Metabolic index
This protocol is extracted from research article:
A committed fourfold increase in ocean oxygen loss
Nat Commun, Apr 16, 2021; DOI: 10.1038/s41467-021-22584-4

The metabolic index Φ38 is defined as the ratio of O2 supply to the temperature-dependent resting O2 demand of an organism and it combines temperature and pO2 as indicators of metabolically viable marine environments. Here, not Φ itself but only changes of Φ are considered48, employing the scripts provided by ref. 49:

where E0 describes the effect of temperature on the critical pO2, i.e., the threshold oxygen partial pressure required for maintaining the resting metabolic rate (hypoxia vulnerability in ref. 40) to temperature, which is different for different species. Parameter kB is the Boltzmann constant and pO2 is the partial pressure of oxygen.

For E0, the species average of ref. 40 is taken (E0 = 0.4 eV). E0 varies considerably among species40 and may be different for deep-sea species, for which such information is not yet available. As an extreme example, a small negative value of E0 = −0.2 eV, indicating an increase in the critical pO2 with decreasing temperature, was found for a species living at the lower oxycline of the oxygen minimum zone in the eastern tropical Pacific50 (where pO2 tends to increase downwards with decreasing temperature). As changes in Φ are dominated by changes in pO2 rather than temperature, the results are relatively similar even for a very low value of E0 = −0.2 eV (Supplementary Fig. 5).

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