Implications of Liebig’s Law of the Minimum for Tree-Ring Reconstructions of Climate

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 and, in dendrochronology, such reconstruction is generally achieved by averaging collections of standardized tree-ring records. Averaging is optimal if growth reflects a single limiting factor and noise but not if growth also reflects locally variable stresses that intermittently limit growth. In this study a collection of Arctic tree ring records is shown to follow scaling relationships that are inconsistent with the signal-plus-noise model of tree growth but consistent with Liebig's Law acting at the local level. Also consistent with law-of-the-minimum behavior is that reconstructions based on the least-stressed trees in a given year better-follow variations in temperature than typical approaches where all tree-ring records are averaged. Improvements in reconstruction skill occur across all frequencies, with the greatest increase at the lowest frequencies. More comprehensive statistical-ecological models of tree growth may offer further improvement in reconstruction skill.