Background |
Field sampling is
one of the major sources of information in empirical research in
ecology, forestry and related disciplines. When decisions are made
about sampling and plot techniques the researcher needs to take into
account the tradeoff between precision/accuracy and cost. Point to
object distance sampling, also called *k*-tree sampling or
fixed-count sampling (because per sample a fixed number of *k*
nearest trees are being taken as sample trees), belongs to a class
of plot design techniques that is very practical and is easily
implemented in the field. Its practicability is frequently stressed
as a major advantage over, for example, fixed area plots. In
ecology, *k*-tree sampling is frequently applied (Krebs 1999),
while forest inventory statisticians tend to advise against it
(Pyandeh and Ek 1986, Mandallaz 1995, Schreuder 2004) because of
concern for bias. An unbiased estimator had only been developed
recently – resulting from DFG project KL894-7 (Kleinn and Vilčko 2006b).
However, that unbiased estimator requires determining
(mapping) the position of various neighbouring trees to be able to
determine the per-sample-tree selection probability which is
required for application of the Horwitz-Thompson estimator.
A number of research questions arise from project KL894-7, in particular regarding the
practicability of the unbiased estimator approach, the possibility
to develop easier to implement proxies and, above all, whether the
approach can also be applied to a class of what we call here
__restricted __*k*-tree sampling, where the *k*
“nearest” trees around a sample point are selected subject to
particular conditions; specifically, the **point-centered
quarter method** and the **T-square sampling
technique**. |

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