Stochastic frontier analysis of a classic self‐thinning experiment

  The classic experiment that gave rise to the self‐thinning rule 40 years ago was re‐analysed using stochastic frontier functions. The estimated slope of the self‐thinning boundary line was almost identical to the original proposed value. However, contrary to the original conclusion that the self‐thinning boundary line remained invariant across the soil fertility gradient, the intercept was found to increase with soil fertility. Stochastic frontier analysis also provided a more realistic estimate of the maximum asymptotic stand density than the original work, by separating the effects of density‐dependent and density‐independent mortalities during self‐thinning in a composed error term in the model specification. The time‐course of self‐thinning across the soil fertility gradient was described by a non‐linear function, which enabled the estimation of a minimum possible stand density that could still maintain full site occupancy (i.e. the maximum asymptotic stand density at the end of self‐thinning). The maximum asymptotic stand density decreased more rapidly on more fertile soils and the difference in maximum asymptotic stand density among the five levels of soil fertility increased non‐linearly with time. Site carrying capacity was defined as stand biomass shown by the point on the self‐thinning boundary line at the end of self‐thinning. This definition led to a direct functional link between the self‐thinning boundary line and site carrying capacity for even‐aged plant populations.