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

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 theorybased 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.