Modeling and evaluating site and provenance variation in height–diameter relationships for Betula alnoides Buch.–Ham. ex D. Don in southern China

Tree height (H) and stem diameter at breast height (DBH) (H-D) relationship is correlated with timber yield and quality as well as stability of forest and is crucial in forest management and genetic breeding. It is influenced by not only environmental factors such as site quality and climate factors but also genetic control that is mostly neglected. A dataset of H and DBH of 25 provenances of Betula alnoides Buch.–Ham. ex D. Don at four sites was used to model the H-D relationship. The dummy variable nonliner mixed-effect equations were applied to evaluate the effects of sites and provenances on variations of the H-D relationship and to select superior provenances of B. alnoides. Weibull equation was selected as the base model for the H-D relationship. The sites affected asymptotes of the H-D curves, and the provenance effect on asymptotes of the H-D curves varied across sites. Taking above-average DBH and lower asymptote of the H-D curves as indicators, five excellent provenances were screened out at each site with a rate of 20%. Their selection gains of individual volume ranged from 1.99% to 29.81%, and their asymptote parameter (k(j) ) and H-D ratio were 7.17%–486.05% and 3.07–4.72% lower than the relevant total means at four sites, respectively. Genetic selection based on the H-D relationship could promote selection efficiency of excellent germplasms and was beneficial for the large-sized timber production of B. alnoides.