A power function for forest structure and regeneration pattern of pioneer and climax species in patch mosaic forests

The DBH-class distribution in natural deciduous broad-leaved forests was el ucidated with a power function. A power function (y = ax(b), y: stem densit y, x: represents DBH class, a and b: constants) fits the distribution bette r than an exponential function (y = a exp bx). The parameter b in the power function is approximately -2. This means that the natural forests studied have a patch-mosaic structure and that tree cohorts regenerate from gaps. P arameter a implies the number of juveniles, and b means size-dependent mort ality. The value of -2 for parameter b means that when trees in a given DBH class double their DBH, the density of the size class should decrease by o ne-fourth. This phenomenon results from self-thinning and is caused by hori zontal space competition among trees, called the 'tile model'. The paramete r describing DBH-class distribution for a forest with self-thinning patches should be approximately -2. I call this the '-2 power law' for DBH-class d istribution. In a typical natural forest dominated by deciduous broadleaf t ree species, trees are recognized as pioneer or climax species by the param eters describing their regeneration patterns. When I applied the power func tional model to the DBH-class distribution of each dominant species, in pio neer species parameter a was high and b was less than -2 (markedly less tha n zero), suggesting that there are many juveniles, but mortality is high. O n the other hand, in climax species parameter a was low value and the value of b was larger (negative, but closer to zero), suggesting that there are not many juveniles, but mortality is low. A power-function analysis of DBH- class distribution can be used to clarify the patch mosaic structure of a f orest, and to clarify the regeneration pattern of pioneer and climax specie s by applying the function for each species.