A new analytical model based on the −3/2 power rule of self-thinning

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Abstract
A nonlinear analytical model is developed to describe the relationship between average plant size (weight or volume) and stand density in single-aged, monospecific plant populations. The model gives estimates of the slope and intercept of the −3/2 power rule asymptote, the nature of the size–density trajectory, and such features as relative density at crown closure and the effects of soil type or site index. The model is tested by growing red alder (Alnusrubra Bong.) seedlings under greenhouse and lath house conditions at three initial spacings (8 × 8, 4 × 4, and 2 × 2 cm) and two soil types (river loam and alder forest soil) for 525 growth days. There are seven harvests, starting at crown closure. All size–density trajectories tend consistently towards the same single asymptote irrespective of initial spacing, soil type, or age. The asymptote slope and intercept are 1.46 and ca. 94 kg tree−1•m−2. The crown closure line is parallel to the asymptote at a relative density of 4.6 × 10−3. The model also adequately describes the size–density trajectories for 20–50-year-old red pines (Pinusresinosa Ait.) growing at six initial spacings. The asymptote slope and intercept are 1.6 and ca. 87 × 103 m3•tree−1•ha−1, respectively.