Global Demonstration of Local Liebig's Law Behavior for Tree-Ring Reconstructions of Climate

Liebig's law of the minimum posits that at any given time the growth factor that is least abundant, relative to physiological requirements, controls plant growth. Dendrochronological reconstructions of temperature and precipitation invoke Liebig's law to justify using tree growth as a proxy for climate and when choosing which trees to sample, but historically reconstruction techniques have not accounted for the influence of Liebig's law on differential growth between sampled trees within a given site. Such an influence implies that site-wide limitations associated with regional climate variability would be most strongly expressed in tree rings experiencing high relative growth in a given year. We demonstrate that local Liebig's law stresses are globally identifiable across ring width and density data sets produced by over 300 different researchers. Furthermore, the local signature of Liebig's law is found at both temperature- and moisture-limited sites. Chronologies based on trees undergoing the highest relative growth in a given year more accurately record climate variability than the mean chronology, especially at sites where more trees were sampled. These results suggest the potential for better reconstructing historical climate variability through pairing intensive tree-ring sampling with a quantitative focus on those trees experiencing the highest relative growth.