The Relationship
between Growth Rate and Emergence in Seedlings of Picea Engelmannii Parry
Department of Botany
University of British Columbia
Vancouver, B. C. V6T 1Z4, Canada
E-mail: jmaze@interchange.ubc.ca
Robson Botanical Consultants
14836 NE 49th Street
Battle Ground, WA 98604, U. S. A.
E-mail: nwplants@teleport.com
Scientificals Consulting
309-7297 Moffatt Road
Richmond, B. C., V6Y 3E4 Canada
E-mail: mishtu_banerjee@telus.net
British Columbia Ministry of Forests
315 Columbia Street
Kamloops,
B. C., V2C 2T7 Canada
E-mail: Alan.Vyse@gems1.gov.bc
© This
paper is not for reproduction without permission of the author.
ABSTRACT
Nursery-grown seedlings of Engelmann spruce were divided into two lots which differed only in fertilizer application, fertilized and unfertilized, when transplanted into a field trial. The seedlings fertilized in the field had faster growth rates and the focus of this study was to explore the relationship between growth rate and the degree of emergence defined as the difference in descriptions between parts and wholes. Seedling growth is the result, and thus a measurement of, energy fixation and flow; emergence is one manifestation of the transformation of matter, the expression of information which accompanies energy flow. This study explores Taborsky’s (1999) argument linking the flow of energy to the transformation of matter (expression of information); a more rapid flow of energy should give a greater transformation of matter and expression of information. The faster growing seedlings did show a higher degree of emergence thereby offering a verification of Taborsky’s (1999) suggestions. This, in turn, provides grounds for suggesting that ontogeny results from the flow of energy and the subsequent transformation of matter, an interpretation that places ontogeny in the realm of events explained by natural laws, i.e., it is inevitable.
Development is a constantly repeated, apparently inevitable event of the natural world that biologists explore and attempt to explain. Theoretical accounts of development often invoke concepts of information, which is continually expressed as development unfolds. In some attempts to explain ontogenetic change, this information expression is linked with entropy. In development, entropy is produced and exported from an organism (Brooks and Wiley 1988; Brooks 2001). This phenomenon is interpreted as a manifestation of entropy increase in complex open systems. Since the outcomes of development and evolution are never fully predictable, this entropic increase may also be interpreted as the generation of novelty.
Another
theoretical approach has relied on the appearance of new information through
the impact of the environment on ontogenetic change (Jablonka and Lamb 1995,
Steele et al. 1998). There is, of course, transfer of information from DNA into
the structures, and their functions, of an organism as described by much of
modern molecular biology. But, the surfeit of details produced in such accounts,
deals with small-scale mechanism - how the changing informational properties of
an organism are correlated with variations in DNA, how information is elicited
from DNA (how the expression of that information is controlled), or how that
information is transferred from DNA out into the cytoplasm. While of interest,
these details beg the question of why that transfer of information occurs; what
global-scale forces and mechanisms would cause information in the DNA to be
transcribed and translated in the first place? The concept of entropy production
has been presented as part of the answer to this question: The expression of information
is the result of (and results in) entropy production and exportation, which is
inevitable under the second law of thermodynamics as expanded to incorporate
open systems (Brooks 2001, Brooks and Wiley 1988, Prigogine 1980). Although
these ideas offer an adequate, ultimate cause of development, they still leave
the general mechanism through which this force acts unexplained - how is
entropy production and exportation carried out?
Taborsky
(1999) has offered a
mechanism for the actions of a force such as the second law of thermodynamics
and for the subsequent expression of novelty in biological systems. She has
argued that energy never exists independent of matter. When energy flows from
one part of a system to another it is through the agency of matter transformation.
For instance, the energy in a cross-membrane hydrogen ion gradient flows and is
then captured in the transformation of ADP + P into ATP. The energy in ATP is
then captured in the transformation of a carbon compound from a three- to a
four-carbon molecule. There are many other examples. This transformed matter is
what Taborsky (1999) calls information.
Thus,
using Taborsky’s arguments, information transfer occurs concomitant with the
flow of energy along energy gradients. This flow is inevitable in a live plant
and information is carried along. The specifics of matter transformation will
be a function of the organism within which it occurs, each transformation being
an expression of the dissipation of entropy – the force that drives the
expression of novelty. We feel it is possible to test Taborsky’s (1999) proposed relationship between the
flow of energy and the expression of information by using two groups of tree
seedlings one of which has a higher growth rate, and thus an increased rate of
energy flow, as the result of differential application of fertilizer.
In
constructing these tests our first assumption is that more energy will be processed
by “faster”, as opposed to “slower”, growing seedlings. As more energy is converted
from sunlight into tissue, more matter will be transformed. In the design of
this experiment the amount of incoming light energy was independent of
fertilizer application; there were no differences in energy available to be
incorporated into a plant body. But most of the light energy that strikes a
plant is not utilized. What is important to the plant is the energy fixed through
photosynthesis and that can be affected by many things, among them fertilizer
application.
The next question is, how will transformed matter, the information, be expressed, and once expressed, how evaluated? One expression of information will be in the production of larger seedlings. However, seedling size alone is inadequate as a means of evaluating information expression since it would not capture the contribution of different plant parts to increasing size. In addition, knowing the size of a seedling does not permit addressing any estimate of integration, of the relationships among parts. Integration is the primary means whereby biological entities are characterized; indeed, what makes organisms unique is how their parts are integrated into a functional whole. The evaluation of information expression should rest ultimately on the interaction of parts, how they are related to each other and how seedling growth rate affects those relationships. One way to evaluate the relationships among parts is to describe and analyze them as correlation matrices, as we demonstrate here.
In
constructing our tests, the next assumption is that the greater expression of information,
resulting from the transformation of a greater amount of matter, should result
in seedlings within which correlation matrices show greater heterogeneity than
those with a lesser amount of matter transformation. This assumption follows
from a relationship between the elements of a correlation matrix, correlation
coefficients, and relative growth rates; the correlation coefficients between
two variables will estimate the growth of those two variables relative to each
other. A high correlation coefficient indicates similar growth rates, lower
correlation coefficients will result from less strongly coupled growth rates,
or weaker relations between these variables. In seedlings with a higher rate of
transformation of matter there will be a greater array of growth rates that
give rise to individual variables with a greater variety of correlation coefficients
and correlation matrices. The appearance of more growth rates with the
transformation of more matter seems, to us, a deductive outcome of the
variation inherent in living things, for, as more matter is transformed, one
expression of biological information will be the appearance of more variable
growth rates.
Correlation
coefficients and correlation matrices are a statistical property of populations.
Thus, to expand our argument, in 100 seedlings of lower energy transfer and
matter transformation, there will be a certain number of growth rates realized,
as revealed by a certain number of correlation matrices. In a collection of 100
seedlings of higher energy transfer and matter transformation, a greater number
of different growth rates will be expressed, resulting in more numerous
differences among correlation matrices seen within those 100 seedlings.
To expand this example, each set of 100 seedlings with certain growth rates can be viewed as having properties of a whole, two 50 seedling subsets, established by randomly dividing the 100 seedlings into two equal portions, of those 100 seedlings can be viewed as having properties of the parts. Thus, there would be a correlation matrix for the whole and two for the parts, one for each subset. In the faster growing seedlings, there would be a greater array of correlation matrices seen among the subsets than would be seen in the subsets of the slower growing set of seedlings. This increase in the number of different correlation matrices in the faster growing set will mean that there will be a greater difference between correlation matrices that describe part of the system; the subsets, and the one that describes the whole system. Or, there will be a greater difference between parts and wholes in systems that are processing more energy than in those that are processing less. We have used this distinction between parts and wholes to generate a descriptive attribute to compare different systems, i.e., emergence (Maze and Bohm, 1997; Maze 1998, 1999; Maze et al. 2000, 2001a, 2001b). Our concept of emergence is derived from Polanyi (1958) where lower hierarchical levels, the parts, have properties different from those of higher hierarchical levels, the whole. The properties of the higher level emerge from those of the lower, but they cannot be reduced to nor fully explained by the lower level properties. One analytical way to characterize Polanyi's formulation of emergence is that descriptions adequate for lower levels (the parts) are inadequate for the higher (the whole). The difference in descriptions between the parts and the wholes is what we call the degree of emergence.
One more point must be made clear. Emergence carries the inference of something new, often a new attribute. But the something new can also be the relationship among attributes, this is how we use it here.
It follows that systems processing more
energy should show a greater degree of emergence - through differences in
descriptions of parts and wholes - than those processing less energy, and ought
to be those expressing more novelty. The purpose of this study is to test these
assertions in seedlings of Picea engelmannii Parry, grown under
conditions where sets of seedlings have been treated with different levels of
fertilizer to produce different growth rates.
This
study was originally designated British Columbian Ministry of Forest SX86126K.
For details of the study site, treatments given and the seedling sources see
Maze and Vyse (1993); they are not required for the arguments we develop. As a
result of the experimental design used in SX86126K, seedlings of 24 different
origins, the combination of six different nursery treatments and four seedlots,
were each given two different fertilizer treatments in the field. Thus we
obtained 24 different contrasts of seedlings, fertilized and unfertilized, in
the field; that is, 24 different instances where we could compare the degree of
emergence in putatively identical groups of seedlings.
The
variables analyzed were the height and diameter at planting, ht86 and dia86,
and the increments of growth in height and diameter for 1987 – 1989, inc87 –
inc89 and incdia87 – incdia89 respectively. These variables mark the growth
response of seedlings subjected to different origins, seedlots, or treatments
in the nursery and in the field.
The
first step was to establish that the fertilized seedlings had, in fact,
undergone a greater amount of growth. The most direct way to do this was to calculate
the relative growth rates (Evans 1972) for height and diameter for the
different treatments in the field for each combination of seedlot and nursery
treatment. We used a modified version of Evans (1972) formula since he used
time as the denominator in his calculation of relative growth rate and all the
seedlings here were analyzed over the same period of time, three years.
The analyses for the degree of emergence, the
features used to compare the seedlings with different growth rates, were
similar to those used in previous studies on emergence (Maze and Bohm, 1997;
Maze 1998, 1999; Maze et
al. 2000,
2001a, 2001b). The basic approach is to describe the degree of emergence for
each group being compared. In this study the groups compared were the seedlings
given different field treatments, fertilized and unfertilized, for each
combination of seedlot and nursery treatment giving 24 comparisons. Those
groups processing the most energy are those with the higher growth rates and
are predicted to show the higher degree of emergence. The analytical steps are
presented below so they can be reproduced.
1. Each system of interest, in this case each
combination of seedlot, nursery and field treatment, are bootstrapped (Efron
1982) 50 times using the random sample generator in SYSTAT 4.1 (Wilkinson
1988).
2. Each bootstrapped sample is divided in
half with each subgroup forming one of the parts and the entire bootstrapped
sample the whole.
3. Each bootstrapped sample is analyzed with
Pimentel’s (1993) MPCA program. For each subgroup (part) and the entire sample
(whole) the program calculates, among other statistics, an angle with a vector
of isometry. This is the angle between the first PCA axis and a theoretical
axis comprised of equal elements. For each combination of seedlot, nursery and
field treatment 50 angles with a vector of isometry were generated for each
subgroup (the parts) and for the entire sample (the whole).
4. The differences between the angles with a
vector of isometry for the two subgroups and the entire sample, are then calculated
and averaged. This we call AVGD (average degree of emergence) and it is a
measure of the degree of emergence for that group analyzed.
5. The degree of emergence for the different field treatments for each combination of seedlot and nursery treatment were then compared using a Kruskall-Wallace non-parametric analysis of variance (see Maze and Bohm, 1997; Maze 1998, 1999; Maze et al. 2000, 2001a, 2001b).
If the predictions made in the Introduction are upheld, then the seedlings fertilized in the field should, for each combination of seedlot and nursery treatment, show a greater degree of emergence, that is, a higher AVGD value.
The raw data we used to assess ontogeny, increments of growth over time, are simple variables. They alone would be inadequate for a definitive test of a relationship between energy flow and matter transformation. The way those variables have been analyzed is what gives credence to our test because our focus is not on the variables used in our analyses, but our evaluation of the integration among those variables. Our comparison of the degree of emergence, expressed as AVGD, among spruce seedlings with different fertilizer regimes is derived from the integration among variables. Although our variables are simple, the way they have been analyzed allows us to assess the relationship between energy flow and matter transformation using concepts central to biology, integration and emergence.
The relative growth rates for height
and diameter for all possible combinations of nursery treatment, seedling and
field treatment are presented in Table 1.
Table 1: Median values for combined relative growth rates (upper and lower hinges) for height and diameter for seedlings unfertilized (1) and fertilized (2) in the field.
Height |
Diameter |
||
1 |
2 |
1 |
2 |
0.56 |
0.73 |
0.73 |
0.92 |
(0.43–0.69) |
(0.57–0.88) |
(0.56–0.92) |
(0.74–1.09) |
There
are 48 combinations of relative growth rate between seedlings that did, or did
not, receive fertilizer treatment in the field, 24 for height and 24 for
diameter. Table 1 does not present all combinations but a comparison of
combined groups. This was done for efficiency of presentation and comparison.
Seedlings fertilized in the field have faster growth rates. The probability
that the values for growth rates for fertilized and unfertilized seedlings in
the field is due to chance is <<<0.001 as based on a Kruskall-Wallace
non-parametric ANOVA.
Table 2 presents the results of comparing
AVGD values for faster and slower growing seedlings, for those that process
more and less, energy respectively.
Table 2: Median combined AVGD values (range between upper and lower hinge) for slower growing (1) and faster growing (2) seedlings.
1 |
2 |
5.63 |
10.45 |
(3.06–9.68) |
(6.01–15.20) |
There
are 24 possible comparisons of all seedlot and nursery treatment combinations.
As in Table 1 the AVGD values were combined and then compared with a
Kruskall-Wallace non-parametric ANOVA. The faster growing seedlings had a
higher AVGD value with a probability <<<.001.
One of
the first requirements of this study was the demonstration of
treatment-dependent differences in growth rates. This does occur and it is
hardly surprising.
Seedlings
with the faster growth rate resulted in seedlings with a higher degree of
emergence, as measured by AVGD. This relationship between growth rate and the
degree of emergence, while significant, is not strong; the η^{2}
for a parametric ANOVA comparing AVGD for the faster and slower growing
seedlings is 0.067. One reason for this may be the heterogeneity of the
environment where the study was carried out. The micro-environmental
differences individual seedlings would encounter could be considerable, from
the small, but relevant, topographic variation to the differences in soil. A
second reason for the weak relationship between growth rate and AVGD could be
the within-seedlot variation in the seedlings planted. Conifers are notoriously
variable, whether growth (Banerjee and Maze 1988; Maze and Vyse 1993; Maze et
al. 1989),
morphological (Chen et
al. 1986;
Lester 1968; Maze and Parker 1983), or molecular (El-Kassaby and Sziklai 1982;
Yeh and El-Kassaby 1980) variables are analyzed. A way to partially circumvent
environmental and organismal variation is to compare the degree of emergence
within single conifers by analyzing needles on long (faster growing) and
shorter (slower growing) branches. An even better approach would be to use
plants that are less variable and grow them under more stringently controlled
conditions.
The
prediction derived from Taborsky’s (1999) linking of energy flow and matter
transformation (information flow) is corroborated though it should be subjected
to further testing. An earlier study demonstrated a positive relationship
between the degree of emergence seen in needles and the size of the tree, a
rough estimator of growth rate, in ponderosa pine (Maze 1999). The degree of
emergence as seen in increments of stem growth in faster growing seedlings of
Douglas fir and increments of annual rings in faster growing mature trees of
ponderosa pine both showed a higher degree of emergence than slower growing
plants. The results from growth increments are presented only anecdotally as
the plants with different growth rates were not the result of a manipulation designed
to affect growth rate, but they are still of interest. One way to look at the
energetics is from an accounting point of view. There is a “cost” for any
change in relationships, or for a new structure. So, under higher growth rates
it is easier to “pay the price” for having more diverse relationships.
The
relationship between the flow of energy and the expression of information can
be visualized as a flow and channel relationship. As energy flows it will do so
along certain paths as determined by the plant itself, these are the material
expression of Polanyi’s (1976) boundary conditions. These boundary conditions,
delimited by phylogenetic history and through the activities of development
itself, will specify how matter is transformed into information.
The
flow of energy, with its concomitant material expression, as directed by the
constraints of the boundary conditions of a plant, is another way of saying
that, given the flow of energy, a plant will develop. To put this in a slightly
different context, energy flow can be viewed as the mechanism through which
novelty and constraint, biological information, are expressed. The “force”
driving biological forms to diverge is limited by the opposing “force” of
evolutionary and developmental history, as expressed through structural
limitations and functionality specifying the form of living things.
This
paper benefited by the input of Cy Finnegan and we are thankful for his time
and wisdom.
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