Author Correction: Optimal Channel Networks accurately model ecologically-relevant geomorphological features of branching river networks

Correction to: Communications Earth and Environment https://doi.org/10.1038/s43247-022-00454-1, published online 31 May 2022.

Four corrections have been made to the original version of this Article to clarify how certain definitions were applied and to clarify related statements in the Abstract, Results and Discussion. The changes are listed below.

The original Article contained an inaccurate statement regarding scale-dependence in the fourth sentence of the Abstract, which read “Here we show that an alleged property of such random networks (branching probability) is a scale-dependent quantity that does not reflect any recognized metric of rivers’ fractal character, and hence cannot be a driver of ecological dynamics.” The corrected Article now reads “Here we show that branching probability of random networks is a scale-dependent quantity in that it varies with the length scale or spatial resolution of observations. Therefore, our findings suggest that this property is not a robust driver of ecological dynamics.”

The original Article omitted a clear definition of how the terms “scale invariant” and scale dependent” were applied in this Article. The corrected Article now includes the following definitions that have been added after the second sentence of the fourth paragraph of the introduction: “Here we use the term “scale invariance” to refer to a property or parameter that does not change with varying scale or resolution of the measured or observed parameter (e.g., the exponent of a power-law relationship). Conversely, we use the term “scale dependence” to refer to a property or parameter that varies depending on the scale or resolution of the measured or observed parameter.”

The original Article contained an inaccurate statement regarding scale-invariance in the fifth paragraph of the section titled “Drainage area and branching ratio: a matter of scale”, which read: “Since the evaluation of p_r depends on the number of nodes N, which, in turn, is defined based on the scale length l, the resulting p_r of a river network under this perspective would depend on the characteristics of the target taxa, which is inconsistent with the alleged role of p_r as a scale-invariant property of river networks.” The correct version reads “Since the evaluation of p_r depends on the number of nodes N, which, in turn, is defined based on the scale length l, then the resulting p_r derived from a random network would depend on the characteristics of the target taxa, which is inconsistent with the assumption of p_r being a scale-invariant property of river networks.”

The original version of this Article contained an error in a sentence in the fourth paragraph of the ‘Ecological implications’ section, which originally read: “In contrast, we note that, if different river networks spanning different catchment areas (say, in km²) are compared, all of them extracted from the same DEM (same l and same A_T in km²), then the larger river network will appear more branching (i.e., have larger p_r). Indeed, by selecting catchments with larger A (in km²) for fixed l and A_T (in km²), one moves towards the top-left corner of Fig. 2a, b (i.e., perpendicular to the level curves A_T/A). The apparent higher “branchiness” of the river network with larger A will result in lower values of CV_M; however, the higher metapopulation stability of the larger network will not be due to its (alleged) inherent more branching character, but only dictated by its larger habitat availability”. In particular, the example provided therein was inaccurately formulated and unsupported by our results and findings (specifically, it was inconsistent with the actual Fig. 2 of the manuscript: the example proposed would imply a movement parallel to the vertical axis, not perpendicular to the level curves A_T/A). The corrected version of the sentence states: “In contrast, we note that, if the same river network (with fixed A in km²) is extracted from DEMs at different resolutions (i.e., different values of l) but same A_T (in km²), then the river network extracted at coarser resolution (larger l) will appear more branching (i.e., have larger p_r). This is because the number of links N_L and the total river length (in km) are primarily determined by A_T and so would remain unchanged. Variation in the pixel size l will impact how the total river length is partitioned into nodes given the length resolution constraints imposed by l. Thus, the number of nodes N would be lower when extracted at coarser resolution (larger l). As p_r = N_L/N this means that p_r will be artificially inflated for rivers extracted at coarser resolutions. This introduces an equivalent effect as selecting catchments with smaller A (in number of pixels) but constant ratio A_T/A, which are located towards the bottom-left corner of Fig. 2a, b (i.e., parallel to the level curves A_T/A). In this case, the apparent higher “branchiness” of the river network extracted at coarser resolution would result in higher values of CV_M (i.e., lower metapopulation stability) because of a reduction in N.”

These changes do not alter the main conclusions of the study.

These points have all been corrected in both the PDF and HTML versions of the Article.