Statistical analyses

FG Folco Giomi AB Alberto Barausse CD Carlos M. Duarte JB Jenny Booth SA Susana Agusti VS Vincent Saderne AA Andrea Anton DD Daniele Daffonchio MF Marco Fusi

This protocol is extracted from research article:

Oxygen supersaturation protects coastal marine fauna from ocean warming

**
Sci Adv**,
Sep 4, 2019;
DOI:
10.1126/sciadv.aax1814

Oxygen supersaturation protects coastal marine fauna from ocean warming

Procedure

* Water temperature and dissolved oxygen*. Environmental monitoring observations were assigned to day or night based on the presence or absence of solar radiation (measured in W m

Table S1 reports the number of valid observations of dissolved oxygen concentration and corresponding water temperature available for the three habitats during day and night, for temperature intervals of 1°C. Only temperature intervals containing more than 13 valid observations were shown through box plots in Fig. 1.

Dissolved oxygen concentration at 100% saturation in seawater was calculated according to the solubility formulation of Garcia and Gordon, as recommended by the U.S. Geological Survey (*37*). Oxygen solubility was calculated at standard atmospheric pressure (1 atm) and corrected for the effect of salinity. A pressure correction factor was not applied to oxygen solubility, given that in this study, it was compared to experimental observations made at shallow depths. For each of the six subplots of Fig. 1 (three habitats, day or night) and for Fig. 4, the salinity value chosen to calculate the salinity correction factor was the median of the salinity observations corresponding to the temperature-oxygen observations included in that (sub)plot (Fig. 1: for the mangroves, this value was 41.76 ppt at night and 41.89 ppt at day; for the coral reef, 41.02 ppt at night and 40.80 ppt at day; and for the seagrasses, 43.85 ppt at night and 43.79 ppt at day; Fig. 4: it was 41.82 ppt, i.e., a value close to the salinity of the laboratory experiments whose measurements were displayed in the same figure, which was 40 ppt).

Before calculating cross-correlations in Fig. 1, the time series of water temperature and dissolved oxygen concentration were detrended by subtracting a 24-hour central moving average to focus on daily rather than long-term variability. Cross-correlations between the detrended time series were calculated using the Pearson correlation coefficient and different time lags for dissolved oxygen concentration.

To map field observations of water temperature and dissolved oxygen concentration to oxygen consumption rates in Fig. 4, we fitted different models to the available laboratory measurements. Laboratory measurements (11 observations) consisted of oxygen consumption rates assessed at different water temperatures and oxygen saturation levels (normoxia and hyperoxia), at fixed salinity (40 ppt). This information was used to calculate the actual dissolved oxygen concentration in the 11 laboratory measurements by using the formulation of oxygen solubility (i.e., dissolved oxygen concentration at 100% saturation) of Garcia and Gordon, as recommended by the U.S. Geological Survey (*37*), at standard atmospheric pressure (1 atm) and correcting for the effect of salinity. A pressure correction factor was not applied to oxygen solubility given the shallow depth at which the observations had been made. The resulting dataset (11 observations) was then used to model oxygen consumption rate as a function of water temperature and dissolved oxygen concentration. Given the small sample size, we fitted simple polynomial models with a maximum degree of 2 to the observed oxygen consumption rates, with a maximum of four coefficients to be calibrated; water temperature and dissolved oxygen concentration were the independent variables. We picked up the best model in an adjusted *R*^{2} sense to map the oxygen consumption rate to field observations in Fig. 4. *R*^{2} adjusted for the model residual degrees of freedom, a good indicator of fit quality when comparing nested models, is$${R}_{\text{adj}}^{2}=1-\text{SSE}\cdot (n-1)/(v\cdot \text{TSS})$$where SSE is the sum of squared errors of prediction, TSS is the total sum of squares, *n* is the number of observations, and ν is *n* − *p*, where *p* is the number of fitted model coefficients including the intercept. The best model to predict oxygen consumption rate *Q* (μmol g^{−1} hour^{−1}) as a function of dissolved oxygen concentration DO (mg liter^{−1}) and water temperature *T* (°C) was$$Q=-1.705+0.1711\cdot T-0.2072\cdot \text{DO}-0.003477\cdot {T}^{2}+0.009181\cdot T\cdot \text{DO}$$

(*R*^{2} = 0.55, adjusted *R*^{2} = 0.25)

Isocurves in Fig. 4 were created by dividing the plot into a 10-by-10 grid of equally spaced boxes. The fraction of all the observations in the plot falling inside each box was computed and then used to draw isolines linking locations with the same densities of observations (as indicated in relative units by the isoline labels in Fig. 4), based on the contour function of MATLAB.

*Physiological performance*. Metabolic differences over increasing temperature (explanatory continuous variable) for the two oxygen conditions (explanatory categorical variable, two levels: hyperoxic, normoxic) were tested using a nonparametric generalized additive model with restricted maximum likelihood [GAM, R package “mgcv”; (*38*)].

A generalized linear mixed model using a quasi-Poisson family error distribution was used to test the difference in the lactate recovery rate (the continuous response variable) for animals exposed to different oxygen saturations (the categorical explanatory variable, fixed and orthogonal, two levels: normoxic and hyperoxic). Each individual ID was considered a random factor in the model to account for paired observations.

After verifying the assumptions of normality and homogeneity of variance (Levene’s test, *F*_{1,10} = 0.57, *P* = 0.466), we carried out an analysis of variance (ANOVA) considering PO_{2}crit as the response variable and oxygen level as an explanatory categorical variable with two levels: hyperoxic and normoxic. All the analyses were performed using the R software (*39*).

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