Ecological Archives A022-009-A3

Laura P. Leites, Andrew P. Robinson, Gerald E. Rehfeldt, John D. Marshall, and Nicholas L. Crookston. 2012. Height-growth response to climatic changes differs among populations of Douglas-fir: a novel analysis of historic data. Ecological Applications 22:154–165.

Appendix C. Diagnostic plots and R script for the selected model (Eq. 1 and Table 2 of main text).

The model showed a good fit and accommodated the hierarchical structure of the data, although the residuals show some degree of curvature (Fig. C1). In this case the use of a non-linear and non-symmetric function may be worth exploring, given the evidence of responses not being symmetric in previous studies. However, given the complex hierarchy of our data and the small degree of curvature in the residuals, we concluded that the quadratic function was adequate. The normal quantile plots and boxplots of the within-group residuals (Figs. C2 and C3) indicate that the assumption of normal distribution with mean zero and equal variance of the within-group residuals is plausible for all random effects. For the plot for the region-level random effects one of the observations deviates from the theoretical quantiles. This is region 1 which comprises the populations with the highest growth potential and with short transfer distances and therefore with better growth across test locations. The better overall growth is accommodated by a larger and positive random effect on the intercept.

The R script for this model is:

mtcm.trds.mtcm.lmer <- lmer (ht3 ~ mtcm + mtcm.trds + mtcm*mtcm.trds + I(mtcm.trds^2)

+ (1|study) + (1|region) + (mtcm.trds + mtcm |pop.id) + (1 |site.i)

 + (1 |rep.i), data = DF.all)

 

FigC1
 

   FIG. C1. Graphical summary of model fit (Eq. 1, Table 2): (a) plot of observed three-year height (mm) vs. fitted values; (b) plot of the inner most residuals versus fitted values.


 

FigC2
 

   FIG. C2. Graphical summary of model fit (Eq. 1, Table 2). Normal plots of the within-group residuals for the population-level intercept and linear terms (a–c), region (d), study (e), and planting (f) intercepts.


 

FigC3
 

   FIG. C3. Graphical summary of model fit (Eq. 1, Table 2). Normal plots of the within-group residuals for the (a) block-level intercept; and boxplots of the within-group residuals for (b) study, (c) population, (d) region, and (e) test site.


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