Studies into abstract properties of individuals. IV.
Emergence in different aged needle primordia of Douglas fir
Jack Maze
a,*, Kathleen A. Robson
b, Satindranath Banerjee
caDepartment Of Botany,Uni
6ersity Of British Columbia,Vancou6er,B.C., Canada V6T 1Z4
bRobson Botanical Consultants,14836 NE 249th Street,Battle Ground,WA 98604, USA cScientificals Consulting,309–7297 Moffatt Road,Richmond,B.C., Canada V6Y 3E4
Received 30 November 1999; received in revised form 17 January 2000; accepted 21 January 2000
Dedicated to the memory of ‘Spence’, Alden Alva Spencer Jr.
Abstract
Young, middle aged and older Douglas fir needle primordia, as determined by distance from the apical meristem, were measured and analyzed to compare levels and patterns of emergence related to development time. Emergence was seen in the differently aged needle primordia, generally most noticeable in the oldest and the least apparent in the youngest. There was also a negative relationship between variation in size and degree of emergence, and a positive one with variation in organization. The increasing level of emergence that appears with age can be related to the continual expression of information and the concomitant increase in complexity that marks ontogeny and is the result of diverging developmental trajectories. The histogenetic events seen in ontogeny can be interpreted as ‘clocks’ generating local time through the interactions among cells and tissues that make up the needle primordia. Emergent properties are manifested through the local events that mark ontogeny, and also through the expression of phylogenetic information, or the local expression of global (historical) levels of organization. © 2000 Elsevier Science Ireland Ltd. All rights reserved.
Keywords:Emergence; Complexity; Ontogeny
www.elsevier.com/locate/biosystems
1. Introduction
This paper is part of a continuing series (Maze and Bohm, 1997; Maze, 1998, 1999) the ultimate goal of which is an exploration of the nature of
the relationship between ontogeny and phylogeny. A first step in this exploration is the description of empirically based properties common to ontogeny and phylogeny. Once those properties are estab-lished they can be used as guides in a search for a common conceptual and theoretical framework for ontogeny and phylogeny.
Some sort of relationship between ontogeny and phylogeny has long been apparent. Both events involve irreversible changes that occur over
* Corresponding author. Tel.: +1-604-8222133; fax: + 1-604-8226089.
E-mail address:[email protected] (J. Maze)
time. It is through ontogeny that the changes which result in phylogenetic pattern are expressed. Ontogeny and phylogeny are the phenomena through which organic form, the part of the bio-logical world available to most people, unfolds. The study of the relationship between ontogeny and phylogeny can even be seen in early evolu-tionary thought through Darwin’s recapitulation-ist views (Richards, 1992). What we want to do is explore the relationship between ontogeny and phylogeny beyond these truisms.
In our search for characteristics to use in ex-ploring ontogeny and phylogeny we rely upon a concept of emergence. In so doing, our first as-sumption is that both ontogeny and phylogeny result in emergence, or emergent properties. Our second assumption is that emergence is of a suffi-cient level of abstraction that we can use it to directly compare the products of ontogeny, indi-viduals, and phylogeny, assemblages of related individuals. Our third assumption is that such a comparison will allow insight into the most basic features of ontogeny and phylogeny, the concep-tual and theoretical constructions that bind them together.
The usual presentation of emergence is the bio-logical truism, the whole is more than the sum of its parts. The credibility of that statement is be-yond doubt. However, there are two prerequisites for the study of emergence as a means to explore ontogeny and phylogeny. The first is a reformula-tion of that truism which will allow its empirical analysis. Second is the establishment of an analyt-ical protocol that will allow direct comparisons between the products of ontogeny, individuals, and phylogeny, groups of related individuals. This second prerequisite is especially important be-cause it establishes a common language to use in talking about ontogeny and phylogeny. A com-mon language is necessary in order to seek the common theories and concepts in phenomena that result in things as complex as organisms.
In the studies done to date (Maze and Bohm, 1997; Maze, 1998, 1999) the depiction of emer-gence used is that of Polanyi (1958); namely, that higher hierarchical levels (wholes) have properties not seen at lower levels (parts), the properties at the higher level having emerged from the lower.
Or, the description of lower hierarchical levels are inadequate to characterize the higher. This char-acterization also allows us to establish an
analyti-cal protocol for comparing the different
hierarchical levels, parts and wholes. First, we can establish a common descriptive morphological language for different hierarchical levels through comparing different levels made up of more inclu-sive groups of like-sized items. In the previous studies (Maze and Bohm, 1997; Maze, 1998, 1999) the like-sized items used were grass spikelets (the
first two studies) or needles of Pinus ponderosa
Lawson (the third study), and the different hierar-chical levels were of smaller and larger aggrega-tions of those parts. This is, of course, the equivalent of the Linnean hierarchy where higher levels are comprised of more and more inclusive groups of individuals. Second, we can characterize those different levels by describing features logi-cally independent of the levels themselves, the organization that they show, and then use those descriptions of organization in an analysis of emergence. What relying on Polanyi’s (1958) char-acterization of emergence allows is to calculate the degree of emergence seen in individuals (the difference between lower and higher hierarchical levels within individual levels) and that seen in aggregations of related individuals (the difference between lower and higher hierarchical levels within the group being analyzed) (Polanyi, 1958). It is that degree of emergence that offers us the common language necessary to explore the rela-tionship between ontogeny and phylogeny; the common language is degree of emergence, the exploration comes through a comparison of indi-viduals and groups of related indiindi-viduals.
In one study of grasses (Maze, 1998) evidence was presented for a time-related increase in the degree of emergence, seen as the difference be-tween the lower and higher levels of a two-tiered hierarchy. However, time in that study was the inferred time of evolution. Degrees of emergence were presented as a continuum, with the lowest level being in ‘youngest’ groups, populations, and the greatest emergence shown in the ‘oldest’ group, a phyletic lineage consisting of two closely
related species, Achnatherum hendersonii (Vasey)
Rob-son. The group presumed to be of ‘intermediate’ age, species, expressed an intermediate level of emergence.
The demonstration in that paper of a possible relationship between phylogenetic time, which is only inferred, and the degree of emergence raises this question: is there a similar relationship be-tween the degree of emergence and time when time is assessed by the real time of development? More specifically, will older needle primordia show a greater degree of emergence than younger? That is the purpose of this paper, to report on an analysis of emergence in an ontogenetic study of differently aged needle primordia of Douglas fir (Pseudotsuga menziesii (Mirb.) Franco).
A broader and more abstract way to envision the real time of ontogeny consists of starting with the histogenetic events that occur during needle development; the division, differentiation and elongation of cells in the needle primordia. As these cells mature, they act as ‘clocks,’ ‘clocks’ referring to a means to measure or perceive time, creating their own local time as they interact with other cells and respond to previous stages as ontogeny progresses. Histogenetic events occur-ring later in the process reference earlier steps in development, or, the cellular communication through which development is coordinated gener-ates local, asymmetric (unidirectional) time (Mat-suno, 1988). The many cells, behaving as ‘clocks’ when they interact with other cells, form the integrated unit we recognize as a conifer needle primordium. A needle primordium, when used as a point of reference, can also be viewed as a higher level ‘clock’ comprised of many component ‘clocks’ formed from individual cells and tissues. This communication, through which form un-folds, also references ‘global,’ or ‘in the record’ phylogenetic information that exists because of the unique history of Douglas fir as a species, as a conifer, and as a vascular plant (Matsuno, 1988; Matsuno and Salthe, 1995). In the context of this study, the initiation of a needle primordium starts a ‘clock’ which forms the reference for subsequent ‘clocks’ that appear with more ontogenetic events. As more needle primordia are initiated, they refer-ence the ‘clocks’ generated by events that pre-ceded them. Upon reaching some threshold, the
primordia move beyond a generalized mass of cells and form a structure that is distinctively a Douglas fir needle. Matsuno’s approach to view-ing ontogeny (local scale) and phylogeny (globally encompassing) as different tiers or sets of time emphasizes the hierarchical nature of biological organization (Matsuno, 1988). This view includes, but is not limited or reduced to, the expression of genetic information. Parts of a bud rely on the ‘clocks’ within a bud, the buds on a tree rely on ‘clocks’ established within a tree, a tree relies on the ‘clocks’ that existed in its parents and so on back through its phylogenetic history. The reverse process does not occur, that is, phylogenetic time does not reference local, developmental events because it is part of the historical record. Thus, what we are studying here, while it is focused on needle primordia in buds, is part of an integrated series with a long history. Using these concepts of time serves to emphasize the historical interrelat-edness of all botanical structures. As well, these self-same concepts identify the kind of compari-sons Goethe identified as the holistic approach necessary to understand botanical events (Arber, 1946).
2. Materials and methods
2.1. Plants
The material for this study came from four full-sib families that were part of a partial diallel of Douglas fir (Maze and Banerjee, 1989). For the plants analyzed terminal buds were taken from the uppermost whorl of branches, with one to four branches being sampled per plant. There were 115 plants, 28 from one family and 29 from the other three, for a total of 230 buds. The buds were sampled in March 1988, fixed in formalin-acetic acid-alcohol (90 cm3
ethanol, 6 cm3
forma-lin, 4 cm3 glacial acetic acid), embedded in
paraplast, sectioned at 15 mm, and stained with
at the midpoint perpendicular to the main axis of
the primordium (m) and length of the needle
primordium along a line from the midpoint of the
attachment to the tip (l) (Fig. 1II). There were
two criteria used in picking needle primordia to measure. First, they had to be from sagittal sec-tions of buds as determined by being able to see the cytohistological zonation in the apical meris-tem and the clarity of image of cell walls. The second criterion was applied to the specific needle primordia. For the youngest, which usually lack procambium, we relied on clarity of cell wall image. For the older we chose those primordia in which the procambium could be seen extending into the stem and also had clear cell wall images. Young, middle age and older needle primordia were chosen by taking two needle primordia on opposite sides of the incipient stem from the uppermost needle primordium in sagittal section, (the young), the bottom-most (the old), and at the
midpoint of the bud (the middle age). Fig. 1 also includes a diagram of a bud showing the relative positions of the primordia chosen (I). Labeling the needle primordia closest to the apical meris-tem as young and those farthest away as old is appropriate even though they all coexist in one bud. The needle primordia at the base of the bud were formed first while the bud was developing in the year before it was sampled, the needle primor-dia nearest the apical meristem were those formed last in the same year. There were 424, 427 and 440 needle primordia for the young, middle age and old, respectively. The difference in numbers is due to the inability to measure certain needle primor-dia because of artifacts of sectioning.
2.2. Analyses
The needle primordia for all four families were combined for the analyses, which gave us a much larger sample size, an advantage when performing the indirect and complicated analyses we used. As well, the families were not strongly different. Based on average r2values for the three variables
measured, the families accounted for only 2.3, 6.3 and 10.4% of the variation in the data for the young, middle age and old, respectively.
Each set of differently-aged needle primordia was used to create two hierarchical levels using the same approach as in Maze and Bohm (1997), Maze (1998, 1999). The differently-aged needle primordia sets, the young, middle age and old, were bootstrapped 50 times to create data sets with a complete set of variables for 400 needle primordia; these 50 bootstrapped samples repre-sented the higher hierarchical level for subsequent analyses. When the 50 samples were drawn, the individual plants from each of the families were scattered, without apparent order, within the orig-inal data file. This was done to eliminate any effect the four different families may have had on the outcome of the analyses even though the family effect was small. In order to create the lower hierarchical level each bootstrapped sample was divided in half. Each of these halves repre-sented a subgroup, the lower hierarchical level, and the entire sample, the whole, the higher hi-erarchical level. The statistic calculated for the
different hierarchical levels was the angle between first eigenvectors, derived from a principal com-ponents analysis (PCA) of a correlation matrix, and a vector of isometry. Only the first eigenvec-tor was used since it alone was consistently derived from a data matrix that was not spherical as determined by either Bartlett’s or Anderson’s test (Pimentel, 1993). Once this statistic was calcu-lated, the degree of emergence was determined as the difference in that angle between the subgroups and the whole and is expressed as the average degree of emergence (AVGD), i.e. the average difference in angles with a vector of isometry between each subgroup, the lower hierarchical levels, and the entire sample, the higher hierarchi-cal level.
In order to explore the relationship between the average degree of emergence and properties of the needle primordia, a multiple regression analysis was done with AVGD as the dependent variable and two estimates of variation as the independent. One of these estimates was variation in size, or the spread of individual structures around a mean value. This is the usual way variation is assessed in a biological context. This was estimated as the within-age group variation in PCA axis scores from the original data set which combined all needle primordia, the young, middle age and old. Again, only the first axis was used. The other estimate was variation in integration and refers to the variation in organization among the variables measured. This is variation in growth rate among the variables relative to each other and could also be called variation in allometry. In spite of the significance of allometry in biological studies, its variation is often not directly addressed. The vari-ation in integrvari-ation was approximated by the variance in eigenvector loadings on the first PCA axis from the original data sets from which the bootstrapped samples were gathered, i.e. from an analysis of all the young, middle age and old needle primordia. Before the multiple regression analysis was done the estimates of variation in size and integration were standardized so that their coefficients could be directly compared through converting the means of both to 0.0. This is the same analysis as was done in Maze (1999).
The bootstrapping was done using the random
sample generator in SYSTAT4.1 (Wilkinson, 1988)
and the angles with a vector of isometry were
calculated by Pimentel’s MPCA program.
Calcula-tion of angles with a vector of isometry in
Pi-mentel’s program relies on the standard
calculation of the angle between vectors, i.e. the ratio of the dot product to the product of the norms of the vectors. Pimentel’s program also calculates the statistics for the entire data set, the within-groups analysis which represents the higher hierarchical level, from the within-groups disper-sion matrix, the weighted average of the group dispersions (Pimentel, 1993). This approach is less sensitive to assumptions about the within-group dispersions, e.g. equality, that describe the lower hierarchical levels. Details are presented in Pi-mentel (1979). Comparisons of AVGD among the differently-aged needle primordia was done using
Tukey’s multiple comparison in SYSTAT 4.1. The
probability level for rejection of similar AVGD values was set at a conservative 0.0001.
The analyses done appear to be very compli-cated, but the basic idea behind them is simple. The organizational properties, as expressed in a correlation matrix of an entire data set, are de-scribed, as are the organizational properties, also expressed as correlation matrices, of two subsets of that entire data set. The description of those organizational properties for the entire data set and the two subsets are then compared. To de-scribe the organizational properties, we used an angle with a vector of isometry, which is related to the properties of a correlation matrix.
We also generated notched box plots for each measured variable for the three differently-aged needles. This offers the most direct graphical rep-resentation of the data and allows simple observa-tions to be made of how patterns of variation change through time for each variable.
Another analysis, a PCA of each of the differ-ently-aged needle primordia, was done. The
pur-pose here was to describe the changing
used since it alone was consistently derived from a non-spherical data set.
3. Results
The comparison of the degree of emergence, as AVGD, for the three different aged needles, young, middle age and old, are presented in Table 1. In no case is the difference between the sub-groups and the whole data set (AVGD) for any one age of needle primordia great, nor is differ-ence in AVGD among the differently-aged needle primordia great. Even so, all are statistically sig-nificantly different, even given a highly conserva-tive probability level for rejection of the null hypothesis of similarity, 0.0001.
Table 2 presents the relationship between the degree of emergence, AVGD, and variation in size, SIZEVAR, and variation in integration, SHAPEVAR. This is a comparison similar to that presented in Maze (1999). Both estimates of varia-tion show a significant relavaria-tionship with the de-gree of emergence (AVGD), with variation in size having the larger absolute effect. In addition, the signs of the two estimates of variation are differ-ent, with the average degree of emergence declin-ing with variation in size but increasdeclin-ing with variation in integration.
Table 3 shows the eigenvectors and percent variation accounted for by the first PCA axis for each entire data set describing young, middle age and older needle primordia, respectively. The pur-pose of this table is to offer insight into how the variable interrelationships change with age, giving more information on patterns of change as emer-gence occurs. The eigenvector elements for each
needle variable measured, b (width at base), m
(width at midpoint) and l (length), decline with
age, with the greatest decline being in m and l.
First axis eigenvalues also decline with age, an indication that the variables become less strongly polarized with age.
Fig. 2 presents the notched box plots. All three variables become larger with age, an expected observation. There are also differences in time-re-lated variation as expressed in the size of the boxes and presence of outliers. The most variable
Table 1
Average AVGD, standard deviations below, for young, middle age and old needle primordiaa
Old
Young Middle age
1.1 2.8
0.4
0.1 0.6 0.5
aAll are significantly different atPB0.0001.
Table 2
Results of multiple regression analysisa
Variable Coefficient Prob
−1.151
SIZEVAR 0.000
SHAPEVAR 0.913 0.000
aAVGD, average degree of emergence; SIZEVAR,
varia-tion of needle primordia as measured by variance in PCA axis scores for young, middle age and old needle primordia; SHAPEVAR, variation in integration for each tree as mea-sured by variance in loadings on first eigenvector. First axis r2=0.834.
Table 3
Eigenvalues and eigenvectors for young, middle age and older needle primordiaa
Old Young Middle age
Eigenvalues 2.4 1.7 1.5
0.819 0.796
b 0.778
m 0.935 0.766 0.697
l 0.910 0.724 0.655
ab, width at base;m, width of needle primordia at midpoint; l, length of needle primordia.
measurements for width at the base of the needle primordia (b) are in the oldest (largest amount of central variation defined by the notched box) and youngest (most outliers expressed) needles. The
least amount of variation for b is seen in the
middle age needle primordia. For the width at the midpoint (m) and the length of the needles (l), the most variable primordia were the youngest, with the middle age and older primordia appearing less variable.
This constraint may be related to the loss of potential that accompanies development. At a more abstract level, this constraint may result as growing needles access information from a higher level phylogenetic clock. This ‘higher level infor-mation’ may be the reason why differences among species become more pronounced at later develop-ment stages.
These changes in variation, while based on notched box plots, were confirmed by Bartlett’s test for homoscedasity (Wilkinson, 1988) and co-efficients of variation. The results of those tests were not included.
4. Discussion
Based on the criteria used here to define emer-gence, and the methods used to describe it, an
increasing trend in the degree of emergence from the youngest to the oldest needle primordia is seen. Thus, there is a relationship between age, as assessed directly, and the degree of emergence. This is not our first attempt to relate the degree of emergence to age. In an earlier study (Maze, 1999), the relationship between the degree of
emergence seen in needles of differently aged P.
ponderosa trees was weaker. The different results in the present study are likely the outcome of directly addressing age in serial homologues. In the previous study (Maze, 1999), the estimation of age was not based on the structures analyzed, mature needles, but the individuals (trees) that bore those structures. The needles of the pon-derosa pines measured were all the same age, 2 years old.
Emergence in needle primordia of Douglas fir is also related to variation among the needle
dia themselves (variation in size) and among the variables measured (variation in integration). There is a negative relationship with the former and a positive one with the latter, with the rela-tionship of emergence to variation in integration being the larger. The same relationship between types of variation and the degree of emergence was seen in P. ponderosa. A slightly different one was seen in grasses where the relationship between size variation and AVGD was positive, as
op-posed to the negative results seen here and in P.
ponderosa. In the study of grasses the strongest relationship was between variation in integration and AVGD, the degree of emergence.
The measure we use here and elsewhere, the degree of emergence, is not part of the lexicon of the botanical consensus. This necessitates relating that measure to concepts more central to current botanical thought. The degree of emergence mea-sures the within-system divergence in organization it being the difference between correlation ma-trices that describe subgroups, the parts, and the correlation matrix that describes the subgroups combined, the whole. Thus for those instances where the degree of emergence is low, young needle primordia, as compared to those instances where it is higher, the old needle primordia, there is also a trend in within-system variation but in this case variation in organization. Because the degree of emergence assesses organization this increasing within-system variation in organization is also measuring expanding constraints of the system. This infers that as the needle primordia increase in physical size there is a concomitant expansion in the constraints on the system, an expansion that may allow that system to explore more potential directions of development.
Emergence, as well as variation, can be viewed as the expression of information. With the expres-sion of more information there will be an increase in the degree of emergence (Maze, 1999). Such an interpretation is consistent with the results pre-sented here; the older needle primordia have been in existence for a longer period of time. More information has been expressed within the older needle primordia as they are farther along in development. This increased expression of infor-mation will be seen as the higher degree of tissue
differentiation expected in older needle primordia, mainly in the appearance of more procambium and the initial steps (cell enlargement) in the differentiation of protoderm and ground meris-tem. Something we find rather interesting is that even though the variables assessed in this study do not reflect any sort of tissue maturation be-yond cell enlargement, there is still evidence for emergence. This leads us to suspect that we have underestimated the level of emergence that has occurred because we were unable to explore the results of the majority of information expressed in the development of the needle primordia.
grows the relationships among the parts may re-main the same, in which case the sole result of growth is an isomorphic increase in size, virtually unknown in biology. Alternatively, relationships among the parts of a structure may change as growth progresses, reflecting not only increasing size, but also changing organization (Maze et al., 1987). Thus, the differences in eigenvector ele-ments seen with age mark changes in the variables relative to each other during growth, reflecting diverging developmental trajectories. The eigen-vector elements decline in value from the youngest to the oldest needle primordia. This indicates a certain element of uncertainty with development; knowing those trajectories at any one age will not allow accurate predictions of the developmental trajectories at a subsequent age. Because the ei-genvalues decline with age, the parts are less strongly related in the older needle primordia, and this also argues for an age-related divergence
among developmental trajectories. The
phe-nomenon of developmental variation has also been observed in the variation among the relative rates of development in different parts of grass florets (Maze et al., 1971, 1972) and in develop-mental trajectories in ovules (Scagel et al. 1985; Maze et al., 1986, 1987). This developmental vari-ation might be viewed as a logical outcome of how a plant responds as it develops. The triggers to which a developing plant responds are at least partially chemical. The plant elicits certain reac-tions from its DNA and the products of at least some of those reactions are chemicals, plant hor-mones, that have an effect on the cell divisions and enlargements through which plant ontogeny unfurls. Adequate synchrony among the different parts of a developing plant requires uniform diffu-sion of two agents throughout the plant. The first agent triggers a response from DNA and the second agent is composed of the hormones that mediate cell division and maturation. The struc-ture of a plant at any one time mitigates against uniform diffusion. Cells themselves, as well as their organelles, are structures that will affect the diffusion and production of hormones, and that production occurs in localized regions, such as areas of greatest meristematic activity.
The focus of this discussion, so far, has been ontogeny and any study ontogentic in nature in-corporates the concept of time. In biology, the passage of time is manifested everywhere and on different levels of an organizational hierarchy. The classical view of time as a discrete and univer-sal constant has been challenged (Matsuno and Salthe, 1995; Matsuno, 1988). These authors dis-tinguish between the asynchronous time that is locally generated by the interactions of any set of objects, and a higher order ‘global’ time that arises secondarily from the interactions of many smaller scale ‘local clocks.’ The argument is made that the local interactions taking place make refer-ence to, and are affected, by the more encompass-ing, global time that has become part of the historical record as phylogenetic pattern and con-straint in biological systems. However, the global patterns do not refer to, and are not altered by, the interactions taking place at the finer scale of local entities, for the large scales of ‘time in the record’ are historical and inviolate. This seems to us an accurate description of ontogeny, where within-structure ‘conversations’ take place while higher-scale phylogenetic information is also ref-erenced. This view of time as hierarchical and emergent also suggests that the phenomenon of speciation must be initiated at the finer scale of ‘local clocks.’ Such an approach offers a clearer understanding of the phenomena of development and speciation; both result from the interaction between ‘local’ and ‘global’ time, between varia-tion and constraint. Such a theory of relative time can be explored through biological systems and their uniquely hierarchical organization (Salthe, 1985).
There is another possible correlate with the greater degree of emergence seen in older primor-dia; they are somewhat independent of the younger primordia and hence are following their own developmental trajectories. In considering that a certain level of independence appears to exist among leaf primordia, the metaphor of a series of ‘local clocks’ (Matsuno, 1988) is useful, especially because it can be approached empiri-cally. Once initiated, these clocks, which mark local development, run somewhat independently of each other, so the ‘time’ read off the clock in
any one old primordium will not be strongly synchronized with the clock in another old pri-mordium, or even among other clocks in the same primordium. This results in an increase in among-primordia variation and also the degree of emer-gence. Matsuno’s idea of the generation of time by local interactions is another expression of the variation in the relative rates of development in different parts of grass florets (Maze et al., 1971, 1972; Matsuno, 1988).
Asymmetry is generated here and emergent properties are manifested in that the historical levels of organization, higher hierarchical levels, cannot be fully described by the interactions of local entities at lower hierarchical levels (Polanyi, 1976). The phylogenetic characteristics that make a conifer or a Douglas fir unique and recognizable can be considered organizational levels of the ‘global’ time that is already in the historical record. As needles create themselves each spring, cells and tissues interpret their positions relative to each other and the messages describing form and function available to them in DNA. Time, information and emergent properties of more en-compassing levels come to exist as local interac-tions take place.
Acknowledgements
We have had the advantage of the insights of Dan Brooks, Cy Finnegan, Koichiro Matsuno and Stan Salthe. Their comments and the time
they took to produce them are greatly
appreciated.
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