Fishing Down the Value Chain: modelling the impact of biodiversity loss in freshwater fisheries - the case of Malawi. Victor Kasulo National Economic Council, Malawi Charles Perrings Environment Department, University of York Abstract An aggregated Gordon-Schaefer model is modified to include both environmental and bioeconomic diversity variables and is fitted to data from a gillnet fishery in Lake Malawi. Despite the inevitable errors involved in using a single species format to analyse a multispecies fishery, it is possible to explain a very high proportion of the variation in estimated stock size, catch and effort if a ‘single-species’ model includes a measure of the diversity of catch. The model is used to consider the importance of the level of diversity in a fishery in open access and profit maximising regimes. Pressure on stocks is greater at all levels of biodiversity in open access than it is in profit maximising regimes. However, in a profit maximising regime both catch and the productivity of fishing effort is highest when there is a single marketed species. By contrast, in an open access regime catches are maximised at higher levels of bioeconomic diversity than in profit maximising regimes. Implications for policy are discussed. Key words Fisheries; biodiversity; open access 1. Introduction A long-held view of the development of fisheries is that they initially exploit more abundant, more easily caught species, and switch over time to increasingly less abundant, less easily caught species. Moreover, it is argued that the rate at which less easily caught species are substituted for more easily caught species is accelerated in open access fisheries. More recently, a study of the mean trophic level of species groups reported in FAO global fisheries statistics has shown that the succession has been from long-lived high trophic level piscivorous bottom fish towards shortlived low trophic level invertebrates and planktivorous pelagic fish (Pauly et al, 1998). The economic explanation for the traditional view is that fisheries, like mining operations, are costdriven. They initially focus on species whose harvesting costs are low, moving on to species involving higher harvesting costs when initial stocks are exhausted. But the shift between fish species involves much greater changes in quality than the shift between low and high extraction cost ores. The economic explanation of the Pauly et al result reflects this. While there may be some correlation between trophic level and extraction cost, a more credible explanation is that consumers prefer higher trophic level to lower trophic level species. That is, the sequence of targeted fish stocks is demand rather than supply driven. We may think of this phenomenon as fishing down the value chain. Whether the fishing sequence is supply or demand driven, it will have an effect on fish biodiversity. There will be a change in the composition and relative abundance of both harvested species, and the species with which they interact. But the change will be different in each case. There is less evidence on changes in the biodiversity of freshwater than marine fisheries. Nonetheless, it is known that the depletion of fish species in freshwater habitats has affected the diversity, dynamics and productivity of freshwater ecosystems. The effects differ depending on the characteristics of the depleted species. Over-exploitation of keystone species can have major effects on the distribution and abundance of other organisms in the ecosystem. For example, removal of zooplankton-feeding fish can cause major changes in the abundance and species of zooplankton, which in turn can have cascading effects on the food web (Moyle and Leidy, 1992). Depletion of predators may have various effects, including replacement of exploited species by alternative species in the same trophic position, an increase in production at a lower trophic level or longer term effects involving changes in the ecosystems (Boechlert, 1996). Aside from the genetic properties of exploited populations, over-fishing causes a reduction in the size of fish in the catch. Because fishing adds to natural mortality of species, it decreases the average life span of the species with implications for both size and value (Heywood, 1995; Roberts and Polunin, 1993). In other words, a change in fish biodiversity alters the productivity and hence the value of the fishery. From a management perspective, it is clearly important to understand the impact of biodiversity change. From an analytical perspective, however, the problem is intractable. Changes in species diversity affect interactions between species in complex ways. Using the Lotka (1925) and Volterra (1931) species interaction equations in a bioeconomic framework to model the optimal exploitation of multi-species systems is extremely difficult. Data constraints add to the problem. Few systems have been sufficiently studied to provide quantitatively valid estimates of interaction coefficients. But practical resource-management decisions cannot wait until all the scientific information is available. Decisions must be made on the basis of available information (Clark, 1990). This paper develops a tractable model of biodiversity in freshwater fisheries. The impact of a change in the diversity of marketed fish species is captured by the introduction of biodiversity variables into an aggregated Gordon-Schaefer fishery model, modified to include the influence of change in environmental conditions. The model is then applied to a freshwater fishery in Lake Malawi. This fishery has been exploited by traditional methods for many centuries, and traditional fisheries still account for around 90 percent of the country's total fish output. Modern commercial fishing started only in 1935 when purse seining was introduced, but it was not until the introduction of trawling in 1968 that the commercial fishery became a significant industry (Tweddle and Magasa, 1989). Since then, the commercial fishery has undergone steady expansion, and the ecological impacts of the combined fishery have been increasing. Between 1971 and 1975 the FAO (1976) carried out a number of experimental trawls. They divided the southern portion of the lake into seven fishing areas and estimated total fish biomass and tentative maximum sustainable yield (MSY) for each fishing area. These estimates were used to specify total allowable catches and to determine the number of trawling licenses to be issued. An initial report on the fishery (Tarbit, 1972) was followed by detailed investigations of changes that occurred as the fishery developed (Turner, 1977; Tweddle and Turner 1977). These studies showed significant changes in the species composition of catches as the trawl fishery intensified, with larger cichlid species disappearing from the catches and smaller species increasing in abundance. The initially abundant medium and large cichlid species, Lethrinops stridei and L. macracanthus, for example, were replaced by small cichlids such as Otopharynx argyrosoma, Pseudotropheus livingstonii and Lethrinops auritus. A decline in the large catfish Bagrus meriodionalis and Bathyclarias spp. was also noted (Banda et al., 1996). Following the FAO (1976) study, the minimum legal trawl cod-end mesh size was increased from 25 to 38 mm. This was intended to reverse the decline in population of the larger cichlid species. However, no attempt was made to see if the hoped-for recovery of the large cichlid species had occurred until 1989, when experimental trawls were again used to estimate total fish biomass and the species composition of the catch. They showed that species such as L. mylodon and L. macracanthus, which had declined substantially in the 1970s, had become locally extinct. Other large species such as Taeniolethrinops furcicauda, T. praeorbitalis and Ctenopharynx spp., had also declined. In the areas where most trawling had taken place, the large and mediumsized benthic zooplanktivores, large sediment feeders and large piscivores had all declined. The standing stock of small sediment feeders and pelagic species had remained largely unchanged (Turner et al., 1995; Banda et al., 1996). The low catches and loss of some species led to a one-year moratorium on trawling in the south east arm of the lake in 1992/3. The closure of the fishery had a marked impact on the stocks. Biomass increased rapidly as the fish grew. Biomass estimates after one year of closure were more than four times that prior to closure, and the species composition after one year of closure was similar to that of other areas. In a follow-up study by Banda et al. (1996), no further major changes in species composition were detected. Traditional fisheries in Malawi are of several types. The most commonly used gear is the gillnet, which accounts for over 40 percent of total traditional catches of around 40,000 tonnes per annum. In this sector, too, there has been substantial change in species composition. Catch per unit effort in the south west arm of Lake Malawi showed a sharp decline from about 20 kg per set in the mid 1950s to 5 kg per set in the early 1970s. The decline was largely accounted for by the disappearance of nchila which had comprised about half of the catch in the 1950s (Walker, 1976). Although there are no published fish stock assessment data for the whole lake, catch figures for the traditional fisheries show that most of the high valued and popular food fish species such as chambo are currently in decline (Munthali, 1997; FAO, 1993). The percentage contribution of tilapiines (Oreochromis spp) to total landings has declined from around 16 percent in 1989 to 5 percent in 1995 while the percentage contribution of usipa (Engraulicypris sardella) and haplochromines (kambuzi, utaka and chisawasawa) has increased from 58 percent in 1991 to 73 percent in 1995 (Munthali, 1997). 2. Measures of bioeconomic diversity in fisheries Given the importance of changes in biodiversity to the functioning and economic productivity of a range of ecosystems, finding appropriate measures of biodiversity has become a central concern in ecology and conservation biology (Ganeshaiah et al., 1997). There are many possible ways to measure distance between species. Two species can be differentiated in terms of their biochemistry, biogeography, ecology, genetics, morphology, physiology or the ecological role that they play in a particular community. As a result of the variety of elements of biodiversity, and of differences between them, there is no single all-embracing measure of biodiversity. This means that it is impossible to state categorically what the biodiversity of an area or of a group of organisms is. Instead, only measures of certain components can be obtained and even then such measures are only appropriate for restricted purposes (Gaston and Spicer, 1998). The literature in ecology provides a variety of indices that can be used to quantify fish diversity. One of the simplest methods suggested in the literature is to count the number of species in the habitat or community. Such an approach is mostly criticised for being too simplistic as it does not account for the extent of representation of each of these species in the community. This method may also not be suitable in most tropical lakes because of the enormous number of species inhabiting the lakes, most of which have not yet been identified and scientifically named. Other indices measure biodiversity based on both number, and abundance of the species. These heterogeneous indices differ mostly in the amount of weight they give to the two elements of number and dominance. Examples of indices in this category include the Shannon, Simpson, McIntosh and Berger-Parker indices (Magurran, 1988). Even with heterogeneous indices, there is still a great deal of disagreement over their efficiency in reflecting the biological diversity of a habitat or community. One major problem cited in the literature is that these indices assume that all species at a site or in a community contribute equally to its biodiversity and ignore biological, ecological and functional differences among the species (Ganeshaiah et al., 1997; Harper and Hawksworth, 1994). To address this weakness, another category of indices has been developed. These indices capture the diversity in taxonomic, morphological and in many other biological features of the species. Examples of indices in this category include, taxonomic relatedness indices (Clarke and Warwick, 1998), the avalanche index (Ganeshaiah et al. 1997), and functional diversity indices (Brisby, 1995). From an economic perspective, the value of biodiversity lies first and foremost in its role in the production of goods and services. An individual harvested species is valued for specific properties that make it useful in either production or consumption. The biodiversity that supports such species derives its value from this. Any measure of diversity should accordingly reflect this (Perrings, 2000; Heywood, 1995). Ecological and economic value are not necessarily the same. It does not, for example, follow that if biodiversity is important to the functioning of some ecological system then it will automatically be valuable to society. Nor does it follow that a species that is rare or occupies a range of restricted size will be economically scarce and hence valuable. There is no necessary correspondence between ecological diversity measures and the economic value of biodiversity. Systems with a high biodiversity value by any of the standard indices may or may not have high economic value. In order to reflect the social-economic value of diversity, the ecological diversity measures need to be modified. The economic value of biodiversity is important because it determines the level of both its use and conservation. Since fishers put their effort where it is worth more, the pressure on the fish resource is not randomly distributed but is highly focused. Market prices influence the exploitation of a fishery. They influence both the level and direction of effort. Targeting of effort toward particular species leads to elimination of highly valued species, and to a reduction in biodiversity and productivity (Barbier et al., 1995). Currently, most studies of the economic value of biodiversity measure the value of specific biological resources rather than the diversity of resources. Earlier studies used the term biodiversity to mean the totality of biological resources (McNeely et al., 1990). Later studies have continued to use the value of biological resources as a proxy for the value of biodiversity because it is easier to estimate (Tacconi, 2000; Pearce and Moran, 1994). In fisheries, since most of the species caught are marketed, fish prices may be used to approximate the economic value of species. Market prices are used because of the pattern of selection and types of preference that they depict (Hanemann, 1988). Since the markets are typically incomplete, however, the use of market prices is not problem-free. Market prices fail to reflect, for example, the contribution of individual species to a range of ecological services. With this caveat, we nevertheless use the set of market prices to weight a Simpson’s index of catch. That is, we use the market value of species catch biomass, rather than actual species catch biomass. Note that a Simpson’s index of catch will always be strictly greater than a Simpson’s index of biodiversity in the aquatic ecosystem, since catch is limited to only a few species at a few trophic levels. A Simpson’s index of catch is: Yi Dt = i=1 Y s 2 (1) where Y represents the total fish catch and Yi is the catch of the ith species. A bioeconomic Simpson’s index of catch is: Pi Y i Bt = i=1 TR s 2 (2) where Pi is the unit price of species i, and TR is the market value of the total fish catch. In both the unweighted and weighted indices, a loss of biodiversity is reflected in an increase in the value of the biodiversity index, which ranges between zero (as the number of species harvested tends to infinity) and one (if the number of species harvested is one). If each species caught has the same market value, then the bioeconomic Simpson’s index of catch is the same as the unweighted index. If different species have different market values, the impact of price weighting depends on the relative abundance of more and less valued species. The economic biodiversity index of a community dominated by species of high (low) market values will be greater (less) than the corresponding ecological biodiversity index of the same community. That is dBt > (<)0 dpt Bt >(<) Dt where Bt and Dt are the bioeconomic and biological diversity indexes respectively. Since the weighted biodiversity index reflects both the economic scarcity and the relative abundance of species, an ecologically dominant species will became more (less) dominant in the weighted index if it is more (less) valuable. 3. An aggregated multi-species model The model developed and estimated in this paper is designed to capture important properties of multi-species fisheries without describing all of the species interactions. It does this by aggregating the different species involved and then modelling the effect of the diversity of those species on the dynamics of the aggregated fishery. In this way we retain the simplicity of the Gordon-Schaefer model, but capture the effect of changes in biodiversity within the fishery. The Gordon-Schaefer model expresses the change in stock biomass as the difference between natural growth and harvest. It assumes a logistic growth function for fish biomass, and a simple Cobb-Douglas production function for fish catch (Y), as a function of fishing effort (E) and fish stock (X). Suppressing time subscripts and ignoring biodiversity and environmental factors others than those affecting the carrying capacity of the supporting ecosystem, this yields the following expression for change in harvested biomass: X = rX(1 – X/K) - qEX. (3) where r is the difference between the birth rate and the death rate, commonly referred to as the intrinsic growth rate or natural rate of increase, K denotes the maximum environmental carrying capacity, q is the catchability coefficient, and E is the level of fishing effort. In the steady state, (when catch, stock and effort all remain constant over time) the production function expresses catch as a function of effort. This implies that, Y = rX(1 - X/K) = qEX Solving for X gives: X = K(1 - qE/r). Hence Y = qEX = qKE(1 - qE/r). (4) This is the usual sustainable-yield function for a Gordon-Schaefer model. Environmental factors play a significant role in determining the productivity of freshwater fisheries. In Lake Malawi, for example, Fryer and Iles (1972) suggested that rises in catch and effort levels in certain years was a result of improved recruitment and survival caused by changes in lake levels. Tweddle and Magasa (1989) later investigated the relationship between lake level fluctuations and recruitment, and showed a clear tendency for falling lake levels to be associated with catch anomalies. The mechanisms are still not clear. It has been argued, for example, that recruitment success may be influenced either by changes in the extent of vegetation for the young, or by fluctuations in food availability. However, no evidence has been found to show that falling lake levels lead to increase in vegetation cover. In fact for Lake Malawi, like other African lakes, the opposite is likely to be true, since rising lake levels increase the extent of peripheral lagoons and marshes, providing excellent nursery areas. The main explanation for the variations in fish productivity is therefore found to be food availability (Tweddle and Magasa, 1989). To capture this we include a measure of the impact of sedimentation and water pollution on fish productivity. The general effect of water pollution on fish diversity and productivity through eutrophication are well documented. Increased nutrient loads lead to increases in production and abundance of phytoplankton, a reduction in the transparency of water or an increase in water turbidity, depletion of oxygen in the hypolimnion, and increases in chemical stratification (Colby et al., 1972). The fish community may respond initially with an increase in production due to increased food supply (Lee and Jones, 1991; Oglesby, 1977), but as the lake becomes more eutrophic, aggregate fish production is likely to fall due to loss of habitat (Hammer et al., 1993). Any decrease in habitat availability due to sedimentation and the volume of deoxygenated water might be expected to influence the productivity of a fishery. Since Lake Malawi is an oligotrophic lake, the process of eutrophication may not be relevant. Moreover, an increase in nutrients through water pollution does not necessarily augment the food supply. Because denitrification minimises the influence of additional nitrogen input, any increase in the supply of nutrients tends to increase in phosphorus rather than nitrogen. Nitrogen-fixing cyanobacteria (blue-green algae) become dominant while the productivity of benthic algae is reduced. Such a shift in phytoplankton species composition may be expected to reduce fish productivity since blue gree algae are a poor source of food compared to benthic algae (Hecky et al., 1999; Bootsma et al., 1999). The productivity of the fishery thus depends on the ability of tilapiines to digest cyanobacteria. Such an environment does not favour zooplanktivorous fish species either because cynobacteria are also a poor food source for zooplankton (Bootsma and Hecky, 1993). Sedimentation on the other hand spoils nursery grounds and may damage fish eggs. Thus, water pollution and sedimentation are likely to have a negative impact on total fish productivity due to reductions in the major food supply and loss of habitat. In the Gordon-Schaefer model, environmental factors can affect fish biomass in three different ways: through an effect on the carrying capacity, K, through an effect on the intrinsic growth rate, r, and through an effect on K and r together (Freeman, 1993; Fréon et al., 1993). Of the three cases, the latter is argued to be the most appropriate. In this paper we assume that environmental conditions affect both r and K, but in ways that preserve the ratio between them. Thus, factors that affect recruitment and survival of fish stocks are assumed also to affect the carrying capacity of the aquatic environment. Specifically, water pollution is assumed to have a negative effect on total fish biomass through its impact on food availability. The growth function for fish biomass takes the form: X = rX(1 – eW – X/K) - qEX. (5) where W is the environmental quality variable, and e is a parameter that gives the amount by which a unit change in the environmental variable depresses the natural growth rate of fish biomass. Now consider the importance of biodiversity. The relative abundance of species depends upon both biological and economic factors. One way of incorporating biological and economic interactions into the fisheries model is by introducing a biodiversity variable that captures the effects of biological as well as economic factors on the system. In the previous section, two biodiversity indices were developed; unweighted and weighted. The unweighted index assumes that all species are of equal values. In this case the biodiversity index is only affected by biological factors. The weighted index, on the other hand, takes into account the different market values of species. By introducing these indices into the model, both biological and economic factors can, thus, be captured. The most tangible effect of any ecological disruption caused by biodiversity loss is likely to be on the productivity of the resource. Changes in fish diversity are often argued to affect fisheries via their impact on the wider aquatic ecosystems that support fish production (Barbier et al., 1995). That is, fish production depends not only by the level of effort and the size of the fish stock, but also by the level of fish biodiversity. This is because fish stocks are exploited from more abundant to less abundant species, from easily caught to less easily caught species, and from high valued to less valued species (Boechlert, 1996; Pauly et al., 1998). This requires the specification of an appropriate production function describing the relationship between fish biodiversity as an input and fish catch as an output. In this paper it is assumed that the effect of species diversity on fish productivity may be captured by the introduction of an additional term into the fisheries production function1. This now becomes: Y = qBEX (6) where B is our economic biodiversity index. When B = 1 the production function reduces to the form generally applied in single species fishery models. B = 1 implies that there is only one valuable harvested species. It is, of course, possible that B = 1 but D 1, i.e. that only one species in a multispecies fishery is valued. In this case the by-catch is assigned a zero weight in the economic biodiversity index. If a caught species has zero value, it implies that their removal from the system has no direct or indirect implications for the production of any goods and (ecological) services. If B < 1, i.e. there is more than one economically valuable harvested species, the productivity of fishing effort is assumed to decline. This may be because of the cost of sorting, clearing by-catch, the use of multiple gears and so on. The growth and sustainable yield functions now become: X = rX(1 – eW – X/K) – qBEX. (7) and Y = qKBE(1 – eW – qBE/r) (8) To see the implications of the extended model for the level of effort and stock size under different property rights, consider the rent exhausting (open access) and profit maximising (private property) values of these variables. The open access case assumes that individual fishers equate total cost and revenue. The profit maximizing case assumes that they equate marginal cost and marginal revenue. The maximum sustainable yield (MSY) values are offered for comparison since the MSY is used by the Malawi Fisheries Department to set total allowable catches. Defining p to be the unit price of harvested fish biomass, c to be the unit cost of effort, and to be the discount rate, the open access steady state level of effort is given by: EOA = r(1 – eW – c/pqBK)/qB (9) and the corresponding stock level is XOA = K(1 – eW – qBEOA/r) (10) The profit maximizing steady state level of effort is a root of: Eo2 2q 2 B 2 Eo qB 2r 1 eW c r 1 eW c 0 1 The fisheries (harvest) production function is also referred to as the catch relationship. It should not be confused with the growth function which is sometimes called the natural production function of the fish stock where r 1 eW and pqBK / r Specifically, qB qB 8q 2 B 2 r 1 eW c Eo 4q 2 B 2 where 2 1 2 (11) 2r 1 eW c The corresponding stock level is XO= c( + r(1 – eW) – qBEO)/(pqB( + r(1 – eW) – 2qBEO) (12) The MSY effort and stock levels for comparison are: EMSY = r(1 – eW)/2qB (13) and XMSY = K(1 – eW)/2 (14) Consider the function linking water pollution and growth. This is negative and monotonic. Increasing water pollution reduces the level of effort under all property rights regimes. It reduces steady state stock size under both open access and regulated (MSY) regimes, but has ambiguous effects under a profit maximising regime. This is summarised in the following proposition: Proposition 1 If falling water quality negatively affects the growth of fish stocks, then a decrease (increase) in water quality implies an decrease (increase) in the MSY, open access and profit maximising levels of effort and stock size. That is: dX MSY dE 0, MSY 0 dW dW dX OA dEOA 0, 0 dW dW dX O dE 0, O 0 dW dW (15) The effect on effort levels and stock size under open access, MSY-regulated and profit maximising regimes reflects the fact that declining water quality scales the fishery down. Now consider the effect of a change in biodiversity on the MSY, open access and profit maximising solutions. This is summarised in the following proposition: Proposition 2 If an increase in biodiversity reduces the effectiveness of fishing effort then, in a multispecies fishery, the maximum sustainable yield level of stock size is not affected by changes in biodiversity but the effort required to catch the MSY increases (decreases) as fish diversity increases (decreases). In open access and profit maximising fisheries, an increase (decrease) in fish biodiversity implies an increase (decrease) in stock size. However, the impact on the open access and profit maximising levels of effort depends on the level of biodiversity. For small numbers of species an increase (decrease) in fish biodiversity implies an increase (decrease) in effort levels. As the number of species rises, the effect on effort levels reverses, and an increase (decrease) in fish biodiversity implies a decrease (increase) in effort. dX MSY dE 0, MSY 0 dB dB dX OA dE 0, OA 0 dB dB dX O dE 0, O 0 dB dB (16) That biodiversity has no impact on MSY is an artefact of the way it has been modelled. In freshwater fisheries where species have been introduced, there is some evidence of an increase in total fish biomass over some time horizon despite a reduction in the number of species. The Lake Victoria fishery in East Africa is an example. The introduction of the Nile Perch into this fishery was associated with the loss of some 200 haplochromine cyclids, but a significant increase in total fish biomass (Kasulo, 2000; Perrings 2000). Where species are merely deleted from an existing fishery, however, the evidence is less clear. It has been assumed here that biodiversity does not affect the productivity of the fishery, but does affect the effectiveness of fishing effort. The impact of the bieconomic diversity of the catch on effort levels depends on parameter values. For B close to1 the addition of a marketed species increases the optimal level of effort. As the number of species increases, however, the effect of an additional species on optimal effort falls, eventually becoming negative. If the diversity of species had no implications for either the value of harvest or for the growth of fish stocks, the optimal strategy would be to reduce the number of species to one. From an ecological perspective, elimination of all species and all trophic levels bar one would effectively destroy the system, but simplification of a fishery to the point where the number of target species is reduced to one is not uncommon. Remember that the value-adjusted or bioeconomic diversity index used in the model measures the diversity of catch weighted by the economic value of the species involved. Indeed, in the empirical case investigated in this paper it measures the diversity of species weighted by their market value. In most cases the aggregate value of the catch is not independent of the diversity of species in that catch. That is, p = p(B), and dp/dB < 0 over at least some range of B: i.e. the value of the aggregate catch increases over at least some range of B. This has implications for the fishery response to any change in environmental conditions. 4. Parameter Estimation There are several methods of estimating parameters of the Gordon-Schaefer model when the only data available are on fish catch and effort (see for example Conrad and Adu-Asamoah, 1986; Ludwig and Walters, 1989 and Uhler, 1980). The three most widely used methods are due to Schaefer (1957), Fox (1970), and Schnute (1977) models. The major differences between the models are that the Schaefer (1957) and Schnute (1977) assume parabolic or logistic growth functions, while Fox (1970) assumes a Gompertz function. In addition, while Schaefer (1957) and Fox (1970) are finite difference models, Schnute (1977) is a continuous dynamic model. Although some studies have used finite difference models, these models tend to perform poorly in non equilibrium conditions. Integrated models are better able to represent the dynamic nature of fishery yield and effort interactions (Schnute, 1977; Hilborn and Walters, 1992; Clarke et al., 1992). They also avoid a major problem with the Schaefer (1957) and Fox (1970) models – that in contradiction to basic theory, the latter predict catch per unit effort without specifying anticipated effort. This paper uses the Schnute (1977) method to estimate the parameters r, q, and K. We first define an equation for catch per unit effort (U). Since Y = qBEX it follows that Y/BE = qX = U and hence that X = U/q (17) The population growth function can therefore be expressed in terms of U: X = rX(1 - X/K -eW) - qBEX may be written in the form: U = rU(1 - U/qK- eW) – qBEU (18) and hence, as: U r = r - qBE U reW U qK (19) Adding time subscripts and integrating from t to (t+1) yields, ln ( r U st+1 ) = r - qE t U t reWt qK U st (20) where U is catch per unit effort. Since integrating over some time period involves time averaging (21) over that period the definition of fishing effort, Et, is total effort per year2. The same applies to Y, the catch rate, so that Ut is the annual catch per unit effort. Equation (24) suggests that a linear regression of ln (Ust+1/Ust) against the three variables Et, Ut, and Wt might be used to estimate the parameters r, K, q and e. However, note that Ust is catch per unit effort at the beginning of year t. This creates a problem in that while typical fisheries data include Et and Ut, they do not include Ust and Ust+1. We proceed by assuming that the catch per unit effort at the start of year t is approximately equal to the annual catch per unit effort for the preceding year3. That is, Ust Ut-1, which also implies that Ust+1 Ut. Using this approximation the key equation becomes, ln ( r Ut ) = r - qE t U t reWt t qK U t -1 (21) A two-year moving average is used to smooth the data, and to reduce bias in the parameter estimates arising from the assumptions made about the error term (t). The estimation equation becomes, ln Xˆ * t = r - q Eˆ *t - r * * Uˆ t - reW t + t qK (22) where ( Eˆ t -1 + Eˆ t ) * ; Eˆ t = Et Bt ; Eˆ t = 2 * Uˆ t -1 + Uˆ t ; ˆ = Y t ; Ut Uˆ t = 2 E t Bt W t -1 + W t * ; Wt = 2 * Uˆ t * ˆ Xt = * . Uˆ t -1 5. Estimation of the model The model is applied to the traditional gillnet fishery of the south west arm of Lake Malawi. The south west arm of Lake Malawi is approximately 50km long, 30 km across and reaches a depth of 100m in the centre. Most of the shoreline, and particularly the south coast is heavily reeded, backed by extensive marshes and small lagoons. The north east coast is rocky, and the north west coast has extensive sandy bays with a few minor rocky outcrops. Three islands called the Maleris are an important feature of this region and an intensive chilimira fishery operates in their vicinity. 2 The integral of the effort rate (E) is the total effort in that year. It is acknowledged, as Schnute (1977) also does, that strictly put, Ut is the average of the ratio Y/E which does not always equal to the ratio of averages Yt/Et, but that this is in many cases the best approximation available. 3 A major river, the Linthipe, flows into the lake opposite the Maleri Islands (Tweddle et al., 1994). The south west arm of the lake is part of the most productive portion of the lake. The northern and central portions of the lake, though employing almost half of the fishers, produce less than one-quarter of total yield. The rest comes from the southern end of the lake (Turner, 1995). The greater fish yields from the south are due to limnological conditions. The northern part of the lake is delimited by geological faults, which create deep steep shores in excess of 200m. The shelf area suitable for fishing is also very narrow. The southern part of the lake has wider gently shelving shorelines with depth of 50 - 60m. This creates suitable conditions for fishing. The southern part of the lake is more productive largely due to the influence of the upwelling of nutrient rich water under the influence of the strong southerly winds. In the shallow southern portions of the lake, winter mixing drives the thermocline to the bottom and the entire water column mixes throughout this region of the lake. The existence of internal waves also helps in mixing the water (Eccles, 1974; FAO, 1993; Twombly, 1983). The study focuses on the traditional fisheries since they contribute about 90 percent of the country’s total fish output. The choice for the gillnet fishery is due to the fact (a) that it is the most favoured fishery, accounting for more than 40 percent of total traditional catches (Tweddle et al., 1994), and (b) that the gillnet is the most nonselective gear of all. In the south west arm of the lake, for instance, it is the main gear used for the exploitation of four groups of highly valued species: tilapia (chambo), kampango (Bagrus meriodionalis), mlamba (clariid catfish) and nchila (Labeo mesops). Thus, no other gear catches more of these species than does the gillnet. We first estimate the parameters of the model. These parameters are then used in the estimation of open access, MSY and optimal solutions of the gillnet fishery. They are also used in the investigation of the biodiversity-productivity relationship, which analyses the impact of changes in biodiversity on open access and optimal solutions. The four equations to be estimated are: ln X *t = r - qE*t - r * Ut + qK (23) ln X *t = r - qE*t - r * U t - reW *t + qK (24) ln Xˆ *t = r - q Eˆ *t - r * * Uˆ t - reW t + qK (25) ln X *t = r - q E*t - r * * U t - reW t + qK (26) where X *t = * * U *t Uˆ t Ut * * ˆ = = ; ; ; Xt Xt * * * U t -1 U t -1 Uˆ t -1 ( ˆ +ˆ ) ( + ) ( E t -1 + E t ) ; Eˆ*t = E t -1 E t ; E*t = E t -1 E t ; Eˆ t = Et * Bt ; Et = Et * Bt 2 2 2 ˆ ˆ + + U t -1 + U t ˆ * U t -1 U t ; Ut = ; U *t = U t -1 U t ; U t = Y t ; Uˆ t = Y t ; U t = Y t . U *t = 2 2 2 E t Bt Et E t Bt W t -1 + W t . W *t = 2 E*t = Yt represents the aggregate fish catch, Et is the level of fishing effort4 and Ut is the catch per unit effort. Wt is an environmental variable and μ is the error term. The annual level of fish biodiversity is measured by Bt. The weighted biodiversity index is represented by B t. The dependent variable for the equations is an index of relative change in fish biomass. The parameters to be estimated are; r, the intrinsic growth rate, q the catchability coefficient, K the environmental carrying capacity, and e the parameter that relates how much a unit of the environment variable Wt reduces the relative growth of fish biomass. Equation 23 is used to estimate the parameters of r, q and K5 when the impact of changes in environmental conditions and biodiversity are ignored. Equation 24 estimates the parameters when the effect of water pollution, as an environmental variable on fish productivity is included. The amount of rainfall in the catchment area of the south west arm of Lake Malawi is used as a rough indicator of the level of water pollution. An ideal measure of water quality should have taken into account the level of chlorophyll A, or the concentration of nutrients and suspended sediment levels in the surface mixed water-layer of the lake. Unfortunately, this detailed information is not available on a long-term basis. However, it has been observed that annual yields of sediments and nutrients deposited in the lake are dependent on the amount of rainfall in the catchment area. In particular, it has been noted that intensive rainfall leads to high deposits of sediments and nutrients into the lake. For example in the high rainfall year of 1997/98, the deposit of suspended sediments from the southern catchment area of Lake Malawi were nearly 50 percent greater than in 1996/97 (Hecky et al., 1999). The amount of rainfall is used as a proxy for the level of water pollution based on the observed dependency of annual nutrient yields, on the amount of rainfall. The use of rainfall figures also indirectly captures the impact of river discharges from Linthipe River, which is one of the largest riverine contributors of nutrients and sediments into the lake (Mwichande et al., 1999). Rainfall data have also been used in other related studies. For example, Mkanda and Barber (1999) have used rainfall energy derived from rainfall data to develop a geographical information system (GIS) model for the prediction of soil loss, and sedimentation in Lake Malawi. In addition to the flow conditions, annual yield of sediments and nutrients are also determined by disturbance of the catchment land surface due to extensive cultivation and deforestation. These practices lead to soil exposure and soil erosion. Extensive agriculture within a catchment causes catchments to have higher than average yields of sediments and nutrients (Hecky et al., 1999). Thus, changes in land use affect the concentration and yield of sediments and nutrients. Intensive use of fertilisers and other chemicals have a similar affect. 4 For the gillnet fishery, effort is expressed in number of sets of 91m (stretched length) net per year. 5 Assuming that r/qK = c, then K = r/qc The economic problem is due to the fact that people earn more from the short-term exploitation of the catchment than from its long-term conservation. The long-term benefits of protecting the catchment area do not stimulate adoption of better land use practices. At the same time, those who benefit from the short-term exploitation of the catchment seldom pay the full social and economic cost of their activities. These costs are largely borne by the lakeshore communities. Conservation of the catchment area can, therefore, be thought in terms of a public good in that those who benefit from it rarely pay the full cost. In this case water pollution and sedimentation can be considered as a function of rainfall amount, runoff, erosion, and fertiliser and chemical use. Thus, a better measure of water pollution can be obtained by including these factors. However, due to data limitations, these factors have not been considered in the measurement of water pollution and sedimentation, but are being highlighted because they have important policy implications for the conservation of biodiversity. Equation 25 includes an environmental variable and a biodiversity measure. The biodiversity measure reflects the fishing-up process whereby fish stocks are gradually depleted from abundant to less abundant species and from easily caught to less easily caught species. Equation 26 is similar to Equation 25 except that it uses the weighted bioeconomic diversity index. The weights reflect market prices. This is based, again, on the observation about the development of a fishery where the sequence of exploitation is from high valued to less valued species (Boechlert, 1996; Pauly et al., 1998). The equations are estimated using data on fish catch and price per species, fishing effort, cost of effort, and rainfall as a proxy for the level of water pollution. The period of study is between 1976 and 1998. In Malawi data on rainfall is collected by the Meteorological Department and is available from the Malawi National Statistical Yearbook. Data on fish catch and price per species and fishing effort were obtained directly from the Malawi Fisheries Department. No data are regularly collected on the cost of effort because it is very difficult to cost fishing effort in a traditional set-up (FAO, 1993). The cost of effort is calculated on the assumption that rents are dissipated due to open access conditions. Thus since, pY cE 0 it follows that c = pY/E (27) where is the net revenue. Regression results for Equations 23, 24, 25 and 26 are reported in Table 1. Table 1: Regression results Equation R Q r/qK 23 -0.1275 -0.00000031 42.813 (-0.4850) (-0.8312) (1.4895) 1.1606 -0.00000052 47.575 24 re -1.221 R2 F Statistic DW Statistic 0.197 2.2094 1.5566 0.431 4.2934 1.4136 25 26 (2.1581) (-1.5740) (1.9059) (-2.6440) 1.4162 -0.0000025 13.184 (3.6076) (-3.9976) (1.4734) (-3.8150) 1.2331 -0.000002 22.6429 -1.244 (3.2994) (-4.6553) (2.0289) (-4.0536) -1.338 0.655 10.7810 1.3628 0.742 16.3267 1.3309 Figures in parentheses are t-statistics The results from Equation 23 are poor. It gives a negative rate of growth, r, and all the parameter estimates are statistically insignificant. The goodness of fit, R2, is very low and the corresponding F-statistic is statistically insignificant. The coefficient of average fish biomass, r/qK, is positive coefficient. Since the coefficient measures the density dependent growth rate, it should be positively related to the relative change in average fish biomass. A decrease in the density dependent growth rate, for example, will lead to a decline in fish biomass. That is, starting with a small level of fish biomass and with little or no exploitation, the average fish biomass index, Ut*, will increase, until it approaches a maximum value (maximum carrying capacity). The density dependent growth rate will fall until it is equal to the intrinsic growth rate, r, and the relative change in average fish biomass will fall as the fish biomass approaches its carrying capacity. The poor performance of the equation matches earlier findings on catch and effort in the gillnet fishery of the south west arm of Lake Malawi. These showed that while there was a trend to decreasing catch per unit effort at higher effort levels, the data were erratic and the trend was not significant. In particular, it was noted that the data were strongly influenced by high catch per unit effort in certain years that were due to environmental effects and not to changes in fishing effort (Tweddle et al., 1994). A similar argument was made for the findings in the south east arm of Lake Malawi (Tweddle and Magasa, 1989; Tweddle et al., 1991a) and Lake Malombe (Tweddle et al., 1991b). For the gillnet fishery of the south west arm of Lake Malawi, no attempt was made to estimate maximum sustainable yield (MSY) levels, because it was obvious that the data could produce grossly misleading results (Tweddle et al., 1994). In other cases where the MSY levels were calculated (for example FAO 1976, Tweddle and Magasa 1989, and Turner 1995) those calculations are treated with caution since they were mostly influenced by high catch and effort levels of certain years. Equation 24 includes a measure of water pollution as one of the explanatory variables. Regression results of the equation (Table 1) indicate a substantial improvement in goodness of fit, from 20 percent for Equation 23 to 43 percent. Moreover, the F-statistic is statistically significant at the 2 percent level of significance. The intrinsic growth rate is positive and significant at the 5 percent level. The coefficient of the environmental variable takes the expected negative sign and is also statistically significant at the 5 percent level. That is, an increase in water pollution negatively affects the rate of change of the average fish biomass. This is in agreement with other studies that find that, controlling for fishing effort, fluctuations in fish catch can be explained by changes in the environmental conditions of the lake (Tweddle and Magasa, 1989). The introduction of an ecological biodiversity index as a factor affecting fish productivity, further improves the model fit (Table 1, Equation 25). The R2 increases to 66 percent and the corresponding F-statistic is significant. Except for the density dependent growth rate, r/qK, all parameter estimates are statistically significant at the 5 percent level. These results are compared to those obtained by using a weighted bioeconomic diversity index, Equation (26). The significance of the density dependent growth rate has improved together with the other coefficients. The model now explains 74 percent of the variation in fish biomass. Diagnostic tests reveal no serious problem with multicollinearity or heteroscadasticity. However, autocorrelation tests using the Durbin-Watson (DW) statistic yielded inconclusive results for Equations 25 and 26. Taking the upper limit of acceptance region as the appropriate significance limit (Maddala, 1992; Gujarati, 1995), this implies the existence of statistically significant first-order positive correlation of the error terms. To improve the efficiency of the parameter estimates, autocorrelation is corrected using a Prais-Winsten transformation (Greene, 1997). Corrected results are reported in Table 2. These are used in the following section. Table 2 Regression results corrected for autocorrelation. Equation R Q r/qK 25 1.3755 -0.0000022 22.563 (3.3150) (-3.462) (2.2750) 1.3591 -0.0000019 27.4507 (3.3330) (-4.232) (2.3140) 26 re -1.4817 R2 F Statistic DW Statistic 0.655 10.7810 1.7615 0.742 16.3267 1.7542 (-4.206) -1.4422 (-4.434) Figures in parentheses are t-statistics 6. The importance of biodiversity in the fishery Now consider the importance of biodiversity. Since we wish to relate biodiversity to the structure of property rights and the regulatory regime in the fishery, we first consider the open access, MSY and profit maximising outcomes in the absence of a bioeconomic diversity index. The corrected parameter estimates are r = 1.3591, q = 0.0000019, K = 25954.98, and e = 1.06. These parameters are used to calculate the open access, MSY and optimal solutions, assuming B = 1. The results are reported in Table 3. The price of output is set at the average beach price for fish in 1997, K562.14 per tonne6. Cost per unit effort is again set at the average for the fishery over the same year, K1.70. Pollution is proxied by rainfall. This takes the form Wtn =Wt/Wav where Wtn is the normalised index, Wt is the amount of rainfall in year t and Wav is the average rainfall. Since the value of B ranges between 1, where only one species is marketed, and 1/s, where s species are marketed, the assumption that B = 1 implies that for this exercise we are ignoring the impact of changes in the marketed value of different species. That is, we are treating the fishery as if it was a single species fishery. Table 3 Estimates of catch, effort and stock levels for open access, MSY and optimal exploitation in the ‘single species’ fishery. Variable Open Access MSY Optimal Actual Average Catch (Y) 879.84 1943.30 1910.40 2194.94 Effort (E) 290936 167227 145468 439490 6 K = Kwacha, the currency in Malawi. Stock (X) 1585.35 6091.92 6884.59 2628.57 These results are typical of single species Gordon-Schaefer fisheries models whether in freshwater or marine fisheries (Conrad and Adu-Asamoah, 1986; Gallastegui, 1983). The open access solution produces the lowest catch level associated with the highest level of effort. The MSY solution gives the highest level of catch and the optimal solution gives the lowest level of effort. Figures for the actual average indicate over-exploitation by comparison with the ‘single species’ fishery, since the average catch is higher than the MSY catch and the average effort is above the MSY effort level. Since MSY does not change with the biodiversity index the overexploitation is not an artefact of the choice of B = 1. Indeed it is widely recognised that the fishery was overexploited during the period analysed, 1986-1997. The results on effort levels would, however, be affected by the diversity of harvest. The bioeconomic index captures the effect of market valuation of harvest. The unweighted Simpson’s index of catch might be a reasonable approximation of a bioeconomic index in a subsistence fishery in which there is no by-catch, and all the species are consumed directly. The weighted index reflects the fact that demand is higher for some species than others, and that this influences which species are targeted by fishers. Lower bioeconomic diversity implies that fewer species are commercially valuable, and/or that fewer species are targeted by fishers. Since most fisheries in Lake Malawi, including the gillnet fishery, are market-driven, the weighted index is the appropriate measure of the diversity of catch. Recall that proposition 2 holds that in both open access and profit maximising fisheries, an increase in the bioeconomic diversity of catch implies an increase in the size of the fish stock, but that the impact on the optimal level of effort in each case depends on the parameters of the model. For B close to 1, an increase in the bioeconomic diversity of catch implies an increase in stock size. As the number of species rises, the effect on optimal stock size reverses, and an increase (decrease) in fish biodiversity implies a decrease (increase) in stock size. To investigate the diversity-productivity link in the fishery, we consider the relationship between biodiversity, fish stock and catch under both open access and profit maximising rules using the same data set. Specifically we calculate the sensitivity of the open access and profit maximising solutions to variation in the bioeconomic diversity of catch. Both cost per unit effort and the discount rate are held constant. Moreover, because we are interested in changes in relative prices only, the average landed price of fish is also held constant. The results are used to fit relationships between biodiversity, fish stocks, effort levels and catch under both an open access regime (Figure 1) and a profit maximising regime (Figure 2). Figure 1 illustrates the relations identified in proposition 2 for an open access fishery. It shows that fish stocks decline as the bioeconomic diversity index rises (i.e. as bioeconomic diversity falls). If the initial bioeconomic diversity of catch is high, both effort and catch initially increase as diversity falls, but later fall along with the stock size. (Figure 1 here) Figure 2 shows the same data for a profit maximising fishery. As in the open access case, stock size declines monotonically as the bioeconomic diversity of catch declines. In a fishery with initially high levels of bioeconomic diversity, effort similarly increases as diversity falls. After some point effort begins to fall as the size of the fishery is itself reduced. Catches nevertheless increase monotonically as bioeconomic diversity falls. (Figure 2 here) In both regimes the impact of bioeconomic diversity loss on stock sizes and effort reflects the assumption that bioeconomic diversity is negatively related to the effectiveness of fishing effort. This relation does not necessarily hold in all fisheries, but it appears to be common in fisheries in which species are successively eliminated. The sharp reaction to a reduction in bioeconomic diversity in initially diverse open access fisheries is consistent with the general results on open access. Gordon’s (1954) observation - that any increase in productivity due to a change in bioeconomic diversity will result in a positive rent that will attract new entrants – holds here. Thus, under open access all the potential benefits of a fall in bioeconomic diversity are dissipated. The result is that fish stocks under open access are lower at all levels of bioeconomic diversity than is the case in a profit maximising regime. We have not considered the relation between the diversity of fish catches and either the value of harvest or the direct cost of effort. However, both are potential policy levers on fisheries. If p = p(B) with dp/dB < 0, implying that the value of harvest is an increasing function of the diversity of catch, or if c = c(B) with dc/dB > 0, implying that the cost of fishing effort is a decreasing function of the diversity of catch, then the change in effort levels associated with a change in the diversity of catch will be strictly less than the case described in this paper, where dp/dB = 0 dc/dB = 0. In the open access case, for example, dEOA rc dp dB r dc dB rq 1 eW rc 2 2 3 2 2 2 dB qb q B pK qB p K qB 2 pK (27) The effect of the last two terms on the RHS of (27) is to reduce the impact of change in the bioeconomic diversity of catch on fishing effort. This would increase the optimal stock size in an open access regime. 7. Concluding remarks What are the inferences to be drawn from this? A Gordon-Schaefer model modified to include both environmental and bioeconomic diversity variables has been shown to fit the data of the gillnet fishery of the south west arm of Lake Malawi much better than a standard GordonSchaefer model. This suggests that despite the inevitable errors involved in using a single species format to analyse a multispecies fishery, it is possible to explain a very high proportion of the variation in estimated stock size, catch and effort if a ‘single-species’ model includes a measure of the diversity of catch. Furthermore, if the measure of diversity is weighted by the economic value (market value in this case) of species, the model turns out to have considerable predictive ability. The bioeconomic diversity measure used in this paper captures the effect of a change both in the relative abundance of marketed species, and in the relative prices of those species. If an increase in bioeconomic diversity reduces the effectiveness of fishing effort, as we assume in this paper, then there will be greater pressure on low diversity than on high diversity systems in both open access and profit maximising regimes. The assumption that bioeconomic diversity may reduce the effectiveness of fishing effort relate to the specificity of fishing gears, the problems of bycatch in non-specific gears and so on. It is an empirical question as to whether the assumption would hold as well for other fisheries as it does for the Lake Malawi fisheries. As one would expect, the pressure on stocks is greater at all levels of biodiversity in open access than it is in profit maximising regimes. However, the sensitivity analyses of section 6 reveals another interesting difference between open access and profit maximising regimes. In both cases effort levels first increase and then decrease as the bioeconomic diversity of catch falls. However, in a profit maximising regime both catch and the productivity of fishing effort is highest when the bioeconomic diversity index is 1 - there is a single marketed species. By contrast, in an open access regime the catch size reaches a maximum at a relatively low value of B. That is, open access catches are maximised at higher levels of bioeconomic diversity than in profit maximising regimes. The efficiency of a profit maximising regime favours specialisation of catch and simplification of fishing markets. The maximum harvest is similar in each case. The stock size corresponding to that harvest is slightly lower in the open access than the profit maximising case, but the diversity of the catch is much higher. This accords with the general evidence on freshwater fisheries, where traditional open access regimes have typically been less selective in the set of harvested species than is the case in commercial fisheries, which tend to be highly selective. The implication of this is that commercial fisheries will tend to focus on the most highly valued species at any one time, and will adapt fishing gear to that species. This implies that optimal exploitation strategies aimed at maximising profits may well lead to a loss of diversity within the fishery through the phenomenon we have called ‘fishing down the value chain’. Traditional open access regimes still lead to the overexploitation of fisheries regardless of the level of biodiversity. Indeed, open access regimes are particularly damaging in single species fisheries. However, they are seemingly less damaging in high diversity than in low diversity fisheries. Given the scope for managing the diversity of fisheries through the use of instruments that work on either the value of catch or the cost of effort, there is scope for policies both to mitigate the damaging impact of open access regimes, and to reduce the biodiversity effects of commercial fishing. Figure 1: The effect of bioeconomic diversity of catch on stock size, effort and catch in an open access fishery 12000 25 20 8000 15 6000 10 4000 Harvest (tonnes) Catch (tonnes), Effort/100 10000 5 2000 1 95 9 0. 0. 85 8 0. 0. 75 7 0. 0. 65 6 0. 0. 55 5 0. 0. 45 4 0. 0. 3 35 0. 0. 25 0. 0. 0. 2 0 15 0 Bioeconomic diversity index Xoa Eoa Yoa Figure 2: The effect of bioeconomic diversity of catch on stock size, effort and catch in an profit maximising fishery 12000 25 8000 15 6000 10 4000 5 2000 Bioeconomic diversity index Xo Eo Yo 1 95 0. 9 0. 85 0. 8 0. 75 0. 7 0. 65 6 0. 0. 5 55 0. 0. 0. 4 0. 45 3 35 0. 0. 25 0. 0. 2 0 15 0 Catch (tonnes) 20 0. Stock (tonnes), effort/100 10000 References Banda, M., T. Tomasson, and D. Tweddle, (1996), ‘Assessment of the deep water trawl fisheries of the South East Arm of Lake Malawi using exploratory surveys and commercial catch data’, in I.G. Cowx (ed.), Stock Assessment in Inland Fisheries, Fishing News Books, Oxford: Blackwell Science Ltd: 53-74. 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