Fig. 5: Empirical support for the conceptual model in Fig. 4.
From: A connectivity threshold between grass patches amplifies coastal dune formation
a–c) Dune height (2023) as a function of nearest-neighbor distance (2013), averaged over the 2, 3, and 5 nearest neighbors. Trend lines show Hill-function fits (Eq. (1)), where k represents the distance threshold (vertical dashed lines). These thresholds closely match the maximum interaction distance predicted from percolation theory (~4.54 m). Shaded bands show the standard deviation. d Using this interaction distance, we calculated the fraction of patches in “spanning” clusters (%) as a function of local patch density. The spanning fraction increases most steeply near the inflection point k from Fig. 3c (0.054 ± 0.003 patches m⁻²) and saturates where dune-height curves level off. e Dependence of k on window radius: k decreases with increasing radius and then approaches a window-independent limit. f Finite-size scaling test: plotting \(k(L)\) against \({L}^{-0.75}\) (x-axis, labeled by the corresponding radii in meters) indeed yields an approximately linear relationship (R² = 0.94).
