2.4 Statistics
We categorized the scaling behavior of relationships between cumulative hyporheic respiration and watershed area for each combination of HEF bin and basin (n = 20) into four allometric classes: Uncertain, Sublinear, Linear, and Super-linear. We visually identified an R2threshold of 0.8 where values exhibit a “knee” (Figure S3A), which we interpret as weak or no allometric scaling. Relationships with mean R2 values < 0.8 were classified as ”Uncertain”. To classify allometric behavior for relationships with R2 values >= 0.8, we used 2.5% and 97.5% confidence intervals (CI2.5 and CI97.5) of slope values as follows: “Linear” for CI2.5 < 1 and CI97.5> 1, “Sublinear” for CI2.5 < 1 and CI97.5 < 1, and “Super-linear” for CI2.5 > 1 and CI97.5> 1 (Figure S3C). We capitalize these terms throughout the rest of this study to clarify when we are referring to these definitions.
To reveal watershed features explaining variation in the spatial distributions of hyporheic respiration across each basin, we used mutual information analysis, which calculates the dependency between two variables based on Shannon’s entropy. Mutual information analysis was conducted with the infotheo R package (Meyer 2022), where each variable was first discretized, then calculated mutual information was normalized to the maximum information within each analysis. For statistical tests with significance values, we used a p-threshold of 0.05. All analyses were performed in R (R Core Team 2023) or Python 3.