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Table 5.1 also shows that there is a relationship between the juvenile growth max-
imum (a) and concavity (b) ( r
6). This relationship is very clear in
the truncated group data fits between (at) and (bt) ( r
=−
0.66, n
=
6). Similarly, the
diminution in ring width over the first 50 years (Table 5.1 , column [rwr]) is strongly
correlated with both (a) and (b). Hence, regardless of the reason, fast-growing trees
will display greater reduction of ring width. Helama et al. ( 2005b ) , by varying (b)
through time (where [a] and [c] are fixed) are standardizing the slower-growing trees
with the 'higher growth rate' RCS curves and the faster-growing trees with 'lower
growth rate' RCS curves (the curve with [a] and [c] held constant will have a higher
rate of radial increase if [b] is small rather than large). The resulting mean values
of the indices will be correspondingly greater for fast-growing trees and lower for
slow-growing trees, in comparison to the means of indices generated by using a
single fixed parameter RCS curve. The low-frequency variance in chronologies is
imparted by changes in the means of index series .
Leaving aside the issue of whether a count of a relatively small number of tree
samples through time is likely to be a realistic representation of between-tree com-
petition when the sample area is very large and varies in its northern boundary by
up to 80 km over past millennia, Helama et al. ( 2005b ) are, in effect, amplifying the
medium- to low-frequency variance in their ECS chronology by an amount that is
directly proportional to the relative growth rate of the trees, regardless of whether
there is any change in their direct competition status. This can be seen in the inverse
pattern of variability through time of their concavity values, on the one hand, and in
the difference in the ECS and RCS chronologies on the other (compare Fig. 4a, b in
Helama et al. 2005b ) .
A positive association between changing concavity and tree-sample number dur-
ing the last 7000 years (see Fig. 4 in Helama et al. 2005a ) may reflect a common
response in both variables to changing temperature forcing; i.e., warmer periods
resulting in faster tree growth (and greater decay rate of ring width) and increased
germination and survival of pine trees. Were this to be true, even to some extent, the
deliberate biasing of the RCS curve implicit in the ECS approach could be question-
able. However, even in subfossil chronologies a period with poor overlap between
two groups of contemporaneous trees can result in a period affected by this 'modern'
sample bias. The most recent section of a long subfossil chronology is invariably
made up of a 'modern sample' from living trees, and the recent end of almost all
such chronologies will suffer from modern-sample bias to some extent.
=−
0.96, n
=
5.7 Discussion and Suggested Directions for RCS Development
It is the unavoidable loss of medium- and low-frequency variance, implicit in curve-
fitting methods, which leads to the necessity of using RCS and the consequent
requirement to recognize and overcome a number of problems associated with its
specific implementation. Had the five sample series in Fig. 5.2b been standardized
by using curve-fitting methods, the means of each series would each be set to 1.0 and
 
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