A Theory-Driven Approach to Tree-Ring Standardization: Defining the Biological Trend from Expected Basal Area Increment

Abstract

One of the main elements of dendrochronological standardization is removing the biological trend, i.e. the progressive decline of ring width along a cross-sectional radius that is caused by the corresponding increase in stem size and tree age over time. The “conservative” option for removing this biological trend is to fit a modified negative exponential curve (or a straight line with slope ≤ 0) to the ring-width measurements. This method is based on the assumption that, especially for open-grown and/or shade-intolerant species, annual growth rate of mature trees fluctuates around a specific level, expressed by a constant ring width. Because this method has numerical and conceptual drawbacks, we propose an alternative approach based on the assumption that constant growth is expressed by a constant basal area increment distributed over a growing surface. From this starting point, we derive a mathematical expression for the biological trend of ring width, which can be easily calculated and used for dendrochronological standardization.The proposed C-method is compared to other standardization techniques, including Regional Curve Standardization (RCS), of tree-ring width from ponderosa pines (Pinus ponderosa Douglas ex P.Lawson & C.Lawson) located at the Gus Pearson Natural Area (GPNA) in northern Arizona, USA. Master ring-index chronologies built from ring area, RCS, and C-method reproduced stand-wide patterns of tree growth at the GPNA, whereas other standardization options, including the “conservative” one, failed to do so. In addition, the C-method has the advantage of calculating an expected growth curve for each tree, whereas RCS is based on applying the same growth curve to all trees. In conclusion, the C-method replaces the purely empirical “conservative” option with a theory-based approach, which is applicable to individual ring-width measurement series, does not require fitting a growth curve using nonlinear regression, and can be rigorously tested for improving tree-ring records of environmental changes.