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Relative growth rate is an ineffective response variable for capturing size effects on tree growth.
MacFarlane, David*,1, Kobe, Richard1, 1 Department of Forestry, East Lansing, Michigan, USA
ABSTRACT- Relative growth rate (RGR) has become the standard response metric for tree growth analysis. It purportedly allows for size differences between trees to be "scaled out" so that other factors that influence growth can be evaluated independently of size. We suggest that RGR is a misleading and ineffective response variable for capturing size effects on growth, and that its mathematical convenience and corresponding ubiquity obscure further progress toward understanding the effects of size, resources, and other environmental factors on growth. We use theory and empirical data sets on tree growth to demonstrate undesirable qualities of RGR as a response variable, including: 1) Rather than scaling out size, RGR scales in size such that it makes size effects intractable and uninterpretable; 2) RGR could lead to false conclusions regarding resource effects on growth because it confounds size and growth. For example, although foliar N is a significant predictor of absolute growth rate in American beech saplings, analyzing the growth response as RGR obscures nitrogen effect through confounding growth and size. 3) In a similar vein, RGR-based models generally resulted in poorer fits than absolute growth models because RGR-based models are size biased and thus decouple the growth response from the predictor variables. To remedy these shortcomings of RGR, we advocate alternative models for growth analysis that relate absolute growth rates to resource supply rates and tree size. These models use size explicitly as a predictor variable, so that size effects on growth can be directly interpreted, rather than simply divided away.
Key words: growth analysis, size scaling, relative growth rate, tree growth