Improving competition representation in theoretical models of self-thinning: a critical review

1 Many theoretical models have been proposed to explain the empirical self-thinning relationship given by Yoda et al. in 1963 for even-aged, monospecific stands of plants, but the models are inadequate to allow consensus on the processes driving variation in density-dependent mortality and self-thinning. 2 Most non-individual based models (non-IBMs), and many IBMs, employ a common representation of competition in which a finite amount of potential crown area remains completely allocated throughout self-thinning, making stand density inversely proportional to mean projected crown area. 3 This representation entails four assumptions regarding the competition process: the population is adequately represented by the mean plant; total stand resource utilization is constant throughout self-thinning; competition is a horizontal packing process; and differences in initial stand conditions may affect the rate of competition but not the process itself. 4 Reviewing published empirical data, the competition literature and the logical implications for the self-thinning process shows that all four assumptions are untenable as generalizations. Unfortunately, their application provides neither a mortality-inducing mechanism nor insight into the relationship between stand growth and mortality. 5 Explaining the observed variation in self-thinning relationships therefore requires improved representation of the competition process. This improvement is likely to require IBMs that explicitly represent variation in plant size or resource acquisition, two-dimensional stand distribution, dynamic rather than static stand resource utilization, and, perhaps, explicit three-dimensional stand development. Most importantly, the requirement for explicitly modelling mortality mechanisms implies that whole plant models may be insufficient for insight into the self-thinning process. 6 The review reinforces the need to assess mechanistic models for more than their ability to reproduce a single, high-level pattern. Such models should be assessed for their ability to simultaneously reproduce multiple features selected from the levels of both the modelled mechanisms and the high-level patterns. 7 Progress in understanding the observed variation in self-thinning currently requires a shift from searching for universal insight into the modelling of specific mechanisms for specific plant types, eventually leading to a broader theory explaining how variation in plants affects the competition process.