Multispecies Models Relevant to Management of Living Resources
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ICES mar. Sei. Symp., 193: 1. 1991 Multispecies Models Relevant to Management of Living Resources Preface Scientific quality is undoubtedly the most important bers of the Steering Committee. In addition, they would aspect of a contribution to a symposium, but the value of like to thank the referees of the papers selected for a contribution is also greatly heightened by a vivid and publication for their invaluable contribution and ex stirring presentation, and the discussion it stimulates. In pertise in formulating many suggestions for improve order to underline the importance of the latter in com ment. It seems only appropriate that the names of these municating scientific results, it was decided to give scientists be listed here: R. S. Bailey, N. J. Bax, W. awards for the “best presentations”. On the basis of a Brugge, S. Clark, E. B. Cohen, W. Dekker, W. Gabriel, plenary vote, the awards were presented to H. Gislason S. Garcia, H. Gislason, J. Gulland, T. Helgason, J. R. (paper) and to M. Tasker, R. Furness, M. Harris, and G. Hislop, M. Holden, E. Houde, G. R. Lilly, J. R. S. Bailey (poster) for their excellent use of audio McGlade, G. Magnusson, R. Marasco, B. M. van der visual aids. Meer, S. Mehl, B. Mesnil, S. A. Murawski, W. J. The Co-conveners would like to express their grati Overholtz, O. K. Pâlsson, D. Pauly, E. K. Pikitch, J. G. tude to J. Harwood (UK), A. Laurec (France), J. G. Pope, J. E. Powers, J. C. Rice, A. Rosenberg, B. J. Pope (UK), and H. Sparholt (Denmark), who put great Rothschild, K. J. Sainsbury, F. M. Serchuk, T. Smith, effort into the organization of the Symposium as mem H. Sparholt, W. Stobo, K. J. Sullivan, and C. Tucker. 1 I. Multispecies virtual population analysis ICES mar. Sei. Symp., 193: 12-21. 1991 Introduction to multispecies virtual population analysis Per Sparre Sparre, P. 1991. Introduction to multispecies virtual population analysis. - ICES mar. Sei. Symp., 193: 12-21. Starting from single-species virtual population analysis, the basic features of multi species virtual population analysis are introduced, with emphasis on the mathematical description and computational procedures. Per Sparre: Marine Resources Service, Food and Agriculture Organization, Via delle Terme di Caracalla, 00100 Rome, Italy. Introduction C = F x N Multispecies virtual population analysis (MSVPA) has where C is the catch in numbers from a cohort, F is the been developed largely as a joint venture within the fishing mortality coefficient, and N is the average num ICES Ad hoc Multispecies Working Group (Anon., ber of survivors from the cohort. 1984a, b, 1986, 1987, 1988). The method integrates the The same mathematical expression applies in the case suitability concept of Andersen and Ursin (1977) for of the number of deaths caused by natural causes (D), describing predator-prey relationships with traditional i.e. all causes other than fishing (predation, disease, virtual population analysis (VPA) as developed by Fry starvation, spawning stress, old age, parasites, etc.) (1949) and Gulland (1965). The first steps in this direc tion were taken by Helgason and Gislason (1979), Pope D = M x N (1979), and Sparre (1980). For a historic review of the where M is the natural mortality coefficient. Figure 1 development of these methods the reader is referred to illustrates the flow of fish (number of fish) as described Pope (1991). by Baranov’s equation. The N-boxes symbolize the MSVPA takes into account predation among number of survivors on the birthday of the cohort, i.e. exploited fish populations. Essentially, it is a number- the number at the beginning of a period. Boxes C and D crunching exercise to estimate fishing and predation symbolize the losses in numbers caused by fishing and mortalities by year and age group simultaneously for a number of species on the basis of catch-at-age data and stomach-content data by age group of predator and prey. This contribution aims at introducing the basic fea tures of this estimation technique, with particular em phasis on the mathematical description and computa N, tional procedures. For more details on VPA, see Beyer and Sparre (1983), Jones (1984), and Sparre et al. (1989). Beyer and Sparre (1983) introduce MSVPA in connection with VPA. c, Single-species VPA VIRTUAL POPULATION The single-species VPA is derived from Baranov’s catch Figure I. Illustration of the model underlying single-species equation (1918) VPA. 12 natural mortality, respectively, during each year of life. is believed to be the dominating source of mortality Boxes D and C are the accumulated numbers of deaths compared to all other sources, including fishing. This during the year and are conceptually different from the idea was inspired by quantitative findings on the con N-boxes. The “virtual population” is the C-boxes in sumption of some predatory fish, notably, North Sea cod Figure 1, that is, the part of the population one can (Gadus morhua) (Daan, 1973, 1975). It was therefore actually see when visiting the fishing harbours. By esti natural to concentrate on the predation mortality when mating the C’s from sampling the commercial landings, searching for a solution to the “M problem”. and assuming that M is known, N, D, and F can be calculated. With this technique, known as VPA (virtual population analysis), it can be calculated how many fish Andersen and Ursin’s model there must have been in the sea to account for the Andersen and Ursin (1977) developed the basic concep number caught. tual framework for predation which allowed extension Fry (1949) introduced the concept of "virtual popu of VPA to MSVPA. This framework was actually em lation” and derived a method for estimating exploitation bedded in a general and comprehensive model of an rate which is virtually the same as that presented by exploited marine ecosystem. Gulland (1965) - the method usually referred to as Although a valuable model, it was not really “oper “V PA” . ational” because of the large number of parameters One feature to be noted here is that in single species which were difficult to estimate. But, by removing a VPA each cohort can be treated separately. The results number of components from their model and by simpli of one cohort have no influence on the results of the fying the remaining part of it, the bases of MSVPA are others. As will be shown later this is not true for revealed. MSVPA. Four alternative reductions of the Andersen and Single species VPA requires the natural mortality Ursin model (AU model) to an “operational model” coefficient as input. The VPA equations link F and M in have been suggested by Helgason and Gislason (1979), a functional relationship, so if M is overestimated the Gislason and Helgason (1985), Pope (1979), Sparre stock numbers (N) will also be overestimated and the (1980), and Ursin (in Sparre, 1980). The following fishing mortalities (F) underestimated, and vice versa. descriptions of the AU model refer to the predator-prey The natural mortality coefficient is difficult to esti relationship, which I consider the cornerstone of the mate for exploited fish stocks because the number of fish Andersen and Ursin (1977) model, and which has served dying from natural causes (D-boxes in Figure 1) is as the basis for the development of the MSVPA version difficult to observe. The traditional approach is to make of this model. a “qualified guess” for M. The flow of biomass between components of the For a stock assumed to be in an equilibrium situation, ecosystem is illustrated in Figure 2. The components of the total mortality Z = F + M can be estimated from age-frequency samples. If the FISHERY stock is unexploited, then F = 0 and consequently M = Z. Thus, in this case there is a simple way of estimating M. Mackerel Haddock However, important fish stocks are usually exploited and not in equilibrium. Although we may be able to estimate Z for exploited stocks, there is no reliable way Herring of estimating the split into M and F for individual age groups. Several attempts to devise simple methods of estimating M, based on general knowledge about the Whiting physiology and behaviour of a fish species, have been suggested. They are all indirect methods and are based on assumptions which are questionable. For a further Saithe discussion of these topics the reader is referred to Chapters 4 and 5 in Sparre et al. (1989). Natural mortality occurs through a variety of causes, e.g. predation, diseases, parasites. In principle, the Other Food number of fish dying from predation by fish can be sampled by analysing the contents of stomachs of preda Figure 2. Flow chart of biomass between components in the AU model for the North Sea considered by the ICES multi tory fish. For young (small) fish the predation mortality species working group. 13 body growth body growth body growth and Fishery recruitment Fishery recruitment Fishery recruitment Other food Other food Other food Mackerel Mackerel Mackerel Saithe Saithe Saithe Cod Whiting Whiting Whiting Haddock Haddock H a ddock Herring Herring Herring Sprat Norway Pout < Norway Pout Norway Pout Sand Eel Sand Eel Sand Eel 1981 1982 1983 Figure 3. Flow of population numbers along the time axis in the AU model. the North Sea considered by the ICES Multispecies and Working Group (Anon., 1984b, 1986, 1987) arc used as an example. Some stocks are predators only, some are D = (M l + M2) X N prey only, and some are both predators and prey. This classification was based on the results from stomach In MSVPA the predation mortality (M2) is estimated content examinations (Anon., 1984a). In addition to within the model whereas Ml still has to be guessed just exploited fish species, a category “other food” is con as M is in single species VPA.