Ecological Clues to the Nature of Consciousness.

Some dynamics associated with consciousness are shared by other complex macroscopic living systems. For example, autocatalysis, an active agency in ecosystems, imparts to them a centripetality, the ability to attract resources that identifies the system as an agency apart from its surroundings. It is likely that autocatalysis in the central nervous system likewise gives rise to the phenomenon of selfhood, id or ego. Similarly, a coherence domain, as constituted in terms of complex bi-level coordination in ecosystems, stands as an analogy to the simultaneous access the mind has to assorted information available over different channels. The result is the feeling that various features of one's surroundings are present to the individual all at once. Research on these phenomena in other fields may suggest empirical approaches to the study of consciousness in humans and other higher animals.

Limits on ecosystem trophic complexity: insights from ecological network analysis.

Articulating what limits the length of trophic food chains has remained one of the most enduring challenges in ecology. Mere counts of ecosystem species and transfers have not much illumined the issue, in part because magnitudes of trophic transfers vary by orders of magnitude in power-law fashion. We address this issue by creating a suite of measures that extend the basic indexes usually obtained by counting taxa and transfers so as to apply to networks wherein magnitudes vary by orders of magnitude. Application of the extended measures to data on ecosystem trophic networks reveals that the actual complexity of ecosystem webs is far less than usually imagined, because most ecosystem networks consist of a multitude of weak connections dominated by a relatively few strong flows. Although quantitative ecosystem networks may consist of hundreds of nodes and thousands of transfers, they nevertheless behave similarly to simpler representations of systems with fewer than 14 nodes or 40 flows. Both theory and empirical data point to an upper bound on the number of effective trophic levels at about 3-4 links. We suggest that several whole-system processes may be at play in generating these ecosystem limits and regularities.

Compartments revealed in food-web structure.

Compartments in food webs are subgroups of taxa in which many strong interactions occur within the subgroups and few weak interactions occur between the subgroups. Theoretically, compartments increase the stability in networks, such as food webs. Compartments have been difficult to detect in empirical food webs because of incompatible approaches or insufficient methodological rigour. Here we show that a method for detecting compartments from the social networking science identified significant compartments in three of five complex, empirical food webs. Detection of compartments was influenced by food web resolution, such as interactions with weights. Because the method identifies compartmental boundaries in which interactions are concentrated, it is compatible with the definition of compartments. The method is rigorous because it maximizes an explicit function, identifies the number of non-overlapping compartments, assigns membership to compartments, and tests the statistical significance of the results. A graphical presentation reveals systemic relationships and taxa-specific positions as structured by compartments. From this graphic, we explore two scenarios of disturbance to develop a hypothesis for testing how compartmentalized interactions increase stability in food webs.

Complexity in quantitative food webs.

Food webs depict who eats whom in communities. Ecologists have examined statistical metrics and other properties of food webs, but mainly due to the uneven quality of the data, the results have proved controversial. The qualitative data on which those efforts rested treat trophic interactions as present or absent and disregard potentially huge variation in their magnitude, an approach similar to analyzing traffic without differentiating between highways and side roads. More appropriate data are now available and were used here to analyze the relationship between trophic complexity and diversity in 59 quantitative food webs from seven studies (14-202 species) based on recently developed quantitative descriptors. Our results shed new light on food-web structure. First, webs are much simpler when considered quantitatively, and link density exhibits scale invariance or weak dependence on food-web size. Second, the "constant connectance" hypothesis is not supported: connectance decreases with web size in both qualitative and quantitative data. Complexity has occupied a central role in the discussion of food-web stability, and we explore the implications for this debate. Our findings indicate that larger webs are more richly endowed with the weak trophic interactions that recent theories show to be responsible for food-web stability.

Biodiversity, functional redundancy and system stability: subtle connections.

The relationship between biodiversity and functional redundancy has remained ambiguous for over a half-century, likely due to an inability to distinguish between positivist and apophatic (that which is missing) properties of ecosystems. Apophases are best addressed by mathematics that is predicated upon absence, such as information theory. More than 40 years ago, the conditional entropy of a flow network was proposed as a formulaic way to quantify trophic functional redundancy, an advance that has remained relatively unappreciated. When applied to a collection of 25 fully quantified trophic networks, this authoritative index correlates only poorly and transitively with conventional Hill numbers used to represent biodiversity. Despite such a weak connection, the underlying biomass distribution remains useful in conjunction with the qualitative diets of system components for providing a quick and satisfactory emulation of a system's functional redundancy. Furthermore, an information-theoretic cognate of the Wigner Semicircle Rule can be formulated using network conditional entropy to provide clues to the relative stability of any ecosystem under study. The necessity for a balance between positivist and apophatic attributes pertains to the functioning of a host of other living ensemble systems.

On the ordinality of causes in complex autocatalytic systems.

The convention in chemical dynamics usually is to identify the reactant and catalytic molecules as the active agencies that combine in mechanical fashion to constitute a reaction process. When macromolecules grow large and complex enough to exhibit some plasticity, however, the subsequent directions in which these molecules change may be guided more by the nexus of chemical reactions in which they participate. In particular, configurations of autocatalytic reactions among plastic macromolecules can come to exert more agency upon the component reactants and mechanisms than vice versa, and the nexus of such processes retains its identity longer than do the latter, more transient participants. Whence, the ascendancy of autocatalytic forms as causal agencies provides a natural example of the phenomenon of "emergence" and affords a way out of the conundrums that currently obfuscate the issue of the origin of life.

Some steps toward a central theory of ecosystem dynamics.

Ecology is said by many to suffer for want of a central theory, such as Newton's laws of motion provide for classical mechanics or Schroedinger's wave equation provides for quantum physics. From among a plurality of contending laws to govern ecosystem behavior, the principle of increasing ascendency shows some early promise of being able to address the major questions asked of a theory of ecosystems, including, "How do organisms come to be distributed in time and space?, what accounts for the log-normal distribution of species numbers?, and how is the diversity of ecosystems related to their stability, resilience and persistence?" While some progress has been made in applying the concept of ascendency to the first issue, more work is needed to articulate exactly how it relates to the latter two. Accordingly, seven theoretical tasks are suggested that could help to establish these connections and to promote further consideration of the ascendency principle as the kernel of a theory of ecosystems.

Quantitative methods for ecological network analysis.

The analysis of networks of ecological trophic transfers is a useful complement to simulation modeling in the quest for understanding whole-ecosystem dynamics. Trophic networks can be studied in quantitative and systematic fashion at several levels. Indirect relationships between any two individual taxa in an ecosystem, which often differ in either nature or magnitude from their direct influences, can be assayed using techniques from linear algebra. The same mathematics can also be employed to ascertain where along the trophic continuum any individual taxon is operating, or to map the web of connections into a virtual linear chain that summarizes trophodynamic performance by the system. Backtracking algorithms with pruning have been written which identify pathways for the recycle of materials and energy within the system. The pattern of such cycling often reveals modes of control or types of functions exhibited by various groups of taxa. The performance of the system as a whole at processing material and energy can be quantified using information theory. In particular, the complexity of process interactions can be parsed into separate terms that distinguish organized, efficient performance from the capacity for further development and recovery from disturbance. Finally, the sensitivities of the information-theoretic system indices appear to identify the dynamical bottlenecks in ecosystem functioning.

Cycling in ecological networks: Finn's index revisited.

A chief cybernetic feature of natural living systems is the recycling of nutrients, which tends to enhance stability and is one of the principal causes of ecosystem complexity. In 1976, Finn proposed a simple and effective measure (later known as the Finn cycling index [FCI]) to assess the quantitative importance of cycles in ecosystems. This index was successfully applied as a gauge of ecosystem health and maturity in a wide variety of studies. It turns out, however, that FCI is biased as a measure of cycling in ecosystems, because it does not include all flows engaged in recycling. A new, more inclusive version of the index is possible. What is called the comprehensive cycling index (CCI) accounts for all of the fluxes generated by cycling. Computing the new measure requires a large amount of time, however, even with ad-hoc software. To obviate the necessity for such heavy computation, a linear transformation of the FCI into the CCI is proposed.

Complexity, stability and self-organization in natural communities.

The search for a functional relationship between diversity and stability has thus far been futile. Recent advances in cybernetics suggest that progress may be achieved if diversity, stability and redundancy are considered to be cofactors in determining the key dependent variable - the capacity for self-organization.

Characterization of the planktonic food web of Takapoto Atoll lagoon, using network analysis.

The planktonic food web of Takapoto Atoll lagoon was studied using network analysis. This analysis includes four types of indices dealing with bilateral interactions of compartments, the trophic structure, biochemical cycles, and the topology of the flows. We found numerous parallel carbon pathways of similar importance, indicating a highly complex system compared to other marine ecosystems. Other characteristics were trophic levels not ranked in the same order as the size classes, the domination of system activity by processes at the first trophic level (and especially by herbivory), and cycling processes that involve many pathways. This is the first use of network analysis to describe completely a planktonic food web, and also the first comprehensive description of the trophic structure of the planktonic system in an atoll lagoon.

The balance between adaptability and adaptation.

In his 1983 book, Adaptability, Michael Conrad explored the quantitative relationship between adaptability and adaptation using the conditional 'entropy' of information theory as his primary tool. The conditional entropy can be used to estimate the connectivity of the network of system exchanges, a key indicator of system stability. In fact, the May-Wigner criterion for the stability of linear dynamical systems can be recast using the conditional entropy to help identify the boundary along which adaptability and adaptation are exactly in balance-the 'edge of chaos' as it is popularly known. Real data on networks of ecosystem flows indicate that in general these systems do not exist nigh upon the edge of chaos, but rather they populate a much wider 'window of vitality' that exists between the realms of chaotic and deterministic dynamics. It appears that the magnitudes of network flows within this region are distributed in power law fashion. The theory also suggests that an absolute limit to the connectivity of natural self-organizing systems exists, at approximately 3.015 effective connections per node.

Quantitative measures of organization for multiagent systems.

A set of "information theoretic" measures has been developed to quantify the degree of constraint inherent in the organization of a multiagent system. Separate measures can be provided to quantify spatial organization, trophic organization and, more generally, the overall structure of interactions. The additive character of these quantities allows them to be distributed in various fashions among species and places in a way that allows one to assign an "Importance Index" to those taxa and places. In addition, a measure to gauge the degree of adaptation of a species to a particular environment is proffered. The proposed measures allow one to formulate the following hypotheses in quantitative fashion: (1). that any disturbance of an ecosystem at a location associated with a high spatial Importance Index will exert a greater impact on the population dynamics than will a similar disturbance aimed at a place where the values of these indexes are lower; (2). that any disturbance in an ecosystem affecting a particular species with high individual Importance Indexes will cause a greater impact on the overall population dynamics than will a disturbance aimed at a species with a lower values of these indexes; (3). that the ascendancy of evolving system has a propensity to increase. The precise quantitative formulation of these hypothesis would permit them to be tested via multiagent simulation. Estimating the probablities pertaining to these hypotheses presents a number of problems that merit discussion.

Ecological network analysis for economic systems: growth and development and implications for sustainable development.

The quantification of growth and development is an important issue in economics, because these phenomena are closely related to sustainability. We address growth and development from a network perspective in which economic systems are represented as flow networks and analyzed using ecological network analysis (ENA). The Beijing economic system is used as a case study and 11 input-output (I-O) tables for 1985-2010 are converted into currency networks. ENA is used to calculate system-level indices to quantify the growth and development of Beijing. The contributions of each direct flow toward growth and development in 2010 are calculated and their implications for sustainable development are discussed. The results show that during 1985-2010, growth was the main attribute of the Beijing economic system. Although the system grew exponentially, its development fluctuated within only a small range. The results suggest that system ascendency should be increased in order to favor more sustainable development. Ascendency can be augmented in two ways: (1) strengthen those pathways with positive contributions to increasing ascendency and (2) weaken those with negative effects.