A mechanistic analysis of self-thinning in terms of the carbon balance of trees

The self-thinning behaviour of a monoculture forest is examined from a mechanistic viewpoint, in terms of the carbon balance of trees at the stand level. Two approaches are described: the first is based on simple assumptions concerning the balance between growth, photosynthesis and respiration; the second uses the process-based I.T.E. EDINBURGH FOREST model, extended to include tree birth and death, to examine the assumptions of the first approach at a more mechanistic level and to interpret the observed variation in the responses to shading and soil fertility in terms of a single model. The first approach leads to a power law relation m varies n-1/y between mean biomass per tree (m) and the number of trees per unit ground area (n), where y is the exponent characterising the rate at which respiration (r) scales with biomass (i.e. r varies m(y)). For values of y less than 1, m and n are predicted to increase and decrease, respectively, as powers of time (t) such that the biomass per unit ground area (M) increases linearly with t for any value of y. When y equals 1, m and n vary exponentially with t and M remains constant. When r is assumed to he proportional to stem cambium surface area, the value of y is shown to lie in the range 0.5 to 1 depending on the rate of stem taper. This leads to slopes on a log m vs. log n self-thinning plot in the range -1 to -2 and typically around -1.5 for rates of taper based on mechanical stability requirements. For the second approach, the I.T.E. EDINBURGH FOREST model, a previously published mechanistic model of plantation growth at the stand level (Thornley, 1991), is extended to natural stands by introducing average stem birth and death rates that are functions of the carbon and nitrogen substrate status of trees. Growth of even-aged and mixed-age forests over about 500 years is simulated under a variety of environmental and physiological conditions. In general, the forest model predicts a curved log m vs.log n thinning line, but has a reasonably well-defined linear section under most conditions. The slope of the linear portion flattens as the rate at which cambium surface area scales with structural biomass increases, in qualitative agreement with the analytical prediction of the first approach. Quantitative differences between the two approaches are interpreted in terms of the processes represented in the forest model. In general, the height of the thinning line increases with irradiance, but is relatively insensitive to soil nitrogen, with no change in slope in either case. However, at very low irradiance or soil nitrogen levels, the slope flattens continuously and the entire thinning line becomes markedly non-linear. Even-aged stands and mixed-age stands have different thinning slopes.