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Zone of influence models for competition in plantations

Published online by Cambridge University Press:  01 July 2016

D. J. Gates  and
M. Westcott
D. J. Gates
Affiliation:
CSIRO Division of Mathematics and Statistics, Canberra
M. Westcott
Affiliation:
CSIRO Division of Mathematics and Statistics, Canberra
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Abstract

A plantation is modelled in terms of discs of random size centred on the points of a two-dimensional lattice, together with rules for partitioning the union of these discs. The resulting sets are functions of random sequences, and some properties of these functions are deduced. Results are given which relate various properties of measurements on a plantation to measurements of individual plants and of plants in isolation. These include limit theorems for complete plantations and for samples. They also lead to a rigorous demonstration of certain well-known empirical relations between typical measurements and survival frequencies and to some new relations which are amenable to test. The model is a formulation of computer simulations which have had success in describing competition in plantations, but are too costly for routine forest management.

Keywords

CENTRAL LIMIT THEOREMCOVARIANCE FUNCTIONERGODIC THEOREMFUNCTIONS OF RANDOM SEQUENCESGEOMETRIC PROBABILITYPLANT COMPETITION MODELSPLANT MEASUREMENTSSURVIVAL PROBABILITIES
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 3 , September 1978 , pp. 499 - 537
Copyright
Copyright © Applied Probability Trust 1978 

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