Modeling individual tree mortality for Austrian forest species

Abstract

Individual tree mortality models were developed for the six major forest species of Austria: Norway spruce ( Picea abies), white fir ( Abies alba), European larch ( Larix decidua), Scots pine ( Pinus sylvestris), European beech ( Fagus silvatica), and oak ( Quercus spp.); a joint model for the remaining broadleaf species was also developed. Data came from 5-year remeasurements of the permanent plot network of the Austrian National Forest Inventory. Parameters of the logistic equation were estimated using maximum likelihood methods. For all species, we found the hyperbolic transformation of diameter ( D −1 ) to be highly significant in predicting the high mortality rates for small diameter trees and decreasing mortality rates for larger diameters. For spruce, a quadratic transformation in D was needed to accurately model the increase in mortality observed for large, low-vigor trees with diameter >70 cm, which resulted in a U-shaped distribution. Crown ratio was also consistently significant, except for oak. We likewise found basal-area-in-larger-trees ( BAL) to be a highly significant predictor of mortality rate for all species except fir and oak. Predicted mortality rate increases as the basal area in larger trees increases and as crown ratio decreases. The resulting logistic mortality model had the same general form for all species, with the signs of all parameters conforming to expectations. In general, chi-square statistics indicate that the most important variable is D −1, the second most important is crown ratio, and the third most important predictor is BAL. The relative importance of crown ratio appears to be greater for shade tolerant species (fir, beech, spruce) than for shade intolerant species (larch, Scots pine, oak). Examination of graphs of observed vs. predicted mortality rates reveals that the species-specific mortality models are all well behaved, and match the observed mortality rates quite well. The D −1 transformation is flexible, as can be seen by comparing the rather different mortality rates of larch and Scots pine. Predicted and observed mortality rates with respect to crown ratio are quite close to the observed mortality rates for all but the smallest crown ratios ( CR<20%), a class with very few observations. Finally, the logistic mortality models passed a validation test on independent data not used in parameter estimation. The key ingredient for obtaining a good mortality model is a data set that is both large and representative of the population under study, and the Austrian National Forest Inventory data satisfy both requirements.