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Annals of Botany 79: 251-257, 1997
© 1997 Annals of Botany Company

Cross-validation of Non-linear Growth Functions for Modelling Tree Height–Diameter Relationships

LIANJUN ZHANG

Faculty of Forestry, State University of New York, College of Environment Science and Forestry, Syracuse, NY, 13210, U.S.A.

Received March 1, 1996 ; Accepted September 4, 1996

Six non-linear growth functions were fitted to tree height–diameter data of ten conifer species collected in the inland Northwest of the United States. The data sets represented a wide range of tree sizes, especially large-sized trees. According to the model statistics, the six growth functions fitted the data equally well, but resulted in different asymptote estimates. The model prediction performance was evaluated using Monte Carlo cross-validation or data splitting for 25-cm diameter classes. All six growth functions yielded similar mean prediction errors for small- and middle-sized trees. For large-sized trees [e.g. DBH (diameter at breast height)>100 cm], however, five of the six growth functions (except the Gompertz function) overestimated tree heights for western white pine, western larch, Douglas-fir, subalpine fir, and ponderosa pine, but underestimated tree heights for western hemlock and Engelmann spruce. Among these five functions, the Korf/Lundqvist and Exponential functions produced larger overestimations. The Schnute, Weibull, and Richards functions were superior in prediction performance to others. The Gompertz function seemed always to underestimate tree heights for large-sized trees.

Sigmoidal growth functions; non-linear regression models; prediction error; model cross-validation; data splitting; Monte Carlo


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