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ŠUMARSKI LIST 1-2/1966 str. 94     <-- 94 -->        PDF

Question 5. What is the minimum number of replicates needed?

Wright (1962) has studied the question of replicate number and comes up
with a table where he presents the number of replicates needed in order to
detect the differences of a certain magnitude when the average range in plot
means is known. The latter value can be calculated from comparing a few
randomly selected plots within a uniform forest population. For the purpose
of provenance studies it seems reasonable to specify that about 1/3 of the range
of variation in plot means for a uniform stand should be detectable. If the
range of variation is very great (low heritability), then the provenance is so
sensitive to environmental differences that its value for practical purposes is
low in view of the risk involved in matching it with the proper environmental
conditions. Small differences between provenances may be of theoretical interest,
but in practice such statistical accuracy is not called for.

If differences equal in magnitude to 1/3 of the range in plot means are
considered as the minimal differences that are of practical interest, then 7
replicates are sufficient to indicate a significance at 5´% level (Wright 1962).
Thus 7 is considered to be the minimal number of replicates.

Question 6. At what age is the neighbour effect severest?

Johnsson (1963) believes that the neighbour effect is relatively unimportant
in a plot of 36 or more trees since, coupled with randomization, there will be
all sorts of neighbours at the different sides of the plot and at different
replicates. He also points out that if a surround is being considered, one should
use the surround of the same progeny or provenance as the plot, since a
standard (hold-over tree) would suppress some plots and improve others.

Thus one could have a larger plot, and either consider the marginal trees
to be a surround, or else include them in the plot, depending on whether this
makes much of a difference.

It is likely that the neighbour effect is severest at the thicket stage when
competition between the trees is at its culminating point (about 15 years).

During that time the need for a surround may be greatest; later, however,
after some improvement thinnings, all the trees in a plot could be used for
the description of a provenance.

To summarize, the six questions posed above lead to the following

1. The minimum number of trees that will describe a stand is 8.
2. The minimum age at which productivity per unit area can be estimated
is 33 years.
3. In order to reconstruct a population, a minimum of 40 trees are needed.
4. The total area of the plantation should not exceed 5 hectares.
5. The minimum number of replicates needed is 7.
6. At the age of 15 years at least one row of surround trees is needed.
To satisfy these minimal conditions, coupled with the need of maintaining
silvicultural treatments that are standard for Central Europe it is proposed to
use the following design for provenance experiments with pine and spruce:
A complete block design, with 8 replicates and 49 pine trees per plot planted
at a 0,60 X 1,20 m spacing and 36 spruce trees per plot planted at a 1,0 X 1,0
m spacing.