Self-Organization Theory Research Paper

1. Historical Background

Self-organization theory is based on the evidence that living systems express distinctive types of intrinsic dynamic order. In the eighteenth century the founder of modern biology, Carolus Linnaeus, regarded his taxonomy as a prolegomenon to a general theory of biology based on the Enlightenment principle which observed that regularities of structure in nature can be explained by underlying generative laws of form. This same idea informed the comparative morphological studies of Goethe, Cuvier, St. Hilaire, Reichert, and Owen in the eighteenth and nineteenth centuries, despite differences of emphasis among them.

A revolution in biological thought occurred when Darwin replaced intrinsic principles of order in organisms by historical and functional contingencies. For Darwin, constraints on morphology came from descent, specifically descent from ancestors whose morphologies were the result of adaptation to particular habitats, realized through the selection of fitter hereditary variants (Mayr 1988).

Within embryology the problem of biological form remained: how does the morphology of the adult organism emerge through growth and transformation of the egg? During the twentieth century this problem was transformed by the rise of genetics into a new question: what are the changes in gene activity that underlie morphological change in developing organisms? In evolutionary studies a crucial question became, what are the changes in genes that underlie the evolution of different species? Developmental and evolutionary genetics are now converging to provide detailed answers to these questions.

What remains problematic is explaining relationships across levels of biological organization, from patterns of gene activity, to phenotypes (morphology and behavior), to community organization, and to higher-level dynamics such as patterns of species extinctions. The difficulty is that there is a hierarchy of organizational levels. Collapsing these levels down to genes and their products does not provide explanations of the different structures of cells, tissues, organs, and/organisms that emerge during development and in the course of evolution. It is here that principles of self-organization in biology have re-emerged in a somewhat different guise from more classical conceptions, sharpening the issues defined earlier and working systematically at different levels of biological order.

The unifying term for this field of study is the sciences of complexity (Cowan et al. 1994). The field focuses on the emergent properties of complex systems during the course of development and evolution (Sole and Goodwin 2000). One of the descriptive terms for these emergent properties is ‘order for free’ (Kauffman 1995), meaning that the order arises spontaneously, can occur at any level, and is not a result of natural selection. In fact, natural selection can do no more than stabilize emergent order if it is adaptive, a principle of evolutionary theory which is sometimes forgotten. This new perspective offers the possibility of integrating the historical and functional explanatory framework of neo-Darwinism with the ‘intrinsic principles’ approach of nonlinear dynamics, the heart of the sciences of complexity. The theory of self-organization now provides the possibility of recasting evolutionary principles in consistently dynamic terms, resolving the tensions that have existed between development and evolution, ontogeny and phylogeny.

2. Development, Behavior, And Life-Cycles

Developing organisms can be understood as self-organizing systems whose morphology emerges from the dynamics of ‘morphogenetic fields.’ These fields are defined by the coordinated properties of cells and their interactions via signaling molecules, the extracellular matrix, adhesion molecules, cell movement, and so on. The particular patterns that emerge are often not obvious at all from the properties of individual cells and require higher-level concepts to be understood.

This principle can be illustrated by the classic example of the cellular slime mold, Dictyostelium discoideum, whose vegetative phase consists of single amoebae that live on bacteria in damp, rotting vegetation, growing and dividing independently of one another. Under conditions of starvation and dessication their metabolism and behavior change so that they begin to interact through pulsatile signals of a metabolite (cyclic adenosine monophosphate) that is released periodically by individual cells and diffuses between them. A cell receiving such a signal emits a pulse itself and moves toward its source, producing dynamic patterns of movement that result in the aggregation of thousands of cells. During this process of aggregation, spiral waves of moving cells are observed. The pattern cannot be explained in terms of individual cell behavior; it requires the higher-level concept of an ‘excitable medium’ which serves as a morphogenetic field for the slime mold (Goodwin 1994).

Initially uniform patterns of aggregating cells break up into streams, another purely dynamic process resulting from an intrinsic instability that breaks the symmetry of the initial aggregate (Hofer et al. 1995). The cells form a shapeless mound of several thousand similar cells around the cell or cells that initiated the signaling process.

Vasiev et al. (1997), who have modeled this whole developmental sequence in the slime mold, point out that ‘this complicated process could take place without the necessity for transcription of new genes. In real life, however, it is known that many different genes are transcribed during aggregation and mound formation.’ For instance, after stream formation, molecules are produced which make cells sticky, reinforcing and stabilizing this pattern. The mound then self-organizes into an elongated shape called a slug, a few millimeters in length. The slug assembles under the influence of continuous periodic signals that come from the same region of cells, which becomes the leading end of the migrating slug. The migration of the slug is a coherent movement of the whole mass of several thousand cells—in other words, the coordinated dynamics of an excitable medium involving three-dimensional waves of activity that propagate through the slug from anterior to posterior (Bretschneider et al. 1999).

During migration of the slug, two types of cell differentiate, involving differential gene activities: the front one-third of the cells of the slug develop stalk characteristics while the posterior two-thirds become the spores. Differential gene activity is a major feature of this process. The slug stops migrating and organizes itself into a fruiting body consisting of a stalk supporting a spherical mass of spores a few millimeters above the surface. When conditions become moist again, resulting in bacterial growth, the spores are released and amoebae emerge to start the life cycle again, growing on the bacteria.

This example illustrates the point that to understand a species’ life cycle it is necessary to understand the dynamics of self-organizing patterns as well as the role of gene activity, which can both initiate and stabilize the morphogenetic changes characteristic of the species. During evolution, changing patterns of gene activity will occasionally produce coherent changes of morphology and behavior, which will persist if they are adaptive. What is becoming clear is that gene activity can stabilize, consolidate, or initiate developmental events, but these processes can only be understood in terms of the self-organizing, coherent dynamics of whole life cycles.

3. Patterns Of Behavior In Social Insects

Entomologists have recognized for many years that communities of insects display high levels of coherent order in their activities and social organization (Holldobler and Wilson 1990). However, these usually cannot be understood simply by observing the behavior and interactions of individuals. For example, several species of ant exhibit a rhythmic pattern of activity–inactivity in the brood chamber, where the workers are tending the queen and the brood, whereas individual ants have no tendency to show such rhythmic behavior. On the contrary, their activity patterns in isolation or at low density have been characterized as chaotic, in the technical sense of the term (Cole 1991). Another example comes from termite colonies, which construct very complex nests with coherently organized passageways, vaults, and ceilings. However, observation of activity in termite ‘construction gangs’ reveals a pattern of behavior that is anything but coherent. Individuals move about, join groups working on different building sites scattered about the construction area, stop suddenly for several minutes, and then scatter randomly to new sites. In these cases, how does coherent order arise from such disorder?

Once again, explanations of pattern require an analysis that goes beyond genes, individual behavior, and natural selection, to models that introduce a new level of complexity in the dynamics of the group. Rhythmic behavior of workers in brood chambers can be shown to arise from chaotic behavior of individuals as a result of stimulatory interactions between ants when they exceed a critical density, as usually occurs in brood chambers (Sole et al. 1993). Furthermore, the range of parameters (e.g., sensitivity of ants to one another and density) that result in rhythmic activity is large, so that this behavior pattern is robust to significant genetic and environmental disturbance, as stable evolutionary characters must be. Similarly, it has been shown (O’Toole et al. 1999) that the coherent architectural results of apparently disorganized termite behavior arise from a dynamic process called ‘self-organized criticality’ (Bak 1988). The attraction of termites to occupied building sites, the sudden immobility at high density (but variable size) of construction gangs, and subsequent scattering to new sites form the basis of a process ensuring that all sites grow at roughly the same rate. With such synchrony the nest components fit together coherently to give organized architectural constructions. Again, this dynamic is stable to parameter perturbation. ‘Order for free’ must be robust if it is to persist in evolution.

4. Emergent Properties Of Ecosystems And The Biosphere

A crucial issue in the study of natural ecosystems concerns the relationship between complexity and stability: are complex ecosystems more or less stable than simple ones? Complexity may be defined, following May (1973), using the notion of ‘degree of connectedness’: ecosystems whose species are richly interconnected are more complex than sparsely connected ones. May’s theoretical study, using conventional population dynamics to model ecosystems and using linear stability analysis, showed that there is a fairly sharp transition between two states. Below a critical degree of complexity (connectivity) ecosystems are stable; above, they are unstable. Detailed analysis of field studies by Keitt and Marquet (1996) showed that there is an interesting inverse relationship between number of species in an ecosystem and their connectivity, supporting May’s conclusion and suggesting an underlying dynamic order. Furthermore, these investigators examined the frequencies of species extinction events of different sizes in ecosystems that were getting more complex as a result of the introduction and establishment of new, exotic species. Their results revealed a regular ‘power law relationship’ that is suggestive of an organized dynamic.

A study by Ellner and Turchin (1995) took stability analysis a step further in identifying a special emergent property of ecosystems. They examined an extensive set of ecological time series within an ecosystem and concluded that they showed chaotic dynamics. Their conclusion supported a conjecture from purely theoretical studies of co-evolving systems, that interacting populations co-evolve ‘at the edge of chaos’ (Wolfram 1986). Langton (1990) then noticed that there are sets of interaction rules that result in highly ordered patterns of stable behavior and others that result in extremely complex activities without any repetitive order (‘chaos’). The rules can be ordered logically and it turns out that in between the ordered and the chaotic regimes there is a realm of complexity whose behavior suggested a potential for ‘emergent computation’ (Langton 1990). Langton suggested that real biological evolution might occur in such a domain of complex dynamics, the edge of chaos, where new order can arise as evolving populations move from order to chaos and on into new order.

Langton’s provocative conjecture has spawned a number of more sophisticated computer models of coevolving populations, among them one by Kauffman and Johnsen (1991). What this model simulates is a dynamic pattern of species extinction sizes of the type described by Pimm (1984) and the time series behavior examined by Ellner and Turchin (1995). A more accurate fit to the data has been obtained by Kauffman (1995) using an extended version of the original model.

A further development of self-organization theory arises from a study of extinction statistics obtained from the fossil record. Sole et al. (1997) showed that extinction has the property of ‘self-similarity,’ a power-law governing the relationship between probability of extinction and size of extinction event (small extinctions are common and large ones are rare). A model of ecosystem dynamics that fits these observations has been constructed (Sole et al. 1996, 1998), suggesting a clear distinction between the dynamics of microevolution (adaptive modifications of species) and macroevolution (patterns of extinction events). Competitive interactions between species and adaptive processes clearly occur in evolution, but they do not explain the large-scale pattern of evolutionary change (extinction sizes and probabilities). The latter arises from the collective dynamics of ecological networks as an emergent property that is not reducible to the competitive interactions and adaptive modifications of species. Micro and macroevolution are then distinct, requiring different explanations.

Finally, unexpected regularities are observed at the level of the whole biosphere in variables such as the oxygen and carbon dioxide content of the atmosphere, the mean surface temperature of the earth, and the concentrations of various ions (calcium, sodium, potassium, chloride, phosphate, sulfate, etc.) in the oceans. Purely geophysical processes are unable to account for the stability of these quantities over geological time periods (millions of years) and the evidence now favors the intimate involvement of biological processes as crucial contributors to global biosphere dynamics. This radical shift of focus for evolutionary thinking comes from the work of James Lovelock (1979, 1991) and the study of microbial communities by Lynn Margulis (1987), who together gave birth to the Gaia Hypothesis. A whole new class of models is under development to account for the capacity of the living earth to regulate variables crucial for life by processes that give rise to emergent stability properties (Harding 1999, Lenton and Watson 2000).

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