Physiological causes and biogeographic consequences of thermal optima in the hypoxia tolerance of marine ectotherms

The minimum O2 needed to fuel the demand of aquatic animals is commonly observed to increase with temperature, driven by accelerating metabolism. However, recent measurements of critical O2 thresholds (‘Pcrit’) reveal more complex patterns, including those with a minimum at an inter-mediate thermal ‘optimum’. To discern the prevalence, physiological drivers, and biogeographic manifestations of such curves, we analyze new experimental and biogeographic data using a general dynamic model of aquatic water breathers. The model simulates the transfer of oxygen from ambient water, through a boundary layer and into animal tissues driven by temperature-dependent rates of metabolism, diffusive gas exchange, and ventilatory and circulatory systems with O2-protein binding. We find that a thermal optimum in Pcrit can arise even when all physiological rates increase steadily with temperature. This occurs when O2 supply at low temperatures is limited by a process that is more temperature sensitive than metabolism, but becomes limited by a less sensitive process at warmer temperatures. Analysis of species respiratory traits suggests this scenario is not uncommon in marine biota, with ventilation and circulation limiting supply under cold conditions and diffusion limiting supply at high temperatures. Using biogeographic data, we show that species with these physiological traits inhabit lowest O2 waters near the optimal temperature for hypoxia tolerance, and are restricted to higher O2 at temperatures above and below this optimum. Our results imply that O2 tolerance can decline under both cold and warm conditions, and thus may influence both poleward and equatorward species range limits. Significance Statement Physiology shapes the ecology, biogeography, and climate responses of marine species. In aquatic ectotherms, accelerating metabolism and lowered oxygen availability generally result in increasing oxygen limitation with warming. Here we present evidence for thermal optima in hypoxia tolerance of diverse species that is explained by a dynamical model of organismal physiology. Our results indicate that this potentially widespread bidirectional pattern explains species biogeographic limits in cold and warm waters. It can be understood using a generalized Metabolic Index of O2 supply to demand, which captures the variable observed trends between temperature and species hypoxia sensitivity. Oxygen limitation of aerobic metabolism in cold water has far-reaching implications for marine biogeography and species migrations under climate change.


Introduction
To examine the prevalence of thermal optima in hypoxia tolerance, diagnose the physiological 82 conditions under which it can arise, and evaluate its relevance to species biogeography, we combined 83 new laboratory experiments, a dynamic model of O 2 supply in marine ectotherms, and species 84 biogeographic distribution data. Among all studied species, we find complex behavior across 85 a broad temperature range. A general model of aquatic water breathers demonstrates the conditions 86 under which thermal optima can emerge from the multi-step nature of the O 2 supply chain, and 87 analysis of prior laboratory data suggests that marine species commonly meet those conditions.

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The behavior of the dynamic model can be reproduced with a generalized Metabolic Index of O 2 89 supply to demand (6) that captures a wide range of observed curves. Finally, we present still others a relatively constant at cold temperatures, followed by a sharp rise at warmer 107 temperatures (N. vectensis, D. opalescens). These new respirometry data combined with published 108 data (17,16), indicate that thermal optima in hypoxia tolerance are found in multiple phyla and 109 across multiple modes of oxygen supply (e.g., gills and a blood vascular system in squid versus 110 cutaneous respiration in anemones) and may therefore represent a widespread pattern. metabolizing body tissues, which may be mediated by a circulatory system ( Fig. 2A). In addition 120 to dissolved O 2 , the model also tracks the concentration of the bound and unbound forms of an 121 oxygen-transport protein such as hemoglobin or hemocyanin (denoted HxO and Hx, respectively), 122 which bind and release molecular O 2 according to the associated chemical equilibrium. This is 123 captured by the pO 2 at half-saturation (denoted 50 ) and the enthalpy (Δ ) of the binding reaction, 124 which governs the temperature dependence of that equilibrium (23, details SI).

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Each of the three O 2 supply processes (ventilation, diffusion, and circulation) is described by a rate 126 that is represented as the product of the pO 2 difference between the respective compartments, 127 Δ 2 , and a temperature-dependent rate coefficientˆ( ) that characterizes the kinetics of that 128 process: The temperature-dependency of the three rate coefficients -flow rates of ventilated water and Simulations across a range of temperatures yield the curve, which integrates the contribution 147 of all traits to a single metric of hypoxia tolerance. Across a wide range of model parameters 148 centered on the most common traits observed in marine organisms (7), the curves exhibit an 149 overall rise with temperature, driven by the increase in metabolic rate.

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Both the chemical properties (Hx, Δ and p50) as well as the rate coefficients of supply and demand 151 (ˆ) have intuitive impacts on the curves. For example, a higher concentration of total Hx 152 acts to lower the curve across all temperatures (Fig. 2C), enhancing the tolerance to hypoxia.
is not always the same across the full temperature range. For instance, a 25 % increase in the ventilation rate does not lower the by the same fraction at all temperatures, but instead has a 158 larger impact under cold conditions than under warm conditions (Fig. 2D). In other words, the 159 curves resulting from a multi-step supply chain can depart from simple exponential relationships 160 with temperature, even when each single supply process accelerates exponentially with warming. 161 We conclude that the well-known non-linearities in blood-O 2 binding are not the essential cause 162 of this behavior, because the variation due to biophysical properties is similar to that induced by 163 variations in blood chemistry. Moreover, we observe complex curves in organisms without 164 O 2 -binding proteins (e.g. N. vectensis in Fig. 1).

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Instead, we focus our analysis on the mechanisms by which the linear combination of biophysical 166 transfer processes in a multi-step O 2 supply chain leads to the complex patterns observed in 167 curves.

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The origins of non-exponential curves can be demonstrated quantitatively in a model with a 169 supply chain consisting only of ventilation and diffusive gas exchange (Fig. 3). In isolation, each step series results in a curve that is the sum of the two curves corresponding to the single steps, 175 and thus exhibits a minimum at an intermediate temperature (Fig. 3C).

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This additive nature of the curve resulting from a linear supply chain can also be derived 177 analytically from the system of model ODEs for more than two supply steps (details in SI).

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Conceptually, this property can be thought of as analogous to an electrical circuit in which a fixed 179 voltage is applied to a series of resistors. Just like the total voltage can be obtained as the sum of 180 the individual voltage drops across each resistor, the total curve of a multi-step supply chain 181 can be obtained as the sum of the pO 2 drops that drive each individual supply process.

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Therefore, a bowl-shaped curve can emerge if the supply chain includes processes that are 183 both more and less sensitive to temperature changes than metabolism. In Fig. 3C, the curve 184 rises under warm conditions because a large pO 2 gradient is required to drive sufficient diffusion 185 at high temperatures. This is due to the fact that diffusion accelerates slower than metabolism with 186 warming. On the other hand, the curve also remains flat or even reverses under cold conditions 187 because a large pO 2 gradient is required to drive sufficient ventilation at low temperatures, since 188 this process has a higher temperature sensitivity than metabolism.

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Because the critical pO 2 differences required to drive the individual supply steps are not the same, 190 the total curve is not equally sensitive to changes in the biologically controlled rate coefficients 191 at all temperatures. In the example above, the change in at high temperatures due to a change in 192 ventilation rate might be small or even negligible while its response to a change in diffusivity might 193 be substantial, even for the same relative increase in the biologically controlled parameter. More 194 generally, a change in the coefficient of any supply process that accelerates faster with warming than 195 metabolism will have the largest impact on under cold conditions, as in the case of ventilation.

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On the other hand, such an increase has the largest impact on under warm conditions for a 197 supply process that accelerates slower than metabolism, such as diffusion.

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This relationship is particularly important for processes under immediate biological control like 199 ventilation and circulation and has implications for understanding their temperature sensitivity.

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Incurring the energetic costs of accelerating heart rate or ventilation across the entire temperature 201 range may not be beneficial if is instead much more sensitive to changes in diffusion at high 202 temperatures. We illustrate this in a model variant with a ventilation rate that has a high temperature 203 sensitivity at low temperatures but reaches an upper limit under warm conditions, as for example 204 observed in (31, 32, 33). The resulting change in at high temperatures compared to a simple 205 exponential ventilation rate is minimal (Fig. S3). In this scenario, increasing the ventilation rate 206 throughout the warm side of the temperature range barely impacts hypoxia tolerance, because O 2 207 supply is largely determined by diffusion. obtained if only volumetric rates (n =12) are considered (Fig. 4).

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These results can be compared to existing estimates of the temperature sensitivity of metabolism

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For the habitat to be viable, this supply rate must be equal to metabolic consumption, such that 257 can be interpreted as the minimum 'voltage' required to achieve an O 2 supply matching demand 258 given the fixed 'conductance' of the biological supply process.

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In a supply chain with multiple steps in series, each step is associated with such a required voltage 260 drop -a pO 2 difference -determined by its single step conductance. Thus, the of the composite 261 chain can be obtained as the sum of the minimum pO 2 differences of the single supply steps, as 262 illustrated in Fig. 3C.

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The temperature-dependent 'conductance' (or rate coefficient)ˆof a single supply step can be 264 expressed as ( ), where denotes the value of the coefficient at reference temperature, 265 which is scaled by an exponential (Arrhenius) function with temperature sensitivity [eV].

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More generally, in a chain with supply steps in series, the total conductance of the chain is the 267 reciprocal of the sum of single step resistances. When divided by metabolic demand ( , ), 268 the resulting expression for the generalized supply-to-demand ratio Φ is where the represent the supply rate coefficients at reference temperature and = −

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The condition for the existence of a bowl-shaped curve, i.e. supply steps having temperature 274 sensitivities both less than and greater than that of metabolic demand, thus reads < < 275 for any two supply steps and . Eqn.
(2) can include any number of supply processes. However, 276 we find that curves generated by the full model ( = 3) can still be appropriately represented cold and warm ends of the temperature range, respectively.

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The metabolic index framework establishes a direct link between physiological traits and biogeo-287 graphical distributions, as the range boundaries of a diverse set of species align more strongly 288 with a specific value of the index than with either temperature or pO 2 alone (7  Fig. S7, 16).

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In all these cases, the generalized Metabolic Index reveals how the reversal in hypoxia tolerance 310 at low temperatures results from physiological traits, and how this bidirectionality is reflected in biogeographic ranges. In particular, it suggests O 2 limitation is the mechanism that restricts habitat 312 towards the cold edges of species distributions.

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The dynamic model of temperature-dependent hypoxia reveals that a series of biophysical O 2 315 supply steps can give rise to thermal optima in hypoxia tolerance as observed in new respirometry 316 data. This occurs when the supply chain includes at least two processes such that one accelerates 317 with temperature more slowly than metabolic demand, and another accelerates more rapidly. In 318 this case, the process with a lower temperature sensitivity drives an increase in under warm 319 conditions, while the more sensitive process leads to a reversal with higher in cold waters. A 320 generalized Metabolic Index adequately captures these complex patterns in a single metric based 321 on mechanistic principles.

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Our analysis of available physiological evidence suggests that such bidirectional effects of temper-323 ature on hypoxia tolerance may not be uncommon in aquatic animals across taxonomic groups.

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Estimates of the temperature sensitivity of ventilation and circulation rates in aquatic ectotherms 325 fall above diffusive gas exchange and below metabolism on average, but imply the existence of 326 thermal optima in a significant fraction of species. However, these results rely on limited physio-327 logical data. In particular, there are only a few teleost and crustacean species for which all required 328 physiological estimates are available. Thus, sampling the involved traits across a broader range of 329 the taxonomic, morphological and ecological diversity is a key step towards further advancing and 330 testing this framework and its implications.

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In contrast to the sparsity of detailed physiological measurements, global occurrence data is avail-332 able for a much larger number and diversity of marine species (e.g OBIS). The generalized index 333 offers further improvements in the analysis of these data compared to its original formulation, 334 especially along the cold edges of species habitats by including a meaningful representation of O 2 335 limitation at low temperatures. In case studies presented here, thermal optima in physiological hypoxia tolerance are also reflected in species' biogeographic state space. Leveraging this approach 337 in a future database-wide analysis of occurrence data will contribute to a fuller picture of how 338 temperature and oxygen shape the biogeography and ecology of marine species.

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Oxygen limitation of aerobic metabolism at low temperature has broad implications for marine

Data and Code Availability
Sensitivity estimates for ventilation and circulation rates obtained from published results are avail-384 able in Dataset S1. Biogeographic and environmental data are publicly available. Full physiological 385 measurements are shown in Fig. S1. and are available from the corresponding author upon rea-386 sonable request. Python code will be made available upon publication. [