Modelling height–diameter relationships in living Araucaria (Araucariaceae) trees to reconstruct ancient araucarian conifer height

To reconstruct a fossil forest in three dimensions, an accurate estimation of tree height is crucial. However, modelling the height–diameter relationship of ancient trees is difficult, because the trunks of fossil trees are usually fragmentary, which makes direct height measurements impossible. One practical approach for reconstructing ancient tree height is to use growth models based on the height–diameter relationships of the nearest living relatives of the fossil taxa. Here we apply 19 growth models to describe height–diameter relationships of living Araucaria trees for establishing good growth models for ancient Araucariaceae trees. Data come from four living populations of the genus Araucaria: Araucaria bidwillii and A. cunninghamii in Queensland, Australia, and A. cunninghamii and A. hunsteinii in New Guinea. According to an AIC-based model selection, a Power model with an exponent of 0.67 (termed here the modified Mosbrugger model) is the best for each population and for the entire dataset (157 trees), but normalization constants differ across populations. To find the best models for the genus Araucaria, 100 random samples (each population generating 25 random samples) from the entire dataset are tested. Based on 100 curve fitting results on each model and multiple performance criteria, three median models are generated from the medians of their parameter estimates. The median Power model works best for Araucaria, but the modified Mosbrugger and Curtis models perform similarly well. In a case study, we revise tree heights of Upper Jurassic araucariaceous logs in Utah, USA, by applying these three models.

Methods
We compiled datasets on tree height–diameter information from three Araucaria species: Araucaria bidwillii, A. cunninghamii and A. hunsteinii. These datasets had originally been collected to determine the size composition of natural stands, describe forest structure, or analyse height–diameter relationships. However, standard in each of these studies was taking the diameter at breast height (DBH) of each tree trunk and the height (H) of the respective tree. In our study, we used both measurements to establish the height–diameter growth models presented here.