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i.e., the cambial zone plays the main role as the target of environmental influence
and then transforms this influence to the next stages of cell differentiation (Vaganov
et al. 1985 ; Vaganov 1996 a ). Reflecting this, equation ( 3.1 ) can be rewritten:
d N
d t
=
f 1 {
x i (t j )
}
d D
d t
=
f 2 {
f 1 }
(3.3)
d CWT
d t
=
f 3 {
f 1 , f 3 }
From this, several theoretical and experimental considerations follow:
1. The hierarchy of control simplifies the common mechanism of environmental
control.
2. There is much evidence of a close relationship between the rate of cell production
and the anatomical characteristics of the cells produced; i.e., the relationship
between two consecutive stages of cell differentiation.
3. The cell dimensions (radial diameter and cell wall thickness) are mainly
determined by the duration of these processes rather than their speed.
4. There is evidence of a nonrandom relationship between the radial dimension
and cell wall thickness (i.e., a relationship between the second and third main
processes of cell differentiation).
5. Frommeasurements of interannual variability of tree-ring characteristics, there is
a decrease in variability from a maximum for tree-ring index (width), to a mini-
mum for radial cell dimension (diameter, cell wall thickness, maximum density).
This result suggests a decreasing influence of climatic variations if one considers
the within-ring components, in contrast to interannual rings with variability.
In the case of hierarchy control, the quantitative description becomes simpler
because only one function must be defined in relation to environmental variables,
and to do this we have enough experimental data from biophysical and physiolog-
ical research of tree growth. This background allows us to create a simple version
of the process-based model of tree-ring formation under changing climatic con-
ditions (weather conditions), and to test this model by simulation of climatically
induced variations of tree-ring width and cell dimension in different climates (from
northern timberline to semiarid regions) (Vaganov et al. 1990 ; Fritts et al. 1991 ;
Shashkin and Vaganov 1993 ; Evans et al. 2006 ; Vaganov et al. 2006 ) . The basic
premise of the model is the principle of a limiting factor, well known in the physiol-
ogy of plant growth. The model is restricted by application only to the quantitative
description of climatically induced growth variations, which means that we do not
use this approach for other factors controlling tree growth, like fertilization (either
carbon dioxide or nitrogen), within-stand competition, growth release after forestry
management, etc.
A significant property of this model is its use of available, commonly mea-
sured meteorological characteristics available from any meteorological station. The
model, therefore, consolidates and compresses our recent knowledge concerning the
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