Estimating the self-thinning line from mortality data

Self-thinning is fundamental to modern density-based forest management. The process of self-thinning arises from the dynamic interaction of stand growth and mortality at equilibrium conditions. However, despite the dynamic basis for the self-thinning process, it is typically modeled using static size-density data. We tested the ability of a simple stand mortality model to estimate the self-thinning line. We used data from long-term silvicultural experiments for six common Eucalyptus species in southeastern Australia. Our approach built on existing mortality model structure that predicts survival trajectories that follow a self-thinning line. We used Poisson and negative binomial generalized linear models for count data as well as a non-linear least squares procedure on the integrated scale to calibrate the mortality model. Derived self-thinning parameters were compared to parameters calibrated on the static allometry between quadratic mean diameter ( Dq ) and stand density ( N ) using two reference methods (linear model and stochastic frontier analysis). Our dynamic mortality models provided estimates of the self-thinning line that were as good as or better than those obtained using reference methods; however, this required accounting for overdispersion of mortality count data. We validated survival trajectories using independent data for the three most abundant eucalypt species and found that they showed excellent behavior. Survival trajectories predicted by the mortality models were consistent with, and accurately estimated, the self-thinning line for the eucalypt species in our study. The simplicity of calibrating mortality models using GLM methods raises the possibility of quantifying how environmental drivers influence the dynamic self-thinning equilibrium.