SUPPLEMENTARY TEXT 2
Constructing CF_SDI
We constructed CF_SDI for each dataset (Global, NAfEu, WAfSAm) as follows: First, for each time interval, we translated the coordinates of the polygon of the area of interest to paleocoordinates based on the PALEOMAP rotation model (Scotese, 2016) using the palaeoverse R package (Jones et al., 2018). While this procedure might not capture the continental polygon perfectly throughout all time slices, when considering the spatiotemporal resolution, we believe that the downstream results are unlikely to be significantly altered from those calculated from a fine-tuned polygon. Then, based on the paleocoastline reconstruction of Kocsis & Scotese (2021), we calculated the coastline length and area of the intersection and calculated the shoreline development index (SDI) based on these values.
It is known that SDI is scale-dependent due to its fractal nature (Seekell et al., 2022). Scale dependence of SDI measurements arises when the resolution of the measurement or the measured area differs significantly for each observation. Seekell et al. (2022) recommended using a bias-corrected SDI, which is defined as:
where d is a shoreline fractal dimension, P is a coastline length, and A is land area. Shoreline fractal dimensions can be estimated by power-regressing coastline length by area and calculating their slope. Figure ST2-1 shows the results of the power regression of coastline length by area. The slope of the regression results corresponds to d/2. When d approaches 1, it becomes scale-independent and bias-corrected SDI converges to a standard SDI (Seekell et al., 2022).
Theoretically, d must be larger than one. However, our regression results show that for all datasets, d s were much smaller than 1, sometimes being negative. This can be expected when the variation in land area is too small to induce a significant linear relationship between land area and coastline length--that is, the differences in land area between time intervals are small. In the case of the NAfEu dataset, the 95% confidence interval of the slope did contain a d value larger than 1, but not significantly larger than 1 (~1.06). Thus, we concluded that we may use the standard SDI instead of the bias-corrected version without much problem.
S2 REFERENCES
Jones, L. A., Gearty, W., Allen, B. J., Eichenseer, K., Dean, C. D., Galván, S., Kouvari, M., Godoy, P. L., Nicholl, C. S. C., Buffan, L., Dillon, E. M., Flannery-Sutherland, J. T., and Chiarenza, A. A. 2023. palaeoverse: A community-driven R package to support palaeobiological analysis. Methods in Ecology and Evolution, 14(9):2205-2215.
https://doi.org/10.1111/2041-210X.14099
Kocsis, Á. T., and Scotese, C. R. 2021. Mapping paleocoastlines and continental flooding during the Phanerozoic. Earth-Science Reviews, 213:103463.
https://doi.org/10.1016/j.earscirev.2020.103463
Scotese, C. R. 2016. PALEOMAP PaleoAtlas for GPlates and the PaleoData plotter program.
http://www.earthbyte.org/paleomap-paleoatlas-for-gplates/
Seekell, D., Cael, B. B., and Byström, P. 2022. Problems with the shoreline development index--A widely used metric of lake shape. Geophysical Research Letters, 49(10):e2022GL098499.
https://doi.org/10.1029/2022GL098499
