• biomass density;
  • density-dependent mortality;
  • growth form;
  • height–diameter allometry;
  • Metabolic Scaling Theory;
  • plant–plant interactions;
  • size-symmetric competition


  1. The form and generality of the biomass–density relationship, especially during self-thinning of crowded stands, have been intensively debated in recent years. All models of self-thinning assume that the trajectory is independent of the initial pre-thinning density, so populations differing in initial density can be analysed together. As plant allometry is a determinant of the self-thinning trajectory, and competition alters plants' allometric growth, initial density may have consequences for the self-thinning trajectory.
  2. To ask whether initial density can influence allometric relationships and the biomass–density trajectory, we grew Fagopyrum esculentum populations at three high densities and measured shoot biomass, density and the height and diameter of individual plants at six harvests.
  3. Initial density did not affect the slope of the log biomass–log density relationship, but there was a clear and significant effect on the intercept. Populations sown at higher densities had significantly more biomass at a given density of survivors.
  4. If the data for all densities and harvests are analysed together, the log biomass–log density relationship is linear with a slope of −0.377, which is consistent with the predictions of Metabolic Scaling Theory. If the independent variable initial density is included as a factor, the estimated slope of the log B–log N relationship is much steeper and consistent with the classical ‘Self-thinning Rule’.
  5. The position of the self-thinning trajectory is determined in part by the biomass density: the relationship between mass and volume. Initial density could affect this by altering allometric growth in a way that influences architectural compactness. An alternative hypothesis is that competition at higher initial density is more size symmetric, which has been shown to reduce growth and mortality.
  6. Synthesis. The self-thinning trajectory is not always independent of initial population density. Interpopulation scaling patterns, even within one species, do not reflect processes within populations, and this conflation lies behind much of the current debate about size–density relationships in plant populations and communities. Interactions among plants and allometry are more important than internal physiological scaling mechanisms in determining the self-thinning trajectory of crowded stands.