Ecological Modelling, 61 (1992) 169-185 169 Elsevier Science Publishers B.V., Amsterdam ECOPATH II -- a software for balancing steady-state ecosystem models and calculating network characteristics * V. Christensen and D. Pauly International Center for Living Aquatic Resources Management (ICLARM), MC P.O. Box 1501, Makati, Metro Manila, Philippines (Accepted 12 November 1991) ABSTRACT Christensen, V. and Pauly, D., 1992. ECOPATH II -- A software for balancing steady-state ecosystem models and calculating network characteristics. Ecol. Modelling, 61: 169-185. The ECOPATH II microcomputer software is presented as an approach for balancing ecosystem models. It includes (i) routines for balancing the flow in a steady-state ecosystem from estimation of a missing parameter for all groups in the system, (ii) routines for estimating network flow indices, and (iii) miscellaneous routines for deriving additional indices such as food selection indices and omnivory indices. The use of ECOPATH II is exemplified through presentation of a model of the Schlei Fjord ecosystem (Western Baltic). INTRODUCTION Since the International Biological Program (IBP) emphasized ecosystem research more than two decades ago, ecologists have studied what may be hundreds of systems or parts of systems worldwide. Thanks to the IBP the focus of many studies has been on describing flows in the systems and we now have well developed methodologies for measuring trophic interaction between most groups in a system (e.g., Vollenweider, 1969; Edmondson and Winberg, 1971; Holme and McIntyre, 1971; Bagenal, 1978; Fasham, 1984). Correspondence to: V. Christensen, International Center for Living Aquatic Resources Management (ICLARM), MC P.O. Box 1501, Makati, Metro Manila, Philippines. * ICLARM Contribution No. 681. 0304-3800/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved 170 V. CHRISTENSEN AND D. PAULY While the IBP focused mainly on the lower part of the ecosystem, where the bulk of the flow occurs, developments in the 1980s have led to an improved picture of what is happening at the higher trophic levels of aquatic systems, especially of those that are commercially exploited. No- table here are a number of complex simulation models developed by fisheries biologists (e.g., Andersen and Ursin, 1977), some of which are now on the verge of serving as management tools (e.g., Sparre, 1991). The ecosystem analyses of the IBP and follow-up studies have led to a large number of excellent scientific papers describing parts of ecosystems. It appears, however, that few of these studies have resulted in the presen- tation of balanced models of whole systems. We think this is due to the absence of a suitable tool, i.e., a versatile approach for balancing ecosystem models. Here we describe a program, the ECOPATH II software system, which may provide such an approach. MODEL DESCRIPTION Programming language ECOPATH II is presently programmed in Microsoft Basic 7.0, Profes- sional Developers Version, and is available with documentation from the authors in an executable version requiring no commercial software (Chris- tensen and Pauly, 1991). It can be run on any IBM-compatible microcom- puter. The present description relates to Version 2.0 of April 1991. The architecture of ECOPA TH H The ECOPATH II model is developed from the ECOPATH model of Polovina (1984), with which it shares its "basic equation" (see below). This equation was originally proposed for the estimation of biomasses in steady-state ecosystems. Pauly et al. (1987) conceived ECOPATH II as consisting mainly of two interacting elements: (i) routines for estimating biomasses, or production/biomass ratios, as well as food consumption by the various elements (boxes) of a steady-state trophic model; and (ii) routines based on the theory of Ulanowicz (1986) for analyzing the flows estimated by applying (i) to data. The version of ECOPATH II described here presents, in addition, a set of miscellaneous routines for deriving further statistics from the biomasses and flows estimated in (i), and further developing the theory in (ii). Notably, it incorporates an attempt to quantify a number of Odum's (1969) 24 indices of system maturity. ECOPATH II FOR STEADY-STATE ECOSYSTEM MODELS AND NETWORK CHARACTERISTICS 1 71 ECOPATH. The basic equations It is assumed that the system to be modelled is in steady state. For each of the living groups in the system this implies that input equals output, i.e. Q=P+R+U (1) where Q is consumption, P production, R respiration, and U unassimi- lated food. From this equation, the respiration can be estimated once the other flows have been quantified. The production part of equation (1) is modelled explicitly in ECOPATH models. Basically, the approach is to model an ecosystem using a set of simultaneous linear equations (one for each group i in the system), i.e. Production by (i) - all predation on (i) - non-predation losses of (i) - export of (i) = 0, for all i. This can be expressed as Pi - M2, - Pi(1 - EEi) - EX i =- 0 (2) where Pi is the production of (i), M2 i is the predation mortality of (i), EE i is the Ecotrophic Efficiency of (i), (1 -EE i) is the "other mortality", and EX i is the Export of (i). Equation (2) can be re-expressed as n Bi" PBi - ~ Bj " QBj " DCji - PBi " Bi " (1- EEi) - EXi = O j-1 or n B~ " PB, " EE, - Y'. Bj" QBi" DCi~- EX, = 0 (3) j=l where B i is the biomass of i, PB i is the production/biomass ratio, QB~ is the consumption/biomass ratio and DC~i is the fraction of prey (i) in the average diet of predator j. Based on (3), for a system with n groups, n linear equations can be given; in explicit terms, BIPB1EE a - BlQB1DCll - B2QBzDC21 - ... - B~QBnDCnl - EX 1 = 0 (3.1) BzPBzEE 2 - BIQB1DCI2 - BzQBzDC22 - ... - BnQB,,DC~2 - EX 2 = 0 (3.2) B.PB.EE. - B,QB,DC,. - B2QB2DC2. -... - B,,QB. DCnn - EX. = 0 (3.n) This system of simultaneous linear equations can be solved using stan- dard matrix algebra. If, however, the determinant of a matrix is zero, or if the matrix is not square, it has no ordinary inverse. Still, a generalized inverse can be found 172 V. CHR|STENSEN AND D. PAULY in most cases (Mackay, 1981). In the ECOPATH II model, we have adopted the program of Mackay (1981) to estimate the generalized inverse. If the set of equations (3.1)-(3.n) is overdetermined (more equations than unknowns), and the equations are not mutually consistent the general- ized inverse method provides least squares estimates, which minimize the discrepancies. Ancillary variables To give guidance for the balancing of ecosystems a number of physiologi- cal variables characterizing groups has been included in ECOPATH II, e.g. gross and food conversion efficiencies, respiration/assimilation ratio, pro- duction/ respiration ratio, and respiration/biomass ratio. The requirements The steady-state requirement of ECOPATH II may appear problematic, but should be taken as implying that the model outputs only apply to the period for which the inputs are deemed valid; the same requirements are implied when any rate variable is estimated for any mathematical represen- tation of reality. For a fast-changing ecosystem such as an aquaculture pond, the steady-state assumption may perhaps be used for a model TABLE 1 Input data for the Schlei Fjord ecosystem (based on Nauen, 1984). Units: t/km2; rates are yearly. Dashes show parameters subsequently calculated by ECOPATH II a Group Catch Biomass Production Consumption biomass biomass 1. Apex predator 0.03 0.1 0.7 6.7 2. Med. predator 0.38 - 1.0 11.3 3. Planktivores 0.05 - 1.8 17.1 4. Temp. planktiv. 2.30 - 1.7 16.4 5. Whitefish 0.12 - 0.5 10.8 6. Small fish 0.00 - 0.2 9.1 7. Zoobenthos 0.00 96.9 1.4 - 8. Zooplankton 0.00 10.2 10.0 36.5 9. Phytoplankton 0.00 89.2 - n.a. 10. Detritus 0.00 100.0 n.a. n.a. a The following additional assumptions were made: (i) other mortality (flow to detritus0 = 5% of production (Groups 2-6 and 9; calculated for Groups 1, 7 and 8); (ii) gross food conversion efficiency of zoobenthos = 0.15. ECOPATH 11 FOR STEADY-STATEECOSYSTEM MODELS AND NETWORKCHARACTERISTICS 173 TABLE 2 Food consumption matrix for the Schlei Fjord system, expressed in percent of consumption on a weight basis. Dashes indicate no consumption (modified from Nauen, 1984) Prey Predator 1 2 3 4 5 6 7 8 1. Apex predator ........ 2. Med. predator 20 ....... 3. Planktivores 50 ....... 4. Temp. planktiv. - ....... 5. Whitefish 5 2.6 ...... 6. Small fish 25 48.7 8.3 ..... 7. Zoobenthos - 48.7 - - 100 80 - - 8. Zooplankton - - 91.7 100 - 20 - - 9. Phytoplankton ...... 5 80 10. Detritus a - ..... 95 20 a Nauen (1984) does not consider detritiory; our interpretation of trophic flows in Schlei Fjord suggests detritiory to be likely for both zoobenthos (95%) and zooplankton (20%). describing 1 month, while for a coral reef model a decade may be appropriate. To illustrate the data requirements for ECOPATH II, we have given the input data for a model of the Schlei Fjord ecosystem (Western Baltic Sea) in Tables 1 and 2 (based on data in Nauen, 1984). The derived flow diagram for the Schlei Fjord system is shown in Fig. 1. To increase the descriptive and explanatory impact of the flow diagram, and to facilitate comparisons between ecosystems we are using some constructional rules. Note that (1) the boxes are placed on the y-axis according to trophic level of the groups, (2) the areas of the boxes are scaled after the logarithms of the group biomasses, (3) flows exiting a box do so from the upper half of the box, while flows entering a box do so via the lower half of the box, and (4) flows exiting a box cannot branch, but they can be linked with flows exiting other boxes.