Andersen and Ursin’s approach in that no attempts MODELLING THE

10.3 Andersen and Ursin’s approach in that no attempts MODELLING THE

NORTH SEA, THE NORTH were made to track numbers of individuals.

Rather, the model strived to maintain mass bal-

PACIFIC AND THE GULF

ance between the cells of a spatial grid, upon which

OF THAILAND

were overlaid the biomass of commercial fishes, and of their prey called ‘forage fishes’, and preda-

Simulation models, incorporating basic elements tors which were mostly marine mammals. Here of the Lotka–Volterra approach, but also incorpo- again, the model and its predictions were not rating components such as those used in yield-per- adopted as such. Rather, the PROBUB model, as it recruit analyses, may be seen as the next logical was later called (Laevastu and Larkins 1981), at- step towards dealing with multispecies interac- tracted the attention of researchers in need of a tool tions. Indeed, several attempts have been made to for modelling biomass flows in a data-sparse sys- conceptualize and parameterize simulation mod- tem, the French Frigate Shoals, Northern Hawai’i els of large marine ecosystems, and three of these (Polovina and Tagami 1980). Stripped of its spatial had a great indirect and direct impact on fisheries and temporal dynamics, PROBUB led to the first research. The North Sea model of Andersen and version of Ecopath, a simple mass-balance ap- Ursin (1977) is unique in terms of its extreme com- proach for estimating biomasses in aquatic sys- plexity and level of details, the consequence of an tems (Polovina 1984). Another indirect effect of attempt to track the numbers of fish from the eggs work on PROBUB is that it motivated a thorough to the adults of dozens of species feeding on each study of the diet of Bering Sea fishes, and thus en-

215 abled the construction of successor models (Trites tion, should be that used for determining one’s use

Ecosystem Models

et al. 1999; also see below). of one or the other formulation. Polovina (1984), Another early simulation model relevant to who developed the original Ecopath formulation, fisheries was that of Larkin and Gazey (1982), de- emphasized the biomasses as the unknowns in his scribing the Gulf of Thailand. Like Andersen and system, thereby making strong assumptions about Ursin for the North Sea and Laevastu and collabo- the fraction of the fluxes retained within the sys- rators for the North Pacific, Larkin and Gazey were tem. In the reformulation of the Ecopath approach faced with the need to parameterize a large number (Christensen and Pauly 1992; Pauly et al. 1993), of coupled differential equations. However, con- this emphasis on biomass was replaced by an op- trary to the situation for the North Sea and the tion to leave other elements of a system of fluxes Pacific, there was, at the time, no hope of obtain- unknown, notably the ecotrophic efficiency (EE), ing the parameters required for a model of the Gulf expressing the fraction of mortality not due to pre- of Thailand, then much less studied than the tem- dation or fishing, a parameter far more difficult perate North Sea, or the North Pacific. Thus they than biomass to estimate in the field. pushed as far as they could the process wherein evo-

The well-known master equation for Ecopath lutionary first principles are used to derive assump- is, for each functional group i: tions about the likely parameter that such values

might take. The result, while establishing their in- B i ◊ ( PB ) i ◊ EE i = Y i + Â B j ◊ ( QB ) j ◊ DC ij , (10.2)

genuity, confirmed that simulation models struc- tured around coupled differential equations could where B i and B j are biomasses (the latter pertaining not be parameterized for most situations such that to j, the consumers of i); P/B i their production/bio- fisheries scientists and managers would feel com- mass ratio, equivalent to total mortality under fortable with the results. Clearly, a route had to be most circumstances (Allen 1971); EE i the fraction found to harness the scattered data on catches, of production (P = B ◊(P/B)) that is consumed with- standing stock estimates, and food consumption in, or caught from the system (usually left as the rates, which marine and fishery biologists have unknown to be estimated when solving the equa- published over the years but which could not be tion above); Y i is the fisheries catch (i.e. Y = F◊ B); straightforwardly used to parameterize models Q /B j the food consumption per unit biomass of j; such as the one of Larkin and Gazey. This, again, and DC ij the contribution of i to the diet of j. leads to the Ecopath model, our next topic.

Herein, solutions for the unknowns, e.g. B i , are obtained by solving the matrix system in equation (10.2) through a robust inversion routine (MacKay

10.4 ECOPATH AND THE

1981). (The right-hand side of equation (10.2) can

MASS-BALANCE APPROACH

also include a biomass accumulation term (B acc ) in cases where the biomass is known to have changed

The basic idea behind the mass-balance approach during the period under consideration, thus allow- incorporated in Ecopath is both trivial and pro- ing for non-equilibrium situations (see below), as found. At any time within the system, and within well as a term for net migration.) the elements of that system, the amounts of matter

Solving the system of equations (10.2) does not that flow in must balance the amount that goes out require the Ecopath software per se. Indeed, they plus the change in biomass. This means that if can be implemented on spreadsheets (see e.g. parts of the fluxes in a system and/or biomass in a Mathisen and Sands 1999). Rather, their key at- system are known, the values for the other parts are tribute is that it is easy to find estimates of various constrained and therefore can be estimated by processes and states in ecosystems which corre- subtraction. This principle can be implemented spond to the parameters of these equations, thus through different sets of equations and we think largely solving the parameterization problem that that the utility criterion, presented in the Introduc- has been besetting earlier modelling approaches.

Chapter 10

Moreover, to correct a false impression created (see models in Christensen and Pauly 1993). Pre- by the title of Christensen and Pauly (1992), the sent applications typically include more groups, Ecopath master equations do not require equilibri- from 20 to 50, as required, to represent a wide range um or steady-state. Rather, they require that mass of ecological and spatial variability and ontogenic balance occurs during the period under considera- diet changes. Whether one uses few or many state tion, e.g. that any excess consumption during part variables, it is important that all taxonomic groups of that period is compensated for by reduced con- occurring in a system be included, whether or not sumption during another part. This is particularly detailed data on them are available. This can be important for models of ecosystems that included done by including a group explicitly, with its own

a strong seasonal component and which either can state variables. This would be for common, well-

be represented by parameters averaged over a year, documented species. Alternatively it can be done which is the option chosen for many applications implicitly as part of broadly defined functional so far, or in which monthly change in biomass, diet groups. A detritus group must also be included, to composition, Q/B and P/B are modelled explicitly. which all fluxes of ungrazed plants and/or uncon-

Constructing an Ecopath model is thus a matter sumed dead animals are directed. Bacteria may or of performing the following steps:

may not be added as an explicit group. If they are

1 Defining the area in which the ecosystem oc- not an explicit group, it is assumed that they feed curs. This should preferably be one in which a dis- from the detritus. In this case, the EE of detritus tinct community of organisms occurs with limited must be <1; this implies that the detritus produced exchange to adjacent ecosystem. This system area in a system is not all consumed within that sys- may comprise several subsystems, e.g. a gulf may tem, i.e. this allows for consumption by bacteria consist of a shallow, mangrove-dominated area, a considered to reside ‘outside’ of that system. rocky or coralline intermediate area and deeper

4 Assembling available estimates of biomass, mud-covered grounds (Opitz 1993). This spatial ar- P/B, Q/B and diet composition . Contrary to the ticulation of a system in the form of subsystems is almost ritually invoked phrase that ‘nothing is important for the spatial considerations discussed known of x’, over a hundred years of quantitative further below.

work by marine biologists, limnologists, fishery

2 Defining the period represented by an ecosys- scientists and others have generated a vast archive tem . Typically, this will be a period during which of valuable information on the aquatic ecosystems major field surveys have been conducted, provid- of the world. Much of it is, admittedly, scattered in ing estimates of biomass, diet composition, and

a vast and still largely untapped literature, some of other important elements for many of the most it obscure. Constructing Ecopath models requires important groups in the system. This period is also access to that literature. This task is facilitated in one during which major changes in the biomass of part by FishBase, which can be made to output P/B, the major ecosystem elements can be assumed not Q /B and diet compositions for the thousands of to have occurred. Thus, wherever massive changes species for which such information has been en- are known to have occurred, it is better to repre- coded, and also provides a starting point for the lit- sent that system by models for each of the periods, erature search in question (Froese and Pauly 2000). before and after the change. Having at least two Only after such a literature search has been con- models also has the advantage that additional in- ducted should field programs be launched aiming ferences on the vulnerability of various species to at estimating missing parameters. Moreover, to their predators and to the fisheries can then be guide both the literature searches and the field made using Ecosim, presented below.

work, routines are available in Ecopath which

3 Defining the state variables explicitly included quantify the uncertainty associated with the avail- in the system . Earlier applications of Ecopath able input values and thus help identify those tended to be composed of 10 to 20 functional components of a model requiring additional field groups representing all species in the ecosystem inputs.

Balancing a model then consists of solving the system of linear equations (10.2), under the con- straint that the EE values remain equal or less than

1, and that the respiration terms are all positive. This balancing often involves revising initial esti- mates and is guided by the quantification of the un- certainties as outlined in (4). Formal approaches for explicitly considering these uncertainties in- volve: (a) the Monte Carlo routine (‘EcoRanger’), which uses the uncertainties in (4) in Bayesian mode, as prior distributions, and outputs both dis- tributions of estimates, and posterior distributions for the input values (Pauly et al. 2000, Fig. 3); and (b) a recently developed approach based on simu- lated annealing, in which fuzzy logic is used to modify qualitative diet compositions within con- straints, until the system of equations is balanced.

Once they are balanced and their key features checked for internal consistency and compati- bility with similar ecosystems, models can be represented in the form of flow charts, which summarize these key features. Such flow charts (Fig. 10.1) can be extremely information-rich and, in the following, we discuss some aspect of this in- formation in terms of trophic levels that are calcu- lated and not previously assumed. This was also the case with the Lindeman pyramids earlier used to represent ecosystems. We then discuss other as- pects of the information contained in ecosystem flow charts.

We stress that the four steps outlined above have now been implemented in hundreds of loca- tions, resulting in over 150 published models. These describe a vast range of ecosystem types from data-rich areas, such as the North Sea and the North Pacific, partly using, for both areas, the same database used for the simulation models dis- cussed above, to the more data-sparse Gulf of Thai- land (Christensen 1998) where the straightforward data requirements of the Ecopath model enabled the parameterization based on empirical data that had eluded Larkin and Gazey (1982). This vast range of applications demonstrates the applicabili- ty of Ecopath as perceived by users who feel thereby empowered, contrary to the situation pre- vailing in programmes such as the International Biological Programme (IBP) where many field biol-

ogists worked ‘for’ rather than ‘with’ the few mod- ellers then working on ecosystems (Golley 1993). This transition has markedly changed the field and made ecosystem-based management a realistic op- tion, as we shall show below, at least as a research- able issue, if not in actual implementation.