catshark), which predict the distinct aerobic habitat distributions of these species (Fig. 2). In all three species, range boundaries in latitude and in depth are closely aligned with a single value of Φ above which the populations are widely distributed and below which reported occurrences are rare and isolated. Geographical range boundaries across a range of depths, latitudes and longitudes also coincided with single isopleths of Φ in other well-mapped species (Extended Data Fig. 4), including species that span multiple ocean basins or different sides of the same basin (Extended Data Fig. 5).

The boundaries of the geographical ranges of species are more strongly aligned with the Metabolic Index than with either temperature or ${p}_{{{\rm{O}}}_{2}}$ alone (Fig. 2 and Extended Data Figs. 4–7). This can be observed geographically: in vertical cross-sections, range boundaries follow a constant Φ value, but tend to cross multiple isotherms (Fig. 2 and Extended Data Figs. 4, 6). In mid-latitude species, range boundaries lean equatorward at shallower depths, opposite to the poleward tilt of isotherms (Fig. 2a, b and Extended Data Fig. 4a–e). At the surface, range limits can be reached as Φ declines towards the Equator, even without a gradient in ${p}_{{{\rm{O}}}_{2}}$ (Extended Data Figs. 4a–e, 6a, c).

The alignment of range boundaries with Φ is most easily observed, however, by projecting the biogeography of species onto the temperature and ${p}_{{{\rm{O}}}_{2}}$ state–space that they inhabit (Fig. 3). Across species from distinct phyla and multiple ocean basins, including those with sparse spatial sampling, the state-space habitat map reveals strong correlations between the temperatures and ${p}_{{{\rm{O}}}_{2}}$ levels that bound the occurrences of species. These relationships are consistent with the expectations based on the Metabolic Index of each species, with opposite slopes for species with positive and negative E_o values, but are incongruent with habitat limitation by either a single temperature or ${p}_{{{\rm{O}}}_{2}}$ level. The predictive ability of Φ to discriminate between inhabited and uninhabited ocean regions is better than that of temperature for 92% of species, better than ${p}_{{{\rm{O}}}_{2}}$ for 67% of species, and better than both temperature and ${p}_{{{\rm{O}}}_{2}}$ for 62% of species (Methods and Extended Data Fig. 7).

Fig. 3: Temperature and ${{\boldsymbol{p}}}_{{{\bf{O}}}_{{\bf{2}}}}$ state-space habitat for three marine species from different phyla, ocean basins and latitude ranges.

a, Summer flounder (Paralichthys dentatus), a fish from the subtropical eastern Atlantic Ocean. b, Nautilus (Nautilus pompilius), a mollusc from the tropical Indo-Pacific Ocean. c, Sea squirt (S. plicata), a cosmopolitan tunicate. The frequency of reported occurrences of each species (log₁₀-transformed values) at each temperature (°C) and ${p}_{{{\rm{O}}}_{2}}$ level (atm) is coloured. Water conditions with no reported occurrences of the species are white, and localities with no modern ocean volume are shaded grey. Measured critical ${p}_{{{\rm{O}}}_{2}}$ levels (P_crit; black dots) indicate the measured threshold for maintaining the resting metabolic rate in laboratory experiments (Supplementary Table 1) and are fitted to the Metabolic Index (equation (1) when Φ = 1 (bottom dashed lines). The boundaries of inhabited ocean conditions follow a Metabolic Index curve, which is elevated above the P_crit curve by a factor Φ_crit (top dashed lines) that represents the ratio of the active-to-resting metabolic rate. Contrary to observations, a species for which the range is limited by temperature or ${p}_{{{\rm{O}}}_{2}}$ alone would have a state-space occupancy delineated by a vertical or horizontal line, respectively.

That the species habitat boundaries coincide with a lower Φ value suggests that an aerobic barrier limits the geographical ranges of marine animals (Figs. 2, 3). We determined the range-bounding value, Φ_crit, for all of the species with hypoxia traits and georeferenced location data, using two independent methods that yield convergent results (Methods and Extended Data Fig. 8a, b). The average of Φ_crit is approximately 3.3 (interdecile range, 1.3–6.5) (Fig. 4). For all species, waters with lower Φ values exist within their inhabited depth range, but lack confirmed sightings (Extended Data Fig. 8c).

Fig. 4: Diversity of the ecological trait governing energetic habitat barriers.

a, Histograms of the lowest values of Φ in the habitat of a species—that is, Φ_crit (bars, light grey for species with fewer than 10 occurrences)—and SMS estimated from measurements of maximum-to-resting metabolic rate ratios⁴¹ (line; see Methods). b, Histogram of SMS for terrestrial species determined in field studies^8,9. The interspecies distributions of Φ_crit are indistinguishable from those of marine and terrestrial SMS (Extended Data Table 1), suggesting that Φ is the operative limit that most frequently acts on the warm temperature and low O₂ edge of the geographical range of marine species (but see Fig. 3c).

If Φ_crit is the operative habitat barrier for marine species, its values should correspond to their sustained metabolic rates relative to rest. Long-term energetic demand is not directly measured for marine organisms, but short-term experimental estimates of maximum-to-resting rate ratios (MMR/RMR) provide an empirical upper bound on SMS (Methods). We find a strong correlation between biogeographically inferred Φ_crit and laboratory measured MMR/RMR values (Extended Data Fig. 9 and Extended Data Table 1), which suggests that SMS lies approximately midway between the resting and maximum rates (that is, SMS = w_R + (1 − w_R)(MMR/RMR); (see Methods, equation 7); w_R = 0.4 ± 0.17 (mean ± s.d.), n = 14) (Extended Data Fig. 9), consistent with independent estimates of SMS from carbon isotopes in the otoliths of Atlantic cod²⁸. Applied to the broadest compilation of MMR/RMR ratios, this scaling yields an interspecies distribution of SMS (n = 106) (Fig. 4a) that is statistically indistinguishable from that of Φ_crit (Fig. 4a, Extended Data Table 1). The Φ_crit values of the few sessile species that we analysed (Styela plicata, Lophelia pertusa and Crassostrea gigas) were among the lowest (Fig. 3c and Supplementary Table 1), which is consistent with their less-active lifestyles. Together, these observations provide strong evidence that Φ_crit corresponds to SMS, and thus represents an energetic barrier to the geographical ranges of species.

The interpretation of Φ_crit as the ratio of sustained active-to-resting metabolic rates can be further evaluated by comparing its frequency distribution across marine species to the SMS data that were directly and independently measured for terrestrial taxa^4,8, including mammals, birds and reptiles (Fig. 4b). The available data reveal no significant differences between the distribution of marine Φ_crit and marine and terrestrial SMS distributions (Fig. 4, Extended Data Table 1), which supports the suggestion that Φ_crit is an operative limit on the geographical ranges of marine species. These results also suggest that the ratios of active-to-resting metabolic rates are a fundamental trait that represents ecological and life-history variation across the animal kingdom.

The SMS of marine taxa has important implications for empirical metrics of thermal tolerance that are widely used to infer the climate sensitivity of marine species. By elevating O₂ demand, ecological and life-history activity increases the vulnerability to hypoxia from a resting threshold (V_h), to an active one, V_h × Φ_crit, that is a key operative constraint on marine geographical ranges. Similarly, because hypoxia tolerance decreases with temperature for most species, ecological activity also reduces the maximum temperature at which aerobic metabolism can be sustained. Maximum temperatures for aerobic metabolism can be derived from the Metabolic Index (Fig. 1a) as the temperature at which P_crit reaches the atmospheric O₂ pressure (P_atm) applied in experimental determinations of thermal tolerance²⁹ (Methods). The distribution of this aerobic thermal limit, denoted AT_max, evaluated in a resting state (Φ = 1, ${{\rm{AT}}}_{{\rm{\max }}}^{{\rm{rest}}}$) is highly variable among species (Fig. 5a), owing to the diversity of hypoxia traits (E_o and V_h). For all species, ${{\rm{AT}}}_{{\rm{\max }}}^{{\rm{rest}}}$ is considerably higher than the temperatures that are encountered by the organisms in their natural habitats^30,31, and for most species it is higher than temperatures found in the ocean (Fig. 5a). Similar findings have been reported based on observed critical thermal maxima, termed CT_max, measured by the loss of physiological performance in a resting state³². Indeed, the frequency distributions of ${{\rm{AT}}}_{{\rm{\max }}}^{{\rm{rest}}}$ and CT_max are remarkably similar (Fig. 5a and Extended Data Fig. 4a–d). In four of the seven species for which both thermal tolerance metrics are known, ${{\rm{AT}}}_{{\rm{\max }}}^{{\rm{rest}}}$ occurs at a temperature at or below CT_max (Extended Data Fig. 10). This correspondence may reflect an aerobic basis for thermal tolerance²⁹, although the link remains controversial^{25,26,27,28,29,30,31,32,33,34,35,36}. Whatever the underlying physiological basis for this similarity, both measures suggest that although there is a large ‘thermal safety margin’ in the face of climate warming^37,38, these are derived from, and applicable to, only a state of rest.

Fig. 5: Thermal tolerance of species measured in laboratory studies (CT_max) and predicted from the Metabolic Index (AT_max).

a, Histograms of the aerobic thermal maxima at rest (${{\rm{AT}}}_{{\rm{\max }}}^{{\rm{rest}}}$; coloured bars) of species derived from measured hypoxia traits and critical thermal maxima (CT_max; green line), which were derived from loss of physiological function experiments. Grey lines depict the relative frequency of global upper ocean temperatures (solid, monthly depth-resolved upper 150 m; dotted, satellite-based daytime Sea Surface Temperature  (Methods), scaled to the peak number of species for visualization. b, Active AT_max based on the hypoxia traits and Φ_crit of all species. Activity levels reduce thermal tolerance from values well above ocean temperatures (grey lines) for species at rest (a) to temperatures that limit species ranges (b). AT_max is the maximum aerobic temperature permitting atmospheric ${p}_{{{\rm{O}}}_{2}}$ to meet resting or active metabolic O₂ demands, computed (see Methods) by solving for T in equation (1), with ${p}_{{{\rm{O}}}_{2}}={P}_{{\rm{atm}}}$ and Φ = 1 (for resting ${{\rm{AT}}}_{{\rm{\max }}}^{{\rm{rest}}}$) or Φ = Φ_crit (for active AT_max).

Under the ecologically relevant energetic demand (Φ = Φ_crit), the active aerobic thermal maximum, ${{\rm{AT}}}_{{\rm{\max }}}^{{\rm{act}}}$, falls well below ${{\rm{AT}}}_{{\rm{\max }}}^{{\rm{rest}}}$ (Fig. 5b). Indeed, calculated values of ${{\rm{AT}}}_{{\rm{\max }}}^{{\rm{act}}}$ closely correspond to the maximum occupied environmental temperatures of individual species (Extended Data Fig. 10). Across species, the distribution of ${{\rm{AT}}}_{{\rm{\max }}}^{{\rm{act}}}$ tracks the global volumetric frequency of ocean temperatures. Thus, species with substantial apparent thermal safety margins at rest are in fact likely to be at the limit of their active thermal tolerance in the ocean³⁹ and will experience habitat compression even at modest levels of warming and without any depletion of O₂.

Implications

The energetic balance of organisms is a powerful framework for explaining biogeographical patterns from temperature-dependent hypoxic tolerances and constituent metabolic rates that have been well studied for decades^4,5,6. Geographical range limits imposed by aerobic energy constraints apply to a greater diversity of ocean species, physiologies and habitats than previously investigated^4,16, from tropical to high-latitude waters and from shallow to deep ocean niches. Our results thus extend and strengthen the hypothesis that temperature-dependent hypoxia has a major role in biogeography, by mediating how ocean temperature and O₂ are experienced by organisms with diverse environmental tolerances and geographical niches. The global applicability of such constraints support their use to predict patterns of extinction caused by climate change in the geological record⁴⁰ and in the future.

Sustained activity levels and the metabolic traits—the resting metabolic rate and its temperature sensitivity—that underlie aerobic energy barriers are not substantially different from the values observed in terrestrial biota. However, the hypoxia traits that shape those energetic barriers—resting hypoxia vulnerability and its temperature sensitivity—cannot be derived from metabolic traits alone because of the strong compensation by O₂ supply mechanisms. Species with fast metabolisms exhibit rapid O₂ supply rates (Fig. 1c and Extended Data Fig. 2), while those with high metabolic temperature sensitivities show strong thermal responses of O₂ extraction (Fig. 1e and Extended Data Fig. 2). The constituent traits of active hypoxia vulnerability are also correlated: species with a lower resting hypoxia vulnerability have a higher active to resting metabolic rate ratio (Extended Data Fig. 2). These correlations act to narrow the interspecies ranges of all three key traits (Extended Data Fig. 2) and suggest that there are strong physiological trade-offs and selective pressures, the nature and causality of which remain unresolved. Whatever their mechanistic origins, these trade-offs and constraints have resulted in a breadth of temperature-dependent hypoxia tolerance and associated spatial habitat limits that allow species to collectively exploit the full range of aerobic conditions found in the modern ocean.

The data needed to calibrate the Metabolic Index and diagnose the relative role of O₂ supply and demand can be derived from standard respirometry data, but currently the number of sampled species comprises only a small fraction of the total marine biodiversity. They include few species without circulatory systems; species without a clear P_crit (‘oxyconformers’); or species pairs with well-characterized predator–prey or other ecological relationships that may modulate the physiological response to climate change. A systematic and concerted effort to expand data on Metabolic Index parameters across a wider variety of marine biota, especially those with rich biogeographical data, and populations that may adapt hypoxia traits over regional scales or between generations, will be key to further evaluating the role of temperature-dependent hypoxia in shaping marine biogeography, ecological interactions and habitat loss in a warming climate.

Methods

Derivation of the  Metabolic Index

The Metabolic Index is defined as per a previous study⁴ as the ratio of the rates of the O₂ supply to and demand by an organism. In general, both rates are dependent on temperature (T) and body mass (B). Following standard metabolic scaling, the O₂ demand can be written:

$$D={\alpha }_{{\rm{D}}}{B}^{\delta }\exp \,\left\{\frac{-{E}_{{\rm{d}}}}{{k}_{{\rm{B}}}}\left(\frac{1}{T}-\frac{1}{{T}_{{\rm{ref}}}}\right)\right\},$$

(2)

where the rate coefficient (α_D) has units of O₂ per unit body mass per time (we use μmol O₂ g^−3/4 h⁻¹). It is scaled by the exponential Arrhenius function of absolute temperature, which captures the temperature dependence often described by a Q10 factor⁴². When estimating parameters, the body mass is normalized to the median experimental body mass so that it is non-dimensional. Thus, when T = T_ref, an organism of median body mass has a resting metabolic rate of D = α_D.

The supply of O₂ to the body may also scale with body size, temperature and ambient O₂ pressure $({p}_{{{\rm{O}}}_{2}})$, such that:

$$S={\hat{\alpha }}_{{\rm{S}}}(T){B}^{\sigma }{p}_{{{\rm{O}}}_{2}}$$

(3)

The function ${\hat{\alpha }}_{{\rm{s}}}(T)$ represents the efficacy of the O₂ supply. It is a rate coefficient (in μmol O₂ g^−3/4 h⁻¹atm⁻¹), but becomes an absolute mass-normalized rate (μmol O₂ g^−3/4 h⁻¹) only when multiplied by the ambient O₂ pressure (we use units of atm). The exponent, σ, for the allometric scaling of the O₂ supply with body mass is typically very similar to that of O₂ demand¹⁸, although the two may differ.

The temperature dependence of ${\hat{\alpha }}_{{\rm{s}}}(T)$ may be complicated, as it reflects the combined effect of multiple steps in the O₂ supply chain, including ventilation and circulation rates that are under biological control, as well as diffusive O₂ flux across the water–body boundary. Because diffusive gas fluxes are governed by physical and chemical kinetics, their temperature dependence follows the known scaling of gas exchange across a diffusive boundary layer⁴³. Standard gas exchange models are well approximated by an Arrhenius function (Extended Data Fig. 3a):

$${\hat{\alpha }}_{{\rm{S}}}(T)={\alpha }_{{\rm{S}}}\exp \,\left\{\frac{-{E}_{{\rm{s}}}}{{k}_{{\rm{B}}}}\left(\frac{1}{T}-\frac{1}{{T}_{{\rm{ref}}}}\right)\right\}$$

(4)

where the scalar coefficient α_S has the same units as the function ${\hat{\alpha }}_{{\rm{s}}}(T)$, but is a constant that does not depend on temperature. The same equation can be applied to ventilation rates and circulation rates, although in contrast to diffusion, for biological rates a single E_s value will not necessarily apply over the entire temperature range of a species (Extended Data Fig. 3b). Even so, equation (4) provides a flexible formula for biological fluxes that vary nonlinearly with temperature over a finite temperature range.

Inserting equations (2)–(4) into the definition of the Metabolic Index, we get:

$$\varPhi =\frac{S(B,T,{p}_{{{\rm{O}}}_{2}})}{D(B,T)}=\frac{1}{{V}_{{\rm{h}}}}{B}^{\varepsilon }{p}_{{{\rm{O}}}_{2}}\exp \,\left\{\frac{{E}_{{\rm{o}}}}{{k}_{{\rm{B}}}}\left[\frac{1}{T}-\frac{1}{{T}_{{\rm{ref}}}}\right]\right\}$$

(5)

where

$$\varepsilon =\sigma -\delta ,$$

(6a)

$${E}_{{\rm{o}}}={E}_{{\rm{d}}}-{E}_{{\rm{s}}}$$

(6b)

and

$${V}_{h}={\alpha }_{D}/{\alpha }_{s}$$

(6c)

The defining formula (equation (5)) is identical to equation (1) in the main text, and to the previously described formula given by ref. ⁴. It differs in form from that described previously⁴ because it is normalized to a reference temperature (T_ref) such that when T = T_ref (here specified at 15 °C), the coefficient (α_S/α_D = 1/V_h, which is denoted A_o in the previous study⁴) is the inverse of P_crit at that reference temperature. We have also chosen a more intuitive annotation for the allometric exponents (σ, for ‘supply’ and δ, for ‘demand’). The only substantial difference in this formulation is that the contributions of the O₂ supply and demand to the temperature sensitivity of hypoxia tolerance (that is, E_o) are made explicit, rather than being accounted for implicitly (for example, see supplementary figure 2 of the previous study⁴). This allows the net temperature dependence of the tolerance of hypoxia to be partitioned into supply and demand effects using equations (6a)–(6c).

Data compilation and parameter estimation

The physiological parameters of the Metabolic Index (Φ) are derived from laboratory measurements of hypoxic thresholds (P_crit) and resting metabolic rates (D) at multiple temperatures. The measurements are taken from published literature, adding to previous compilations^7,40,44. The original studies and parameter values are listed in Supplementary Table 1, and yield 145 species with metabolic rate parameters, and 72 species with hypoxia parameters (including four based on lethal thresholds (LC₅₀)). The species with P_crit data range over 8 orders of magnitude in body mass, from 5 phyla (Annelida, Arthropoda, Chordata, Cnidaria and Mollusca), including 31 malacostracans, 26 fishes, 9 molluscs, 2 copepods, and 1 species each for ascidians, thaliasceans, scleractinian corals and annelid worms.

Metabolic traits (δ, α_D, E_d) are derived from fitting equation (2) with mass-normalized resting metabolic rates (μmol O₂ h⁻¹g^−3/4) that have been experimentally determined at multiple temperatures. Hypoxia traits (ε, V_h and E_o) are derived by substituting paired experimental temperatures and P_crit data (atm) in equation (5) (as variables T and ${p}_{{{\rm{O}}}_{2}}$), and solving for the parameters that give Φ = 1, the condition in which the physical O₂ supply and resting metabolic demand are balanced. Parameters describing the net O₂ supply (α_S and E_s) were estimated from equations (6a)–(6c), that is, α_S = α_D/V_h and E_s = E_d − E_o, for the subset of species for which P_crit and metabolic rates are both available at multiple temperatures. The temperature dependence of the net O₂ supply is compared to independent estimates based on the individual steps in the O₂ supply chain: diffusion, ventilation and circulation (Extended Data Fig. 3). With species for which body mass varied by less than a factor of 2, we set δ = 3/4 and ε = 0, values that typify most species, including those investigated here.

We analysed the parameters of the Metabolic Index in two complementary ways. First, we compare the interspecies frequency distributions of each parameter, which emphasizes the diversity of traits and their relationships across marine biota, and enables comparisons between traits that are not all measured in all species. Second, we examine the intraspecies relationships between traits whenever multiple traits from the same species are available. Such analyses provide a more direct test of physiological mechanisms, but are taxonomically restricted and more sensitive to random errors in the experimental determination of parameters.

We use MATLAB’s nonlinear fitting routine (fitnlm.m) to solve for species traits (parameters) that minimize the squared residual errors. We report the central estimate of each parameter, the Pearson correlation coefficient (r²) and the P value based on two-sided Student’s t-tests, and the number of raw observations in Supplementary Table 1. With species parameters obtained from equations (1), (2), (6), relationships between traits are subsequently analysed using a standard linear least squares MATLAB routine (regress.m). Regression parameters, their 95% confidence intervals, correlation coefficients (r²), the P value based on two-sided t-tests and the number of raw observations for each relationship are reported in Extended Data Table 1.

To maximize the number of species analysed, we include those for which experiments were conducted at as few as 2 temperatures. However, all reported relationships among traits were confirmed using the subset of species (n = 14) for which regressions of metabolic rates and P_crit data against temperature were statistically significant (P < 0.05, two-tailed t-test) (Extended Data Fig. 2).

Determination and validation of Φ _crit

The limiting value of the Metabolic Index in each species habitat (Φ_crit), was estimated by pairing species location data with hydrographic conditions at those locations. Occurrence data were downloaded from the Ocean Biodiversity Information System (OBIS; http://iobis.org) in September 2019. Of the 72 species with hypoxia traits, OBIS contains georeferenced presence data for 68. To estimate the hydrographic conditions at each specimen location, we used monthly climatological temperature and O₂ fields at a resolution of 1° latitude and longitude and at 33 depths from the World Ocean Atlas^45,46. For analysis of temperature at the sea surface (z = 0 m) (Fig. 5), we include the diurnal temperature range from satellite remote sensing (data downloaded from https://www.ghrsst.org/ghrsst-data-services/products/) to estimate the globally resolved peak daytime surface temperatures.

Species occurrences were paired to hydrographic data by binning them to the World Ocean Atlas grid for every month based on the locations provided in OBIS. Hydrographic conditions were determined at the central depth of the minimum and maximum depths reported by OBIS, or from either depth alone if only one metric was provided. Occurrences were discarded if the range of conditions within that depth range differed from the central estimate by more than 2 °C for temperature or 20% for O₂. For occurrences that did not have depth information altogether, we assigned a minimum depth at the sea surface and maximum depth at the seafloor⁴⁷. In cases in which even this maximum uncertainty in depths satisfied the error tolerance (2 °C for temperature and 20% for O₂) the location data were retained. The Metabolic Index (that is, equation (5)) was computed based on species-specific traits and the paired hydrographic data for the occupied sites of each species.

Of the more than 1.5 million OBIS occurrences used here, only 0.1% mapped to climatological conditions in which Φ falls below 1. This environmental condition is physiologically unsustainable, yet may arise from transient species movements, or a mismatch between the climatological temperature and O₂ fields used to compute Φ and the true in situ hydrographic conditions at the time occurrence data were recorded. Only three species in our dataset had more than 5% of OBIS occurrences for which Φ < 1, and two of them (Sergia tenuiremis and Sergia fulgens) are known to be vertical migrators. Because of the likelihood that these occurrences do not reflect viable long-term habitats, but instead are being used as a temporary refuge that requires metabolic suppression, we report the Φ_crit values that do not include such locations. Of the three species with more than 5% of locations that had Φ < 1, the removal of those points affected the estimate Φ_crit by <0.3 for two of them (S. fulgens and M. pammelas), and thus has a negligible effect on our results. We report the Φ_crit estimates both with and without the inclusion of rare locations for which Φ < 1 (Supplementary Table 1).

We evaluated the Φ value that best defines the boundary of the geographical range of each species in two independent methods, which use identical data but differ in the degree of data aggregation over space and time. The first equates Φ_crit with the lower tail in the frequency distribution of Φ across all occupied sites in OBIS, for each species. The second computes the Φ value that maximizes its predictive skill in segregating inhabited and uninhabited grid cells globally, using a machine-learning technique. The two methods, which are described below, give highly consistent results (Extended Data Fig. 8a), but the first approach is presented in the main text (Fig. 4), owing to its conceptual and computational simplicity.

Occurrence histogram

The ecological parameter, Φ_crit, is estimated from the cumulative distribution function as the value of Φ above which the most of the occurrences of each species are found (5th and 10th percentiles). The two values yield similar Φ_crit values, and their range encompasses the Φ_crit derived from a machine-learning algorithm (see ‘The F₁-score’; Extended Data Fig. 8a), but can be applied objectively to species for which the three-dimensional distribution is too complex or sparsely sampled to identify a clear boundary to the geographical range. We present the median of Φ_crit in our primary results, but include both values in Supplementary Table 1.

As sampling density decreases, the lowest observed Φ value may not reflect the true minimum within a species habitat. However, we found that the distribution of Φ_crit for all species was similar regardless of sampling intensity (Extended Data Fig. 8b), and not biased towards higher values of Φ_crit (Fig. 4). We therefore did not restrict the analysis based on the number of occurrences.

The F ₁-score

We evaluated the ability of Φ to separate the ocean into inhabited and uninhabited portions for each species, using a standard statistical categorization metric, the F₁-score^48,49. The F₁-score is computed based on the presence and absence of a species on a regular grid (latitude, longitude, depth and month), for which the environmental conditions fall above and below a threshold value, which we varied. The value of the environmental threshold that yields the maximum F₁-score is the one that best segregates global grid cells into inhabited and uninhabited conditions for the environmental parameter of interest. Φ_crit is estimated as the Φ value that optimizes the predictive skill of categorizing habitat (maximum F₁-score).

The F₁-score is calculated as the harmonic mean of precision and recall, with equal weighting given to both measures. Precision measures the probability that the presence of the species in waters for which Φ ≥ Φ_crit is a true positive (TP; specimen reported in the space in which they are predicted to occur) rather than a false positive (FP; specimen reported in a space predicted to be below the Φ threshold). Recall is the probability that a specimen is actually reported where Φ > Φ_crit (that is, how likely is a true positive relative to a false negative (FN); missing observations above Φ_crit). In terms of these variables, the F₁-score can be expressed as:

$${F}_{1}={\left(\frac{{{\rm{recall}}}^{-1}+{{\rm{precision}}}^{-1}}{2}\right)}^{-1}=\,\frac{2{\rm{TP}}}{2{\rm{TP}}+{\rm{FN}}+{\rm{FP}}}$$

(7)

This metric does not give weight to true absence data (species known to be not present), which are infrequently and inconsistently reported in marine species data. It is thus well suited to categorization problems based on OBIS data. A model with perfect precision and recall would have F₁ = 1. The absolute F₁-score cannot be meaningfully compared between species, as it depends on the total number of grid cells included, as well as the total number of occupied sites. However, when applied to the same species and geographical region, the variations in F₁-scores between different values of the same environmental parameter, or between different environmental parameters (for example, Φ versus T), are a meaningful metric for the relative skill of a given parameter and its threshold value. Optimal F₁-scores were used to compare the predictive skill of different environmental parameters.

Comparison to SMS

To determine whether Φ_crit is consistent with independent estimates of the ratio of active-to-resting metabolic rates, we compared the frequency distributions of both metrics. An appropriate direct comparison of the habitat constraint (Φ_crit) to metabolic rate ratios would be based on active metabolic rates sustained over the time scales of population maintenance (termed ‘SusMR’)⁸. Such rates are not measured in marine species. However, maximum rates of metabolism are commonly measured in laboratory experiments. Long-term sustained metabolic rates can be expressed as a weighted average of the maximum rates (MMR) obtained under extreme exertion and the minimum rates that apply in a state of rest (RMR):

$${\rm{SusMR}}\,=\,{w}_{{\rm{R}}}\times {\rm{RMR}}+(1-{w}_{{\rm{R}}})\times {\rm{MMR}}$$

where w_R represents the effective weight of the resting state in the time–mean sustained metabolic rate. Dividing both sides by RMR, and noting the definition of SMS (SMS = SusMR/RMR), yields the equation in the main text:

$${\rm{SMS}}={w}_{{\rm{R}}}+(1-{w}_{{\rm{R}}})({\rm{MMR}}/{\rm{RMR}}),$$

(8)

which can be rearranged, substituting the definition of factorial aerobic scope (FAS = MMR/RMR) to estimate the weighting factor, w_R:

$${w}_{{\rm{R}}}=\frac{{\rm{FAS}}-{\rm{SMS}}}{{\rm{FAS}}-1}.$$

(9)

Carbon isotope analyses of the otoliths of Atlantic Cod²² suggest that SMS ≈ 2, whereas FAS⁵⁰ ranges from 3.3 to 3.8, yielding a range of w_R from 0.39 to 0.47. We estimated the weighting of resting metabolic rates (that is, w_R) using the measured ratios of MMR/RMR and Φ_crit for the species in our dataset (Supplementary Table 1), and find a mean and interspecies variation (s.d.) (w_R = 0.40 ± 0.17, n = 14; Extended Data Fig. 9 and Supplementary Table 1) that is consistent with the direct geochemical estimate for cod. Extending the mean value from these 14 species to a broader group of species with measured FAS⁴¹ (n = 106) but no SMS or Φ_crit, we find a distribution of SMS that is statistically indistinguishable from the overall distribution of Φ_crit (Extended Data Table 1). Interspecies variation in the estimates of w_R probably reflects both real biological differences in activity levels and the substantial methodological uncertainties that originate from both laboratory rates (MMR and RMR) and biogeographically derived Φ_crit values. Regardless of the precise values of w_R and their uncertainties, the fact that they are all positive (FAS values are at or above Φ_crit) and that Φ_crit is significantly correlated with laboratory-derived SMS and MMR/RMR measurements (Extended Data Table 1 and Extended Data Fig. 9) indicates that aerobic energy availability is a habitat constraint.

Estimation of AT_max

The maximum temperature at which aerobic respiration can be sustained is estimated by extrapolating the empirical relationship between P_crit and temperature to the mean atmospheric ${p}_{{{\rm{O}}}_{2}}$ (P_atm), at which CT_max experiments are carried out. We thus find the solution to the equation:

$${A}_{{\rm{o}}}{P}_{{\rm{a}}{\rm{t}}{\rm{m}}}\,\exp \,\left\{\frac{{E}_{{\rm{o}}}}{{k}_{{\rm{B}}}}\,[\frac{1}{{{\rm{A}}{\rm{T}}}_{max}}-\frac{1}{{T}_{{\rm{r}}{\rm{e}}{\rm{f}}}}]\right\}=\{\begin{array}{cc}1 & {{\rm{r}}{\rm{e}}{\rm{s}}{\rm{t}}{\rm{i}}{\rm{n}}{\rm{g}}{\rm{A}}{\rm{T}}}_{max}\\ {\varPhi }_{{\rm{c}}{\rm{r}}{\rm{i}}{\rm{t}}} & {{\rm{a}}{\rm{c}}{\rm{t}}{\rm{i}}{\rm{v}}{\rm{e}}{\rm{A}}{\rm{T}}}_{max}\end{array}$$

(10)

Because the P_crit data are all below P_atm, the solutions to this equation (AT_max) are necessarily extrapolated beyond the experimental range of temperatures over which E_o is estimated. If E_o was constant across the full range of temperatures, this extrapolation would only be influenced by the random errors in P_crit measurements, but would not incur a systematic bias across all species, yielding a histogram of AT_max with a robust mean value. However, the available data indicate that E_o increases systematically (albeit slightly) with temperature (Extended Data Fig. 3). We correct for this bias in the extrapolation of P_crit curves to the aerobic thermal maximum, by including an empirically derived linear increase in E_o with temperature, as discussed next.

The slope of the relationship (denoted by the derivative of E_o with respect to temperature, dE_o/dT) is estimated in multiple ways, to evaluate the uncertainty in these extrapolations. First, we use the intraspecies difference in E_o among species for which it can be separately estimated both above and below T_ref, as discussed in the main text and shown in Extended Data Fig. 3. This yields a mean intraspecies dE_o/dT = 0.036 eV/°C (0.55 eV/15 °C, where 15 °C is the difference between the two temperature bins 0–15 °C and 15–30 °C). Second, we consider the differences in E_o between colder waters (T < T_ref) and warmer waters (T > T_ref) for all species. This estimate, dE_o/dT = 0.013 eV/°C (0.2 eV/15 °C; Extended Data Fig. 3) gives a lower value because it includes interspecies variation. Finally, as a third method for estimating the potential variation in E_o with temperature, we directly fit the P_crit curves (equation (5) for all species with more than 2 temperatures, including a linear relationship between E_o and temperature. We discard any fits that predict a P_crit that declines towards zero at high temperatures (T ≫ 30 °C), as this would imply an unrealistic (infinite) tolerance for hypoxia at high temperatures. As a second check on the curve fits, we compare the Akaike information criterion (AIC) for the model with a linear increase in E_o to our standard model with a constant E_o. We only retain those curve fits in which the AIC did not decrease, indicating that the additional parameter did not reduce the information content of the model despite the additional parameter. Across species, this yields a mean value of dE_o/dT = 0.022 eV/°C, which falls in between the previous two values. We apply this interspecies mean value as a default value for all species (Fig. 5), since it yields results that are not biased relative to values derived from species-specific dE_o/dT wherever both are available (Extended Data Fig. 10). The range of dE_o/dT estimates is used to generate the error bars of the estimates of AT_max plotted in Extended Data Fig. 10.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this paper.

Extended data figures and tables

Extended Data Fig. 1 Species metabolic rates and hypoxia tolerances from laboratory studies.

a, b, Measured metabolic rates (μmol g⁻¹ h⁻¹) (a) and critical O₂ pressures (P_crit) (b) versus temperature (°C) in published laboratory experiments (circles). For clarity, metabolic rates are shown only for the subset of species with P_crit data. c, Location data from OBIS for all species with P_crit measured at multiple temperatures, yielding calibrated Metabolic Index parameters. The number of species with occurrences in the Pacific, Atlantic and Indian Oceans are labelled. Maps of the occurrences of individual species are available at https://obis.org/.

Extended Data Fig. 2 Correlations and diversity in traits that govern geographical range boundaries.

a–c, The key traits that make up resting hypoxia vulnerability (V_h = α_D/α_S) (a), its temperature sensitivity (E_o = E_d − E_s) (b) and the elevated hypoxia vulnerability under activity (V_h × Φ_crit) (c) all exhibit significant correlations (standard linear regression, two-tailed t-test, P < 0.05) between their constitutive parameters, regardless of whether we use all 72 species (dashed lines) or the subset of 14 species (dotted lines) for which the traits themselves were derived from statistically significant fits to equations (1) and (2) (see Methods and Extended Data Table 1). As in Fig. 1, points and error bars (centred dot, if shorter than marker) are mean ± s.e.m. for species with more than two independent experimental temperatures. See Supplementary Table 1 for the number of independent temperature experiments used for each species. The number of species used in each correlation is n = 48 (a, b) and n = 56 (c). See Extended Data Table 1 for statistics on two-sided t-tests of trait correlations. d–f, Observed diversity in resting hypoxia vulnerability (V_h) (d), its temperature sensitivity (E_o) (e) and active hypoxia vulnerability (V_h × Φ_crit) (f), is measured as the interquartile range (IQR) among all species (red bars). We also quantified the diversity in species traits in the absence of observed correlations in the underlying metabolic traits. The correlations are removed by replacing species variation in the indicated parameter with the interspecies mean value. The diversity of the resulting trait is recomputed from the IQR (blue bars). Specifically, we replace the variable α_S (a) with its mean value to derive a new distribution and IQR of V_h (d, blue bar); replace the variable E_s (b) with its mean value to derive a new distribution and IQR of E_o (e, blue bar) and replace the variable Φ_crit (c) with its mean value to derive a new distribution and IQR of the active hypoxia tolerance (V_h × Φ_crit; f, blue bar). For all three central traits, the correlation and putative trade-offs among the underlying constitutive parameters act to reduce the interspecies diversity of the trait that governs habitat range limits.

Extended Data Fig. 3 Temperature sensitivity of processes that govern the O₂ supply.

a, The rate of diffusive flux across the boundary layer increases with temperature in proportion to Scⁿ, where the Schmidt number (Sc) is the ratio of seawater viscosity (υ) to O₂ diffusivity (κ). Typical values of the exponent, n, are −1/2, −2/3 and −1, depending on the underlying model of boundary layer renewal²³. In all cases, the empirically derived curves (solid) are well approximated by an Arrhenius function (dashed) with corresponding activation energy parameters (that is, E_s) ranging from 0.21 eV (for n = −1/2; blue) to 0.27 eV (for n = −2/3; green) and 0.42 eV (for n = −1; red). b, Experimental measurements of rates of the ventilation (solid) and circulation (dashed) of animals. Rates at multiple temperatures are from published studies of six species, including three annelids²⁴ (Nereis virens, blue; Nereis succinea, brown; and Nereis diversicolor, gold; all with n = 6 independent experiments) and three chordates (Lepornis macrochirus²⁶, red; Oncorhynchus mykiss⁵¹, green; Leiopotherupon unicolor²⁵, cyan; all with n = 7 independent experiments). c, For each species, the temperature sensitivity of each rate is determined by fitting to an Arrhenius function above and below 20 °C, the approximate thermal midpoint of all data. Histograms of activation energy in each temperature range (insets) are significantly different (two-sample Kolmogorov–Smirnov test; P = 5× 10⁻⁴) for warm conditions (E_s = 0.04 ± 0.18 (mean ± s.d.)) and cool waters (E_s = 0.55 ± 0.15 (mean ± s.d.)). d, Distributions of E_o computed from experimental data at temperatures at or above 15 °C (red bars) are higher than for the same parameter computed using only temperatures at or below 15 °C (blue bars). For species for which at least two P_crit values were available both above and below T_ref, the difference between E_o for warm and cold temperatures (green bars) is always greater than zero, and has a mean value (0.55 eV) similar to the change in temperature dependence of ventilation and circulation rates across cold and warm temperatures (green bars in c).

Extended Data Fig. 4 Spatial distributions of the Metabolic Index, temperature and ${{\boldsymbol{p}}}_{{{\rm{O}}}_{2}}$ compared to occurrences of species that occupy diverse latitude and depth ranges.

a–e, Species inhabit mid to high latitudes. f–h, Species are found in tropical waters. Fields of Φ (colours), temperature and O₂ pressure are zonally averaged over the longitudinal range of each species. a, Cyclopterus lumpus (95 °W–35 °E). b, Tautogolabrus adspersus (50–80 °W). c, Gadus morhua (75 °W–40 °E). d, Zoarces viviparus (10 °W–30 °E). e, Gadus ogac (110 °W–40 °E). f, Penaeus aztecus (40–120 °W). g, Funchalia villosa (100 °W–40 °E). h, Gennadas valens (100 °W–47 °E). Observed species occurrences are plotted (blue dots). A single lower limit of Φ bounding each species range is contoured (Φ_crit; black lines) alongside isotherms of temperature (white lines; °C) and isopleths of ${p}_{{{\rm{O}}}_{2}}$ (grey lines; atm). Published upper thermal limits (CT_max) are contoured in green where available, based on maximum monthly ocean temperatures (°C). Green asterisks denote species for which CT_max occurs above all mapped maximum monthly temperatures. For most species, Φ_crit more skilfully categorizes occupied habitat than either upper temperature limits or lower ${p}_{{{\rm{O}}}_{2}}$ considered individually. This skill is shown by the ratio of F₁-scores of Φ relative to temperature or to ${p}_{{{\rm{O}}}_{2}}$ (in parentheses, respectively) from the full four-dimensional species distribution. For G. morhua, the monthly range of Φ_crit is also mapped (dashed black lines). For G. ogac, mapped occurrences, Φ and water properties are from the Atlantic Ocean only. Land regions are shaded in grey.

Extended Data Fig. 5 Maps of the Metabolic Index, temperature and ${{\boldsymbol{p}}}_{{{\rm{O}}}_{2}}$ compared to species distributions.

a–f, Mapped variables are averaged from the surface to the 95th percentile depth of each species. a–c, P. borealis (0–450 m). d–f, Stenobrachius leucopsarus (0–225 m). A single lower limit of Φ (Φ_crit; black lines) is consistent with habitat range limits found in the Pacific and Atlantic Oceans for P. borealis (a) and different sides of the Pacific Ocean for S. leucopsarus (d). By contrast, no single maximum temperature or minimum ${p}_{{{\rm{O}}}_{2}}$ is consistent with each species’ range limit across those regions. The increased skill of Φ_crit is encapsulated by the higher F₁-scores of Φ relative to temperature (b, e) or to ${p}_{{{\rm{O}}}_{2}}$ (c, f) (in parentheses, respectively) from the full four-dimensional species distribution. Occurrence data for each species are shown (blue dots).

Extended Data Fig. 6 Spatial distributions of the P. borealis, S. canicula and S. plicata compared with the Metabolic Index, temperature and ${{\boldsymbol{p}}}_{{{\rm{O}}}_{2}}$.

a–i, Spatial distributions of the species shown in Fig. 2 (P. borealis, S. canicula and S. plicata) were compared with the Metabolic Index (a, d, g), temperature (b, e, h) and ${p}_{{{\rm{O}}}_{2}}$ (c, f, i). a–c, P. borealis. d–f, S. canicula. g–i, S. plicata. A single lower limit of Φ bounding each species range is contoured (Φ_crit; black lines). For all species, Φ_crit more skilfully categorizes occupied habitat than either temperature limits or lower ${p}_{{{\rm{O}}}_{2}}$ considered individually. This skill is shown by the higher ratio of F₁-scores of Φ relative to temperature or to ${p}_{{{\rm{O}}}_{2}}$ (in parentheses, respectively) from the full four-dimensional species distribution. Occurrence data for each species are shown (blue dots). Regions for zonal averaging are as in Fig. 2.

Extended Data Fig. 7 Predictive skill of the Metabolic Index in delineating the species geographical range, compared with temperature or ${{\boldsymbol{p}}}_{{{\bf{O}}}_{{\bf{2}}}}$ alone.

The F₁-score measures the ability of each environmental variable at a given threshold value to categorize the ocean into inhabited and uninhabited regions. The maximum F₁-score for Φ is then compared with the maximum value for temperature or ${p}_{{{\rm{O}}}_{2}}$ thresholds and plotted on a log₁₀ scale such that positive (negative) values indicate a stronger (weaker) predictive skill for Φ. Printed numbers (n) on the graph indicate the number of species that fall within each quadrant (for numbers in quadrants) or to each side of the axes (for numbers on axes). For example, Φ outperforms T in 44 species, and underperforms in only 4, and outperforms both T and ${p}_{{{\rm{O}}}_{2}}$ in 30 species. A maximum F₁-score was found for 48 species, while 8 additional species had no clear maximum in F₁-score.

Extended Data Fig. 8 Critical value of the Metabolic Index at the limit of species geographical range (Φ_crit).

a, The values of Φ_crit are compared using two independent methods. The first (y axis) is determined from the peak in the F₁-score for categorization into occupied and unoccupied sites (see Methods). The second (x axis) is determined from the bottom percentile (5–10%) of Φ values inhabited by the species. b, The histogram of Φ_crit is not sensitive to the number of occurrence observations. c, For all species, waters with lower Φ values than Φ_crit exist within the depth range of these species, but lack confirmed specimens. The dashed line indicates the 1:1 line.

Extended Data Fig. 9 Relationship between Φ_crit and the ratio of maximum-to-resting metabolic rates (MMR/RMR), among all species with empirical estimates of both parameters.

Blue dots, species with empirical estimates of both parameters (Supplementary Table 1). Lines of constant w_R (see equation (9) are shown for a sustained metabolic rate that is equal to the resting rate (SMS = 1; w_R = 1; blue line), the maximum metabolic rate (SMS = FAS; w_R = 0; red line) or the mean apparent species value (w_R = 0.4; green line) in which sustained the metabolic rate is approximately midway between minimal (resting) and maximal rates. Independent geochemical estimate of SMS based on carbon isotopes in the otoliths of Atlantic cod²⁸ are shown as a triangle.

Extended Data Fig. 10 Relationship across species between thermal tolerance of species measured in laboratory studies and predicted from the Metabolic Index.

Critical thermal maxima (CT_max), reported in previous studies, were measured at the onset of loss of physiological function in a resting state. The AT_max are predicted from the Metabolic Index, as the temperature at which the O₂ threshold for metabolic rate in either resting state (P_crit) or under sustained activity levels (P_crit × Φ_crit), reaches the mean atmospheric O₂ pressure, P_atm (see Methods, equation (10)). The extrapolation of P_crit curves to the atmospheric pressure is based on n = 3 independent estimates of the linear increase in E_o with temperature (see Methods). Points for each species are the mean, and error bars show the range among the resulting n = 3 estimates of AT_max. Data are shown for all species in Fig. 5, for which all parameters are available (n = 7). For four out of seven species, the AT_max is reached before the CT_max, even in a resting state. For all seven species, the active AT_max is reached at a lower temperature than the CT_max, and is comparable to the maximum temperature that the species inhabits at atmospheric pressure.

Extended Data Table 1 Summary statistical tests of the relationships between metabolic and hypoxia traits and between distributions of Φ_crit and SMS