Korčak’s law of the predicted suitable patches. The fractal dimension of the patches is derived from the scaling exponent, ε=D
/2, of the probability of exceedance of the patch size (Equation 3) for SNPL, PIPL, and REKN. The probability of exceedence of the patch size is represented for the years 2006, 2020, 2040, 2060, 2080, and 2100. The probability of exceedance is compared against the box-counting scaling laws for the years 2002-2010. Additional file 1: Table S2 reports the values of D
. The insets represent the probability density functions (pdfs) of the patch size that show a heavy-tailed behavior.