PARTICLE-SIZE SPECTRA IN ECOSYSTEMS

10.8 PARTICLE-SIZE SPECTRA IN ECOSYSTEMS

Using data from particle-size counters, Sheldon et al. (1972), proposed that the size spectrum of ma- rine organisms is a conservative feature of marine ecosystems, characterized by a constant slope, for which they provided the rationale, using thermo- dynamic considerations. The controversy which ensued, still festering among marine biologists, who tend to consider only the small range of organ- ism sizes sampled by automatic plankton particle counters, was largely ignored by fisheries scien- tists, who quickly established not only that fish abundances also neatly fit (log) linear size spectra, but that the slope of such spectra reflect the exploitation level to which a multispecies fish community is subjected, being steeper where ex- ploitation is high (Pope and Knight 1982; Bianchi et al. 2000).

This provides another constraint for multi- species and/or ecosystem models, which should be expected to generate such spectra as one of their output (as did, the North Sea model of Andersen and Ursin already described).

Individual-based models such as OSMOSE (Shin and Cury 1999) can generate such spectra, as may perhaps be expected (Shin 2000; see also Huse et al., Chapter 11, this volume). Perhaps more sur-

prisingly, it turns out, however, that mass-balance models can also be used to generate size spectra of the ecosystem, and thus build a bridge between the hypotheses advanced by marine ecologists and those of fisheries scientists. We briefly describe the routine of Ecopath which is used to re-express the biomass of fish, invertebrates and marine mam- mals in various ecosystems in the form of stan- dardized size spectra, whose slope can then be compared. This routine, while assuming steady- state, does the following: • uses the von Bertalanffy growth curves and the values of P/B (i.e. Z) entered for each group in the model to re-express its biomass in term of a size–age distribution; • divides the biomass in each (log) weight class by the time, Dt, required for the organisms to grow out of that class (to obtain the average biomass present in each size class); • adds the B/Dt values by (log) class, irrespective of the groups to which they belong.

Figure 10.2 compares size spectra obtained in this fashion for a trophic model of the Gulf of Thailand. The spectra are based on 40 ecosystem groupings ranging in size from phytoplankton to dolphins. The spectra are obtained by running a model describing the 1973 situation, where fishing pressure and resource depletion were moderate, with observed fishing pressure through to 1994, where fishing pressure was high, and the resources severely depleted. Further, a simulation was performed with fishing pressure removed, and the long-term equilibrium used to estimate a spectrum without fishing.

The dots on Fig. 10.2 indicate the actual size spectrum obtained for the 1973 model. It is far from a straight line, but shows a hump in the size range dominated by benthos. This hump is likely to be caused by poor resolution for the benthic groupings, and would probably not appear if these groups were split into finer taxonomic groups than used for the model presented.

The three straight lines on Fig. 10.2 show that the slope of the size spectra, as expected, increases with fishing pressure, here from (-0.17) for the unfished situation, to (-0.18) for the moderately fished, and to (-0.22) for the situation with high

Ecosystem Models

221

Chapter 10

No fishing (–0.17) 2.0 Moderate fishing (–0.18)

1.5 High fishing (–0.22) )

Biomass (log g m –1.5 –2.0

Body weight (log g)

Fig. 10.2 Ecosystem-level size spectra for the Gulf of Thailand. The spectra are derived based on a trophic model with 40 ecosystem groupings (see www.ecopath.org). The thin line associated with ‘moderate fishing’ describes the 1973 situation in the Gulf, while the broken line indicates the slope of the model situation at long-term equilibrium without fishing, and the thick line indicates the 1994 situation, with resources severely depleted by over-fishing. Note that the slopes of the spectra (in brackets) increase with fishing pressure.

fishing pressure. The increased slope is caused by d B i d t = g i ◊ Â Q ij - Â Q ji +- I i ( M 0 i ++ F i EB i ) i ,

the removal of virtually all higher trophic-level (10.5) organisms in the Gulf during the time span studied

(see Christensen 1998; Pauly et al. 1998b). where dB/dt is the rate of biomass change, g the The example given here only serves as a taster growth efficiency (i.e. P/Q), F the fishing mortality

for how size spectra may be of use as ecosystem (i.e. Y/B), M

0 the natural mortality (i.e. excluding indicators of exploitation level, and no gener- predation), I is the immigration rate, E the emigra-

alizations have been drawn so far of how the slopes tion rate, and Q ij (Q ji ) the consumption of type j (i) of the spectra relate to exploitation. We anticipate, biomass by type i (j) organisms.

however, that the ease with which ecosystem- This set of coupled differential equations could level size spectra can now be constructed through

be easily integrated as they are over time, thus the Ecopath approach will lead to a blossoming yielding a simulation model with the help of

of spectral analysis in the foreseeable future, which various scenarios resulting from changes and that valuable insights will be gained in the in fishing mortality F, could be explored. This process.

simulation model, however, would be of the Lotka–Volterra type, wherein the amount con-

10.9 sumed of a given prey ‘i’ is proportional to the ECOSIM, REFUGIA

product of its biomass times the biomass of its

AND TOP-DOWN VS.

predator(s). Such ‘top-down controlled’ systems,

BOTTOM-UP CONTROL

however, are inherently unstable, and usually fluc- tuate in unrealistic fashion. As animals do not live

The system of coupled linear equations that is in reaction vats, modelling predation must reflect behind a balanced Ecopath model (see equation the ability of potential prey to hide or camouflage

10.1) above can be re-expressed in terms of the themselves, or generally to evolve strategies that change implied by:

limit their exposure to predators (see Krause et al.,

223 Chapter 13, Volume 1). In Ecosim, the dynamic terms of the implementation presented here, inter-

Ecosystem Models

counterpart to Ecopath, the existence of physical mediate control, which is a form of control that is or behavioural refugia is represented by prey bio- neither fully top-down, nor bottom-up, is required mass consisting of two elements: one, vulnerable for simulated ecosystems to behave in realistic to predators, the other invulnerable. It is then the fashion, this being a major finding obtained rate of transfer between these two partial compo- through Ecosim (Walters et al. 1997, 1999; Pauly et nents of a prey’s biomass which determine how al. 2000; Christensen et al. 2000; and www.eco- much of the prey can be consumed by a predator. path.org may be consulted for further information When the exchange rate is high, part of the bio- on this rapidly evolving software). mass which is vulnerable is quickly replenished and hence we still have top-down control and Lotka–Volterra dynamics. On the other hand,

10.10 SPATIAL

when the replenishment of vulnerable biomass

CONSIDERATIONS IN

pool is set to be slow, it is essentially that slow rate

ECOSYSTEM MODELLING

which determines how much the predators can consume. We speak here of ‘bottom-up control’, As mentioned in the introduction, adding com- since it is the dynamics of the prey which shape the plexity to ecosystem models does not necessarily ecosystem. Issues of top-down versus bottom-up make them ‘better’. Rather, to increase the useful- control are addressed further in the food webs ness of models, what is required is to identify those chapter by Polunin and Pinnegar (Chapter 14, improvements of existing models for which the Volume 1) and Persson (Chapter 15, Volume 1).

gain in new insights outweighs the added com- These different control types can be represented plexity and data requirements. As it turned out, by replacing Q ij in the above equation by:

the major improvements that can be added to models such as Ecopath and Ecosim are spatial

(10.6) considerations, capable of representing explicitly some of the refugia implied in the above Ecosim where v ij and v ij ¢ represent rates of behavioural ex- formulation. change between vulnerable and invulnerable state

Q ij = vaBBv ij ij ij ( ij + v ij ¢+ aB ij j ) ,

The formulation developed for this, still based and a ij represents the rate of effective search by on Ecopath parameterization and its inherent predator j for prey i, i.e. the Lotka–Volterra mass- mass-balance assumptions, is one wherein the action term.

ecosystem is represented by say, a 20 ¥ 20 grid of Thus, Ecosim, which allows users to change the cells with different suitability to the different rates of exchange, allows testing the effect of as- functional groups in the system. Movement rates sumptions about bottom-up vs. top-down control. are assumed symmetrical in all directions around As it turns out, these effects are profound: pure the cell, but are higher in unsuitable habitat. Their top-down control, which is the Lotka–Volterra exact value is not important. The survival of assumption, generates, upon the smallest shock, various groups and their food consumption are violent oscillations such as do not occur in real assumed higher in suitable habitat, but they other- ecosystems. Conversely, under bottom-up control, wise consume prey as they do in Ecopath and depletion of one species, as, for example through Ecosim, as they encounter them within a given fishing, tends to affect the biomass of only that cell. species and less strongly its key prey and predators;

Starting from the Ecopath baseline where func- the system as a whole generally remains unaffect- tional groups are distributed evenly over suitable

ed even when the species in question is one of habitats, Ecospace simulation iterates towards a its major components (the astute reader will note solution wherein the biomass of all functional this to be the unstated assumption behind single- groups is spread over a number of cells, given the species population dynamics). Thus, at least in predation they experience and the density of prey

Chapter 10

organisms they encounter in each cell. The distrib- ution maps thus predicted can be compared with existing distribution maps and inferences drawn about one’s understanding of the ecosystem in question and the functional group they are in. The rich patterns obtained by the application of this approach to a number of Ecopath files, thus turned into spatial models, suggest that the broad pattern of the distribution of aquatic organisms can be straightforwardly simulated (Walters et al. 1998).

One particularly interesting aspect of Ecospace is that it allows for explicit consideration of eco- system effects when evaluating the potential im- pact of Marine Protected Areas (MPA) in a given ecosystem, thus allowing for a transition towards ecosystem-based fisheries management, our last topic.