Metabolic index

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 k_B 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).