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The Self-Thinning Surface

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This article introduces a generalized expression of the self-thinning rule, B = KS α N β, where B is stand biomass per unit area, N is stand density, S is relative site index, and K, α and β are parameters. On log scales, this equation becomes a self-thinning surface that defines a density-dependent upper frontier of stand biomass over a gradient of site productivity for a given species. This equation is formulated for parameter estimation as a stochastic frontier function with two error components that have different distributional properties. As an example, maximum likelihood estimates of the self-thinning surface and its confidence envelope were shown for Pinus radiata (D. Don). Furthermore, site occupancy was estimated through one of the error components of the stochastic frontier function. The conditional response of mortality at any given site occupancy was revealed by using regression quantiles. Light mortality was associated with increases in site occupancy, while heavy mortality caused a reduction in site occupancy. Changes in the estimated site occupancy had a linear relationship with changes in log stand density. The dynamic interplay between site occupancy and mortality, together with the random external effects on the self-thinning frontier, was suggested to drive the growth trajectories of individual stands during stand growth and self-thinning. Consequently, individual stands seldom travel along their self-thinning frontiers but are more likely to converge toward them during the self-thinning phase of stand development. FOR. SCI. 47(3):361–370.

Keywords: Pinus radiata; Stochastic frontier function; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; mortality regression quantile; natural resource management; natural resources; site occupancy; site productivity; stand dynamics

Document Type: Miscellaneous

Affiliations: Senior Research Scientist Research and Development Division, State Forests of NSW, PO Box 100 Beecroft, NSW, Australia, 2119, Phone: 61 2 9872 0168; Fax: 61 2 9871 6941

Publication date: 2001-08-01

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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