# «ECOPATH II - a software for balancing steady- state ecosystem models and calculating network characteristics. Ecological Modelling 61: 169-185. 169 ...»

Christensen, V. and D. Pauly. 1992. ECOPATH II - a software for balancing steady-

state ecosystem models and calculating network characteristics. Ecological Modelling

61: 169-185.

169

Ecological Modelling, 61 (1992) 169-185

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) ABSTRACf 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, (ij) 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

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 presentation 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, Professional Developers Version, and is available with documentation from the authors in an executable version requiring no commercial software (Christensen and Pauly, 1991). It can be run on any IBM-compatible microcomputer. The present description relates to Version 2.0 of April 1991.**The architecture of ECOPATH II**

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 aI. (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.

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## ECOPATH II FOR STEADY-STATE ECOSYSTEM MODELS AND NETWORK CHARACTERISTICS

ECOPATH. The basic equationsin 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 generalized inverse method provides least squares estimates, which minimize the discrepancies.

**Ancillary variables**

To give guidance for the balancing of ecosystems a number of physiological variables characterizing groups has been included in ECOP ATH II, e.g.

gross and food conversion efficiencies, respiration/ assimilation ratio, production/ 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 representation 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: tjkm2; rates are yearly. Dashes show parameters subsequently calculated by ECOPATH II a

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. The flows are balanced so that input equals output for all boxes.

**Ascendency**

ECOPATH II links concepts developed by theoretical ecologists, especially the theory of Ulanowicz (1986), with those used by biologists working in fisheries and aquaculture. Most notable is the inclusion of a routine for calculating "ascendency" in the form suggested by Ulanowicz and Norden (1990). Ascendency is a measure of average mutual information in a system, derived from information theory and scaled by system throughput.

1.0 (7274) Fig. 1. Flow diagram of the Schlei Fjord system (based on Nauen, 1984). Flows are expressed in t/km2/year.

Thus, if one knows the location of a unit of energy the uncertainty of where it will go next is reduced by an amount known as the "average mutual information"

Qi' as a probability, is scaled by multiplication with the total throughput of the system, T, where n n E ETij T= i= 1 j= 1 Further A=T.[ where it is A that is called "ascendency". The ascendency is symmetrical and will have the same value whether calculated from input or output.

There is an upper limit for the size of the ascendency. This upper limit is called the "development capacity" and is estimated from C=H.T where H is called the "statistical entropy", and is estimated from n E Qi. log Qi H= i= 1 The difference between capacity and ascendency is called "system overhead". The overheads provide limits on how much the ascendency can increase and reflect the system's "strength in reserve" from which it can draw to meet unexpected perturbations (Ulanowicz, 1986) Judged from the theoretical foundation of the concept it has been stated that ascendency "correlates well with most of Odum's (1969) 24 properties of 'mature' ecosystems" (Ulanowicz and Norden, 1990).

However, only a few ecosystems have been analyzed using Ulanowicz's theory. It thus remains to be shown how close the correlation is between ascendency and maturity.

**Trophic level**

Lindeman (1942) introduced the concept of trophic levels. Further, by treating the ecosystem as a thermodynamic unit, he could describe the efficiencies of transfers between trophic levels. However, some authors disagreed. Cousin (1985), noting that "a hawk feeds on five trophic levels", suggested abandoning the trophic level concept.

Alternatively, species can be placed on fractional trophic levels, as suggested by Odum and Heald (1975). ECOPATH II includes such fractional trophic levels.

Detritus and primary producers such as phytoplankton and benthic producers have, by definition, a trophic level equal to unity. For all other groups the (mean weighted) trophic level (TL) of group (i) is defined as 176 V. CHRISTENSEN AND D. PAULY

This equation system is solved using a standard inverse method. Following this approach a consumer eating 40% plants (TL = 1) and 60% herbivores (TL = 2) will have a trophic level of 1 + [0.4. 1 + 0.6. 2] = 2.6.

Trophic aggregation In addition to the calculation of fractional trophic levels, we have included a routine that aggregates the entire system into discrete trophic levels sensu Lindeman. This routine is based on an approach suggested and described by Ulanowicz (in press); it reverses the routine for calculation of fractional trophic levels. Thus, 40% of the flow through the consumer,,,,, ~

group mentioned above would be attributed to the herbivore level and 60% to the first-order earn ivory level.

This leads to a further development of the pyramid metaphor: one can give them three dimensions, just as they have in Egypt. An example of this is given for the Schlei Fjord system in Fig. 2, where the volume of each of the pyramidal compartments representing discrete trophic levels is proportional to the total throughput of the trophic level.

The trophic aggregation produces as its main result calculated estimates of trophic transfer efficiencies by trophic levels, e.g., the transfer efficiencies in the Schlei Fjord system are 4.9% for the herbivory level, and 10.3,

8.2 and 6.1% for the first three carnivory levels, respectively.

Omnivory index

where n is the number of groups in the system, TLj is the trophic level of prey j, TL is the average trophic level of the preys, i.e. one less than the trophic level of predator i, and DCij is the fraction of prey (j) in the average diet of predator (i).

If a predator only has prey on one trophic level its omnivory index will equal zero, while a large omnivory index indicates that the trophic positions of a predator's preys are variable. Cousin's hawk would have a high omnivory index.

**Selection indices**

One of the most widely used indices for selection is the Ivlev electivity index, E; (Ivlev, 1961) defined as E; = (r; - P;)/(r; + Pi) where r; is the relative abundance of a prey in a predator's diet and P; is the prey's relative abundance in the ecosystem. In ECOPATH II, the r;

and P; refer to biomass, not numbers. E; is scaled so that E; = - 1 corresponds to total avoidance, E; = 0 represents non-selective feeding, and E; = 1 shows exclusive feeding.

178 V. CHRISTENSEN AND D. PAULY

where rj and Pj are defined as above and n is the number of groups in the system.

As implemented in ECOPATH II, the forage ratio has been transformed such as to vary between -1 and 1, where -1,0 and 1 can be interpreted as the Ivlev index.

Recycling index An index of how much of the flow of an ecosystem is recycled has been included in ECOP ATH II. This recycling index, developed by Finn (1976), is expressed as percentage of total throughput. It was originally intended to quantify one of Odum's (1969) properties of system maturity. However, its interpretation is apparently not as simple as E.P. Odum conceived, with recycling increasing as a system matures. Wulff and Ulanowicz (1989) suggest that the opposite may indeed be the case.

**Cycles and pathways**

A routine based on an approach suggested by Ulanowicz (1986) has been implemented to describe the numerous cycles and pathways that are implied in an ecosystem (Table 3).

In addition, a measure of the average path length is included, defined as the average number of groups/boxes a flow passes through. The average path length (pL) is calculated from a steady-state version of the equation presented by Finn (1976). We have

Leontief (1951) developed a method to reveal the direct and indirect interactions in the economy of the USA, using what has since been called the Leontief matrix. This matrix was introduced to ecology by Hannon (1973) and Hannon and Joiris (1989). The latter developed the method further so that it becomes possible to give qualitative statements of the impact of direct and indirect interactions (including competition) in a system.

Ulanowicz and Puccia (1990) developed a similar approach, and a routine based on their method has been implemented in the ECOP ATH II system. In this approach the positive effect (gjj) a prey (j) has upon a predator (i) is expressed as the proportion the prey constitutes to the diet of the predator. We have = DC., gj J ' IJ