The following is a paper I wrote for an excellent course I took at Reed College in 1991, titled "Plant Communities",
from a now emeritus Dr. Bert Brehm. This was one hell of a course. In
addition to great coursework and lectures, every Saturday everyone would
pile into a bus and trek out to various locations in Oregon. Ancient
Hemlock Climax (?) forests, the Oregon Coast, the High Desert, Reed's
property along the Sandy river (where we all went skinny dipping and got
stung by bees, luckily enough not at the same time!), and more. One hell
of a course....
Anyway, a lot of what I was pontificating about in this paper has been
written elsewhere since (and probably a lot of it before as well). I
would really love to write a sequel to the paper- update the outdated and
non-existant refs, make some new figures. I'll get around to it, but in
the meantime, read on.
It is becoming increasingly evident that many of the patterns
generated in nature are products of chaotic or complex interactions. The
structure of a fern frond, for instance, can be modeled by a very simple
computer program which uses fractal geometry. Patterns in large
populations are also governed by chaos. The classic example in this area
is the equation Xn+1 = RXn(1-X), where X is the number of individuals in a
population and R is a constant. Depending on the value of R, this simple
equation can generate non-linear, chaotic results when iterated. In
addition, as with most chaotic systems, extremely small variations in the
starting value of R can generate drastically divergent X values after a
short time. It has also been found that certain kinds of complex systems,
which may start out in a wide range of highly disordered states, will end
up in one of a few highly ordered states. Recent research in this area
indicates that these complex systems are capable of self-organization.
While studying the organization of plant communities, in particular the
argument between reductionists and holists, I became interested in the
cellular automaton as a model for the organization and evolution of plant
communities. Reductionists claim that a plant community may be almost
completely described by concentrating on the individual plants, ie. the
whole is merely the sum of the parts. The holists hold that while
examining the individual parts of the system may be informative and even
necessary, this is not sufficient to characterize the community, ie. the
whole is greater than the sum of its parts. My view, loosely visualizing
communities as a type of chaotic system known as a cellular automaton, is
not just a middle ground between these two positions but is a different
and better way of thinking about plant communities.
A plant community consists of a vast population of interacting
plants. In the community model which this paper proposes, it is useful to
think of the species not as the individual but rather as a
quality of the individual; individuals can be treated like
mathematical variables. For instance in a temperate forest a particular
individual’s "species value" may be douglas fir, hemlock, vine maple
or any number of other types of plants native to that area. In addition,
each of these individuals exert influences over some area and thus some
number of other individuals. These influences-shade, pollination,
allelopathic inhibition, etc.- are limited by various intrinsic and
environmental factors-size and density of canopy, wind patterns and other
pollination vectors, genetic disposition, etc. If we attempt to assemble a
simplified model of the plant community we must first consider the
possible types of individuals. An individual may consist of an individual
organism of a certain species or of a group of organisms of different
species that seem to often associate. If a model of a coniferous forest
were assembled, for instance, it would be certainly necessary to include
douglas fir, hemlock, pine, etc. as possible individual types. It might
also be useful to add in other individual types such as meadow patch,
swamp patch, etc. Patches are individual types that are typified by
reproducible, consistent interactions with other individuals. A patch of
meadow may consist of many different species of grasses and other
herbaceous plants distributed in a somewhat random fashion, but a patch of
meadow in one area of the forest will interact with its neighbors in much
the same way as a patch of meadow in any other area of the forest. Models
may be constructed with varying degrees of resolution, that is the scale
at which the model differentiates between individuals. For instance even
as it makes little sense when studying a forest to make a distinction
between two kinds of meadow flower, it also makes little sense to call an
area of grass and other herbaceous plants "meadow" when studying a
marshland community in detail. In the latter case a finer distinction must
be made between grasses and flowers and a correspondingly smaller scale
must be used. The final aspect that must be considered when constructing
this simplified model is that of interactions between individuals. Each
individual will exert some influence upon surrounding individuals and in
turn it will be acted upon by those surrounding individuals. Plants may
influence other plants in competitive, beneficent and even regulatory
ways. Again the details and resolution of these interactions depends on
the purpose and depth of the study. The intent of this paper however is
not to construct an actual model of plant communities, for no universal
one exists, but rather to propose a new tool that can be used when
studying plant communities.
A cellular automaton consists of a population of interacting cells,
each cell being represented by a variable in computer memory. The
population of cells is arranged in a two-dimensional array (technically
the array may have n dimensions however only the two-dimensional case is
relevant to this paper). Each cell has a value that is referred to as its
state. Cells are also influenced by some number of other cells in the
population, this group is called a cell's neighborhood. The automaton is
generated iteratively with a cell's state at time n+1 dependent on the
states of all of the cells in its neighborhood at time n. A set of rules
determines how the cell in question will be affected by its neighborhood
(See Figure 1). One of the surprising things about cellular automata is
that even the simple system outlined above can generate such complex
patterns (see Figure 2).
Often intricate, repeating patterns grow out of
the simple interactions that govern an automaton. Research in this area
has also revealed a counterintuitive and very exciting aspect of cellular
automata. Certain dynamic systems of this type, starting from a highly
disordered, chaotic state can "spontaneously 'crystallize' into a high
degree of order". Cellular automata have been programmed that, through
this order, are capable of simple information processing. This potential for self-organization in
automatonic systems has tremendous implications for the study of plant
ecology.
Benoit Mandelbrot, the "father of fractals", proposes that most
objects and phenomena in nature have a hidden chaotic order. For instance
highly accurate renditions of snowflake patterns can be generated by a
very simple cellular automaton program in which the cells are hexagonally
shaped. In fact it seems that snowflakes are probably actually formed by a
process analogous to this in nature. The basic components of plant
communities and cellular automata display strong functional similarities.
It may therefore be hypothesized that both systems may
exhibit general qualities and behavior that are similar to one another. In
fact it does seem to be the case that many aspects of community dynamics
and structure can be explained by referring to the cellular automaton
model. This cellular automaton model for plant communities deals with some
questions raised by plant ecologists in a very new and, I believe,
productive manner.
Although it is evident and accepted that individual organisms
evolve according to Darwin's theory of evolution, the issue of whether a
community as a whole is capable of true evolution, is still much debated.
The critical process of evolution for individual organisms is the passage
of information contained in genes from parent to progeny. It is commonly
accepted that natural selection acts on these genes in populations to
drive evolution. Communities are acted upon by natural selection,
certainly regions of a community which are ill-suited to their environment
will not persist. Critics of community evolution claim however that there
is no mechanism inherent in a plant community that is analogous in
function to the genetic information of an individual. Because of this
deficiency there is no way of ensuring that valuable adaptations will
persist and be passed along thus evolution does not occur. A mechanism to
preserve this vital information in a community is important in that it
would provide some kind of order, analogous to the organization observed
in individual organisms, that natural selection could act upon. Poorly
organized communities would cease to exist while communities better suited
to their environment would survive and accumulate more useful variations,
possibly increasing in size and thereby propagating the "better"
organization (this is, in fact, an oversimplification: natural selection
would probably not work by eradicating whole communities but rather by
eradicating small sections of the communities [see Whittaker for ref]). If
such a mechanism existed in communities then community evolution would not
only be possible, it would have to occur.
Stuart A. Kauffman asserts while speaking of evolution, "it is
possible that biological order reflects in part a spontaneous order on
which selection has acted". That is to say, spontaneous patterns may arise
from complex biological systems upon which selection is able to act. Some
members of the class of mathematical systems that cellular automata
belong to, called Boolean networks, are capable of developing such
spontaneous order. This spontaneous order arises when the system
approaches the boundary between order and chaos, ie. the border between a
fixed, non-dynamic system and a completely disordered, kinetic one.
Kauffman goes on to state,"networks on the boundary between order and
chaos may have the flexibility to adapt rapidly and successfully through
the accumulation of useful variations." Individual organisms preserve
their order in a material way, genetic information is encoded in DNA
contained in each cell. In self-organizing Boolean networks order is
preserved by the interactions of the individual elements, in other words
the mechanism of preservation is not materially embodied. The "spontaneous
order" of Boolean networks will be discussed in depth later. If
communities are Boolean networks on the boundary between order and chaos
there may indeed be order generated by the interactions of the individual
plants upon which selection may act. As Aarssen and Turkington stated in
1983, "the community acquires adaptations through the effect of its
component species on it." This model allows individuals in the community
to contribute order, order that is stable and that may be acted upon by
selection, to a greater whole about which they have no knowledge of.
The order that arises from systems poised on the boundary between
order and chaos has some interesting qualities that apply directly to
community dynamics. As the system approaches this boundary it can develop
a stable, frozen core that will spread through the system leaving islands
of unstable, changeable elements. Kauffman draws a loose analogy between
these types of systems and phases of matter. Maximally disordered, chaotic
systems are likened to gasses while maximally ordered, static systems are
likened to solids. Self-organizing systems are an intermediate between the
two, containing both frozen and unfrozen components. The frozen core of
these systems is stable on a system wide basis and, barring perturbation,
will remain relatively unchanged for an indefinite time. Kauffman
claims;
Communities first establish themselves in a stochastic manner. In
an area recently cleared by fire or other catastrophic factors, fairly
random distribution of species occurs according to various innate factors
and factors in the environment. In these early successional, pioneer
stages, chaos rules. J.H. Whittaker states, "early stages are ... cases of
evident instability". At some point this chaos seems to abate and is
slowly replaced by more orderly interactions of species. The community
goes through a series of successional stages which are accompanied by a
general increase in productivity, species diversity and relative
stability. The community may eventually reach a climax stage which
represents the apex of the general trends mentioned above. Whereas the
dynamics of the successional stages of communities are directional the
climax community is characterized by fluctuations around a mean state. Due
to its stability the climax community is resistant to perturbation, most
perturbations are compensated for by the ecosystem. The climax community
therefore represents a self-maintaining, steady state system. [see
Whittaker,Communities and Ecosystems, for references]
Dynamic, non-linear systems, such as cellular automata, may begin
with periods of very chaotic behavior but then settle into a stable cyclic
pattern which is referred to as a dynamic attractor or state cycle. "Every
network must have at least one state cycle; it may have more". The system
will generally fall into its dynamic attractor regardless of the state
which the system starts out in. The state cycles of self-ordering systems
are much more stable than those in other systems, "the ordered network
regime is therefore characterized by a homeostatic quality : networks
typically return to their original attractors after perturbations". The
succession of communities can be explained by using the model of
self-organizing Boolean networks outlined above. The pioneer stages
correspond to the chaotic state of the pre-ordered Boolean network. The
system may start out in any number of disordered states but will still
eventually fall into one of the state cycles. The community system at some
point crystallizes into a relatively low degree of order. Further
successional stages are characterized by the "accumulation of useful
variations". That is, the organization of the community increases, with a
corresponding increase in productivity and stability, until the climax
community is reached. The climax system, at the apex of the successional
trends, is a dynamic attractor. The dynamic attractor is resistant to
perturbation and is a state cycle, fluctuating around a mean state and not
proceeding in any directional manner.
In this model of community evolution, the evolution of the system
as a whole will have feedback effects upon the evolution of individual
species. That is, species with genotypes more suited to fit into this
ordered system may be more likely to propagate. Individuals in each
species may also be selected for their ability to fulfill certain roles in
specific portions of the ordered systems. An example of this selection
might be found in the plant defense guilds outlined by Aarssen and
Turkington. [explanation, maybe also mycorrhizal associations]. This model
also implies feed-forward effects. That is, because certain plants may be
more suited for certain roles, or niches, in the organized community they
will have an effect upon the evolution of the community itself. The
successional evolution discussed above could therefore have wider reaching
implications than just the attainment of the climax community. The
evolution of successional stages would feedback to cause species to evolve
toward the formation of useful interactions between individuals. This
tendency to form useful interactions in species would then feed-forward to
favor the formation of communities that would tend more strongly toward
order. As Aarssen and Turkington write,
Interactions lie at the heart of complex systems. A very important
but still quite enigmatic aspect of plant interactions is that of
mycorrhizal associations. Mycorrhizzae, the symbiotic fungi that grow in
association with the roots of higher plants, are ubiquitous and seem to
form a vast network that interconnect plants regardless of species.
Mycorrhizae have been found to provide an advantage to plants in certain
cases by providing essential nutrients, in turn the mycorrhizae receive
essential products of photosynthesis. However, it seems that the scope of
this relationship is not limited to simply nutrient exchange. The
mycorrhizae provide a means for exchange of materials between plants. A
study by [Woods, F.W. and K.Brock. 1964. Interspecific transfer of
45Ca and
32P by
root systems. Ecology 45:886-889] showed that radiolabeled calcium and
phosphorous applied to a root stump appeared, within 8 days, in 43% of all
species in a radius of 7.3m. Mycorrhizae can and do mediate the exchange
of hormones and other regulatory factors between plants.
It is important at this point to note that the cellular automaton
model for plant communities is not necessarily limited to the successional
scale where a change in state of a cell implies the death of one
individual and the growth of another. Plants, unlike animals, are able to
express a wide variety of phenotypes given the same genetic information.
Transplant experiments in which a plant from a distinct environment is
removed and planted in a quite different environment have shown that some
plants are able to alter their phenotypic expression to such a degree that
they resemble another, native species more than their original phenotype.
Phenotypic expression is a very broad subject encompassing such factors as
dormant cycles of some plants, expression of allelopathic factors, aspects
of morphology, etc. Plants also have a modular, open-ended growth
patterns. This means that plants are able to adapt to particular needs
placed on them by their environment by, for instance, growing toward an
area that affords the most sunlight. These needs are most often placed by
the acts of their neighbors on them which allows the formation of a
complex, automatonic system. Phenotypic plasticity and the growth patterns
of plants allow them to express a wide variety of states without actually
being replaced by another species.
Given the wide variety of plant interactions and the phenotypic
variation of the individual plants it seems reasonable to propose a model
in which plants might alter their phenotype in response to forces exerted
by neighboring plants. These forces might include competitive
interactions-competing for sunlight, nutrients, water, etc.-and beneficent
interactions-modifying the availability of light, evaporative regime, wind
flow, soil composition, nutrient transfer, etc. This model represents a
cellular automatonic ecosystem that is dynamic during a time period that
is much shorter than the evolutionary scale discussed above. A study by
[whoever] demonstrated that an insect infestation contained to one area of
a forest elicited a defensive response from trees well removed from the
site of the infestation itself in a short amount of time. It is this kind
of stimulus-response behavior which hints at the possibility of more
complex informational processing in community systems.
Is the issue of community evolution and organization then solved?
If one accepts that a plant community can act as a Boolean network capable
of self-ordering behavior, then it seems that communities would indeed
evolve. I strongly suspect that pertinent data collected in this area will
support this model, however at the present supporting data, though strong,
is still too scarce to "prove" the model. It is important to keep in mind
that with a computer program to generate self-organizing cellular
automata, the observer has a unique perspective from which they are able
to see the system in its entirety. Plant ecologists, unfortunately, have
no perspective analogous to this. Theirs is limited by vast amounts of
time, space and complexity. It is impossible to gain a perfectly complete
picture of the community. In fact, it is quite difficult to obtain a
limited picture of a small portion of a community. These limitations,
present in most areas of scientific research, make discerning the level of
actual organization of communities very difficult.
Conceptualizing of communities in this way is a beautiful way of
embracing both holism and reductionism. The holist may study the patterns
and evolution of the whole in a very useful and perhaps even quantitative
manner. The reductionist may usefully consider how individual cells
interact and evolve and how the parts may form the whole. Whittaker
states, "successions give the impression of a hit-or-miss interplay of
species populations that reach and can tolerate the habitat replacing one
another in ways that may be only loosely predictable" (Whittaker, 1972).
This may be true but, in the light of the science of Chaos, the integrity
of the complexity, evolution and organization of plant communities is not
compromised. The science of chaos, I believe holds some very interesting
and valuable insights into the structure and even function of plant
communities.References used in this paper
Aarssen & Turkington, What is Community Evolution?,
(1983) Evol. Theory 6:211-217
Bak, Per and Kan Chen, Self-Organized Criticality, Scientific American,
January 265:46-53 (1990)
Dewdney, A.K., Computer Recreations : The failings of a digital eye
suggest that there can be no sight without insight, Scientific American,
251:22-30 (1984)
Kauffman, Stuart A., Antichaos and Adaptation, Scientific American,
August 265:78-84 (1991)
Whittaker, R.H., Evolution of Natural Communities, pp. 137-159 [in]
Ecosystem Structure and Function (Ore. St. Univ. Colloquim,
1972)
Wolfram, Stephen, Cellular automata as models of complexity, Nature,
311:419-424 (1984)
Wolfram, Stephen, Computer Software in Science and Mathematics,
Scientific American, 251:188-203 (1984)