Search

For over 40 years, Professor Bernie Patten, offered a course on Field Systems Ecology at the University of Georgia in Athens, Georgia, USA. The course combined systems analysis approaches and natural field ecology in a way that gave the students new perspectives on making conceptual and formal models of the natural world. The course employed extensive use of outdoor field laboratories at a nearby park, which had multiple ecological habitats. The main progression was to go from simple observations to “seeing systems” to modeling by learning how to ask pertinent systems-oriented questions. This started with a structured walk through the six identified subsystems (forest ridgetop, forest slope, field, lake, stream, and wetland) and proceeded to specific field sampling techniques for the terrestrial and aquatic environments. In addition to the field labs, the course required two weekend camping trips, one to the Great Smokey Mountain National Park in the Appalachian Mountains and one to the Okefenokee Swamp/Cumberland Island National Seashore. The idea was to use the two weekend trips to frame the local watershed scale processes at the continental scale. In this manner, students could observe and measure ecosystem processes and interactions at multiple scales. The notes, which are reproduced below, have been further modified for use at Towson University which utilizes a local park in Baltimore County called Oregon Ridge Park and weekend trips to Catoctin National Park and Chesapeake Bay. The general approach of these notes should have universal appeal to anyone teaching or taking a systems ecology course.

Aspects of ecology-based environmentalism may run counter to how nature works; it is important to get the science right. The Janus Enigma Hypothesis is formulated as a flow–storage network approach to holistic ecological understanding. It proceeds from primary energy–matter consumption toward maximization of throughflow. When transferred material is energy, the goal function is maximum power (energy flow). The Janus Hypothesis has the following line of development: 1. The 2nd Law of Thermodynamics requires that the environments of aggrading (anti-entropic) processes become themselves degraded. To restrict such degradation is to limit life's processes. 2. A maximum power conjecture holds that aggrading systems self-organize to maximize power generating work. Maximal resource use, work production, and environmental degradation necessarily follow. This applies also to material flow in generalized energy–matter (throughflow) processing. 3. In maximizing power (throughflow), biota perform work to maximize their fitness (Type I, biological), but at the expense of degraded environments. Zero-sumness of conservative, consumptive transfers produces a proximate life–environment relationship that is win–lose. 4. But covert mechanisms also operate such that maximizing throughflow also maximizes a system-wide, nonzero-sum, network property— dominant indirect effects . 5. These maximize another property of network organization, network synergism . This transforms proximate, tangible, zero-sum, agonistic, (+, −) transactions into ultimate, intangible, nonzero-sum, mainly positive (+, +) and synergistic relations . The proximate transactions lead by network processes to ultimate nonzero-sum benefits > costs, which is network synergism. 6. By the indirect line from maximum power (throughflow) to network synergism, biotic work maximizes both biological and ecological fitness (Type II), and the life–environment relationship becomes win–win. This cannot be seen from pure empiricism because it plays out diffusely as limit processes in networks that are virtual. Three lines of evidence are presented in support of the Janus Hypothesis: (1) “Building a biosphere” by progressively adding nodes and links in simple compartment models shows throughflow and network synergism to be positively correlated. (2) Decomposing the utility measure of network synergism in these models into its constituents shows them to be largely made up of throughflows; maximum network synergism likely follows from the maximization of throughflow. (3) Comparing total system throughflow with network synergism in 31 food webs described for Ukrainian pasturelands shows the two measures to be positively correlated in this large empirical database. The Janus Hypothesis has a built-in paradox. Because the positive benefits derived from the nonzero-sum maximum throughflow → network synergism → Fitness-II line exceed the negative costs generated by the zero-sum maximum throughflow → Fitness-I line, applied programs designed to reduce environmental degradation will reduce not only Fitness-I, but also Fitness-II by foregoing the implicit benefits of network synergism that inherently exceed the explicit costs of maximizing throughflow. This is the Janus Enigma. It means that well-meaning but misguided environmental programs may actually, in fact must, induce a lose–lose relationship between life and environment. If the Janus Hypothesis proves scientifically valid, environmentalism must resolve and manage the apparent conflict, and ecology as its parent science must expand its dimensions and become a complex systems science competent in understanding and methodology to meet the challenges of complex, intractable, non-obvious holism in nature's living networks.

Causality in Complex Adaptive Hierarchical Systems (CAHSystems) is bipolar. In the hierarchical organization, within-scale contributions come both from below (reductionistic) and above (holistic). Holoecology is ecology that seeks to bring holism and formalism into the traditional mix of descriptive, empirical approaches to elaborating ecological cause and effect. The holism is philosophical and methodological, ecological modeling being an important element in the latter. The formalism (presently) is built around a body of environmental system theory called the Theory of Environs. This theory encompasses a set of “principles” of transactional network organization, where a transaction is a flow of conservative substance (energy or matter) between two system components. These are numbered, and referred to not as principles, but as cardinal hypotheses, because they are conditioned on verification or falsification by empirical or theoretical means. Presently, there are 20 of them: 1. Network pathway proliferation—increase of pathway numbers with length. 2. Network nonlocality—dominance of indirect effects. 3. Network homogenization—trend to uniform distribution of transaction based causation. 4. Network aggradation—network growth and development properties move systems away from thermodynamic equilibrium. 5. Network throughflow maximization—system-wide virtual goal function. 6. Network storage maximization—system-wide concrete goal function. 7. Network boundary amplification—benefits of agency in boundary crossing. 8. Network interior amplification—benefits of high node in-degree. 9. Network enfolding—entwinement of boundary relations into deep interiors. 10. Network unfolding—conversion of networks to macrochains. 11. Network centrifugality/centripetality—expansion and contraction of influence from node storage in, respectively, output and input environs. 12. Network topogenesis—quantitative determination of stocks and flows by topological properties of qualitative digraphs. 13. Network synergism—system-wide benefits > costs emergent in network organization. 14. Network interaction typing—structural determination (by digraph topology) vs. parametric determination (by quantitative flow-storage transactions) of qualitative relations specifying binary interaction types (e.g., predation, competition, mutualism) between component pairs in systems. 15. Network mutualism—emergence of positive interaction types (symbioses) in network organization. 16. Network Janus Enigma Hypothesis—stronger adjacent transactions produce stronger ultimate expression of positive binary relations (network synergism), but also stronger proximate environmental degradation. 17. Network clockwork stockworks (holon autonomy)—time delay of substance flow in storage causes nodes to dominate in determining network properties; “‘net’works” are really more like “clockwork ‘stock’works” that contribute constrained autonomy to their entities. 18. Network environ autonomy—boundary-based partitioning of transactional stocks and flows in systems, causing environs to be isolated “small worlds” spanning intra-system organization and expressing implicate order. 19. Network distributed control—Expression among system components of distributed (indirect, decentralized, or remote) control at a network distance. 20. Network ecogenetic coevolution—system-wide coevolution of mutually implicated parts and wholes to achieve and sustain systemic coherence and life. These hypotheses are grouped into sections by shared affinities. Eight of them are identified as having special potential to: transform ecology into a systems science that integrates bipolar causality; unify the reductive and holistic modes of science; and shift the ecological worldview more towards holism.

Black locust colonization of floodplains can exacerbate the problems associated with increasing nitrogen inputs into the riparian area and river ecosystem. In this study we compare the nitrogen budgets of two sites of floodplain ecosystem, one is colonized by invasive black locust and the other is forested by the indigenous willow species. Our data report the considerably higher N-flow rates, nitrogen storage and the faster total N-related ecosystem processes in the Robinia site in comparison to the indigenous Salix site of the study floodplain. Black locust affects the nitrogen cycle in the study riparian ecosystem through the N-fixation, high N-content litterfall and rapid litter decomposition that results in the increase of the nitrogen flow into the river and contaminates the water. Black locust appeared to reduce the conservation values of colonized areas and adjacent river. Restoration strategies that remove the black locust from invaded sites and prevent the further invasion will slow down the contamination. However, high availability of nitrogen in soil and soil degradation might have a long-term effect on floodplain ecosystem after the restoration.

This paper gives a possible explanation for how changes in holistic network organization can come to be reflected in changes in mechanistic processes thought to be under local control by organisms and abiota. Most point-contact, or node(●)-link ( — , → ), networks in science are qualitative. Their complexity is great and quantification is difficult. Networks depict wholeness and are models for holism. Mathematically, they are graphs, unweighted when unquantified, and either undirected ( ●– ●; most social networks) or directed ( ●→ ●; most ecological food webs). Directed graphs are digraphs. The question of this paper is, can unweighted digraphs be used to quantify mass–energy link flows? A methodology, link tracking , is developed to achieve this. Simple paths (no repeated nodes) and cycles in the network are identified. Links for different node pairs are tallied along these pathways, and used to calculate transition probabilities. These are extended to all pathways (direct + indirect) by matrix inversion; the resultant coefficients are used in conjunction with boundary inputs to generate flows. Applied to an ecological stock-and-flow model, empirical measurements lay within ±2 times the corresponding link tracking values. This reinforces the intuition that digraph structure and flow function are intimately related, which is the principal general finding of the paper. However, only one “structure-based” parameterization is calculable per digraph by link tracking, whereas many “functional” empirical flows are possible. The meaning of the link tracking values is therefore to be resolved. In discussion, it is hypothesized that link tracking structural flows are basins of attraction – centrally tending mean flows around which realizable empirical flows are constrained by structure to be distributed. The methodology sheds light on previously unexplained results from an early radiotracer study of experimental ecological networks. Uses of link tracking to expand existing knowledge of food webs and other kinds of qualitative networks are considered.

An important question in ecology is whether the food-web structure and ecosystem functions are related. This paper provide an empirical evidence for the food-web complexity–ecosystem properties relationships using the comparative analysis of food webs in seven mountain pastoral grasslands located in the Carpathian Mountain area of the Chernivtsi Region, Ukraine. Biomass of plant functional groups; grazing intensity; richness of different functional groups of the soil microorganisms; and geographical location of the study grasslands are observed ecosystem properties. Trophic networks consisting of N food and feeding categories (nodes, compartments) joined by L food transfers (links) were constructed for each studied pasture and the following network measures of their graph characteristics (“topology”) determined: food-web size ( N ), number of links ( L ), link density ( LD = L / N ), and connectance ( C = L / N 2 ). Also the number of trophic classes and size of each trophic class are incorporated as the properties of the food-web architecture. Our data reveal that increase in species richness and food-web complexity increases the biomass of forbs within the study grasslands. Grazing intensity shows negative but statistically insignificant correlation with network measures. Our findings also reveal the longitudinal changes in connectance variation across the study food webs. It shows that temperature and elevation changes may also contribute toward the food-web connectance variation within the study area. Overall, our findings report plants to be the defining in network architecture. Furthermore grazing-susceptible plants show to be the driving variable in a food-web structure of the study grasslands. Our findings also reveal new aspects in behavioral patterns of food-web properties in relation to each other. Our data report link density to be the most sensitive parameter in relation to the other food-web measures. In contrast, connectance shows the least sensitivity to all other network measures, but the most sensitivity to the observed ecosystem parameters.

Compartmental, or “stock-and-flow”, models describe the storage and transfer of conservative energy or matter entering and leaving open systems. The storages are the standing “stocks”, and the intra-system and boundary transfers are transactional “flows”. Network environ analysis (NEA) provides network methods and perspectives for the quantitative analysis of compartment models. These emphasize the distinction between direct and indirect relationships between the compartments, and also with their environments. In NEA, each compartment in a system has an incoming network that brings energy or matter to it from the system’s boundary inputs, and an outgoing network that takes substance from it to boundary outputs. These networks are, respectively, input and output environs. Individual pathways in environs have an identity not unlike spaghetti in a bowl, each strand of which originates at some boundary input and terminates at some boundary output. All strands originating at the j’th input collectively comprise, no matter where they terminate, the j’th output environ; similarly, all strands terminating at the i’th output comprise, no matter where they originate, the i’th input environ. Thus, any substance freely mixing in the system as a whole runs in pathways consigned to one and only one output environ traced forward from its compartment of entry, and also one and only one input environ traced backward from its compartment of exit. The environs are partition elements – they decompose the interior stocks and flow according to their input origins and output destinations. Moreover, each environ’s dynamics and other systems and network properties are unique, and sum over all the environs to give the aggregate dynamics and properties of the whole. It is this composite, aggregate whole that empirical methods measure; empiricism unaided by theoretical analysis is blind to the environ pathways that actually compose the wholes. A previous study of nitrogen dynamics in the Neuse River Estuary (NRE), North Carolina, USA ( Whipple et al., 2007 ) described within-environ transfers using a throughflow-based network analysis, NEA-T. Throughflow (Tin, Tout) is the sum of flows into or out of each compartment. This paper extends this work using a companion storage-based methodology, NEA-S, re-notated from its antecedent and originating contributions ( Barber, 1978a , Barber, 1978b , Barber, 1979 , Matis and Patten, 1981 ). Time-series data implementing 16 seasonal steady-state network models of nitrogen (N) storage and flow in the Neuse system were constructed for spring 1985 through winter 1989 by Christian and Thomas, 2000 , Christian and Thomas, 2003 . Network topology was constant over time, but the storage and transfer quantities changed. Environ analysis of this model showed that nitrogen storage and residence times differ within the different environs composing the compartments, and moreover, that these differences originate in the system’s interconnecting network as a whole. Thus, environs function within themselves as autonomous flow–storage units, but this individuality derives from, and at the same time contributes to the entire system’s properties. Environ autonomy is reflected in unique standing stocks and residence times, and whole empirical systems are formed as additive compositions of these. Because storage is durable and transfers ephemeral, storage environs revealed by NEA-S have more autonomy than flow environs computed using NEA-T. We quantified this autonomy by comparing the heterogeneity of extensive environs in models driven by actual inputs with intensive environs normalized to unit inputs. The former is more storage-heterogeneous than their unit reference counterparts, with dissolved nutrients NOx, DON, and NH4 exhibiting greatest heterogeneity. A previous NEA study of distributed control in this same model by Schramski et al. (2007) showed that NOx controls the system whereas sediment is controlled by the system. In the present study, NOx dominates storage in extensive environs, and therefore, is controlling in actuality. However, in the intensive unit, environs sediment accounted for most of the storage, reflecting greater control potential. This potential is expressed by the sediment acting like a capacitor for N, seasonally sequestering and releasing this element in the role of a biogeochemical regulator.

Ecosystems can be abstracted into models consisting of compartments containing matter or energy, transactional flows of matter or energy between compartments, inputs into the system, and outputs from the system. Although direct transactions are measurable in the field, indirect transactions have been demonstrated to have dominant effects. Integral network utility (U) is a summation of all direct and indirect net transactions in a network presented in matrix format and developed as a feature of Network Environ Analysis (NEA). While U can provide qualitative information about ecological interactions between compartments, the nonzero-sum nature of indirect net transactions has made ecological interpretation of quantitative network utility challenging. Here we aimed to examine U for nine 2- or 3-compartment ecosystem models from a throughflow perspective. For each model, we assigned inputs, outputs, and flows algebraically using flow components traceable across the model, developed corresponding flow (F) and throughflow (T) matrices based on these values, and used symbolic Matlab to calculate the net adjacent flow intensity matrix (D) and U. Substituting algebraic combinations of flow components with corresponding throughflow values allowed us to reduce elements of U to throughflows to the maximum extent possible. Models with only simple input environs were fully throughflow reducible, while models with more complex input environs exhibited one to three nonreducible elements in U. Throughflow reducibility was sufficient, but not necessary, for topological determination of ecological relations of a model, as described by sign(U). Parametrically determined elements of sign(U), along with the specific flow components influencing the sign of that element, could be readily identified based on quantitative consideration of nonreducible flow components. We provide an example showing that considering throughflow as a centrality measure can allow the identification of a quantitative basis for network synergism. By allowing identification of specific subsets of transactional flows relating to ecosystem complexity and qualitative differences between human-designed systems in the conventional industrial model and evolved ecological systems, the throughflow perspective of U opens avenues for designing more sustainable human systems.

Red spruce ( Picea rubens Sargent) has exhibited widespread growth decline and high mortality for the last half century in the eastern United States. Good prediction of this species’ distribution in relation to environmental conditions is critical for effective management. This study projects red spruce distribution in response to multiple causal mechanisms in the Great Smoky Mountains National Park (GSMNP) of the Southern Appalachian Mountains by coupling a temporal simulation model of tree growth (ARIM.SIM) to a species distribution model (ARIM.HAB). ARIM.HAB computed habitat suitability, estimated from ARIM.SIM-generated red spruce growth, for every spatial 30 m grid cell in GSMNP. ARIM.SIM showed that different factors were responsible for habitat suitability and growth at higher vs. lower elevations. The air pollution variables (acid rain and cloud immersion frequency) caused low habitat suitability at higher elevations (1800–2028 m). Reduced air pollution but greater stress from climatic variables (high temperatures, reduced precipitation) caused medium suitability at lower elevations (1400–1600 m). And less stress from air pollution and climate variables combined with ample water to produce highest suitability at intermediate elevations (1600–1800 m). The projected range was verified with an existing geospatial database for red spruce and showed excellent correspondence with present-day distribution (AUC = 0.99, kappa = 0.87 and TSS = 0.88). This research shows that species distribution models coupled with a process-based temporal simulation models can improve the precision and accuracy of, respectively, habitat suitability and range projections for species at local scales.

We investigated the potential effects of projected climate change on red spruce (Picea rubens Sarg.) growth in the Great Smoky Mountains of Southeastern USA. A model called Annual Radial Increment Model (ARIM) was used to capture ecosystem complexity manifested as direct and indirect effects in multifactorial within- and across-scale interactions. The model was run under different scenarios, including projected climate change under reduced, no change, and increased atmospheric pollution. Modeled red spruce growth at end of 21st century (2080–2099) was compared to modeled growth at end of the 20th century (1980–1999). Red spruce growth at high elevations (≥1700 m) declined by 10.8% when climate change interacted with a 10% increase in air pollution, but red spruce growth increased by 8.4% when air pollution decreased by 10%. In contrast, red spruce growth at low elevations (

This is the first of two numbered papers for this Special Issue dealing with the ecological basis of environmentalism. The second follows, in a subsequent issue if not here. Patten (2013) gives a short preview of both papers. Problems of environmentalism—environmental protection, conservation, and preservation—are now widely appreciated as important to human enterprise and destiny. Called to attention by advances in descriptive empirical ecology, the new problems are too complex for this same ecology to solve without further expansion of basic knowledge. To understand how nature works two kinds of science are needed, one empirical, describing what is immediate and tangible, the other theoretical, developing first-principles understanding of what is indirect and intangible. Development of a complex systems theory based ecology is hindered by over-commitment of attention and resources to applied environmentalism. This may in its inadequacy run counter to how nature works, which could be detrimental to both humanity and nature. It is important to get the science right. As background for a revisionary hypothesis presented in Part II, five elements of basic ecology and five of applied environmentalism are here reviewed. The basic topics are ecological energetics, linear vs. nonlinear dynamics, steady vs. non-steady states, epistemic mediation, and indirect effects. The environmental topics are overpopulation, biodiversity, invasive species, sustainability, and global change.

An unlimited variety of within- and across-scale constraints generated by self-organizing processes in ecosystems presents problems for life to solve. Solutions reached at all levels of the ecological hierarchy spawn further constraints in an endless spiral of ecosystem growth and development. Diversification, exposed to natural selection, produces differentiated function within organized wholes. This paper reviews such differentiation over the span of organizational levels from atoms and biochemical molecules to cells and their genetics, from organs and organisms to species and their phylogenetics, from populations and communities to their compositions as ecosystems, and thence to the cosmos itself. On Earth, life occurs in non-extreme and extreme environments, enabled by a biphasic adaptive radiation that drills into and fills available niche space. The first phase is diversification, which is the generation of variations. The second phase is selective differentiation that sculpts meaningful function from an endless stream of diversified, niche-filling possibilities. The paper asks, from the apparent universality of this diversification/differentiation pair, whether or not there is a force in Nature that drives the phenomenon. Diversification arises more in atomism and differentiation in holism, in a part/whole resolution between particulate and aggregate spheres of existence. Examples from Okefenokee Swamp and extreme environments exemplify the two-phase process—deep sea, intertidal zones, carnivorous plants in nitrogen-poor conditions, insects in winter, and creatures of deep caves and, perhaps, subglacial lakes. Diversification (Darwin's generation of variants) and differentiation (via natural selection, and other agencies) of Nature's living forms is a prerequisite for Adaptation (our next installment) and the ultimate expression of (our final chapter) systemic Coherence. Liberation through in-system interaction, bonding, and coupling—all antithetical to degrees of freedom—is the paradoxical result.

This paper analyses the transient dynamics, steady states, and a set of diagnostic system-wide properties of a linear flow-quantified pastoral food web from the Chernivtsi Region of Ukraine. The web in question is one of 31 so-described; it contains 86 nodes and 496 links. On-line simulation and network analysis software EcoNet was used to quantify transient dynamics, steady states, and eleven system-wide index parameters. Food-web flows were classified into inputs, interior flows, and outputs. The last two (endogenous) were represented by linear, mass-balance, flow coefficients. The three sets, inputs plus these coefficients, were systematically manipulated in their entirety in different combinations over seven orders of magnitude to determine their effects on system properties. The results of these trials are described and interpreted. They show that linear descriptions of empirical food webs harbor considerable dynamic and relational complexity.

Ecosystem constraints are both ontic and epistemic. They limit activity, and as problems to be solved they drive organization, which is our hypothesis: The driver of organization is constraint . Solutions proliferate further constraints in an unending spiral of problem (constraint) generation and solution. As constraints proliferate, behavior narrows, and species diversify to compensate (paradox of constraint). Resource enrichment reduces constraints, releases behavior, and reduction of challenges decreases diversity (paradox of enrichment)—high diversity is expressed in low-resource environments and low diversity in high-resource environments. A three-part model of constraints is formulated for non-living systems, and also for goal-directed, problem-solving biota. Mode 1 : dynamical means behavior is co-determined by internal states and external inputs. Mode 2 : cybernetic employs negative feedback to keep dynamics within goal-oriented operating limits. Mode 3 : model-making entails ability to represent (model) physical reality and respond to both phenomenal (modeled) and physical inputs; this property distinguishes living from nonliving systems. Principal sections of the paper elaborate dynamical constraints (three classes), boundary constraints (expressed in edge effects and trophic dynamics), physical constraints (space, time, temperature), chemical constraints (environment fitness, ecological stoichiometry, chemical evolution, limiting factors), coding constraints (environmental vs. genetic coding), network and pathway constraints (connectivity), and natural selection constraints (fitting to the biosphere). Consideration of how the world would look without constraints suggests how fundamental these are in ecosystem emergence, and how the next property in this series, differentiation , would be unmotivated without them. We conclude that constraints as a category are under-studied in ecology, poorly understood in ecological phenomenology, and (our hypothesis) comprise a ubiquitous organizing force in nature.

This study provides a method for assessing a multiplicity of environmental factors in red spruce growth in the Great Smoky Mountains National Park (GSMNP) of Southeastern USA. Direct and indirect factors in the annual growth increment are first organized into a schematic input–output envirogram (ARIRS), and this information is then used to construct a simulation model (ARIM). The envirogram represents a structured conceptualization of most environmental factors involved in growth, as developed from relevant literature. This interdisciplinary synthesis distinguishes direct vs. indirect factors in growth and takes account of the systems ecology concept that indirect factors may be as important as or more important than direct ones in regulating growth. The ARIRS envirogram summarizes hierarchically organized, within- and cross-scale, local-to-global interactions, and its construction makes it obvious that growth is influenced by many cross-scale spatiotemporal interactions. More research on genecology is still needed to clarify the role of phenotypic plasticity and adaptive capacity in nutrient cycling, global change, and human disturbance.

The steady-state assumption is a mainstay for the analysis of ecological systems with more than three or four states. However, it is well accepted in ecology that inputs to large systems come in pulses assumed to have a reasonably constant magnitude and frequency. Steady pulse inputs and the use of electro-chemical–mechanical control systems methodology enables limited short term dynamic responses of ecological systems of a scale often occurring in systems of potential engineering importance to be analyzed. This paper explores and presents a survey of multi-input–multi-output (MIMO) control systems analysis of ecosystem network models to better understand pulse frequency issues and further develop experimentally verifiable approaches to testing the MIMO concept. The analysis process is demonstrated using two network model exemplars. Two aspects of MIMO analyses appear relevant to understanding ecological systems: (1) Eigenvalue invariant analyses and singular value decomposition (SVD) analyses enable assessment of stability and relative strength of states. Eigenvalues reflect time constants and provide a check on experimentally determined system matrices. (2) Analysis of SVD versus frequency for each output indicates maximum pulse frequencies that allow system components to benefit from pulsing. As a group, MIMO analyses complement other analytical methods and provide a theoretical systems focus convenient for analyzing ecosystems from an engineering perspective.

Ecosystems are often modeled as stocks of matter or energy connected by flows. Network environ analysis (NEA) is a set of mathematical methods for using powers of matrices to trace energy and material flows through such models. NEA has revealed several interesting properties of flow–storage networks, including dominance of indirect effects and the tendency for networks to create mutually positive interactions between species. However, the applicability of NEA is greatly limited by the fact that it can only be applied to models at constant steady states. In this paper, we present a new, computationally oriented approach to environ analysis called dynamic environ approximation (DEA). As a test of DEA, we use it to compute compartment throughflow in two implementations of a model of energy flow through an oyster reef ecosystem. We use a newly derived equation to compute model throughflow and compare its output to that of DEA. We find that DEA approximates the exact results given by this equation quite closely – in this particular case, with a mean Euclidean error ranging between 0.0008 and 0.21 – which gives a sense of how closely it reproduces other NEA-related quantities that cannot be exactly computed and discuss how to reduce this error. An application to calculating indirect flows in ecosystems is also discussed and dominance of indirect effects in a nonlinear model is demonstrated.

Ecological network analysis (ENA), predicated on systems theory and Leontiev input–output analysis, is a method widely used in ecology to reveal ecosystem properties. An important ecosystem property computed in ENA is throughflows, the amount of matter/energy leaving each compartment of the ecosystem. Throughflows are analyzed via a matrix N representing their relationships to the driving input at the boundary. Network particle tracking (NPT) builds on ENA to offer a Lagrangian particle method that describes the activity of the ecosystem at the microscopic level. This paper introduces a Lagrangian throughflow analysis methodology using NPT and shows that the NPT throughflow matrix, N, agrees with the conventional ENA throughflow matrix, N, for ecosystems at steady-state with donor-controlled flows. The matrix N is computed solely from the pathways (particles’ histories) generated by NPT simulations and its average over multiple runs of the algorithm with longer simulation time agrees with the Eulerian N matrix (Law of Large Numbers). While the traditional NEA throughflow analysis is mostly used with steady-state ecosystem models, the Lagrangian throughflow analysis that we propose can be used with non-steady-state models and paves the way for the development of dynamic throughflow analysis.

The Reynolds transport theorem (RTT) from mathematics and engineering has a rich history of success in mass transport dynamics and traditional thermodynamics. This paper introduces RTT as a complementary approach to traditional compartmental methods used in ecological modeling and network analysis. A universal system equation for a generic flow quantity is developed into a generic open-system differential expression for conservation of energy. Nonadiabatic systems are defined and incorporated into control volume (CV) and control surface (CS) perspectives of RTT where reductive assumptions in empirical data are then formally introduced, reviewed, and appropriately implemented. Compartment models are abstract, time-dependent systems of simultaneous differential equations describing storage and flow of conservative quantities between interconnected entities (the compartments). As such, they represent a set of flexible and somewhat informal, assumptions, definitions, algebraic manipulations, and graphical depictions subject to influence and selectively parsed expression by the modeler. In comparison, RTT compartment models are more rigorous and formal integro-differential equations and graphics initiated by the RTT universal system equation, forcing an ordered identification of simplifying assumptions, ending with clearly identified depictions of the transfer and transport of conservative substances in physical space and time. They are less abstract in the rigor of their equation development leaving less ambiguity to modeler discretion. They achieve greater consistency with other RTT compartment style models while possibly generating greater conformity with physical reality. Characteristics of the RTT approach are compared with those of a traditional compartment model of energy flow in an intertidal oyster-reef community.

Network particle tracking (NPT), building on the foundation of network environ analysis (NEA), is a new development in the definition of coherence relations within and between connected systems. This paper evaluates three ecosystem models in a comparison of throughflow- and storage-based NEA and NPT. Compartments in models with high indirect effects and Finn cycling showed low correlation of NEA storage and throughflow with particle repeat visits and numbers of particles in compartments at steady state. Conversely, the correlation between NEA and NPT results was high with two models having lower indirect effects and Finn cycling. Analysis of ecological orientors associated with NEA showed NPT to fully support conventional NEA results when the common conditions of donor control and steady state are satisfied. Particle trajectories are recorded in the new concept of a particle “passport”. Ability to track and record particle in-system histories enables views of multiple scales and opens the possibility of making pathway-dependent modeling decisions. NPT may also enable modeling of time, allowing integration of Newtonian, organismal and stochastic modeling perspectives in a single comprehensive analysis.

An environ is a within-system partition of the environment associated with each ecosystem component. The methodologies for calculating throughflow-based and storage-based environs have heretofore been considered quantitatively and qualitatively different. Below, we show, from the fundamental environ equations, that these two approaches are mathematically equivalent by proving the throughflow-storage-equivalence relationship, T E = S E . This implies that ecosystem flows of energy or matter to storage and throughflow are one and the same, differing only in storage delays (flow impedances) along the way in the storage case.

The methods of network environ analysis (NEA) currently apply to steady-state models. Networks of real ecosystems are near steady-state in long-term mean characteristics, but are dynamic in short-term responses. A formal mathematical approach to dynamic NEA analysis has never been fully developed, though Hippe [Hippe, P.W., 1983. Environ analysis of linear compartmental systems: the dynamic, time-invariant case. Ecol. Model. 19, 1–26] offers one approach. Another potential approach to addressing this limitation is to analyze a discrete-time series of steady-state models, each a snapshot for the time period it represents. Using concepts from open-loop control theory, four throughflow-based ecological control terms (control ratio, CR; control difference, CD; system control, scj; and total system control, TC) as developed using an environ framework are evaluated for 16 consecutive seasons of nitrogen cycling in the Neuse River Estuary, North Carolina, USA. Results of this assessment offer a quantitative measure of the quasi-dynamic distributed control in this network. The NOx and Sediment components assume opposing but dominant roles (high scj magnitudes) in all 16 seasons. Low total compartmental throughflow (Ti) to respective boundary inflow (zi) or outflow (yj) ratios are shown to be indicators of component control dominance, suggesting a role for boundary flows in the consideration of a system component's dominance. This conclusion may also be a property of the high cycling nature of this nitrogen model (average Finn cycling index of 89% for all 16 seasons). TC appears to be correlated with total system throughflow (TST), suggesting that TST may indicate a system's distributed control patterns. This correlation may likewise be fruitful if TST proves to be an indicator for system stability, an important and logical consideration in the notion of control.

Network environ analysis is motivated by a desire to investigate ecosystems from a holistic perspective. It provides a quantitative measure of the integral (direct plus indirect) relationship between compartments and their within-system environments. In this analysis, each compartment within a system has an incoming interactive network that brings matter to it from the system's boundary inputs, and an outgoing network that takes matter from it to boundary outputs. These are, respectively, input and output environs. Methods described herein are used to compare environs from a time series of ecological networks for which the flow structure remains constant while flow quantities change. Observed differences in environs are analyzed with respect to: (a) differences between the steady-state seasonal ecosystem networks, and (b) which compartment receives the ‘analytical input’ in output-environ analysis. The Neuse River estuary is an ideal subject for this because a time series of 16 seasonal steady-state networks of nitrogen (N) storage and flow were constructed for the period spring 1985 through winter 1989 by Christian and colleagues. We explore two levels of analysis. The first is macro-level analysis of whole environs; total environ throughflow, an index of whole-environ activity, is computed and compared. The second is micro-level analysis which involves the individual intercompartmental flow and boundary output elements of output environs for two selected focal compartments, phytoplankton (x1-PN-Phyto) and nitrate/nitrite (x5-NOx). Our findings indicate that most of the observed variation in environs is being driven by differences in the seasonal networks analyzed. The macro-scale patterns observed for the environs show the same seasonal patterns evident in the whole steady-state network time series. These results support and extend the constancy of temporal indirect effects results reported by Borrett et al. [Borrett, S.R., Whipple, S.J., Patten, B.C., 2006. Indirect effects and distributed control in ecosystems: temporal variation of indirect effects in a seven-compartment model of nitrogen flow in the Neuse River estuary, USA—time series analysis. Ecol. Model. 194, 178–188]. When comparing different environs within the same season, the macro-scale patterns show that the environs are quantitatively very similar; however, when micro-scale patterns are observed, it is found that the environs are indeed unique. Macro-scale similarities are thought to be driven by high cycling indices and high network homogenization. A conclusion from the comparative analysis of the Neuse estuary networks is that these environs display a weak autonomy. We hypothesize that the individuality of the environs is suppressed by two characteristics of the Neuse estuary networks: they are strongly connected graphs, and they contain many linked autocatalytic cycles. Two aspects of our results provide a means to link ecological measures important to the Neuse River estuary and environ analysis. Environ throughflow ( T E ¯ T ) is driven by boundary inputs, which is equivalent to the ecological measure of N loading, with dominance of total T E ¯ T by DON (x4-DON), nitrate–nitrite (x5-NOx), and ammonium (x6-NH4), which receive the largest boundary inputs. Previous network analysis demonstrated that, on average, one-half of the nitrogen needs of phytoplankton are met by nitrogen that once resided in the sediments. Phytoplankton (x1-PN-Phyto) and sediment (x3-Sed), and ammonium (x6-NH4) had distinctly different T E ¯ T pattern than the steady-state TST pattern. The key ecological driver of the sediment source for N needs of phytoplankton is the release of N from sediments in the warmer months as ammonium which is taken up by phytoplankton; low T E ¯ T during winter for phytoplankton (x1-PN-Phyto), sediment (x3-Sed), and ammonium (x6-NH4) reflects the low levels of ammonium release and low growth rates; high T E ¯ T during summer corresponds to greater release of ammonium (x6-NH4) from the sediments (x3-Sed) and greater uptake of ammonium (x6-NH4) by phytoplankton (x1-PN-Phyto).

Network environ analysis (NEA) was used to analyze a seven-compartment, steady-state model of nitrogen flow in the Neuse River Estuary, North Carolina, USA. Four perspectives for analyzing network properties emerge: (1) throughflow-specific oriented to output environs; (2) throughflow-specific oriented to input environs; (2) storage-specific oriented to output environs; (4) storage-specific oriented to input environs. Analysis of the model is based on a decomposition of total system throughflow, TST, into total environ throughflow, TET, for each of the seven compartments, and a further decomposition of total environ throughflow into compartmental boundary exchanges and environ flows generated by boundary inputs and outputs at individual compartments. The analysis provided a quantitative basis for the development of indirect effects between compartments and is the basis for analyzing the fate of nitrogen entering the system and the origin of nitrogen leaving the system. The decomposition of TST is also the basis for analyzing four network properties: pathway proliferation, ratio of indirect effects to direct effects, homogenization and amplification. Results indicate dominance of indirect effects within the model due to cycling. Moreover, insight about the interrelationship of all model compartments is developed quantitatively based on the NEA methodology.

Indirect effects, the ability of one element in a system to impact another without direct interaction, are critical components of complex adaptive systems. Network environ analysis (NEA) is an environmental extension of economic input–output analysis that characterizes and quantifies indirect effects transmitted by a specific currency (e.g., carbon, nitrogen) within a steady state system. Previous NEA results suggest that indirect effects tend to dominate direct effects in ecosystems. Although steady state models may be useful, ecologists are often interested in system dynamics. In this article, we use NEA to investigate the temporal dynamics of indirect effects in 16 steady state models of nitrogen cycling in the Neuse River Estuary, USA. These models were originally constructed by Christian and Thomas [Christian, R.R., Thomas, C.R., 2003. Network analysis of nitrogen inputs and cycling in the Neuse River Estuary, North Carolina, USA. Estuaries 26, 815–828]. Our work had two primary objectives: (1) describe and quantify the temporal dynamics of indirect flows and (2) identify the importance of model factors in determining the magnitude of indirect flows. Our results indicate that indirect flows transmitted by the network of nitrogen transactions, especially microbial transformations, dominated direct flows in the Neuse River Estuary between spring 1985 and winter 1989. When we examined the indirect flow index (ratio of indirect to total system throughflow), we were surprised by the relatively small amount of temporal variation within the Neuse River Estuary. In all seasons, indirect flow was more than 80% of TST, and there was no significant interannual variation. Our analysis also revealed no clear relationship between boundary or direct flow and indirect flow, but a strong association between cycled and indirect flow. We conclude that while an increase in boundary, direct, and cycled flows can influence indirect flows, in the Neuse River Estuary models indirect flows are predominantly due to cycling. If nitrogen loading had been reduced during our study period, this system likely would have remained eutrophic for an extended period of time. If we assume the system remained similar in 1997, we would expect the legislated reduction of nitrogen loading to have little immediate effect, although this action will be important for long-term change. Dominance of indirect flow due to cycling makes this system state relatively difficult to change rapidly by external forcing. In this sense, the indirect effects stabilize the system, making it more resistant to external perturbations, though it may be more sensitive in the long-term.

Comparative network environ analysis (NEA) is used to holistically explore controlling relationships in ecosystems. The term, distributed control, for the present series of papers, is adopted to describe a diffuse and decentralized concept of control residing in the complexity of organization. Starting with “open-loop” control theory parlance, three ecological control terms (control ratio, control difference, and system control) are derived in an environ framework by considering pair-wise and system-wide distributed control relationships. These control relationships are then explored using the seven compartment steady-state model of average nitrogen flow in the Neuse River Estuary, North Carolina, USA (Christian, R.R., Thomas, C.R., 2003. Network analysis of nitrogen inputs and cycling in the Neuse River Estuary, N.C., USA. Estuaries 26 (3), 815–828). Sediment and nitrates–nitrites (NOx) are shown to participate in opposing roles. If magnitude denotes dominance and therefore control, the control metrics reveal that sediment is overwhelmingly controlled by all components where NOx exhibits control over all components. However, if a limiting factor perspective is used (e.g., sediment sequestering N with a controlled release to NOx), the conclusions are opposite; sediment controls all other components and all other components control NOx. As such, the overall direction of the control relationship is the subject of further review. Thus far, the results are preliminary and this remains a throughflow based steady-state analysis with additional discrete time analyses planned.

Queensland fruit fly, Bactrocera (Dacus) tryoni (QFF) is arguably the most costly horticultural insect pest in Australia. Despite this, no model is available to describe its population dynamics and aid in its management. This paper describes a cohort-based model of the population dynamics of the Queensland fruit fly. The model is primarily driven by weather variables, and so can be used at any location where appropriate meteorological data are available. In the model, the life cycle is divided into a number of discreet stages to allow physiological processes to be defined as accurately as possible. Eggs develop and hatch into larvae, which develop into pupae, which emerge as either teneral females or males. Both females and males can enter reproductive and over-wintering life stages, and there is a trapped male life stage to allow model predictions to be compared with trap catch data. All development rates are temperature-dependent. Daily mortality rates are temperature-dependent, but may also be influenced by moisture, density of larvae in fruit, fruit suitability, and age. Eggs, larvae and pupae all have constant establishment mortalities, causing a defined proportion of individuals to die upon entering that life stage. Transfer from one immature stage to the next is based on physiological age. In the adult life stages, transfer between stages may require additional and/or alternative functions. Maximum fecundity is 1400 eggs per female per day, and maximum daily oviposition rate is 80 eggs/female per day. The actual number of eggs laid by a female on any given day is restricted by temperature, density of larva in fruit, suitability of fruit for oviposition, and female activity. Activity of reproductive females and males, which affects reproduction and trapping, decreases with rainfall. Trapping of reproductive males is determined by activity, temperature and the proportion of males in the active population. Limitations of the model are discussed. Despite these, the model provides a useful agreement with trap catch data, and allows key areas for future research to be identified. These critical gaps in the current state of knowledge exist despite over 50 years of research on this key pest. By explicitly attempting to model the population dynamics of this pest we have clearly identified the research areas that must be addressed before progress can be made in developing the model into an operational tool for the management of Queensland fruit fly. (C) 2003 Published by Elsevier B.V.

Ecosystem-based management of resource populations is not a reality but a vision for the future. We liken it to instrument flight of an aircraft. An aircraft cannot be controlled without visual reference to the ground (VFR—Visual Flight Rules) or a cluster of flight instruments (IFR—Instrument Flight Rules). Instrument pilots are trained to develop a rhythmic scan of the cluster to obtain information about flight path and attitude. The untrained tendency is to fixate on a single gauge. When this occurs, the aircraft deviates from its desired attitude and trajectory, and control may be lost. This is analogous to single-factor management in which variables, like habitat quality, recruitment, predator control, or harvest rates, are singled out for manipulation without regard to the others. Exploited populations are no less complex than an aircraft in flight. They move through time and space, and can only be effectively managed using the multiplicity of instruments nature has provided. These include distal as well as proximate variables because populations are embedded in ecosystems that holistically propagate indirect effects to them. Therefore, whole-ecosystem-based management is needed, giving attention to multiple control variables as in the case of instrument flight. Only modeling can identify a suite of sufficient controls, both direct and indirect, and place them in a coherent, operational framework. “Flying the resource”, then, is what we conceive as modeling-assisted, ecosystem-based management. We advocate that management institutions should employ ecosystem-based modeling as an ongoing organizational activity in which scientists, managers, and others cooperate in framing conceptual models from which further steps in modeling can proceed. We call this Institutionalized Model-Making (IMM), with two purposes: (1) building teams from indigenous expertise, and (2) producing models to serve in the same relation to nature as flight simulators do to actual aircraft. The models mimic responses to control actions, simulating multifactorial management analogous to the instrument scans and control manipulations of instrument flying. We illustrate our ideas with a STELLA simulation model of the North American white-tailed deer (Odocoileus virginianus Miller) in the Adirondack Mountains of New York State, USA. Sensitivities of control parameters are ranked, and use of the model in the instrument flight sense is demonstrated. The results reflect on current styles and fashions in ecological modeling.

In ecosystems network, structure determines adjacent (direct) and non-adjacent (indirect) pathways over which energy, matter, and information can flow. The more pathways, the more possible ways the conservative substance can move in zero-sum transactions between network nodes that the pathways interconnect, and the more possible non-conservative, nonzero-sum relations can be secondarily derived from these. Structural analysis is a tool we employ, from a family of input–output methods for exploring zero- and nonzero-sum attributes of environmental networks, to count pathways of varying length between network nodes. In this paper, we examine the relationship between pathway length (k) and number (Pk) as determined by system size (n, number of nodes) and extent and pattern of connectance (C). We develop a measure (ma) of pathway growth in numbers with increasing length, and then normalize this to the maximum rate possible (ma/mc) for a given system size. These measures apply to two pathway types—paths, ma(0) and ma(0)/mc(0), which forbid adjacent node repetitions, and walks, ma(1) and ma(1)/mc(1), which allow them. We find that network size has a curvilinear effect on the pathway number versus length relationship, and extent and pattern of connectance are convolved. Values computed for the paths and walks of three ecosystem models (oyster reef, freshwater marsh, and reservoir cove) are used to compare their pathway structure.

This fifth paper in the series on Ecosystems Emerging treats the properties of ecosystem growth and development from the perspective of open (paper four), nonequilibrium, thermodynamic systems. The treatment is nonrigorous and intuitive, interpreting results for living ecosystems based on parallels between these and the much simpler nonliving ones treated rigorously in thermodynamic theory. If an (open, nonequilibrium) ecosystem receives a boundary flow of energy from its environment, it will use what it can of this energy, the free energy or exergy content, to do work. The work will generate internal flows, leading to storage and cycling of matter, energy, and information, which move the system further from equilibrium. This is reflected in decreased internal entropy and increased internal organization. Energy degraded in the performance of work is exhausted as boundary outputs to the system's environment. This is reflected in decreased organization and increased entropy of the surroundings, the dissipative property (paper three). All properties rest on the conservation principle (paper two). Growth is movement away from equilibrium, which occurs in three forms: (I) when there is a simple positive balance of boundary inputs over outputs, which increments storage; (II) when, with boundary inputs fixed, the ratio of internal to boundary flows increases, which reflects increase in the sum of internal flows, which contribute to throughflow; and (III) when, somewhat coincident with but mostly following upon I and II, system internal organization, reflecting its energy-use machinery, evolves the utilization of information to increase the usefulness for work of the boundary energy supply. These three forms of growth are, respectively, growth-to-storage, growth-to-throughflow, and growth-to-organization. Forms I and II are quantitative and objective, concerned with brute energy and matter of different kinds. Form III has qualitative and subjective attributes inherent in information-based mechanisms that increase the exergy/energy ratio in available energy supplies. The open question of this paper is, which of many possible pathways will an ecosystem take in realizing its three forms of growth? The answer given is that an ecosystem will change in directions that most consistently create additional capacity and opportunity to utilize and dissipate available energy and so achieve increasing deviation from thermodynamic ground. The machinery for this synthesized from the three identified growth processes is reflected in a single measure, exergy storage. Abundant and diverse living biomass represents abundant and diverse departure from thermodynamic equilibrium, and both are captured in this parameter. It is the working hypothesis of this paper that ecosystems continually maximize their storage of free energy at all stages in their integrated existence. If multiple growth pathways are offered from a given starting state, those producing greatest exergy storage will tend to be selected, for these in turn require greatest energy dissipation to establish and maintain, consistent with the second law. Energy storage by itself is not sufficient, but it is the increase in specific exergy, that is, of exergy/energy ratios, that reflects improved usability, and this represents the increasing capacity to do the work required for living systems to continuously evolve new adaptive ‘technologies’ to meet their changing environments. Exergy cannot be found for entire ecosystems as these are too complex to yield knowledge of all contributing elements. But it is possible to compute an exergy index for models of ecosystems that can serve as relative indicators. How to compute this index is shown, together with its use in developing models with time-varying parameters. It is also shown how maximization of exergy storage distinguishes between local and global optimization criteria. In ecological succession, energy storage in early stages is dominated by Form I growth which builds structure; the dominant mechanisms are increasing energy capture (boundary inputs) and low entropy production (dissipative boundary outputs). In middle stages, growing interconnection of proliferating storage units (organisms) increases energy throughflow (Form II growth). This increases endogenous inputs and outputs and, in consequence, throughflow/boundary flow ratios, entropy production, and on balance, biomass. In mature phases, cycling becomes a dominant feature of the internal network, increasing storage and throughflow both. Biomass and entropy production are maximal, but specific dissipation (as dissipation/storage ratio) decreases, reflecting advanced organization (Form III growth) typified by cycling. Specific exergy (exergy/energy ratio) increases throughout succession to maturity, in early stages mainly due to mass accrual, and in the later stages to gains in information and organization. During senescence, storage, entropy production, specific dissipation, and specific exergy all decrease, reflecting a declining ecosystem returning toward equilibrium.

This paper formally introduces the rheomode orientation to network flow analysis and provides a quantitative test for the ecological property of network homogenization. Using network flow analysis, it is possible to identify and quantify the direct, indirect, and integral contributions of flow between any two components in a reticulated system. Inspection of the integral (direct plus indirect) flow matrix reveals many interesting properties not obvious from an empirical investigation of proximate transactions. Using network flow analysis, we observe that the composition of direct flows is comprised of a fairly uniform mixture of resources from all the system components. We call this evening out of flow network homogenization (Patten, B.C., Higashi, M., Burns, T.P., 1990. Ecol. Model. 51, 1–28). Here we introduce a standard statistical technique to provide a quantitative test for network homogenization. This property is the direct result of a flow oriented analysis of ecological systems. This has broader implications for the standard trophic dynamics paradigm currently dominating ecological research. The central results from this approach indicate that networks are holistic entities which must be analyzed as such.

This third paper in the series on Ecosystems Emerging deals with properties resulting from the second law of thermodynamics. Dissipation of energy and matter, which is degradation from more to less organized states, causes cycling of matter and origination of networks. The second law is presented in two forms: the classical one and by means of exergy which measures useful energy. Energy and matter dissipation condition the formation of structures, growth, development and evolution. In contrast to the ecological cliche that energy does not cycle in ecosystems, it becomes evident that energy must cycle like matter because the two are coupled. Matter cycling is necessary for the continued existence of ecosystems on earth because the closed planet has only a finite supply of material resources. Biological dissipation takes a variety of forms: respiration, excretion, egestion, natural and predatory mortality and others. Relations of dissipation by organisms to size and temperature are causes of similar relations for a number of life processes and also for certain ecological characteristics of organisms. This underlies the theory of ecosystem size and structure. Recognition of matter dissipation leads to substantial changes in ecological paradigms. For example, dissipation of nutrients can have positive effects on ecosystem production. Grazing mortality can speed primary production. Therefore, ecological studies must focus more on fluxes than standing biomasses. Detrital and microbial food paths play a significant role in ecosystems. The classical ideas of trophic pyramids and ecological efficiencies are changed completely by studies of dissipation. Dissipation of information relates to decreasing biodiversity and the present crisis of environment can be explained as a dissipation-driven entropy crisis.

Many momentarily important concepts in science pass after a time with little enduring consequence. Sustainability has the potential to become a really significant idea, but it could also disappear if it never becomes formally implemented to make it operational. To do this requires clarifying its various meanings, then integrating these into a measure or model, preferably quantitative. This paper makes a start at this employing propositional logic—first to establish that the success of any species requires proportional disadvantage to others in a zero-sum world (the AWFUL theorem), and then to explore three possible properties of sustainability (stability, continuation, and longevity) at two different levels of system organization (whole and part). The following conclusions are reached and discussed: at a given scale of organization, for sustainability (1) stability is a necessary but not sufficient condition, (2) continuation is sufficient but not necessary, and (3) longevity is also sufficient but not necessary. Across scales, between wholes and parts: (1a) part stability is sufficient for whole system sustainability, and part instability can be compensated by system design to achieve sustainability; (1b) system instability is sufficient for part unsustainability; (2a) part continuation is sufficient for system continuation, and therefore system sustainability; (2b) part noncontinuation is necessary for system unsustainability; (3a) part longevity is sufficient for system longevity, and therefore system sustainability; and (3b) failure of parts to achieve longevity is a necessary condition for system-level unsustainability. These attributes of sustainability in the part–whole context do not exhaust the possibilities. There are also comparisons to be made of relations between different sustainability attributes. The examples given indicate that sustainability is not a simple concept and that considerable development will be necessary to mold it into a permanently useful scientific tool.

Traditional evolutionary theory depicts survival of the fittest as a difficult existence based on danger, conflict and strife. But, another view is emerging of a more synergistic organization in which ecosystems on the whole provide hospitable conditions for life. This world is populated by organisms mutually adapted and beneficial by virtue of their direct and indirect interactions. Many examples of mutualism have been explicitly observed (Bronstein, J.L., 1991. Bull. Ecol. Soc. Am. 72, 6–8; Cushman, J.H., Beattie, A.J., 1991. Trends Ecol. Evol. 6, 193–195; Casti, J.L., Karlqvist, A. (Eds.), 1995. Cooperation and Conflict in General Evolutionary Processes, Wiley, New York, 435 pp.), and we view mutualism as an implicit consequence of indirect interactions and ecosystem organization. This paper extends a methodology based on input-output analysis that models these synergistic relationships (Patten, B.C., 1991. Theoretical Studies of Ecosystems: The Network Perspective, pp. 288–351; Patten, B.C., 1992. Ecol. Modell. 62, 29–69). We show for simple storage-flow models that direct zero-sum resource transactions between organisms, when considered in context of the whole-system organization, produce integral (direct plus indirect) relationships more positive than the direct ones. This phenomenon, `network synergism', is demonstrated for two simple networks and a complete three component model. We also show, by looking at a limiting case, that system-wide synergism is ubiquitous, occurring in all models of any size or complexity. Network synergism emerges in these models because of three network properties: symmetry, indirectness and openness.

Black bears on the 6000-ha Huntington Wildlife Forest, in the central Adirondack region of upper New York State, were modeled using the stella II simulation software. The purposes were to (1) express black-bear biology as a population system inseparably derived from its ecosystem; (2) demonstrate how chaos, with origins in nonlinearity, and sustainability, related to linearity, can be incorporated into dynamical models, minimizing the use of mathematics that may not be well-chosen due to an inadequate rationale; and (3) demonstrate how qualitative biology, natural history, and ecology can be realistically built into a model despite many unknowns and initially limited data. A rationale is presented for synthesizing chaos and sustainability in ecological models. From this and the good behavioral properties observed in simulated baseline and sensitivity dynamics, it is concluded that a useful approach in ecological modelling may be to put nonlinear attributes into the parameter space and linear ones into the state space to conform the two opposed properties of well-behavedness and surprise. The role of linearity in modelling, and in formulating humanity's future ecological paradigm of existence, should not be overlooked.

This second paper in the series on Ecosystems Emerging treats some properties of ecosystems derivable from the single elementary principle of conservation. These go beyond the mere balancing out of the matter and forces of nature. A brief sketch of a conservationless world is given, followed by an elementary background review of energy, matter and information. The main conservative quantities are matter, energy, momentum and electric charge. The difference between sun and earth surface temperatures is the source of useful energy (exergy) and information to motivate matter. The earth acts as a photon multiplier in this process, and generates entropy radiated to the universe at large. Neither exergy, information, nor photons are conservative quantities. Four phases of matter are recognized: solid, liquid, gaseous and living. These contribute to five realms of the earth's ecosphere: lithosphere, atmosphere, hydrophere, biosphere and noosphere. An additional category, the semiosphere, represents informational aspects of the materialistic ecosphere. Information is related to Aristotle's four causes: formal, material, efficient and final. Information has a material basis; its physical carriers are conservative markers, or avatars. Information is always produced by bonding of masses to form higher-level systems; the energy to achieve bonding is released in degraded form (heat) and carried away by low-energy photons in entropy production. All systems owe their cohesion to bonding (interaction). System bonding may be by conservative substance exchange (transactions) or nonconservative information exchange (relations). In both cases, identity constraints of coupling mediate the bonds. A universal metamodel for system change is described under state-space determinism. Exogenous conditions (inputs), and endogenous conditions (states) are lawfully mapped into behavioral dynamics (outputs). There are two fundamentally different kinds of state-space systems: objects (nonliving, which respond reactively to physical inputs); and subjects (living, which can respond proactively based on phenomenal inputs, which are models of physical inputs). The ability to make models is conjectured as a new definition of life. In living processes, elements of the materialistic ecosphere and informational semiosphere are combined to produce the phenomenal noosphere. All three categories are mutually implicative. Arguments are made to consider space as locally conserved and time as conserved. The nature of transactional (materialistic) and relational (informational) bonding in the origin of systems, under state-space determinism, is described. The conservation principle underlies this because transactions are always the prior basis of relations. Environments arise under the same considerations as origin of systems; conservation is at the root. Input environment, output environment and indirect environment are described as elements of a general concept of environment. Indirect environments are bounded by the speed of light, and (closer in) by the boundaries of defined systems. The within-system portions of component-level environments are environs. Energy balance and photon multiplication in the ecosphere are described as a series of electromagnetic cascades. Charge-discharge cycles of energy and matter are mechanisms for progressively degrading solar photons to heat in coupled solar → trophic → biochemical interactions at different scales of hierarchical organization. The conservation principle underlies all these processes. A review of the broad phenomena, concepts and principles of ecology reveals that many of these have strong dependence on conservation of mass, energy, momentum and electric charge, as well as local space and time. Just as conservation laws are basic in the organization of reality, they are also rightly reflected in much of the subject matter of ecology.

This paper explains the rationale behind measuring first passage flows of conservative substances in ecological networks by a simple modification of input-output flow analysis (Higashi et al., 1993a, Ecol. Model., 66: 1–42). Pilette and Kincaid (1992, Ecol. Model., 64: 1–10) posed this “first flow-through” problem and described a different method to solve it. This method, however, does not account for their intended “all non-duplicated routes and transfers” from one compartment to another, and consequently underestimates indirect transfers. In addition, it incorrectly treats storages as equivalent to flows. We correct their version, according to the discrete time input-output flow-storage analysis of Higashi et al. (1993b, Ecol. Model., 66: 43–64), and derive a correct evaluation of direct transfers. This, however, turns out to be equivalent to simple flow ratios obtained from standard, continuous time input-output flow analysis.

Self organization in ecosystems has been postulated to be directed by a number of seemingly unrelated goal functions or extremal principles. These include exergy , the useful work content of energy, which measures distance from thermodynamic ground; emergy , which increases in proportion to the number of steps energy has taken away from its point of input to a system; power , which is work per unit time, and can be measured as the total energy flow in an ecosystem; ascendency , which combines a mutual information measure of the distribution of flows in a system network with the total flow; and indirect effects , which concern relationships at a distance in energy networks. S.E. Jorgensen recently obtained high correlations between exergy, emergy, ascendency, and the ratio of indirect to direct effects, in a set of ecosystem models. These results suggest that these optimality criteria may be formally related. This paper shows, for systems at macroscopic steady states, that they are. Exergy, emergy, power, ascendency, and indirect effects all have common origins in the path structure and associated microscopic dynamics of energy and matter flows and storages in ecosystem networks. Thus, these organizational measures, originally derived from different perspectives on ecosystems, are in fact related through a common basis.

Sustainability of the biosphere requires conscious and responsible management of available resources on a global scale. Up to now it has not been possible to deal with the full complexity of interaction between human society and nature. The complexity of tasks required to assure the base of human existence calls for means to overcome disciplinary fragmentation of knowledge. This paper discusses how modelling activities can contribute to interdisciplinary planning on a regional scale as parts of a global interaction network. Conceptual modelling workshops are advocated as the basis for a new type of institution elaborating management scenarios and political decision alternatives on the level of geographic landscape units. Interdisciplinary modelling, in its conceptualization phases, is seen as the basis for organizing such institutions to provide an interface between science and government, and achieve a more integrative science of holism to meet the needs of the next decades.

The concept of progressive efficiency is generalized from food chains to food networks of arbitrary structure. Two distinct modes and corresponding pathways of contribution to energy-matter utilization are identified and formulated using continuous time models of energy-matter flows in ecosystems. First passage or root utilization involves first time transfer and transformation (of assimilated substance only) along all direct and indirect food paths originating at a defined source compartment and terminating at a defined destination compartment. First passage paths include acyclic paths plus cyclic paths that do not pass through the destination compartments. Recycling or reutilization involves the subsequent retransformation of previously utilized but not dissipated energy-matter by consumers. Recycling pathways start and end at the defined destination compartment. Total or ultimate utilization by destination compartments is the sum of first passage and recycling utilization. Two properties of ecosystems are demonstrated which depart from those of conventional trophic dynamics. Network virtual amplification is the increase of energy-matter ultimately utilized at destination compartments compared to the quantities originally introduced at source compartments. This is due largely to recycling; no energy is created, no thermodynamic law violated. Network homogenization is the tendency in food cycles for introduced energy-matter to become more or less evenly distributed to all compartments. These properties are illustrated with two models of ecosystem energy-matter flows.

Energy moves with varying temporality in ecosystems, and as a result becomes unevenly aged. This paper examines the time dependency of energy-matter flux in ecosystems modeled as flow-storage networks. The temporality of passage is governed by storage, which can be viewed as transport delay, a process contributing to the availability of energy to ecosystem compartments over time. Availability is a prior condition for utilization, which nevertheless is measurable from flow considerations alone. Combined flow-storage analyses are required to determine the temporality of substance availability; flow-only analyses are sufficient to specify utilization. The relations between the two are developed. What we term “tempo” involves the transport and delay as standing stocks of variously aged substance over the direct and indirect pathways of ecosystem networks. Our concept of “mode” refers to utilization alone, without regard for timing or the age distribution of flowing substance. Temporal analysis highlights the importance of turnover time, and thus body size and mass of individual organisms, in the dynamics of energy dependencies in ecosystems.

Environs are a model of J. von Uexkull's theory of environment. They have affinities with embodied energy (emergy), transformity and energy value in H.T. Odum's energy-circuit theory. Energy circuits and output environs are both networks defined by a single input; environ theory also has reciprocal input environs which extend back from outputs. Feedback cycling exerts control functions in Odum's model. In environs, control is distributed nonspecifically over highly reticulated cyclical pathways. These networks can be unfolded into straight chains with an indefinite number of steps. Distance from sources motivates Odum's measure of energy quality as embodied energy, or emergy, measured by transformity. Any unfolded network may have such measures computed for individual output (or input) environs. Each transfer level contains contributions from many compartments, and each compartment occupies many transfer levels. The subnetworks of output (or input) environs become commingled to form the whole-system network, which environ analysis unravels mathematically, preserving the reticulated (vs. straight-chain) conception. Transformities measure network value, in individual environs or entire systems. A different approach to energy value is provided by utility measures; both direct (local) and direct plus indirect (global) values may be computed. Comparison of local vs. global utilities has both quantitative and qualitative aspects. The latter define ecological interaction types (competition, predation, etc.) from internodal flows. Network organization tends to synthesize global positive relationships from local negative ones. Environ-value theory differs from embodied-energy theory, but is not in conflict with it. Together, they provide complementary perspectives on quantifying subjective values from objective flow processes.

This is the first paper in a projected series which will attempt to identify a set of elementary principles that can be considered to provide a sufficient basis for a comprehensive theory of complex ecosystems. These principles emerged from studies of ecosystems by means of mathematical models. Our approach will be holistic, as opposed to the still dominant reductionism that prevails both in ecosystem studies and ecological modelling. We hold that a full reductionistic recognition of major ecosystem components not only exceeds what is possible to do, but also that it is inadequate because an ecosystem is more than the sum of its parts. The principles delineated in this paper for further subsequent elaboration arise from strict applications of elementary laws of physics, chemistry, biology and ecology, extended to higher level rules derived from nonlinear, far-from-equilibrium thermodynamics, cybernetics and network analysis.