Annals of Botany 76: 569-577, 1995
© 1995 Annals of Botany Company
In Defence of the -3/2 Boundary Rule: a Re-evaluation of Self-thinning Concepts and Status
Institute of Grassland and Environmental Research, Aberystwyth, UK, Dept. of Plant Science, Massey University, Palmerston North, New Zealand and INRA, Station d'Écophysiologie des Plantes Fourragères, Lusignan 86600, France
The -3/2 power rule, or -3/2 self-thinning rule, was accepted 10 years ago as an important generalization, but has recently been questioned by a number of authors. This paper assesses what remains of the rule. While it has been empirically established that size-density trajectories followed by self-thinning plant populations do not necessarily follow a -3/2 slope, a more general power rule describing a density-dependent upper limit to mean shoot biomass per plant (the '-3/2 boundary rule') remains largely intact.
Principal component analysis (PCA) overestimates the steepness of the thinning slope if y:x variance ratio is greater than 1:1. Lonsdale's (Ecology 71: 1373-1388) overall mean PCA slope of -0·6 for biomass-density suggests a true mean slope close to the theoretical value of -0·5. Reduced major axis (RMA) regression appears a reasonable approximation for the -3/2 but not the -1/2 formulation of the rule. Fitting of a linear functional relationship (LFR) is a more appropriate slope estimation procedure, not previously used for data on thinning. None of these procedures estimates a boundary line that is not transgressed by any data point except through errors of measurement.
Mortality due to overcrowding ensues when a small, suppressed plant no longer holds its leaves high enough in the canopy to maintain a positive carbon balance. It follows that LAI should remain constant during thinning, and that self-thinning theory should be developed in terms of maximum leaf area index and the biomass required to support it. A derivation is presented and some of its consequences are examined.Copyright 1995, 1999 Academic Press
Self-thinning, -3/2 power rule, -3/2 self-thinning rule, boundary line, size-density compensation, regression methods
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