John R. Schramski

Network environ theory, simulation, and EcoNet® 2.0

We introduce and codify the mathematics of Ecological Network Analysis (ENA) in general and Network Environ Analysis (NEA) in particular used by the web-based simulation software EcoNet? 2.0. Where ecosystem complexity continues to drive an increasingly vast environmental modeling effort, ENA and NEA represent maturation, in part, of the compartment modeling approach. Compartment modeling mathematically represents compartment storages with both internal-connecting and external-environmental flows as ordinary differential equations. ENA and NEA expand these mathematics into complex systems analysis and corresponding network theory. EcoNet was developed to facilitate the mathematical modeling, to enhance the overall presentation, and to improve the subsequent long-term progress of ENA and NEA systems analysis. Thus, as a continuing enhancement to the overall understanding, but more importantly, to the future growth of environmental modeling associated with ENA and NEA, we derive and summarize the canonical mathematics of ENA, NEA, and EcoNet, which facilitates their future use.

Human domination of the biosphere: Rapid discharge of the earth-space battery foretells the future of humankind

Earth is a chemical battery where, over evolutionary time with a trickle-charge of photosynthesis using solar energy, billions of tons of living biomass were stored in forests and other ecosystems and in vast reserves of fossil fuels. In just the last few hundred years, humans extracted exploitable energy from these living and fossilized biomass fuels to build the modern industrial-technological-informational economy, to grow our population to more than 7 billion, and to transform the biogeochemical cycles and biodiversity of the earth. This rapid discharge of the earth’s store of organic energy fuels the human domination of the biosphere, including conversion of natural habitats to agricultural fields and the resulting loss of native species, emission of carbon dioxide and the resulting climate and sea level change, and use of supplemental nuclear, hydro, wind, and solar energy sources. The laws of thermodynamics governing the trickle-charge and rapid discharge of the earth’s battery are universal and absolute; the earth is only temporarily poised a quantifiable distance from the thermodynamic equilibrium of outer space. Although this distance from equilibrium is comprised of all energy types, most critical for humans is the store of living biomass. With the rapid depletion of this chemical energy, the earth is shifting back toward the inhospitable equilibrium of outer space with fundamental ramifications for the biosphere and humanity. Because there is no substitute or replacement energy for living biomass, the remaining distance from equilibrium that will be required to support human life is unknown.

Metabolic theory predicts whole-ecosystem properties

Significance A theory is presented which shows how the metabolism of individual organisms controls the flow of carbon through ecosystems. The theory synthesizes top-down, ecosystem-level and bottom-up, organism-level approaches to ecological energetics and material cycles. The theory predicts a very simple straight-line relationship between residence time of carbon molecules and the ratio of whole-ecosystem biomass to primary productivity. This and additional predictions for total throughfow and recycling are supported by numerical models and data from real ecosystems. The theory provides a powerful way to understand the roles of organisms in ecosystem processes at scales from local habitats to the biosphere. Such an understanding is important for addressing the impacts of human-caused changes in climate, land use, and biodiversity. Understanding the effects of individual organisms on material cycles and energy fluxes within ecosystems is central to predicting the impacts of human-caused changes on climate, land use, and biodiversity. Here we present a theory that integrates metabolic (organism-based bottom-up) and systems (ecosystem-based top-down) approaches to characterize how the metabolism of individuals affects the flows and stores of materials and energy in ecosystems. The theory predicts how the average residence time of carbon molecules, total system throughflow (TST), and amount of recycling vary with the body size and temperature of the organisms and with trophic organization. We evaluate the theory by comparing theoretical predictions with outputs of numerical models designed to simulate diverse ecosystem types and with empirical data for real ecosystems. Although residence times within different ecosystems vary by orders of magnitude—from weeks in warm pelagic oceans with minute phytoplankton producers to centuries in cold forests with large tree producers—as predicted, all ecosystems fall along a single line: residence time increases linearly with slope = 1.0 with the ratio of whole-ecosystem biomass to primary productivity (B/P). TST was affected predominantly by primary productivity and recycling by the transfer of energy from microbial decomposers to animal consumers. The theory provides a robust basis for estimating the flux and storage of energy, carbon, and other materials in terrestrial, marine, and freshwater ecosystems and for quantifying the roles of different kinds of organisms and environments at scales from local ecosystems to the biosphere.

Assessing upstream fish passage connectivity with network analysis

Hydrologic connectivity is critical to the structure, function, and dynamic process of river ecosystems. Dams, road crossings, and water diversions impact connectivity by altering flow regimes, behavioral cues, local geomorphology, and nutrient cycling. This longitudinal fragmentation of river ecosystems also increases genetic and reproductive isolation of aquatic biota such as migratory fishes. The cumulative effects on fish passage of many structures along a river are often substantial, even when individual barriers have negligible impact. Habitat connectivity can be improved through dam removal or other means of fish passage improvement (e.g., ladders, bypasses, culvert improvement). Environmental managers require techniques for comparing alternative fish passage restoration actions at alternative or multiple locations. Herein, we examined a graph-theoretic algorithm for assessing upstream habitat connectivity to investigate both basic and applied fish passage connectivity problems. First, we used hypothetical watershed configurations to assess general alterations to upstream fish passage connectivity with changes in watershed network topology (e.g., linear vs. highly dendritic) and the quantity, location, and passability of each barrier. Our hypothetical network modeling indicates that locations of dams with limited passage efficiency near the watershed outlet create a strong fragmentation signal but are not individually sufficient to disconnect the system. Furthermore, there exists a threshold in the number of dams beyond which connectivity declines precipitously, regardless of watershed topology and dam configuration. Watersheds with highly branched configurations are shown to be less susceptible to disconnection as measured by this metric. Second, we applied the model to prioritize barrier improvement in the mainstem of the Truckee River, Nevada, USA. The Truckee River application demonstrates the ability of the algorithm to address conditions common in fish passage projects including incomplete data, parameter uncertainty, and rapid application. This study demonstrates the utility of a graph-theoretic approach for assessing fish passage connectivity in dendritic river networks assuming full basin utilization for a given species, guild, or community of concern.

Engineering Education as a Complex System.

This paper presents a theoretical basis for cultivating engineering education as a complex system that will prepare students to think critically and make decisions with regard to poorly understood, ill-structured issues. Integral to this theoretical basis is a solution space construct developed and presented as a benchmark for evaluating problem-solving orientations that emerge within students’ thinking as they progress through an engineering curriculum. It is proposed that the traditional engineering education model, while analytically rigorous, is characterised by properties that, although necessary, are insufficient for preparing students to address complex issues of the twenty-first century. A Synthesis and Design Studio model for engineering education is proposed, which maintains the necessary rigor of analysis within a uniquely complex yet sufficiently structured learning environment.

Dynamic modeling of potentially conflicting energy reduction strategies for residential structures in semi-arid climates.

Globally, residential energy consumption continues to rise due to a variety of trends such as increasing access to modern appliances, overall population growth, and the overall increase of electricity distribution. Currently, residential energy consumption accounts for approximately one-fifth of total U.S. energy consumption. This research analyzes the effectiveness of a range of energy-saving measures for residential houses in semi-arid climates. These energy-saving measures include: structural insulated panels (SIP) for exterior wall construction, daylight control, increased window area, efficient window glass suitable for the local weather, and several combinations of these. Our model determined that energy consumption is reduced by up to 6.1% when multiple energy savings technologies are combined. In addition, pre-construction technologies (structural insulated panels (SIPs), daylight control, and increased window area) provide roughly 4 times the energy savings when compared to post-construction technologies (window blinds and efficient window glass). The model also illuminated the importance variations in local climate and building configuration; highlighting the site-specific nature of this type of energy consumption quantification for policy and building code considerations.

Flow Decomposition in Complex Systems

Complex systems can be represented as weighted digraphs. Cycles play an important role in complex systems because they define relationships consisting of unique groupings of nodes. A grouping of connected nodes contains rich contextual meaning because of the relationships defined by its connecting edges. Cycle bases are a description of the set of all independent cycles within a graph. The work herein outlines a computational methodology to decompose the total through flow of a complex system into a set of coefficients over its cycle bases. A coefficient is computed for each cycle representing the cyclescontribution to the total system through flow. This vector of coefficients provides information for data mining and information clustering applications to analyze the system. The proposed methodology provides a powerful framework for analyzing symbolic data by assigning magnitude values to the contextual meaning within groupings of symbols.

A unifying theory for top-heavy ecosystem structure in the ocean

Size generally dictates metabolic requirements, trophic level, and consequently, ecosystem structure, where inefficient energy transfer leads to bottom-heavy ecosystem structure and biomass decreases as individual size (or trophic level) increases. However, many animals deviate from simple size-based predictions by either adopting generalist predatory behavior, or feeding lower in the trophic web than predicted from their size. Here we show that generalist predatory behavior and lower trophic feeding at large body size increase overall biomass and shift ecosystems from a bottom-heavy pyramid to a top-heavy hourglass shape, with the most biomass accounted for by the largest animals. These effects could be especially dramatic in the ocean, where primary producers are the smallest components of the ecosystem. This approach makes it possible to explore and predict, in the past and in the future, the structure of ocean ecosystems without biomass extraction and other impacts.Evidence of inverted trophic pyramids in marine food webs has been enigmatic owing to lack of theoretical support. Here, Woodson et al. use metabolic and size-spectra theory to show that inverted pyramids are possible when food webs have generalist predators and consumers with large body sizes.

System decomposition for temporal concept analysis

Temporal concept analysis is an extension of formal concept analysis (FCA) that introduces a time component to concept lattices allowing concepts to evolve. This time component establishes temporal orderings between concepts represented by directional edges connecting nodes within a temporal lattice. This type of relationship enforces a temporal link between concepts containing certain attributes. The evolution of concepts can provide insight into the underlying complex system causing change, and the concepts evolving can be seen as data emission from that complex system. This research utilizes models of complex systems to provide frequency histograms of activity in well-defined sub-networks within a system. Analyzing systems in this way can provide higher levels of contextual meaning than traditional system analysis calculations such as nodal connectedness and throughflow, providing unique insight into concept evolution within systems.