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.