Points of view The problems of estimating potential ...

Reviews in Fish Biology and Fisheries 8, 473±480 (1998)

Points of view The problems of estimating potential yield in data-sparse lake ®sheries: a new family of approximate models with examples from African lakes TO N Y J. P I T C H E R  and ALI DA B UNDY Fisheries Centre, University of British Columbia, Vancouver, Canada V6T 1Z4

Keywords: African lakes, approximate models, data-sparse lake ®sheries, lake ®sheries, morphoedaphic index

Introduction Estimation of the potential yield of ®sheries in the African lakes is important not only on account of a ®shery's ecological, economic and social impacts but also because, when compared to current harvest, it may provide an approximate assessment of status and sustainability. But estimating potential yields presents problems in many African lakes, because catch and effort data with which to perform such estimation are sparse and highly uncertain. In this Point of View we discuss a new family of approximate estimation models in an attempt to encourage new ways of dealing with this problem. The method, based on numerical comparison of the productive potential of the lake ecosystem and of the ®sh, takes advantage of better information being available from one lake than from others. The principal uncertainties in process and estimation errors are described and the models' scope and prospects evaluated in the light of preliminary results that aim to solicit further attempts at validation and improvement. Description of model The essential feature of the new model is the use of an assessment of potential sustainable yield for a ®shery in one lake, termed the baseline lake, as the basis of a projection to a ®shery for a similar species in a second lake, termed the target lake. This potential yield from the baseline lake is then scaled to the target lake using the ratio of the logarithms of primary production: (1) Y ˆ f(Y =A ) A  ln (P ‡ 1)=ln (P ‡ 1)g ‡ î t

b

b

t

t

b

where Yt represents the potential sustainable yield of ®shery in the target lake (tonnes yearÿ1 ), Yb is the potential sustainable yield of ®shery in the baseline lake (tonnes yearÿ1 ), At denotes the area of the target lake (km2 ), Ab is the area of the baseline lake  Author to whom correspondence should be addressed (e-mail: tpitcher@®sheries.com). 0960±3166 # 1998 Chapman & Hall

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(km2 ), Pt represents the average primary production in the target lake (gC mÿ2 dayÿ1 ), Pb is the average primary production in the baseline lake (gC mÿ2 dayÿ1 ), and î is the process (model) error. The addition of 1 to the primary production values ensures that the logs do not become negative for lakes where primary production is less than 1 gC mÿ2 dayÿ1. In addition, the curve intersects a linear model at the values for the baseline lake. To date, the model has been developed for two situations: ®rstly where baseline and target lake ®sheries are for the same ®sh species that has been introduced to the target lake (Pitcher, 1995) as shown in the formula above; and secondly, where the baseline and target lake ®sheries are for different species that occupy an analogous ecological niche (Pitcher et al., 1996). Where such ®sh belong to different taxa, the potential yield is scaled in proportion to the ratio of the two productive capacities, as expressed by the production-to-biomass ratio, Ù: (2) Y ˆ f(Y =A ) A  ln (P ‡ 1)=ln (P ‡ 1) Ù =Ù g ‡ î t

b

b

t

t

b

t

b

where Ùt represents the production-to-biomass ratio for the target lake ®sh species, Ùb is the production-to-biomass ratio for the baseline lake ®sh species, and î is the process error. Where data are available, several baseline lakes may be used and the results incorporated in the estimated potential yield for the target lake. In this way, approximate 95% con®dence limits may be attached to the potential yield estimates. In work on small pelagics in African lakes, Pitcher et al. (1996) employed the auximetric growth parameter, ö9 (phi prime; ö9 ˆ log k ‡ 2 log L1 , where k is the von Bertalanffy growth rate parameter and L1 is the von Bertalanffy asymptotic length; Pauly and Munro 1984), as a surrogate for Ù. Evaluation of process errors The principal uncertainty in this model is the assumption that primary production is correlated with ®sh yield. The use of the logarithm re¯ects the main non-linearity in this relationship, as examined by Downing et al. (1990), but this assumption suffers from three main sources of error. Firstly, the averaging of annual production conceals wide seasonal, geographical and inter-annual variation in photosynthetic ®xation of carbon (Imboden, 1990). Moreover, the relationship probably does not hold for very shallow and seasonal lakes and ¯oodplains, where macrophytes dominate habitat structure and provide surfaces for algal and bacterial ¯ora. Secondly, relatively small changes in the nutrient status of a lake render trophic pathways labile and may divert production away from ®sh into microbes (Reimann and Christoffersen, 1993). Thirdly, the cascade effect (Carpenter et al., 1985) generates alternate high and low biomass levels in lake food chains (see Ochumba, 1995, for an example from Lake Victoria) so that correlations with primary production at successive trophic layers may obey different rules. These uncertainties are discussed in more detail in Pitcher et al. (1996). When used for an introduced species, the model bypasses all the complex ecology of establishment by assuming that the introduced species ¯ourishes in its new lake, entering a vacant niche in the case of a human-made lake, or displacing endemic species in a natural lake. Moreover, all differences in lake ecology are effectively subsumed into the primary production ratio (see Pitcher, 1995, for a more detailed discussion). The model makes no prediction about the success of any ®sh introduction. The two-taxa version of the model assumes that the ratio of Ù's re¯ects the differing

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productive capacities of the two species in proportion. Using ö9 as a surrogate for productive capacity among the four taxa of small African lake zooplanktivores from Pitcher et al. (1996) is a reasonable approximation (Table 2 loc. cit.; n ˆ 17; Pearson correlation between Ù and ö9 ˆ 0:59; P ˆ 0:013). However, more recent investigations among wider groups of taxa suggest that ö9 is not consistently related to productive capacity (Pitcher, unpublished data) and the use of Ù is therefore likely to provide better predictions. Estimates of Ù can be made from the total mortality rate, Z (Allen, 1971). Reducing the process error outlined above requires detailed knowledge of the ecology of the ®sh species, lakes and their ®sheries. But, paradoxically, if we knew this much about lake and ®sh ecology, there would be no need to try to invent an approximate model. This model is, therefore, discussed in the light of the inevitable, large and irreducible process error attached to any simple model that reduces the ecology of two lakes to eight parameters, which for some will doubtless doom the model to failure. On the other hand, we feel that simpli®cation may be validated by proof of utility, and so this paper is written to encourage trials of the new method. Evaluation of estimation errors Estimation uncertainties may be accommodated in the structure of the model by a series (usually 1000) of Monte Carlo simulations. Each simulation comprises making an estimate of Yt by choosing values randomly from the error distribution attached to each input parameter of the model. The simulations were implemented using proprietary software on a Microsoft Excel spreadsheet (Crystal Ball Inc., Denver, CO, USA). Bajdik and Schneider (1991) show that different error distributions (such as gamma or normal) in lake ®sheries models have differing consequences for model predictions. To take account of this problem, actual error distributions for the baseline lake parameters may be employed when they are available, and the procedure allows error distributions to be normal, log normal, or indeed any shape including uniform between upper and lower bounds. This means that in the absence of anything more de®nitive, guesstimated error bands may be used and no information is wasted. For example, primary production values are often available over a season or between years, and these may be used to set up the guesstimated distributions for the simulation. Likewise, in the two-taxa version of the model, a uniform distribution of Ù values taken from the literature may be used directly. Examples Pitcher (1995) examined potential yields for introduced sardine and Nile perch ®sheries in 13 natural and 7 human-made African lakes, showing, for example, that between 800 000 and 1.2 million tonnes of sardines might be harvested from human-made lakes in Africa. Table 1 sets out the calculations for putative sardine (Limnothrissa) introductions to four African lakes, and the results are illustrated in Fig. 1, together with 95% con®dence limits from Monte Carlo simulation of estimation errors. Of the two different baseline lakes employed, the estimates based on Lake Kariba have the most credibility on account of the much better documentation of its ®shery yields than for Lake Tanganyika. Sardines were introduced to the only natural lake of the four, Kivu, in the 1950s, and so this model provides one of the few estimates of the potential yield of that lake. Lake Kivu is located on the border of Congo and Rwanda in what has long been a war zone,

476 Table 1. Examples of the application of the potential ®sh yield model for introduced species in one natural and three human-made African lakes. Lakes Tanganyika, a natural lake, and Kariba, a human-made lake, act as alternative baselines. Country codes: Bur, Burundi; Con, Republic of Congo; Tan, Tanzania; Zam, Zambia; Zimb, Zimbabwe. Con®dence limits obtained from 1000 simulated runs of the model using random values drawn from the error distributions on each parameter.

Pitcher and Bundy

Potential yield of African lake ®sheries

477 Kariba baseline Tanganyika baseline

Potential Fish Yield, tonnes yr21

1000000

100000

10000

1000

Kainji

Kivu

Itezhitezhi

Nasser

Fig. 1. Examples of the model for potential ®sh yield for introduced species applied to four African lakes. Calculations are shown in Table 1.

so this estimate has added relevance when sardines are used for food by the large refugee population. The success of a recent introduction of sardines to the human-made Lake Itezhi-tezhi in Zambia has yet to be determined, but this model provides one of the few estimates of potential yield. The model may soon be tested in the Lake Kainji ®shery for clupeids, currently the subject of a new, well-designed survey (Turner, 1996 and pers. comm.). For the Monte Carlo simulations, errors were taken as a uniform distribution from 4.9 to 6.8 tonnes kmÿ2 for Lake Kariba sustainable sardine yield, and 8.5 to 11.5 tonnes kmÿ1 for Lake Tanganyika (both based on 95% tiles of estimates discussed in Pitcher and Bundy, 1994, but replacing the normal distribution with a more conservative uniform one). Error distributions on average primary production were taken as log normals with a COV of 20% (based on reported year-to-year variation in average primary production). Using the second form of the model, to estimate potential yield of poorly documented species from better documented ones, Pitcher et al. (1996) estimated the potential annual sustainable yield of the Lake Victoria Rastrineobola (dagaa) ®shery to be between 5.2 and 8.1 tonnes kmÿ2 , indicating that the ®shery might be expanded over the recorded 1990 levels of around 2 tonnes kmÿ2 . Sardines in Lakes Kariba and Tanganyika were used as baselines, and errors on ö9 were set as uniform distributions covering the range of values used to assemble the means. We are aware of no other estimates of potential yield for this large but poorly documented ®shery. Choice of baseline lake One critical feature of the model is that the potential yield of the baseline lake ®shery must be well assessed. For sardine ®sheries in African lakes, the Lake Kariba ®shery is the best example available (e.g. Pitcher and Bundy, 1994). The ®sheries for the two species of sardines in Lake Tanganyika are more uncertain, because reported high

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potential ®sh yields (Coulter, 1992) may not be realizable. The Lake Victoria Nile perch ®shery (Pitcher and Bundy, 1995) constitutes the most appropriate baseline lake available for Nile perch ®sheries. In all cases, the errors in estimating the potential yield for the baseline lake ®shery may be used in the error bootstrapping. Where possible, the simultaneous use of several different baseline lakes in the model should lead to more accurate potential yield estimates and con®dence limits. For example, in Pitcher et al. (1996), both Kariba and Tanganyika sardine baselines are employed for the model predicting Rastrineobola yields.

Prospects for the new family of models In a review of approximate ®sh yield models for lakes, Leach et al. (1987) complain of a lack of models of intermediate complexity between the two-parameter morphoedaphic index and full ecosystem simulation. The new family of empirical models suggested here has the advantage of being simple to implement and relies on a number of published ®sh growth and limnological data, together with an established ®shery as a baseline. Obtaining estimates of stock status is a great problem in the data-sparse ®sheries of many of the African lakes. If the method presented here were to be fully validated, it would be a considerable help to ®shery managers and development of®cers trying to work with remote and under-researched ®sheries. Approximate assessments could be made where there are ®gures for current yield in relation to model predictions of potential yield, at least for species which occupy similar enough niches for this method to be employed, and thereby effectively make use of the greater amount of work on other lakes. For example, the sardine ®shery in Lake Kivu has been subjected to only preliminary study (de Iongh et al., 1995), yet the sardine stocks were heavily exploited during the recent serious unrest in the region and large undocumented catches of sardines were a vital source of protein for unfortunate inhabitants of lakeside refugee camps in both Rwanda and Congo. The model suggests that some 7000±9000 tonnes (3± 4.2 tonnes kmÿ2 ) might be taken from Kivu (Pitcher, 1995). This is slightly larger than the 6000 tonnes minimum, based on areal yields only, by Marshall (1992), but considerably greater than most of a series of hopeful guesses over the years documented in Marshall (1992), some of which were nevertheless actually used in development policy. Provided that further work increased con®dence in the present model, we hope it could be helpful in such situations. One way of checking the model's predictions is to cross validate them. A preliminary cross validation of the method may be found in Pitcher (1995), where yields in some of the baseline lakes themselves were checked using other lakes as baselines. For example, sardines in Lake Kariba, the main, well-studied baseline lake, were estimated using Tanganyika sardines as a baseline, with the result, allowing for two species of sardine in Tanganyika, of around 28 000 tonnes (about 5.2 tonnes kmÿ1 ), very close to the best estimate from more formal assessments in Kariba of 31 500 tonnes (5.9 tonnes kmÿ2 ). The model might be validated and extended by applying it to heavily documented North American lakes with introduced species, where the actual process error could be revealed by comparison with known ®sh yields (e.g. Lake Ontario salmon: Jain and DePinto, 1996). Because the relationship of primary production with ®sh yield is

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different in temperate and tropical lakes, and in the oceans (Nixon, 1988; Downing et al., 1990), the lake pairs have to be chosen within related climate and habitat sets. There is evidently a need for further empirical work linking primary production and sustainable ®sh yields, and we present this model in the hope of encouraging such advances in understanding. For example, it is easy to envisage a series of improvements that could increase the precision of estimates made with the new type of model. It may be possible to use life history parameters that re¯ect frequency of breeding and cohort structure to approximate differences in production per unit area. Perhaps the most exciting prospects for this type of approximate empirical model lie in the possibility of addressing multispecies concerns, arguably one of the most serious de®ciencies of present ®sheries assessment science (Pitcher and Pauly, 1998). For example, the rapidly increasing harvest of dagaa from Lake Victoria has raised trophodynamic concerns because this ®sh forms one of the prey of Nile perch and eats lake prawns, themselves the food of juvenile Nile perch. This family of models would become of greater value if it were possible to tune potential yields for predator and prey ®sh using trophic ¯uxes from an ecosystem model such as Ecopath (e.g. Moreau, 1995) or Ecosim (Walters et al., 1997). References Allen, K.R. (1971) Relation between production and biomass. J. Fish Res. Board Can. 28, 1573±1581. Bajdik, C.D. and Schneider, D.C. (1991) Models of the ®sh yield from lakes: does the random component matter? Can. J. Fish. Aquat. Sci. 48, 619±622. Carpenter, S.R., Kitchell, J.F. and Hodgson, J.R. (1985) Cascading trophic interactions and lake productivity. Bioscience 35, 634±639. Coulter, G.W. (1992) Fisheries. In Coulter, G.W., ed. Lake Tanganyika and its Life. Oxford: Oxford University Press, pp. 139±150. Downing, J.A., Plante, C. and Lalonde, S. (1990) Fish production correlated with primary production not the morphoedaphic index. Can. J. Fish. Aquat. Sci. 47, 1929±1936. Imboden, D.B. (1990) Mixing and transport in lakes: mechanisms and ecological relevance. In Tilzer, M.M. and Serruya, C., eds. Large Lakes: Structure and Function. Berlin: Springer-Verlag, pp. 000±000. de Iongh, H.H., Spliethoff, P.C. and Roest, F. (1995) The impact of an introduction of sardine into Lake Kivu. In Pitcher, T.J. and Hart, P.J.B., eds. The Impact of Species Changes in African Lakes. London: Chapman & Hall, pp. 277±298. Jain, R. and DePinto, J.V. (1996) Modeling as a tool to manage ecosystems under multiple stresses: an application to Lake Ontario. J. Aquat. Ecosyst. Health 5, 23±40. Leach, J.H., Dickie, L.M., Shuter, B.J., Borgmann, U., Hyman, J.B. and Lysack, W. (1987) A review of methods for prediction of potential ®sh production with application to the Great Lakes and Lake Winnipeg. Can. J. Fish. Aquat. Sci. 44 (Suppl. 2), 471±485. Marshall, B.E. (1992) Limnothrissa miodon and its ®sheries in the African lakes. Consultancy report to Renewable Resources Assessment Group, London, 63 pp. Moreau, J. (1995) Analysis of species changes in Lake Victoria using ECOPATH, a multispecies trophic model. In Pitcher, T.J. and Hart, P.J.B., eds. The Impact of Species Changes in African Lakes. London: Chapman & Hall, pp. 137±161. Nixon, S.W. (1988) Physical energy inputs and the comparative ecology of lake and marine ecosystems. Limnol. Oceanogr. 33, 1005±1025. Ochumba, P.B.O. (1995) Limnological changes in Lake Victoria since the Nile perch introduction. In Pitcher, T.J. and Hart, P.J.B., eds. The Impact of Species Changes in African Lakes. London:

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Chapman & Hall, pp. 33±43. Pauly, D. and Munro, J.L. (1984) A simple method for comparing the growth of ®sh and invertebrates. Fishbyte 2(1), 21. Pitcher, T.J. (1995) Thinking the unthinkable: a candidate model for predicting sustainable yields of introduced ®sh species in African lakes. In Pitcher, T.J. and Hart, P.J.B., eds. The Impact of Species Changes in African Lakes. London: Chapman & Hall, pp. 495±526. Pitcher, T.J. and Bundy, A. (1994) Successful species introductions in the African lakes: assessment, uncertainties and strategies for ®shery management. In Kruse, G., Eggers, D.M., Marasco, R.J., Pautzke, C. and Quinn, T.J., eds. Management Strategies for Exploited Fish Populations. Fairbanks, AL: Alaska, Sea Grant College program 93-02, pp. 545±570. Pitcher, T.J. and Bundy, A. (1995) Assessment of the Nile perch ®shery in Lake Victoria. In Pitcher, T.J. and Hart, P.J.B., eds. The Impact of Species Changes in African Lakes. London: Chapman & Hall, pp. 163±180. Pitcher, T.J. and Pauly, D. (1998) Rebuilding ecosystems, not sustainability, as the proper goal of ®shery management. In Pitcher, T.J., Hart, P.J.B. and Pauly, D., eds. Reinventing Fisheries Management. London: Chapman & Hall, pp. 311±329. Pitcher, T.J., Bundy, A. and Neill, W.E. (1996) The ®shery for Rastrineobola argentea in Lake Victoria: estimation of potential yields using a new approximate model based on primary production. Fish. Res. 28, 133±149. Reimann, B. and Christophersen, K. (1993) Microbial dynamics in temperate lakes. Mar. Micr. Food Webs 7, 69±100. Turner, G.F. (1996) Maximisation of yields from African lakes. In Cowx, I.G., ed. Stock Assessment in Inland Fisheries. Oxford: Fishing News Books, pp. 465±481. Walters, C.J., Christensen, V. and Pauly, D. (1997) Structuring dynamic models of exploited ecosystems from trophic mass-balance assessments. Rev. Fish. Biol. Fish. 7, 139±172.

Accepted 4 April 1998