B. B. Cael, Jeremy Biggs, David Seekell

Global-scale characterizations of Earth's lakes and ponds assume their surface areas are power-law distributed across the full size range. However, empirical power-laws only hold across finite ranges of scales. In this paper, we synthesize evidence for upper and lower limits to power-law behavior in lake size-distributions. We find support for the power-law assumption in general. We also find strong evidence for a lower limit to this power-law behavior, although the specific value for this limit is highly variable (0.001 - 1 km$^2$), corresponding to orders of magnitude differences of the total number of lakes and ponds. The exact mechanisms that break the power-law at this limit are unknown, but we are able rule out mapping errors as a first-order factor. There is no evidence for an upper limit to power-law behavior at the global scale. There is inconsistent evidence for an upper limit at regional-scales. Explaining variations in these limits stands to improve the accuracy of global lake characterizations and shed light on the specific mechanism responsible for forming and breaking lake power-law distributions.