Title: "Liebig's Law and dendroclimatology: Finding hidden climate signals in tree rings using ecological theory"
Abstract: A basic principle of ecology, known as Liebig's Law of the Minimum, is that plant growth reflects the strongest limiting environmental factor. This principle implies that a limiting environmental factor can be inferred from historical growth patterns, and in dendrochronology such reconstruction is generally achieved by averaging collections of standardized tree-ring records. Averaging is optimal if growth records are composed of a signal of interest plus unrelated noise, but if variable growth across trees reflects the operation of the Law of the Minimum, averaging is no longer optimal because certain variations reflect a local, more-limiting factor. Here we use a large collection of Arctic tree-ring density records to show that growth patterns reflect operation of Liebig's Law. Recognition that the Law of the Minimum operates at the level of individual trees can be leveraged to improve the skill of dendroclimatological reconstructions. Reconstruction of Arctic-wide temperature using a reconstruction method that takes advantage of the law of the minimum increases the squared cross-correlation with instrumental records from 0.14 to 0.42. The greatest increases in reconstructive skill occur at the lowest frequencies and result in recovery of recent trends in Arctic warming, eliminating the so-called "divergence problem" in tree-ring density reconstructions of arctic temperature. More comprehensive models of tree-growth may offer still greater improvement in reconstructive skill.