Ecosystem Approaches for Fisheries Management, Part 7

Since 1981, the Benguela Ecology Programme has aimed at increasing ecological understanding of a large marine upwelling region of importance to fisheries. In an attempt to summarize results of this program, experts brought together both published and unpublished data at a workshop held in Cape Town in 1989. This was in an attempt to construct simple input-output carbon budgets of the Northern and Southern Benguela ecosystems. Based on these results, and together with more recently published data, ECOPATH models of the two systems during the 1980s have been prepared. In the Northern Benguela system, the dominant pelagic fish species during the 1980s was horse mackerel, whereas in the Southern Benguela, anchovy were dominant. In both systems, sardine were at low levels and hake were commercially important. These, together with different structures in the zooplankton communities and the different fishing levels in the respective systems, are used as a basis upon which to compare the trophic functioning of the two parts of the Benguela ecosystem during the period 1980-1989. Preliminary EcoSim analysis highlights differences in the impact of fisheries on selected groups in the two systems. 528 Shannon & Jarre-Teichmann — Trophic Flows in Upwelling Systems Introduction There are four major marine upwelling systems in the world (Fig. 1). The Benguela upwelling system is subdivided into relatively distinct upwelling systems: the Northern Benguela off Namibia, and the Southern Benguela off South Africa. The trophic functioning of the Northern Benguela system has been examined in two periods, namely 1971-1977 and 1978-1983 (JarreTeichmann et al. 1998; Jarre-Teichmann and Christensen 1998a, 1998b). In addition, an ECOPATH model of the Northern Benguela has also been developed for the 1990s (Heymans 1996). Preliminary models of trophic flows in both the Northern (Shannon and Jarre-Teichmann 1999) and Southern (Jarre-Teichmann et al. 1998) Benguela systems during the 1980s have been constructed. The present paper serves as a preliminary comparison of the trophic functioning of the upwelling ecosystems of the Northern and Southern Benguela during this decade. The paper aims to stimulate and encourage further revision of the data and models, so that more detailed interdecadal and intersystem comparisons can be made. It is planned that this work will form part of a fuller comparison of the trophic functioning of both the Northern and Southern Benguela ecosystems during periods dominated by different species. Using an approach such as this, it would be possible to compare the way in which harvest and conservation strategies impact the northern and southern systems under different species dominance regimes. This would be of benefit to both South Africa and Namibia, particularly as the fisheries have been managed in different ways in the two systems over the last few decades. Researchers and managers in each system could learn from the other, and both could work together towards improving fisheries management and conservation in the future. Methods Trophic flow budgets for the Northern and Southern Benguela ecosystems during the 1980s were constructed using ECOPATH. The latter is a widely used ecosystem modeling tool that has been under development since 1987 by the International Centre for Living Aquatic Resources Management (ICLARM). Christensen and Pauly (1992, 1995) describe the ECOPATH model in detail. ECOPATH is based on a model by J.J. Polovina of the U.S. National Marine Fisheries Service, Honolulu, Hawaii (Polovina 1984). The steady state approach was recently extended to a dynamic simulation tool called ECOSIM by scientists of the Fisheries Centre, University of British Columbia, Canada (Walters et al. 1997). At a workshop held in 1989, experts on the different species groups in the Benguela upwelling region brought together both published and unpublished data to construct a simple input-output carbon budget. These data, together with those which have since become available, have been used to construct preliminary Ecopath models of both the Southern (JarreEcosystem Approaches for Fisheries Management 529 Teichmann et al. 1998) and the Northern (Shannon and Jarre-Teichmann 1999) Benguela upwelling systems. The model of the Northern Benguela comprises the shelf region to about 500 m depth, extends from 15oS to 29oS and covers an area of 179,000 km2. The model of the Southern Benguela comprises the shelf region to about 500 m depth, extends from 29oS, around the southern tip of Africa and eastwards to 28oE, covering an area of 220,000 km2. The Southern Benguela model, presented by JarreTeichmann et al. (1998), has been slightly modified to separate some components for clarity, and to incorporate some new hake data, which only recently became available. Parameters used are tabulated in Shannon et al. (1999). The two systems are compared in terms of flow diagrams, primary system statistics, relative consumption by components, primary production equivalents, and so on. In addition, analyses such as mixed trophic impact assessment (Ulanowicz and Puccia 1990) are used to highlight overall competition between species and the effects of species on others within an ecosystem. ECOSIM has only been released in an alpha form at this stage. We show here how it can be used to perform preliminary analyses of the impacts of changing fishing mortality in the two systems. All settings were default, with interactions assumed to be of the mixed control type (0.5). Once thorough testing and validating of ECOSIM have been done, this work will be taken further. Figure 1. Map showing the four major upwelling regions of the world, with the inset showing the Northern and Southern Benguela systems (after JarreTeichman et al. 1998). 530 Shannon & Jarre-Teichmann — Trophic Flows in Upwelling Systems Results and Discussion Northern Benguela Model In the Northern Benguela, there was heavy fishing on both sardine (Sardinops sagax) and hake (Merluccius capensis and M. paradoxus) during the 1970s. Sardine, the dominant pelagic species between 1971 and 1977 (Jarre-Teichmann and Christensen 1998a), was severely reduced from 1.5 million t to 134,000 t in the 1980s. Anchovy (Engraulis capensis) was also less abundant, decreasing from 593,000 t in the 1970s to 252,000 t in the 1980s. The dominant pelagic species was horse mackerel (Trachurus trachurus capensis), at 2.5 million t (Shannon and Jarre-Teichmann 1999). Biomass of hake (both species combined) was 1.3 million t in the 1980s. In order to balance the model, it was necessary to estimate the biomass of some groups, so that there was sufficient to support the consumption of other predatory groups. For example, the model required that biomass of demersal fish was half that of hake, an estimate that seemed reasonable (Shannon and Jarre-Teichmann 1999). Hewitson and Cruickank’s (1993) estimate of biomass of pelagic goby (Sufflogobius bibarbatus) was doubled in the model. The proportion of cephalopods in the diets of many species was reduced to avoid consumption of cephalopods exceeding production. Estimates of benthic fauna and production are lacking. Therefore the model was used to estimate required benthic biomass. That the benthic biota in the northern ecosystem are less abundant (at ony 25% of that in the southern Benguela) is to be expected (Shannon and Jarre-Teichmann 1999); the northern model is of an upwelling area whereas the southern model extends over shelf (Agulhas Bank) and upwelling areas. Further, low oxygen levels are frequently found in shelf waters off Namibia (Bailey 1991). Southern Benguela Model During the 1980s, anchovy was the dominant pelagic fish, at a biomass of 1.1 million t off South Africa. Sardine was at a low level of only 129,000 t, mesopelagic fish (lanternfish, dominated by Lampanyctodes hectoris and lightfish, Maurolicus muelleri) at 1.7 million t, and hake at about 624,000 t (both species combined). In order that the model balance, some of the parameters of a few groups had to be reevaluated. Hake and other demersal fish caused major problems in the model, particularly related to diet composition of the various size groups. The proportion of these groups in the diet of others was reduced in many cases and it was necessary to allow the model to estimate the predatory biomass of these groups, based on the amount required as prey and catches. Hake biomass was required to be about 64% higher than estimated, and that of other demersal fish, 7.5 times higher. These adjustments can send ripple effects through the system as a result of prey species being consumed in larger amounts. As in the Northern Benguela, cephalopods were not abundant enough to support demands by other components, and the proportion in the diets of some groups had to be reduced dramatically. Ecosystem Approaches for Fisheries Management 531 Comparison of Northern and Southern Benguela Upwelling Systems Summary Statistics Total biomass (excluding detritus) was higher in the Northern Benguela (360 t per km2 ) than in the Southern Benguela (297 t per km2). With the exception of total catches, all major flows were higher in the Southern Benguela (Table 1), indicating that the Southern Benguela is a more productive system. Mean path lengths (sensu Finn 1976) in the two systems were similarly short, at 3.02 in the Southern and 3.19 in the Northern Benguela. Flow Diagrams Trophic levels of the components of the systems, biomasses, and flows through the two systems are compared (Fig. 2). Many components in the Southern Benguela occupy higher trophic levels than the same groups in the Northern Benguela. Consumption Consumption by anchovy, redeye, hake, and other demersal fish and mesopelagic fish are most important in the Southern Benguela (Fig. 3b). In the Northern Benguela (Fig. 3a), horse mackerel and goby also consume large portions of production. Primary Production Required Use of primary production equivalents enables the effects of fishing at different trophic levels to be compared (Pauly and Christensen 1995). The Table 1. Comparison of summary statistics in the Northern and Southern Benguela upwelling systems in the 1980s. Flows are in tons per km2 per year. Northern Benguela Southern Benguela Sum of all consumption 11,743 14,196 Sum of all exports 1,254 4,300 Sum of all flows to detritus 4,265 10,170 Total system throughput 23,327 36,435 Sum of all production 10,034 15,427 Net system production 1,254 4,300 Sum of all respiratory flows 6,065 7,769 Total net primary production 7,319 12,068 Total catches 7 3 532 Shannon & Jarre-Teichmann — Trophic Flows in Upwelling Systems Figure 2. Diagrams of the trophic flows in the Northern (top) and Southern (bottom) Benguela during the 1980s. Boxes arranged along vertical axis by trophic level. Flows are tons wet mass per km2 per year. Biomass of components denoted by B where B >1 t per km2. Flows leave boxes in upper half, enter in lower half. Values are indicated for respiration and flows to detritus, with those less than 5 t per km2 per year (i.e., around 0.3-0.4 ppt of total consumption) omitted for clarity. Ecosystem Approaches for Fisheries Management 533 Figure 3. Production consumed by predators in the Northern (a) and Southern (b) Benguela during the 1980s. 534 Shannon & Jarre-Teichmann — Trophic Flows in Upwelling Systems greatest proportions of total primary production required to support catches in the Southern Benguela are those of anchovy, large pelagic fish, and hake (Fig. 4). Catches of horse mackerel and hake require far greater proportions of total primary production in the Northern Benguela system. Primary production required for fisheries is 5.8% in the Northern and 3.6% in the Southern Bengeula. That the fraction of primary production required to sustain catches in the Southern Benguela is so small, could be explained by the mismatch of phytoand zooplankton productivity and fish consumption, as suggested by Hutchings (L. Hutchings, pers. comm., Marine and Coastal Management, South Africa). This seems not to be the case in the Northern Benguela. By contrast, the ratio of primary production required by the fisheries, to harvest, is 179 in the Southern Benguela, compared to only 96 in the Northern Benguela. This indicates that fishing in the Southern Benguela is ecologically more expensive than in the Northern Benguela, despite lower catches in the south. The mean trophic levels of catches are similar in the southern (4.7) and northern (4.6) systems. Primary production required to sustain (i.e., support the consumption) of top predators (large pelagics, seals, sharks, seabirds, whales, and dolphins) in the Southern Benguela was 1,553 t, compared to 657 t in the Northern Benguela system. This indicates that top predators are far more important in the Southern Benguela system, as also reflected in the catches of species serving as their prey. Trophic Aggregation Biomass was concentrated in trophic level I in the Northern Benguela and trophic level II in the Southern Benguela (Table 2). Transfer efficiencies were comparable between the two systems at most levels, with the exception of transfer through level IV in the southern system being twice as efficient as that in the northern system. As expected for upwelling systems (Christensen and Pauly 1993), the transfer efficiency at these high trophic levels is low, as are those at the herbivore level. There are some long food chains in both systems, resulting in a total of nine discrete trophic levels. Mixed Trophic Impact Assessment Mixed trophic impact assessment is a technique measuring the relative impact of a change in the biomass of one component on other components of the ecosystem (Ulanowicz and Puccia 1990). It assumes that trophic structure is constant; i.e., the technique cannot be used for predictive purposes, but should rather be used as sensitivity analysis. In the Southern Benguela, microzooplankton benefited mesozooplankton, anchovy, sardine, redeye (Etrumeus whiteheadi), and other small pelagic fish, such as saury (Scomberesocidae) and flying fish (Exocoetidae), by providing a food source for these groups and by serving as food for others upon which Ecosystem Approaches for Fisheries Management 535 Figure 4. Percent of total primary production required to sustain catches in the Northern and Southern Benguela ecosystem during the 1980s. Table 2. Trophic aggregation in the Benguela upwelling systems during the 1980s. Transfer efficiency, Total throughput Trophic Biomass (t per km2) % (all flows) (all flows) level Northern Southern Northern Southern Northern Southern I 206.87 89.60 11,584.02 22,238.61 II 86.91 147.78 9,670.81 10,936.25 III 48.83 40.77 10.6 7.5 1,028.39 823.36 IV 14.55 14.58 12.3 22.1 123.15 180.62 V 3.02 4.27 17.5 20.5 19.63 35.99 VI 0.22 0.46 9.2 8.8 1.27 2.80 VII 0.01 0.02 7.3 6.3 0.06 0.13 VIII 0.00 0.00 3.0 2.9 0.00 0.00 IX 0.00 0.00 2.9 1.5 0.00 0.00 X 0.00 0.00 0.2 0.4 0.00 0.00 536 Shannon & Jarre-Teichmann — Trophic Flows in Upwelling Systems these groups prey (Fig. 5). By contrast, in the northern system, microzooplankton competed with these groups (goby replaces redeye in the northern system) for phytoplankton food, thereby having a net negative impact on them. Mesozooplankton, through consuming phytoplankton, negatively affected pelagic goby in the Northern Benguela. However, mesozooplankton was an important prey item for its counterpart in the Southern Benguela, the redeye. Owing to its greater biomass in the south, anchovy had more pronounced impacts on other groups in the Southern Benguela. Similarly, horse mackerel, the dominant pelagic species in the Northern Benguela, had greater effects on its competitors in the north. Sardine showed small net effects in both systems. As expected from higher catches in the Northern Benguela, groups in this system were more severely affected by fishing. ECOSIM Analysis of the Effects of Altered Levels of Fishing Mortality Altered fishing mortality has different effects in the two systems (Fig. 6ac). Increasing fishing mortality (F) on the three most abundant small pelagic fish in each system (namely anchovy and sardine in both systems, and redeye in the south and goby in the north) had less pronounced effects on other components in the Northern than in the Southern Benguela (Fig. 6a). Anchovy and sardine stocks in both systems crashed under this scenario of fishing. Further, in the Southern Benguela, there was a sharper decline in large pelagic fish when their prey of anchovy and sardine were severely fished. Redeye and goby catches were very low and therefore increasing these by a factor of four appears to have little effect. Despite such low fishing effort on redeye and goby in the southern and northern systems, respectively, the ecotrophic efficiencies of these two groups are very high (greater than 0.9), indicating that they are in high demand as food for other groups. Fishing at higher absolute levels would have major implications for the systems. In the Southern Benguela, chub mackerel and horse mackerel were favored by decreases in anchovy and sardine biomass, leaving more zooplankton available to their competitors (refer also to Fig. 5b). When fishing mortality was increased fourfold as above, but only for the first 4 years of the simulation, sardine in the Northern Benguela began to recover, although only reaching about one-third of its original biomass by year 10 (Fig. 6b). Anchovy did not recover. In the Southern Benguela, both species recovered by year 10. Increasing fishing mortality of hake fourfold in the first four years of simulation reduced hake biomass, thereby favoring some of the prey species of hake, such as mesopelagic fish and squid (Fig. 6c). However, in the Northern Benguela, other small pelagic fish (e.g., saury) were reduced and did not recover once fishing on hake was restored to its original level. In both systems, horse mackerel were negatively affected by increased fishing on hake, stabilizing at a lower level of abundance once fishing on hake Ecosystem Approaches for Fisheries Management 537 Figure 5. Mixed trophic impacts of selected groups in the Northern and Southern Benguela during the 1980s. Bars extending above the line of zero impact for each species represent net positive impacts. Conversely, bars extending below the zero line represent net negative impacts. 538 Shannon & Jarre-Teichmann — Trophic Flows in Upwelling Systems Figure 6. Results of ECOSIM simulations. Biomass plotted as a proportion of original biomass. (a) Effects of a fourfold increase in fishing mortality (F) of anchovy, sardine, and redeye (Southern Benguela) or goby (Northern Benguela) over 10 years. (b) Effects of a fourfold increase in fishing mortality (F) of anchovy, sardine, and redeye (Southern Benguela) or goby (Northern Benguela) for the first 4 years, after which Fs are set back to original levels. (c) Effects of a fourfold increase in fishing mortality (F) of hake for the first 4 years, after which F is set back to original level. Ecosystem Approaches for Fisheries Management 539 was restored to its original level. The effect was more severe in the Southern Benguela. This is explained by the greater net negative impact which mesopelagic fish had on horse mackerel, by competing with them for zooplankton food (Fig. 5b). As horse mackerel were lightly fished in the Southern Benguela, increasing F by a factor of 4, for example, had little effect. In the Northern Benguela, increasing F on horse mackerel fourfold for 4 years reduced horse mackerel biomass dramatically, so that by year 10, biomass was only at half its original level. Horse mackerel had a negative effect on chub mackerel by competing with them for zooplankton prey (Fig. 5a). Therefore chub mackerel were favored by this scenario, leveling off at a biomass factor of 1.7 that at the start. Conclusions There are clearly differences in the functioning of the Northern and Southern Benguela systems, related to abundances of the various components, as well as to the level of harvesting on these. Catches were higher in the Northern Benguela, despite the higher overall production in the Southern Benguela. However, fishing was more ecologically expensive in the southern system. Top predators were more important components in the Southern Benguela, as indicated by twice the primary production required to support consumption by top predators in the south. Demersal fish biomass required to support consumption in the Southern Benguela was double that in the Northern Benguela. However, when hake biomass is taken into account, the overall demersal component was only slightly higher in the Southern Benguela, and is explained by the fact that the Southern Benguela system is a continuum from upwelling to shallow bank. Although only lightly fished in both systems, mesopelagic fish, redeye, and pelagic goby were required to sustain the production of other components within the systems, and their heavier exploitation should be considered with caution. Zooplankton was more abundant in the Northern Benguela, but not as efficiently transferred to higher trophic levels. Preliminary ECOSIM analyses show that increasing fishing mortality (in proportion to its original value) has different effects in the two systems, and that these are complex responses to indirect and direct competition. In the Southern Benguela, large pelagic fish were more severely affected by fishing strategies that reduce their small pelagic prey. Also, horse mackerel and hake were more closely linked, so that reducing hake biomass had a more pronounced effect on horse mackerel in the Southern Benguela. 540 Shannon & Jarre-Teichmann — Trophic Flows in Upwelling Systems Acknowledgments We would like to thank Coleen Moloney, Patti Wickens and John Field for their foresight in organizing the workshop held in 1989, for which much of the basic data used in this model were prepared and presented by local experts. We thank Coleen Moloney for her encouragement and support in this first comparative attempt. We are grateful to the European Union Framework Programme IV, Cooperation with Third Countries and International Organisations, Part C, Scientific and Technological Cooperation with the Developing Countries “Putting fishing effects in the ecosystem context” for funding which enabled us to work together on this project. We thank Villy Christensen for his efforts to make available to us the alpha version of EcoSim used in this paper. Intentions to model this system for the period 1980-1989 were presented at the International Symposium on Environmental Variability in the South-east Atlantic, held 30 March-1 April 1998 in Swakopmund, Namibia, and parts of the manuscript presented were incorporated into this paper. References Bailey, G.W. 1991. Organic carbon flux and development of oxygen deficiency on the modern Benguela continental shelf south of 22oS: Spatial and temporal variability. In: R.V. Tyson. and T.H. Pearson (eds.), Modern and ancient continental shelf anoxia. Geological Society Special Publication 58:171-183. Christensen, V., and D. Pauly. 1992. ECOPATH II: A software for balancing steadystate ecosystem models and calculating network characteristics. Ecol. Modell. 61:169-185. Christensen, V., and D. Pauly (eds.). 1993. Trophic models of aquatic ecosystems. ICLARM Conference Proceedings 26. 390 pp. Christensen, V., and D. Pauly. 1995. Fish production, catches and the carrying capacity of the world oceans. NAGA (ICLARM Quarterly) 15(4):26-30. Finn, J.T. 1976. Measures of ecosystem structure and function derived from analysis of flows. J. Theor. Biol. 56:363-380. Hewitson, J.D., and R.A. Cruickshank. 1993. Production and consumption by planktivorous fish in the northern Benguela ecosystem in the 1980s. S. Afr. J. Mar. Sci. 13:15-24. Heymans, J.J. 1996. Network analysis of the carbon flow model of the northern Benguela Ecosystem, Namibia. Ph.D. thesis, University of Port Elizabeth, South Africa. 213 pp. Jarre-Teichmann, A., and V. Christensen. 1998a. Comparative modelling of trophic flows in four large upwelling ecosystems: Global vs. local effects. In: M.-H. Durand, P. Cury, R. Medelssohn, C. Roy, A. Bakun, and D. Pauly (eds.), Global vs. local changes in upwelling ecosystems. Proceedings of the First International CEOS Meeting, ORSTOM, Paris, pp. 423-443. Ecosystem Approaches for Fisheries Management 541 Jarre-Teichmann, A., and V. Christensen. 1998b. Modelling trophic flows in large eastern ocean ecoystems: Temporal and spatial comparisons. ICLARM Studies and Reviews 24. In press. Jarre-Teichmann, A., L.J. Shannon, C. Moloney, and P. Wickens. 1998. Comparing trophic flows in the Southern Benguela to those of other upwelling ecosystems. In: S.C. Pillar, C. Moloney, A.I.L. Payne, and F.A. Shillington (eds.), Benguela dynamics: Impacts of variability on shelf-sea environments and their living resources. S. Afr. J. Mar. Sci. 19:391-414. Pauly, D., and V. Christensen. 1995. Primary production required to sustain global fisheries. Nature 374:255-257. Polovina, J.J. 1984. Model of a coral reef ecosystem. I. The ECOPATH model and its application to French Frigate Shoals. Coral Reefs 3:1-11. Shannon, L.J., and A. Jarre-Teichmann. 1999. A model of the trophic flows in the Northern Benguela upwelling system during the 1980s. S. Afr. J. Mar. Sci. 21. In press. Shannon, L.J., A. Jarre-Teichmann, and P. Cury. 1999. Comparing trohpic flows and effects of fishing on the Southern Benguela ecosystem during two decades. Submitted to ICES Symposia (ICES/SCOR Symposium “Ecosystem effects of fishing,” March 1999, Montepelier, France). Ulanowicz, R.E., and C.J. Puccia. 1990. Mixed trophic impacts in ecosystems. Coenoses 5:7-16. Walters, C., V. Christensen, and D. Pauly. 1997. Structuring dynamic models of exploited ecosystems from trophic mass-balance assessments. Rev. Fish Biol. Fish. 7:139-172. Ecosystem Approaches for Fisheries Management 543 Alaska Sea Grant College Program • AK-SG-99-01, 1999 Modeling of Chub Mackerel (Scomber japonicus) and Sardine (Sardinops sagax melanosticta) During the Annual Migration Cycle Mikhail V. Pavlychev Far East State Technical University, Natural Science Institute, Vladivostok, Russia V.A. Belayev Pacific Scientific Research Fisheries Centre (TINRO-Centre), Vladivostok, Russia E.Y. Frisman Institute for Automation and Control Processes, Vladivostok, Russia Vadim P. Pavlychev Pacific Scientific Research Fisheries Centre (TINRO-Centre), Vladivostok, Russia Abstract In this work we have attempted to mathematically describe chub mackerel (Scomber japonicus) and sardine (Sardinops sagax melanostricta) migrations, and construct a model and verify it by retrospective forecast. Three models are described. The first is constructed based on a linear migration model excluding any environmental factors. The second is constructed by taking into account the thermocline depth. The third model adds the additional characteristic of a temperature gradient in the thermocline. Positive results permit predicting migrations one month in advance for April-June and September-October for chub mackerel and for January-April and September-October for sardine.In this work we have attempted to mathematically describe chub mackerel (Scomber japonicus) and sardine (Sardinops sagax melanostricta) migrations, and construct a model and verify it by retrospective forecast. Three models are described. The first is constructed based on a linear migration model excluding any environmental factors. The second is constructed by taking into account the thermocline depth. The third model adds the additional characteristic of a temperature gradient in the thermocline. Positive results permit predicting migrations one month in advance for April-June and September-October for chub mackerel and for January-April and September-October for sardine. 544 Pavlychev et al. — Modeling Mackerel and Sardine During Migration Introduction Fish of the genus Scomber are one of the most numerous fishes found in the pelagic waters of temperate and subtropical zones of the Pacific Ocean. Chub mackerel is widely distributed and occurs in the temperate waters around Japan, where it has periods of high abundance. Large aggregations of Pacific sardine are also observed in this area. The least understood aspects of the biology of these commercially targeted fish is their foraging and spawning migrations (Figs. 1 and 2). Therefore, forecasting these occurrences is very important for the fishing fleet. The mathematical modeling of the spatial-temporal distribution of biological populations and communities is not well developed, as is the modeling of dynamics of their biomass (Bocharov 1990). Therefore the problem of modeling the migrations of pelagic fishes is quite practical. Based on the scientific research of the distributions and migrations of chub mackerel and Pacific sardine, a problem arose in describing the seasonal migrations of these fishes by mathematical methods; i.e., constructing a model to obtain model coefficients and verify them with actual data. We constructed three models based on a chamber model, where the considered biological population is divided into subpopulations (chambers), which are connected only by migrations between chambers. The first model is constructed with no environmental factors being considered. The second model is constructed on the basis of the scientific assumption that chub mackerel and sardine, as well as many other pelagic fishes, inhabit the upper layer of water, i.e., in a layer above the thermocline. The third model is constructed by including in the second model the additional characteristic of a vertical gradient in the thermocline. Chamber Model In construction of a chamber model (Tuzinckevich 1989) the area of habitation of the biological object is divided into p fragments (chambers), which are independent and connected to each other only by migration flows: d d u t f (u ,...,u ) M (u ,...,u ) ik ik 1k nk ik i1 ip = + where uik is biomass (abundance) of species i in fragment k; fik is intrapopulation interaction of species i in fragment k; Mik is inflow of migrants of species i in fragment k; and n is number of species. The main advantage of the chamber approach is the simplicity of the model. Considering the use of ordinary differential equations, chamber Ecosystem Approaches for Fisheries Management 545 Figure 1. Distribution of chub mackerel in the northwest Pacific (Belayev 1984). 1 = Spawning region, 2 = Foraging region, 3 = Migrations, 4 = Month. models carry out the analysis rather easily, which was one of the factors for selecting them for the mathematical description of migrations of the studied biological objects. In considering the construction of the migration models, we divide the ocean surface into equal squares and attach each square to a coordinate grid [i, j]. Use data on catch per effort (in kilograms) as density of fish concentration in each square in the given month and designate it as Xi,j. By considering one of the squares in the given month (n) we take four adjacent squares on the horizontal and vertical, and assume at the current time the fish migrate from square to square; i.e., movement between squares (subpopulations) occurs.