Density dependence of plant population processes has been analyzed independently of physiological processes. Recent evaluation has demonstrated that tree-size-distribution-based models with one-sided competition along vertical canopy profile readily reconstruct density-yield relationship, self-thinning, and time trend of size structure. However, an individual is expressed by one size dimension (i.e. trunk diameter), such models cannot demonstrate geometric scaling of self-thinning and dimensional allometric change with time.

We took an alternative,shoot-based approach to reproduce population consequence of density dependence. We constructed a simulator named PipeTree to describe annual shoot growth and branching in three-dimensional space. Constraints included were simple allometric relationship at current-year shoots, branching rule, pipe-model relationship that relates stem sectional area and the above foliage mass, available light resource at every shoot tip that control assimilation of shoot foliage, and operational assimilate allocation rules. We tuned it to subalpine fir populations for quantitative validation.

We could reproduce the development of size hierarchy due to crowding, geometric rule of self-thinning, and time course of trunk diameter vs. tree height allometry observed in real fir stands. Quantitative patterns of density dependence of plant populations were considerably explained by light-resource limitation in packed foliage distribution. The model further predicted the population-level response to increasing photosynthetic capacity by increasing atmospheric carbon dioxide. Resulted change was no mere acceleration of stand growth, but architectural modification. We concluded that a simple individual-tree-based forest development simulator with single individual size parameter was not powerful enough to describe the forest response to global change.

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