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Rit Fiskideildar 16 (1999) 295-305 Biological interactions in fish stocks: models and reality Kjartan G. Magnússon Science Institute, University of Iceland Dunhaga 3, IS-107 Reykjavík, Iceland ABSTRACT Three types of biological interactions; predation, competition and cannibalism are discussed in the context of marine ecosystems. Their effects on stock dynamics are considered and the empirical evidence for biological interactions reviewed. The main predictions from various population models which include some of these interactions are discussed and compared to empirical observations of stock dynamics, in order to see how well the predictions accord with observations. Although some limited evidence exists, showing that interactions - predation in particular - can be important, the fact remains that due to the high level of noise in data from marine ecosystems as well as the confounding effects of environmental varibility, it has proved difficult to find evidence demonstrating conclusively that biological interactions play a significant role in regulating stock dynamics. The purpose of large- scale multispecies models incorporating biological interactions is discussed, a range of such models for boreal ecosystems is reviewed and the necessary and desirable features which such models should have are given. Keywords: Predation, competition, cannibalism, multispecies models. INTRODUCTION lakes (Seip 1997), which are relatively constant and predictable compared to for example pelagic marine ecosystems. Nevertheless, the results of Seip (1997), looking at interaction pairs of phytoplankton and zooplankton in a Norwegian lake and attempting to relate observations to prototype predation, competition and mutualism phase-plane diagrams, were less than conclusive. There are essentially three types of interspecies interactions: predation, competition and mutualism. Predation is the one most easily observed and quantified, since consumption rates of one species on another can be observed and calculated from measurements of stomach contents given suitable models of digestion or stomach evacuation. Nevertheless, the effect of Biological interactions in marine ecosystems, between species as well as within species, may have a significant influence on stock dynamics and can contribute to the high variability frequently observed in recruitment and stock sizes. However, it has proved difficult to determine and quantify the dynamical effects of biological interactions since these effects are usually confounded by effects due to environmental variability, the relative importance of the two in determining abundance being the subject of much debate. Effects of biological interaction may be more easily observed and tested in more stable environments, such as inshore benthic ecosystems (Branch et al. 1987) or freshwater Dedicated to Professor Unnsteinn Stefánsson in honour of his contributions to oceonography and education. 295 predation on the dynamics and abundance of the stocks involved is less tangible. Competition is more difficult to observe and empirical verification of its effects is scarce. Mutualism is probably much rarer in marine ecosystems than predation and competition and evidence for it is even more difficult to find. It will therefore not be considered here. Intra-species interactions may take the form of competition for resources – as with competition between species – or cannibalism. Again, empirical evidence for density dependent effects are hard to come by, but cannibalism has been observed in a number of species and can play an important role (Smith and Reay 1991). The effects of biological interactions can be studied in two complimentary ways; by looking for empirical evidence and statistical relationships, and by the investigation of mathematical models. In this article we will consider three types of interactions in turn; i.e. predation, competition and cannibalism, and review, admittedly rather superficially, models and model results and see how they relate to observations of the real world. dependent on capelin abundance is given further support by the observation that total consumption by cod decreases as the consumption of capelin decreases, showing that cod is only partially able to compensate for a decreased availabilty of capelin by switching to other prey types (Magnússon and Pálsson 1991). Mathematical models of populations with predator-prey interactions tend to be of two types: 1. Fairly abstract models where the population sizes are usually modelled by systems of coupled differential equations and general assumptions are made about the nature and form of the interaction of the predator and prey. The qualitative behaviour of these models is usually studied by analytical techniques and computer simulations play a secondary role. 2. Concrete models, often pertaining to particular species and areas, where the various biological processes involved, such as feeding, reproduction, mortality, migration, etc. are modelled explicitly. Such models tend to be very large and data intensive and cannot be studied analytically. Computer simulations are the only option. Predator-prey systems and/or competition systems of the first type have been extensively studied as regards existence of long term equilibrium states and their stability properties, existence of oscillatory solutions, existence of chaotic dynamics and persistence of the system. The main relevance of these studies in understanding actual predator-prey systems is in throwing some light on the qualitative dynamics of such systems, e.g. whether oscillatory behaviour is a common feature and under which conditions is it most likely to occur, which processes and which functional forms tend to be stabilizing and which destabilizing, how the dynamical behaviour (stability or oscillations) depends on the number of predator species and the number of prey species and on the number and strengths of the trophic interactions, and so on. General predator-prey systems with one predator and one prey have been shown to have either a stable equilibrium or stable sustained oscillations under fairly general and reasonable assumptions (May 1972). Furthermore, if there is a stable equilibrium state then it is generally a PREDATION The main emphasis in theoretical and empirical studies of species interactions has been on predation since it is relatively easy to observe, and probably more important than competition. It is usually straightforward to observe and quantify predation using stomach content data, together with a digestion rate model. Mortality rates due to predation can also be calculated using stomach contents, catch-at-age data and/or abundance data; either indirectly as in Multispecies Virtual Population Analysis (Helgason and Gislason 1985) or directly as in Magnússon and Pálsson (1989). However, demonstrating that predation has a measurable and significant effect on stock dynamics and long-term stock sizes is more difficult. Direct empirical evidence is scarce, but there are strong indications from Icelandic waters that the abundance of cod has a significant effect on the population development of shrimp and that the abundance of capelin has a significant effect on individual growth rate of cod (Stefánsson et al. 1998). The hypothesis that cod growth rate is 296 spiral point, i.e. the system will oscillate with decreasing amplitude towards the equilibrium state. Existence of stable sustained oscillations has been demonstrated for a variety of predatorprey models and the existence of chaotic dynamics for Lotka-Volterra type systems with one predator and two prey and for a three species food chain was shown in Klebanoff and Hastings (1994, 1994a). The general conclusion which can be drawn from these theoretical studies is that oscillatory behaviour is a common and indeed almost universal feature of predator-prey models, the oscillations being either decreasing with time or sustained. If the model predicts a stable equilibrium, then the stock sizes will tend towards this equilibrium in an oscillatory manner. For reallife systems, perturbations due to external influence (i.e. environmental) are constantly taking place. Therefore, an otherwise stable system will in general not be in a steady state, i.e. it is constantly being perturbed from its equilibrium state, oscillating back only to be perturbed away once more. Oscillations are therefore predicted to be the “natural state“ of predator-prey systems. It has not been easy to verify these predictions. Oscillations are a common feature of marine fish stocks, but it is difficult to separate the effects of biological interactions and environmental variability. Fairly simple predator-prey models with one predator and two prey species can predict the suppression of one of the prey species. A predator and a prey species can coexist in a stable long-term steady state, but the presence of a second prey species may disrupt this co-existence and result in the suppression of the original prey species, since a high predator abundance can be maintained due to the alternative food source. Some examples of this phenomenon exist for terrestrial mammals (e.g. wolf-caribou-moose, lynx-snowshoe hare-arctic hare, see Bergerud (1983)), but no definite cases are known for marine ecosystems. However, the cod-capelinshrimp complex in Icelandic waters appears to be a possible candidate. The purpose of theoretical models is to gain some insight into the qualitative dynamics of predator-prey systems. However, it is usually only possible to draw general conclusions and it is not easy to relate such models to specific ecosystems. Large-scale models, aiming for more “ecological and biological realism“, have therefore been developed to deal with a variety of situations and areas, modelling the various processes – biological and environmental – which are thought to be important, e.g. migration, recruitment, predation etc., explicitly. Submodels of these processes are combined to form a large-scale model representing the ecosystem. Such models are generally termed multispecies models, but usually the primary interaction between species is via predation. The purpose of multispecies modelling is manifold: 1. As a tool for formal testing of whether or not certain interactions or effects exist. Formal statistical testing of the presence of interactions and effects involves estimating parameters, carrying out sensitivity studies and comparing log likelihood values (in order to see if the fit is improved). Thus, some idea of the importance of various features (such as predator-prey relationships, environmental conditions, area structure, variable migration rates etc.) can be obtained. 2. As a simulation tool to answer “what if“ questions and to provide insight into the system. The model should be able to reproduce observed time series of variables deemed to be of importance. This does not mean that large-scale multispecies models are to be regarded as a “true“ representation of the real system. Many such models have sufficient degrees of freedom to be able to reproduce most time series by selecting appropriate parameter values. However, by a suitable parameterization of the model and estimating parameters in a statistically sound manner, some degree of confidence may be obtained that the model is a reasonable representation of the actual system. 3. To obtain parameter estimates which can be used as input in other management procedures or to provide direct or indirect management advice. Such models will in general be a very simplified representation of the real world with few parameters to estimate. 4. As a system model (operating model) for use as a representation of the real system. This type is used to generate data for testing mana- 297 gement procedures. This has been done by the Scientific Committee of the International Whaling Commission to test proposed management procedures (Kirkwood, 1992). The management procedures must be tested under a variety of assumptions about the various processes modelled, and it is therefore not necessary to get the formulation and parameter values in the processes precisely right. The model must necessarily include a stochastic component in the data-generating procedure. Several multispecies models have been developed in the past two decades or so. The models mentioned here are primarily those with some applicability to Arcto-boreal regions. MSVPA (Multi Species Virtual Population Analysis) was developed in the early eighties (Helgason and Gislason 1985). The main purpose was to calculate predation mortalities in a VPA-like manner, in addition to the fishing mortalities as obtained in single species VPA, based on formulations by Anderson and Ursin (1977). MSVPA can also be used in a forward mode (when it is referred to as MSFOR) to simulate the effects of changes in for example mesh size, effort etc. Predation mortalities are modelled in MSVPA but feeding rates and predator growth are taken to be constant, which is an unrealistic assumption for Arcto-boreal systems. In its present form, MSVPA does not include area structure and migration, and in fact migration may be difficult to model backwards in time. The continuum model of Reed and Balchen (1982) is probably the first attempt to construct an ecological model of an Arcto-boreal system. It includes many of the features required for a multispecies model of such a system, that is predation – on capelin by cod and marine mammals- and area structure, which is of fundamental importance in Arcto-boreal models. In the MULTSPEC model (Bogstad et al. 1997), developed at the Institute of Marine Research in Bergen, Norway, area structure and migrations are considered explicitly and feeding rates are variable, depending on total food abundance according to formulations adapted from Anderson and Ursin (1977). The Arcto-boreal model BORMICON (BORreal MIgration and CONsumption) was developed at the Icelandic Marine Research Institute (Stefánsson and Pálsson 1997). This model relies to some degree on MULTSPEC, but has the advantage of being more recent and therefore being coded using more recent programming methodology and making use of the experience gained in the development of MULTSPEC. BORMICON is more general and more flexible than MULTSPEC, for example as regards components included in the model, types of data which can be utilized and likelihood functions. The ECOPATH and ECOSIM models (Walters et al. 1997) consider all components of the ecosystem (not just a selection as for example MULTSPEC) in a holistic way. The former is a stationary model. It sets up mass balance equations for the flow between the various components of the system. On the other hand, ECOSIM is a dynamic model which replaces the mass-balance equations by sets of differential equations for the various components. The equilibrium assumptions of ECOPATH are used to obtain values for some of the parameters used in ECOSIM. Values of other parameters are basically guesswork. An attractive feature of both models is that the ecosystem is considered as a whole and, furthermore, that they are not too complex in the sense that parameter values can in many situations be obtained and simulations carried out. ECOPATH has in fact been used on some Arctoboreal systems such as in the Bering Sea and Icelandic waters. However, it is not statistically based and the empirical foundation for many parameter values is weak. The ECOSIM model is only designed to answer “what if“-questions, such as what happens if effort directed towards one group of species is varied. Unlike MULTSPEC or BORMICON, these models are not able to give parameter estimates or to test for the presence of effects or interactions. The ecological model for the Barents Sea, being developed at the University of Bergen, Norway by Giske and others, also deserves a mention (Giske et al. 1998). The approach taken there is quite different from that taken in MULTSPEC, in that the spatial distribution and behaviour of cod and capelin is predicted using dynamic programming (and other methods) to optimize fitness functions. Interactions between cod and capelin are included in the model via spatial overlap. Other models have been designed for more re- 298 stricted situations, e.g. a model of cod-capelin interactions in Icelandic waters (Magnússon and Pálsson 1991) and a simulation model for codcapelin-shrimp interactions based on statistically obtained empirical relationships (Daníelsson et al. 1997). There are some notable differences between Arcto-boreal systems and temperate systems. The former have fewer biological components, a large part of the diet consists of a few key prey species (in particular capelin) and the reservoir of other food is probably smaller than in temperate systems, such as the North Sea where MSVPA has found its primary application. Thus “other food“, as defined in the MSVPA and acts as a buffer to ensure that fish always obtain the required amount of food, is only available to a much lesser extent in boreal systems. This means that individual consumption is more variable and, consequently, so is individual growth. Another important difference between the two types of systems is the variability in the environment, which is much greater in Arcto-boreal systems. This entails the necessity of including some environmental variables, temperature being the minimum requirement. Initially, the values of these variables may not be modelled, but the values read from an external file. In general, the number of fleets and their diversity is smaller in Arcto-boreal systems. Modelling the fishing operations should therefore be easier and, in addition, management strategies easier to implement since there are fewer participants. There are a number of features and components which it is necessary or desirable to include in a simulation model of an Arcto - boreal marine ecosystem (Stefánsson and Pálsson 1998): 1. Variable environment (e.g. temperature, nutrients, primary production) 2. Components: Fish predators (e.g. cod, herring), prey (e.g. capelin, herring, shrimp), apex predators (marine mammals and man). 3. Spatial structure and hence variable overlap between species 4. Relatively fine temporal structure (e.g. time interval of one month), as things can happen fast in time and space (e.g. capelin migration) 5. Stock structure (e.g. age, length, maturity) 6. Sub-models a) Predation mortalites dependent on predator abundance, prey abundance, abundance of other prey and on spatial and temporal overlap. The form of the relationship between prey abundance and predation rate is of major importance in models as in real life: a relationship where the mortality rate due to predation decreases with decreasing prey abundance at low prey densities – the so-called type III functional feeding response (Holling 1959) – will in general have a stabilizing effect on the predatorprey dynamics, whereas the opposite is the case for a type II relationship (predation mortality rate increases with decreasing prey abundance at all prey densities). The dynamics of both predator and prey may therefore be substantially different depending on the functional relationships used. b) Variable growth rates depending on the availability of food (prey abundance for fish predators, plankton density for prey and on environmental conditions). c) Migration (and feeding movements). A submodel of migration can for example be based on transition matrices (Bogstad et al. 1997, Stefánsson and Pálsson 1997) or partial differential equations (Reed and Balchen 1982). d) Recruitment as a function of environmental conditions, size and composition of the spawning stock and might include cannibalism. 7. Parameter estimation (with a flexible likelihood function, flexibility with respect to the incorporation of a number of available data sources) and the ability to test the significance of effects such as interactions. An interesting result from studies of multispecies models is the demonstration that sometimes changes in one component in the system can lead to changes in the other components which are counter-intuitive. An example is provided by the model of fur seals and hake off South Africa (Punt 1994). It turns out that if hake is modelled as one species (it is managed as one species at present) then a seal cull would lead to an increased stock of hake. However, if hake is modelled as two species, the larger preying on the smaller (which is in fact the case) then predatorprey interactions between the two species of hake 299 together with differential predation rates by seals on the two species, could mean that the result of a seal cull is a smaller hake stock. This is contrary to what might be expected. Bogstad et al. (1997) provide another example of this phenomenon. It is well known that minke whales consume capelin, so it is reasonable to expect that an increased whale stock would lead to a smaller capelin stock. In fact, model results indicate that the opposite might be the case. This is due to strong predator-prey interactions between herring and capelin and the fact that herring is also preyed on by whales. An increased whale stock leads to increased whale predation on herring which in turn reduces herring predation on juvenile capelin. A third example is the effect of mesh size changes on long-term yield. Single species models generally predict that a higher yield will result from an increase in mesh size, but in multispecies models the opposite can occur. The reason is that the abundance of predators may increase by increasing the mesh size, leading to higher predation mortalities especially on younger fish (both from cannibalism and predation by other species). This will in turn lead to lower stock sizes and hence to lower yields. The real possibility of such effects has been demonstrated using the MSVPA/MSFOR model for the North Sea (Pope 1991). From a mathematical point of view, these results are not very surprising for a system with many interacting variables, but they nevertheless draw attention to the fact that ecosystems are very complex and even the direction of changes resulting from certain actions is not always easy to predict. Multispecies models are therefore of considerable value in demonstrating how ecosystems can behave in ways which are both complex and at times counter-intuitive. It is still too early to pass judgement on the success or otherwise of large-scale multispecies/ ecosystem models. They have in many cases been shown to be fairly successful in reproducing historical time series such as weights-at-age for Barents Sea cod (Anon. 1996) and early computer runs of BORMICON are promising (Stefánsson and Pálsson 1997). However, formal statistical comparisons between retrospective predictions from single species models and multi- species models – e.g. running both models using historical data such as catch and recruitment series, and comparing the observed time series of other variables such as weights-at-age and stock numbers with the predictions from the two models, thereby testing rigorously for the presence of predation effects – will be a real test of the importance of multispecies effects as well as of the usefulness of multispecies models. COMPETITION A range of mathematical models have been constructed to describe inter-species competition, ranging from simple ordinary differential equations models of the Lotka-Volterra type to more elaborate age- and/or size-structured models. A common feature of these models is the existence of multiple steady states with one or more species at low stock levels. A change in the abundance of one species due to external effects such as changing catch rates or different environmental conditions can result in a transition to a different steady state. Such transitions in a competition system to a state with different stock levels, with one stock significantly lower and another stock significantly higher than before, have been termed competitive species replacements. In order to investigate whether these model predictions have been observed in real ecosystems and if there is any empirical evidence for species replacements, one should look for cases where a species has apparently filled an ecological niche which has become vacant due to a decrease in a competing species. The potential examples are generally of pelagic species. The best known examples are the pilchard-anchovy pairs in various parts of the world, but other possible cases are herring-blue whiting and herring-capelin in the North-Atlantic, and herringAtlantic mackerel off New England and the Canadian Maritime Provinces (Skud 1982). The question of whether these and other pelagic fish species compete with one another and whether the reduction of one species led to its replacement by another has attracted considerable attention. However, pelagic fish occupy regions where environmental fluctuations are high and therefore evidence for such inter-specific competition has proved elusive. What little evi- 300 dence there is, is circumstantial. Stocks of California pilchard, Peruvian pilchard, Far Eastern pilchard, and South African pilchard have all collapsed and have been followed by apparent increases in the size of anchovy stocks. This has led to speculations that the increases in anchovy stocks were due to reduced competition by pilchard (Kawasaki 1983). The possible competitive replacement of South African pilchard by anchovy in the Benguela ecosystems off Southern Africa has been extensively studied. Models of this interaction show that a decrease in one stock is followed by an increase in the other, either in an alternating way (Silvert and Crawford 1988), or the anchovy stock increasing when the pilchard stock was reduced by overfishing, and pilchard again becoming dominant when the fishing pressure on it is reduced (Korrubel 1992). However, data supporting the theory of competitive species replacement is limited. Admittedly, there is a strong negative relationship between the catches of the two species, but the interpretation of this is confounded by a number of other factors (Branch et al. 1987). Furthermore, the estimates of anchovy biomass show it to have been fairly constant after the collapse of the pilchard stock and far from replacing the lost biomass of pilchard. In this case, the suggestion of competitive replacement is therefore ambiguous and the supposed replacement of pilchard by anchovy could simply be a reflection of the collapse of the former species due to overfishing and the subsequent switch of effort to the latter. Evidence of replacement is even weaker in most of the other possible cases. A review of the literature by Daan (1980) identified only one possible example of species replacement, i.e. in the Californian anchovy-pilchard pair, and even this is uncertain. However, the lack of evidence does not imply that competition between species is non-existent, only that evidence for it is hard to find, perhaps because the effects of environmental variability dominate and the effects of competition are of secondary importance (Branch et al. 1987). The possibility of competition for food between herring and capelin in northern waters has been suggested (Nikolsky and Radakov 1968). Based on commercial catches, it might be hypo- thesized that competitive species replacement took place in Icelandic waters with the capelin stock increasing following the collapse of the herring stock in the 1960’s. There is however, no evidence to support this hypothesis since the size of the capelin stock prior to the collapse of herring is not known. The stock of capelin may in fact always have been large and there are indications of large stock sizes of capelin earlier in this century (Hjálmar Vilhjálmsson pers. comm). The possible replacement of the Atlanto-Scandian herring by blue whiting is more plausible, but the evidence for that is circumstantial (Daan, 1980, Hjálmar Vilhjálmsson pers. comm.). The competition between herring and capelin in the Barents Sea has been suggested, i.e. grazing by juvenile herring on low stocks of zooplankton in the mid-1980’s may have caused food shortages for capelin (Skjoldal and Rey 1989), and the reduced food competition due to a low herring stock in the 1970’s may have contributed to the high stock of capelin in this period (Dragesund and Gjøsæter 1988). However, this is highly speculative and the real effect of herring on capelin dynamics may in fact be through predation by juvenile herring on capelin larvae and juveniles (Hamre and Hartlebakk 1998). It would therefore appear that the predictions of competition models are not substantiated by observations. There seems to be little direct evidence for inter-species competition among fish. There are some suggestions or indications, based either on general considerations such as two species occupying a similar trophic niche or on changes in commercial catches , i.e. a decline in the catch of one species was followed by an increase in the catch of the other. The more obvious explanation for the changes in catches is simply a change in the relative fishing effort due to one of the species being reduced by overfishing. However, inter-species competition may be observed indirectly by responses to changing environmental conditions. A dominant (i.e. more abundant) species may respond positively to environmental conditions such as temperature, whereas the subordinate species responds negatively. The negative response of the subordinate species may be a reaction to a change in the abundance of the dominant species, and hence increased competitive pressure, rather 301 than a direct effect of the physical environment. The response might othervise have been positive in the absence of the dominant species. The abundance of the subordinate species is thus controlled by the dominant species. This behaviour is easily described and “explained“ by a competition model consisting of two ordinary differential equations. Cases where the response to changing environmental conditions is positive when a species is dominant and negative when it is subordinate would strongly indicate some sort of competition or interaction. Examples of this behaviour are found in the herring-mackerel pair off the east coast of USA and Canada as well as in sardines and anchovies off California (Skud 1982). Similar phenomena have been observed in freshwater species. Occasionally a negative correlation between the abundance of two candidate competing species is observed. Two “competing“ species may interact in other ways and the important interaction, as well as the explanation for a negative correlation in abundance, may be predation rather than competition. Cases in point are predation of juvenile herring on capelin larvae mentioned earlier and predation by pilchard and anchovy on each other’s eggs and larvae. tant effect on the dynamics of the cod stock. For example, there is a significant negative relationship – probably due to cannibalism – between recruitment in Icelandic cod and the abundance of immature cod (Bogstad et al. 1994) and including cannibalism gives a better fit between abundance indices from surveys and the VPA estimates for cod age groups 1-3 in the Barents Sea (Tjelmeland and Bogstad 1998). It is therefore believed that cannibalism is sufficiently important to be taken into consideration in the assessment and management of the Barents Sea cod stock (Anon. 1996a) and it is suggested that cannibalism is a factor contributing to the observed fluctuations in recruitment of three year old cod (Ulltang 1996; Moxnes 1998). Some estimates of mortality rates due to cannibalism have been obtained for Icelandic waters and for the Barents Sea. Stefánsson et al. (1997) gave a point estimate of 0.19 for the annual mortality rate of 1 year old cod in Icelandic waters due to cannibalism. By relating observed recruitment for Iceland cod to the abundance of immature cod, Bogstad et al. (1994) estimated that the value of the cannibalism mortality rate on 0-2 year old cod is 0.71 on the average over the period 1970-1991, i.e. an average annual value of 0.24. Estimates for the Barents Sea are even higher (B. Bogstad, pers. comm.) and the mortality rate is probably negatively related to the abundance of capelin, the main prey of cod. In their analysis of data up to 1992, Bogstad et al. (1994) found no evidence that cod cannibalism decreased with increasing biomass of capelin. However, using more recent data, Bogstad has found strong indications that increased capelin biomass has a negative effect on cannibalism in cod (Bogstad, pers. comm.). Theoretical studies of population models have shown that cannibalism can have a considerable effect on population structure and dynamics. This effect can even be positive. For example, Kohlmeier and Ebenhöh (1995) have shown that cannibalism by the predator can in some cases lead to a higher long term predator stock size. Furthermore, cannibalism can enable a population to survive when food for the adults is scarce – the so-called life boat effect (van der Bosch et al. 1988). CANNIBALISM Cannibalism has been observed in a great variety of fish species. It is common among piscivores and can make a significant contribution to the diet (Smith and Reay 1991). Rates of losses due to cannibalism can sometimes be very high, e.g. 60% annual mortality of the 0+ age group has been observed in walleye pollock in the Eastern Bering Sea (Dwyer et al. 1987). It has been demonstrated, that adult Atlantic cod eat large numbers of their young, especially those of ages 0 to 2 years (Bogstad et al. 1994), and that the frequency of occurrence of cannibalism in the Barents Sea increases with the abundance of juvenile cod. Although the contribution of cannibalism to the diet of Atlantic cod is fairly small – it does not exceed 9% on the average, even for the largest cod, and is somewhat higher in the Barents Sea than off Iceland – (Bogstad et al. 1994), it can nevertheless have an impor- 302 It has been shown that cannibalism can in some cases have a stabilizing effect on a predator – prey system. Kohlmeier and Ebenhöh (1995) studied a two-dimensional predator-prey system of a Lotka-Volterra type with predator satiation, where cannibalism is incorporated by letting the total food supply for the predator be a weighted sum of the prey biomass and the predator biomass. They show that cannibalism can stabilize a predator-prey system by eliminating cycles that can otherwise occur in the absence of cannibalism. These cycles are caused by the interaction between prey carrying capacity and predator satiation. Recently, van den Bosch and Gabriel (1997) showed that cannibalism can stabilize a predator-prey system where the oscillations are due to age structure. Their model is essentially a system of two differential equations for the adult predator population and the prey population, with delays in the equation for the former. This system can oscillate due to the delays, but the stability region (in a two dimensional parameter space) is enlarged by increasing the “cannibalism pressure“. The results of those two papers lead van den Bosch and Gabriel to conclude that „In predator – prey systems, cannibalism by predators can stabilize both externally generated (consumer-resource) as well as internally generated (age-structure) fluctuations.“ There are, however, exceptions to this and in Magnússon (1999) an example is given of a predator-prey system where cannibalism can lead to oscillations in both predator and prey abundance in a system which is otherwise stable. It is shown that sustained oscillations are not possible without a high juvenile mortality rate and low recruitment rate. For cod, the mortality rate for juveniles is likely to be high, in particular under harvesting, and the age at maturation of 6-7 years is high. Thus, only a small portion of the total juvenile population will be recruited in any given year and the recruitment rate to the mature population is therefore fairly low. The necessary conditions for sustained oscillations are therefore likely to be satisfied for the cannibalistic predator-prey system consisting of cod and capelin, but it is not possible at this stage to draw any firm conclusions whether cannibalism might contribute to the fluctuations that characterize the dynamics of the stocks of cod and capelin in the Atlantic. Both stocks are heavily harvested, also at the juvenile stage in the case of cod. It is therefore worth noting that harvesting juvenile fish will make oscillations more likely, since not only does harvesting increase the juvenile mortality rate but also decreases recruitment rate since a smaller fraction of the total juvenile stock will survive to reach the age of maturity. The main result in Magnússon (1999) is that sustained oscillations are not possible for low levels of cannibalism, but at sufficiently high levels oscillations can set in. Therefore, cannibalism can be a destabilizing force in a predator-prey system. This is contrary to the results of Kohlmeier and Ebenhöh (1995) and van den Bosch and Gabriel (1997). The main reasons for this discrepancy are the following: In the Kohlmeier and Ebenhöh model, predators are not separated into juveniles and adults. All individuals are therefore vulnerable to cannibalism and all individuals indulge in cannibalism. The model of van den Bosch and Gabriel is fully age structured, but the only effect of cannibalism is an increased mortality rate of juveniles. The adults do not benefit in terms of increased growth rates. The conversion efficiency of juvenile biomass to adult biomass via cannibalism is therefore zero. In view of this, it can be postulated that all of the following features are necessary for cannibalism to be destabilizing: 1. Predator population is separated into adults and juveniles, with adults feeding on juveniles. 2. Low recruitment rates to the adult population, e.g. due to a high age at maturity and/or high mortality of juveniles. 3. Cannibalism leads to increased growth rates of adults as well as increased mortality rates of juveniles. However, the effect of cannibalism on the dynamics of predator-prey systems are not straightforward and a number of other factors can be important. Cycles and oscillations can occur in predator-prey systems without cannibalism and can indeed also be caused by environmental fluctuations. The main issue is however that cannibalism may be yet another factor contributing to the variability of fish stocks. 303 SUMMARY REFERENCES. We have reviewed superficially some of the dynamical models used to describe interactions between fish species. Fundamental parts of the models are the functional relationships between the various components, for example those used to describe how the rate of predation depends on prey abundance, predator abundance, abundance of other prey and so on. This important topic has hardly been touched upon here, nor has density dependence in recruitment, mortality rates, growth, etc. been addressed, although such density dependence would certainly classify as biological interaction. We have mentioned the main results of simple generic predator-prey models and competition models as well as models of cannibalism. The main use of such models is in showing how these interactions can affect the qualitative dynamical behaviour of the stock sizes under consideration. It has proved difficult to verify the predictions of these models, partly due to poor and limited data in some cases but mainly because of the confounding effects of environmental variability. In fact, effects of biological interactions on the stocks may often become swamped by effects caused by variations in the physical environment. It is, for example, not easy to determine whether observed fluctuations and cycles in stock abundance are due to predator-prey interactions, cannibalism or environmental cycles/ fluctuations. While all three of these variables may contribute, one factor may be dominant. Similarly, it has not been easy to find evidence of competition between species and species replacement as predicted by many models. It is one of the major future tasks in marine research to identify and quantify biological interactions and assess their importance relative to the influence of the physical environment. There are a number of ways whereby this can be addressed and using large-scale multispecies models to test statistically for interactions may be a promising avenue of investigation. These large multispecies models have primarily been used as research tools, essentially to reproduce observed time series and to answer “what if“ questions. Demonstrations of their full validity and usefulness are yet to come. 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