Elsevier

Ecological Modelling

Volume 189, Issues 3–4, 10 December 2005, Pages 251-269
Ecological Modelling

Theory of materials and energy flow analysis in ecology and economics

https://doi.org/10.1016/j.ecolmodel.2005.03.011Get rights and content

Abstract

Materials and energy flow analysis (MEFA) has been widely utilized in ecology and economics, occupying unique positions in both disciplines. The various approaches to materials and energy flow analysis in ecology are reviewed, the focus being on the linear network system introduced from input–output economics. After its introduction in the early 1970s, the calculus and system definition for materials and energy flow analysis have been diversified, causing problems in comparing the results of different studies. This paper uses a materials and energy flow analysis framework that is a generalization of the major approaches in ecology and economics to illuminate the differences and similarities between the approaches on the basis of a set of consistent principles. The analysis often shows that seemingly different calculus and interpretations employed by different approaches eventually lead to the same outcome. Some issues of interpretations that conflict or require cautious interpretation are further elaborated. A numerical example is presented to test the generalized framework, applying major analytical tools developed by other approaches. Finally, some parallels, convergents, and divergents of the perspectives of ecology and economics and their implications for endogenized resources economy are discussed as they are reflected in the materials and energy flow analysis frameworks.

Introduction

Since Lotka (1925) and Lindeman (1942), materials and energy flows have been among the central issues in ecology (Lindeman, 1942, Lotka, 1925). Energy flows in ecological systems have often been presented in the form of so-called Lindeman spines, which illustrate uptake, utilization, and dissipation of energy in a chain-like diagram. A more comprehensive representation of energy flows based on a network structure rather than a chain was introduced in the 1970s (Heal and MacLean, 1975). It was Hannon (1973) who first introduced the use of a system of linear equations, taken from input–output economics, to analyze the structure of energy utilization in an ecosystem (Hannon, 1973). Using an input–output framework, the complex interactions between trophic levels or ecosystem compartments can be modeled, taking all direct and indirect relationships between components into account.

Shortly after its introduction, Hannon's approach was adopted by various ecologists. Finn, 1976, Finn, 1977 developed a set of analytical measures to characterize the structure of an ecosystem using a rather extensive reformulation of the approach proposed by Hannon (1973) successfully demonstrating how some key properties of a complex network system could be extracted (Finn, 1976, Finn, 1977). Finn's cycling index (FCI), for instance, is still one of the most frequently applied indicators in ecological network analyses. The contributions by Finn, 1976, Finn, 1977 have led the materials and energy flow analysis framework to be more widely utilized in general ecological applications (Baird et al., 1991, Baird and Ulanowicz, 1989, Heymans and Baird, 1995, Heymans and Baird, 2000a, Heymans and Baird, 2000b; Heymans and McLachlan, 1996, Loreau, 1998, Szyrmer and Ulanowicz, 1987, Vasconcellos et al., 1997). For instance, Baird et al. (1991) evaluated E.P. Odum's definition of ecosystem maturity using FCI. The analysis of six marine ecosystems by Baird et al. (1991) showed that FCI and system maturity were inversely correlated. The result was generally confirmed by Vasconcellos et al. (1997) on 18 marine trophic models.

Another important development in the materials and energy flow analysis tradition in ecology is environ analysis. Patten (1982) proposed the term environ to refer to the relative interdependency between ecosystem components in terms of nutrient or energy flows. Results of environ analysis are generally presented as a comprehensive network flow diagram, which shows the relative magnitudes of materials or energy flows between the ecosystem components through direct and indirect relationships (Levine, 1980, Patten, 1982, Patten et al., 1990).

R.E. Ulanowicz and colleagues have broaden the value of materials and energy flow analysis both theoretically and empirically. A comprehensive study on Chesapeake Bay by Baird and Ulanowicz (1989) found that the extended diets of bluefish and striped bass they calculated showed considerable differences, although, as both are pelagic piscivores, the differences in their direct diets are not apparent. The finding helped to explain why the concentration of the pesticide Kepone detected in the flesh of bluefish was much higher than that in striped bass. The methodology used in Baird and Ulanowicz (1989) is based on, for instance, Szyrmer and Ulanowicz (1987).

Finally, a number of researchers have contributed to further enriching and broaden the materials and energy flow analysis in ecology. Higashi (1986a) and Han (1997a) concerned the residence time of materials in ecological systems, and Higashi (1986b) and Han (1997b) further extended the ecological network analysis. Savenkoff et al. (2001) and Allesina and Bondavalli (2003) developed procedures for balancing input–output network data.

These important developments in the materials and energy analysis tradition in ecology were rather isolated from major developments in network analysis in economics, notably Input–Output Analysis (IOA). Szyrmer and Ulanowicz (1987) wrote:

Unfortunately, the authors are aware of no instance in which these novel adaptations of IOA by ecologists have been implemented by economists.

An economist perhaps could have made a similar statement. Because of the lack of interaction with input–output economics and the different needs of ecologists, the materials and energy flow analysis tradition in ecology has followed its own path, resulting in considerable differences in its appearance from that used in economics. Furthermore, the system definitions and calculi used by different studies are surprisingly different from each other, hampering a fruitful communication among ecologists themselves.

The present paper reviews the tradition of materials and energy flow analysis (MEFA) in ecology focussing on the input–output formulation of ecological network analysis (ENA). The existing approaches are analyzed and compared by means of a MEFA framework that represents a generalization of the major approaches. The analysis presented here may be used as a point of departure in facilitating a common language and dialogue between and among the network flow analysts in ecology and economics.

In this paper, bold characters represent matrices (upper case) and vectors (lower case), while lower case italics are used for scalars and elements of the corresponding matrix or vector (with subscripts). Prime (′) denotes transpose of matrices or vectors. Hat () diagonalizes vectors. Italics of i, j, and m are used as indices for ecosystem components and k for energy or nutrient inputs from outside the system.

Section snippets

The tradition of materials and energy flow analysis in ecology

The calculi and the system definitions of major MEFA approaches in ecology are summarized below, emphasizing their similarities and differences.

A generalized framework for materials and energy flow analysis

In the development of MEFA approaches in ecology, little attention has so far been paid to horizontal integration and comparison between studies. Except for a few well-known indicators such as FCI, different studies often employ different sets of indicators, hampering communications and comparisons between results. The differences in system definitions are another source of difficulties in comparing and understanding the approaches (Table 1). In input–output economics, statistical bureaus have

Interrelations between existing MEFA approaches

In this section, the interrelations between existing MEFA approaches are derived by means of the generalized MEFA framework presented in the previous section.

A numerical example

Table 3 and Fig. 4 show an example of a MEFA problem involving five ecosystem components and two types of primary input.

Two types of dependency coefficients can be defined: supply-driven dependency and demand-driven dependency. Supply-driven dependency is calculated from Eq. (22) by (IA¯)1I (Table 4), while demand-driven dependency is derived from (23) by (IA)1I (Table 5).

The ijth cell in Table 4 shows the production of j induced by one unit of availability of i, and the ijth cell in

Discussion and conclusions

This paper has analyzed MEFA methodologies in ecological studies, and presented a generalized MEFA framework that embraces ecological as well as economic systems. Using the generalized MEFA framework, it has interpreted and compared existing methods, while discussing a few critical issues of interpretations and calculi as well. Finally, it has demonstrated the generalized MEFA framework by means of a numerical example. Below I discuss a few issues arising from the analyses.

Acknowledgements

The author is thankful to R.E. Ulanowicz, and B. Hannon for their comments and suggestions. B.C. Patten and S. Allesina offered thorough reviews and suggestions which greatly helped improving the clarity of the current paper. The author is indebted to G. Huppes, E. Dietzenbacher, F. Duchin and J. Klerkx for the kind reviews and advices on an earlier version of this paper and to E. de Roos for getting the literatures. This material is based upon work supported in part by the National Science

References (61)

  • M. Higashi

    Residence time in constant compartmental ecosystems

    Ecol. Model.

    (1986)
  • M. Higashi

    Extended input output flow-analysis of ecosystems

    Ecol. Model.

    (1986)
  • M. Lenzen

    Environmentally important paths, linkages and key sectors in the Australian economy

    Struct. Change Econ. Dyn.

    (2003)
  • S. Levine

    Several measures of trophic structure applicable to complex food webs

    J. Theor. Biol.

    (1980)
  • B.C. Patten et al.

    Trophic dynamics in ecosystem networks—significance of cycles and storage

    Ecol. Model.

    (1990)
  • S. Suh

    A note on the calculus for physical input–output analysis and its application to land appropriation of international trade activities

    Ecol. Econ.

    (2004)
  • J. Szyrmer et al.

    Total flows in ecosystems

    Ecol. Model.

    (1987)
  • M. Vasconcellos et al.

    The stability of trophic mass-balance models of marine ecosystems: a comparative analysis

    Ecol. Model.

    (1997)
  • M. Augustinovics

    Method of international and intertemporal comparison of structure

  • R.U. Ayres et al.

    Industrial Ecology: Towards Closing the Materials Cycle

    (1996)
  • R. Bailey et al.

    Applying ecological input-output flow analysis to material flows in industrial systems. Part I: tracing flows

    J. Ind. Ecol.

    (2004)
  • R. Bailey et al.

    Applying ecological input-output flow analysis to material flows in industrial systems. Part II: flow metrics

    J. Ind. Ecol.

    (2004)
  • D. Baird et al.

    The comparative ecology of 6 marine ecosystems

    Philos. Trans. Roy. Soc. London Ser. B: Biol. Sci.

    (1991)
  • D. Baird et al.

    The seasonal dynamics of the Chesapeake Bay ecosystem

    Ecol. Monogr.

    (1989)
  • J.E. Cohen et al.

    Improving food webs

    Ecology

    (1993)
  • P. Dasgupta et al.

    Optimal depletion of exhaustible resources

    Rev. Econ. Stud.

    (1974)
  • J. Defourny et al.

    Structural path analysis and multiplier decomposition within a social accounting matrix framework

    Econ. J.

    (1984)
  • B.D. Fath et al.

    Review of the foundations of network environ analysis

    Ecosystems

    (1999)
  • Finn, J.T., 1977. Flow analysis: a method for tracing flows through ecosystem models. Thesis/Dissertation. University...
  • R.A. Frosch et al.

    Strategies for manufacturing

    Scientific Am.

    (1989)
  • Cited by (0)

    View full text