Whereas the open-grown tree relationship shows a monotonically decreasing form, this is only partially matched by the predictions of the individual tree growth models.

In some cases there is a peak at the beginning of the simulation period, before height:diameter ratios decrease. The monotonically decreasing pattern was predicted by Moses and BWIN on all sites, except for pine on good-average sites by BWIN. Prognaus correctly predicts open-grown tree patterns for spruce on poor sites and for pine on good CP-673451 mouse sites. Silva predicts monotonically decreasing patterns for spruce on good and poor sites. The dimensions of open-grown trees at the age of 100 years for different site indices for the four growth models are shown in Table 11. Generally, predicted AZD2281 research buy diameters are always higher on good

sites than on poor sites for each of the simulators. On good sites the predicted diameters range from 68 to 245 cm for spruce and from 44 to 85 cm for pine. The diameter predicted by BWIN for spruce is considerably higher than the diameter predicted by the other simulators. On poor sites, predicted diameters for both spruce and pine range from 24 to 42 cm. Please note that predictions of the four individual-tree growth models agree best for the average site. Another detail regarding the predicted diameters deserves attention (Table 11): excluding BWIN, differences in the diameter of an open-grown tree between good and poor sites can be as large as 78 cm and as small as 26 cm. Thus, the influence of site on diameter growth is clearly different among the different individual-tree growth models. Crown ratios for open-grown trees can be found in

Table 12. By constraint, Moses always yields a crown ratio of 1. Prognaus predicted a crown ratio for spruce >0.96 and a crown ratio for pine >0.67. Crown ratios obtained from BWIN and Silva were highly variable during the simulation period. For BWIN, they ranged almost from 0.39 to 0.99 for spruce and 0.3 to 0.81 for pine. For Silva, they ranged from 0.50 to 0.70 for spruce and from 0.28 to 0.67 for pine. We found a bias of diameter increment that ranged from 0.01 to 0.23 cm year−1 (absolute values) depending on the growth model and region. Our results do not indicate the superiority of any particular model, since it was the same growth model that had both the smallest and the highest bias. This prediction bias agrees well with results from numerous comparable studies, which report a bias of 0.002–0.273 cm year−1 (absolute values) (Pretzsch and Dursky, 2001, Sterba et al., 2001, Pretzsch, 2002, Froese and Robinson, 2007, Schmidt and Hansen, 2007 and Härkönen et al., 2010). If bias exists, it can be temporal or spatial in nature. Temporal bias is frequently found in evaluations of forest growth models (Sterba and Monserud, 1997, Pretzsch and Dursky, 2001 and Pretzsch, 2002).