Control system approaches to ecological systems analysis: Invariants and frequency response

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.     

The Reynolds transport theorem: Application to ecological compartment modeling and case study of ecosystem energetics

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.     

Implications of network particle tracking (NPT) for ecological model interpretation

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.     

Cycling in ecosystems: An individual based approach

Cycling index is an important ecological indicator used in ecosystem analysis. The higher the cycling in an ecosystem, the higher the utilization of mass and energy within the system before it is lost due to respiration and other factors. For a stock-flow type ecosystem model at steady state, Finn’s cycling index (FCI) can be computed using simple matrix algebra. However, it is difficult to measure how well this index represents the actual cycling occurring in the system. In this paper, we study cycling in ecological networks using an individual based approach (particle tracking algorithm). This new simulation method provides access to the pathway data of individual particles that flow in the system, therefore one can quantify cycling using this pathway data quite literally. We used particle tracking simulations (PTS) to compute a cycling index using Finn’s idea of flux based cycling. Our simulation based results (using no matrix algebra) agree with Finn’s cycling index, verifying the accuracy of both the PTS, and the original linear algebraic formulation of FCI.     

The archaeology of deforestation in south coastal Turkey

The Rough Cilicia Archaeological Survey Project investigates landscape transformation as a component to its regional survey of ancient Rough Cilicia (south coastal Turkey opposite Cyprus). Rough Cilicia was celebrated during antiquity for pristine cedar forests that stood between 1500 and 1800 m in altitude along the slopes of the Taurus Mountains. Today along the front range of the Taurus Mountains this forest is completely denuded or otherwise replanted with recent growth in the past 80 years. We employ paleoenvironmental analysis of relic cedar forests in the Taurus Mountains to construct a timeline of anthropogenic disturbances associated with population growth over time and thereby assess the sustainability of ancient forestry practices. To obtain these data, the team recovers pollen and carbon samples from geomorphologic trenches excavated in the cedar zone, tree ring data from dendrochronological survey of the existing forest, and archaeological data from remains of ancient highland settlements. Preliminary results indicate that current perspectives about the timing of deforestation in this region are flawed and that the initial deforestation coincided with regional site abandonment and population decline at the end of antiquity.     

Urban/rural division in environmental justice frameworks: revealing modernity-urbanisation nexus in Turkey’s small-scale hydropower development

Environmental justice frameworks predominantly focus on exploration of socio-environmental inequalities faced by racial, ethnic, religious, cultural and low-income groups. This article aims to expand this mainstream focus of the environmental justice concept on these groups by conceptualising urban/rural division as a group difference, based on which rural communities face with socio-environmental burdens of environmental policies in relation to their urban counterparts. It is based on the analysis of Turkey’s small-scale hydroelectricity power plant (HPP) development policies, referring to the planning and constructions of approximately 1500 hydropower plants across the country, along with country’s modernist agenda, i.e. achievement of economic development, social progress and urban transformation of Turkey. These power plants are also strongly associated with numerous socio-economic, environmental and cultural impacts on local rural communities and local environments with dozens of local opposition movements, while favouring needs, interests and lifestyles of urban communities. This point deserves a systematic conceptualisation within the environmental justice frameworks as it helps to further explain deep causes of socio-environmental inequalities particularly in developing country contexts. Thus, this article is built on such a conceptualisation arguing the necessity to integrate urban/rural division as a separate group difference to environmental justice frameworks by examining modernisation and urbanisation nexus in Turkey’s small-scale HPP development process.     

Dynamic environ analysis of compartmental systems: A computational approach

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.     

Throughflow analysis: A stochastic approach

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 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, , agrees with the conventional ENA throughflow matrix, , for ecosystems at steady-state with donor-controlled flows. The matrix 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 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.