Models for plant self‐thinning

Plant self‐thinning, which is density‐dependent mortality, has several observed characteristics, including a certain mathematical relationship between growth and density. The original equation that describes self‐thinning is logw¯=C−(3/2)×logdensity, w¯ = mean weight. The basic equation is supported by data from ecology and forestry, but there have been a number of reported slopes that differ from −3/2. This study proposed that change in plant density over time decreases exponentially and that plant growth (weight or volume) increases over time according to one of two models: either exponential growth or sigmoid growth. Exponential growth with a finite time limit, in conjunction with exponential decrease in density, led to the equation log w = C + α/γ × log density, where α/γ < 0, w is total weight, but did not imply any particular value for its slope. Sigmoid growth, in conjunction with exponential decrease in density, led to the equation log (w/(a₁ + a₂w)) (or v) = C + a₁/γ × log density, where a₁/γ < 0, w (or v) is a total, but did not imply any particular value for its slope. For the data examined, exponential density decrease was supported by all data sets. For eight data sets, exponential growth was supported and in 7 of 8, log w = C + β log density was a good fit with α/γ a good predictor of β. For 31 data sets, sigmoid growth was supported, and in 29 of 31, log (w/(a₁ + a₂w)) (or v) = C + β log density was a good fit with a₁/γ a good predictor of β. The numerical value of β can be regarded as an index, and there was some indication that a wide range of values (or lack) is associated with a wide (or narrow) range of environments to which the species is adapted. For the larch data, the initial spatial distribution of trees was aggregated but changed toward a random distribution of individuals over time.