Estimating the age-diameter relationship of oak species in Switzerland using nonlinear mixed-effects models

Tree growth plays a key role in forest dynamics, yet little attention has been paid to quantifying tree age-diameter relationships. Predicting diameter growth of oaks is especially important due to their role in nature conservation and adaptive forest management under climate change. Thus, we (1) identified environmental variables that shape age-diameter relationships of oaks and (2) quantified the accuracy of predictions based on these variables. We determined the age-diameter relationship of 243 oaks (Quercus spp.) growing in Switzerland by using tree-ring samples. Nonlinear mixed-effects models based on a modified Chapman-Richards equation were fitted with environmental variables included as covariates. The fixed effects elevation, slope and water-holding capacity were most important in shaping the age-diameter relationships. Lower elevations, steeper slopes, north-facing aspects, higher water-holding capacities and moister summers resulted in larger maximum diameters. For 75 % of the oaks, age-diameter relationships predicted by the fixed effects matched fairly well the observations (root mean square error between predictions and observations <6 cm); the inclusion of random effects reduced root mean square errors for 86 % of the trees. These results suggest that water runoff plays a key role for the age-diameter relationships, accompanied by limiting temperature effects at higher elevations. The fixed effects covered variability in site quality, whereas the random effects included tree-specific deviations from expected age-diameter relationships, potentially due to neighbourhood effects such as stand density and competition.