# 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 organisms1,2,3. 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.

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## Data availability

The data used in this study are described in the Methods. The data that support the findings of this study are available from the corresponding author upon reasonable request.

## Code availability

The MATLAB code is available at GitHub (https://github.com/cadeutsch/Metabolic-Index-Traits).

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## Acknowledgements

We thank T. Brey for contributing data, E. Howard for statistical advice, H. Frenzel for computational support and W. Verberk, M. Pinsky and A. Bates for insightful suggestions that improved the clarity of presentation. This work was made possible by grants from the Gordon and Betty Moore Foundation (GBMF#3775) and the National Science Foundation (OCE-1419323 and OCE-1458967) and the National Oceanic and Atmospheric Administration (NA18NOS4780167).

## Author information

Authors

### Contributions

C.D and J.L.P. analysed the data and wrote the paper with input from B.S.

### Corresponding author

Correspondence to Curtis Deutsch.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Amanda Bates, Malin Pinsky and Wilco C. E. P. Verberk for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## 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 (Pcrit) (b) versus temperature (°C) in published laboratory experiments (circles). For clarity, metabolic rates are shown only for the subset of species with Pcrit data. c, Location data from OBIS for all species with Pcrit 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.

ac, The key traits that make up resting hypoxia vulnerability (Vh = αD/αS) (a), its temperature sensitivity (Eo = Ed − Es) (b) and the elevated hypoxia vulnerability under activity (Vh × Φcrit) (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. df, Observed diversity in resting hypoxia vulnerability (Vh) (d), its temperature sensitivity (Eo) (e) and active hypoxia vulnerability (Vh × Φcrit) (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 αS (a) with its mean value to derive a new distribution and IQR of Vh (d, blue bar); replace the variable Es (b) with its mean value to derive a new distribution and IQR of Eo (e, blue bar) and replace the variable Φcrit (c) with its mean value to derive a new distribution and IQR of the active hypoxia tolerance (Vh × Φcrit; 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, Es) 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 (Es = 0.04 ± 0.18 (mean ± s.d.)) and cool waters (Es = 0.55 ± 0.15 (mean ± s.d.)). d, Distributions of Eo 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 Pcrit values were available both above and below Tref, the difference between Eo 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.

ae, Species inhabit mid to high latitudes. fh, 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 (Φcrit; black lines) alongside isotherms of temperature (white lines; °C) and isopleths of $${p}_{{{\rm{O}}}_{2}}$$ (grey lines; atm). Published upper thermal limits (CTmax) are contoured in green where available, based on maximum monthly ocean temperatures (°C). Green asterisks denote species for which CTmax occurs above all mapped maximum monthly temperatures. For most species, Φcrit 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 Φcrit 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.

af, Mapped variables are averaged from the surface to the 95th percentile depth of each species. ac, P. borealis (0–450 m). df, Stenobrachius leucopsarus (0–225 m). A single lower limit of Φ (Φcrit; 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 Φcrit 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 $${{\boldsymbol{p}}}_{{{\rm{O}}}_{2}}$$.

ai, 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). ac, P. borealis. df, S. canicula. gi, S. plicata. A single lower limit of Φ bounding each species range is contoured (Φcrit; black lines). For all species, Φcrit 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 (Φcrit).

a, The values of Φcrit 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 Φcrit is not sensitive to the number of occurrence observations. c, For all species, waters with lower Φ values than Φcrit 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 Φcrit 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 wR (see equation (9) are shown for a sustained metabolic rate that is equal to the resting rate (SMS = 1; wR = 1; blue line), the maximum metabolic rate (SMS = FAS; wR = 0; red line) or the mean apparent species value (wR = 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 (CTmax), reported in previous studies, were measured at the onset of loss of physiological function in a resting state. The ATmax are predicted from the Metabolic Index, as the temperature at which the O2 threshold for metabolic rate in either resting state (Pcrit) or under sustained activity levels (Pcrit × Φcrit), reaches the mean atmospheric O2 pressure, Patm (see Methods, equation (10)). The extrapolation of Pcrit curves to the atmospheric pressure is based on n = 3 independent estimates of the linear increase in Eo with temperature (see Methods). Points for each species are the mean, and error bars show the range among the resulting n = 3 estimates of ATmax. Data are shown for all species in Fig. 5, for which all parameters are available (n = 7). For four out of seven species, the ATmax is reached before the CTmax, even in a resting state. For all seven species, the active ATmax is reached at a lower temperature than the CTmax, and is comparable to the maximum temperature that the species inhabits at atmospheric pressure.

## Supplementary information

### Supplementary Table 1

Table containing species metabolic and hypoxia traits, and model statistics.

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Deutsch, C., Penn, J.L. & Seibel, B. Metabolic trait diversity shapes marine biogeography. Nature 585, 557–562 (2020). https://doi.org/10.1038/s41586-020-2721-y

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