Coefficients in Taylor's law increase with the time scale of water clarity measurements in a global suite of lakes

Identifying the scaling rules describing ecological patterns across time and space is a central challenge in ecology. Taylor's law of fluctuation scaling, which states that the variance of a population's size or density is proportional to a positive power of the mean size or density, has been widely observed in population dynamics and characterizes variability in multiple scientific domains. However, it is unclear if this phenomenon accurately describes ecological patterns across many orders of magnitude in time, and therefore links otherwise disparate observations. Here, we use water clarity observations from 10,531 days of high-frequency measurements in 35 globally distributed lakes, and lower-frequency measurements over multiple decades from 6342 lakes to test this unknown. We focus on water clarity as an integrative ecological characteristic that responds to both biotic and abiotic drivers. We provide the first documentation that variations in ecological measurements across diverse sites and temporal scales exhibit variance patterns consistent with Taylor's law, and that model coefficients increase in a predictable yet non-linear manner with decreasing observation frequency. This discovery effectively links high-frequency sensor network observations with long-term historical monitoring records, thereby affording new opportunities to understand and predict ecological dynamics on time scales from days to decades.