© 2005 International Council for the Exploration of the Sea
Estimation of Atlantic salmon smolt carrying capacity of rivers using expert knowledge
a Department of Biological and Environmental Sciences, University of Helsinki PO Box 65, FI-00014 University of Helsinki, Finland
b Finnish Game and Fisheries Research Institute, Oulu Game and Fisheries Research Tutkijantie 2 A, FI-90570 Oulu, Finland
*Correspondence to L. Uusitalo: tel: +358 9 191 58992; fax: +358 9 191 58257. e-mail: laura.uusitalo{at}iki.fi.
A mixed salmon fishery with both natural wild salmon stocks and reared salmon exists in the Baltic Sea. The agreed-upon goal of management is to safeguard the wild stocks, and the practical management objectives have been agreed to attain at least a 50% maximum salmon production capacity in each river. This natural production capacity is, however, largely unknown. Here, a new approach has been used to estimate the salmon maximum production capacity of northern Baltic Sea rivers. A probabilistic salmon production capacity model was built entirely upon expert knowledge. The model describes the external physical and biological factors of the rivers and the juvenile salmon stocks' response to these factors. We found that the experts estimated the carrying capacity to be considerably higher than former estimates. A very high uncertainty was, however, connected with these estimates. We also found considerable disagreement over the general carrying capacity level among the experts; the major uncertainty emerged from the conflicting views of the experts. The result implies that perhaps operational management objectives other than those based on maximal smolt production levels should be considered to decrease the uncertainty connected with evaluation of management success.
Keywords: Baltic salmon, Bayesian belief network, carrying capacity, expert knowledge, probabilistic modelling, smolt production, smolt production model, wild salmon
Received 18 June 2003; accepted 22 October 2004.
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Introduction |
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The Baltic Sea (Figure 1), located in Northern Europe, is one of the world's largest brackish-water bodies, covering an area of 420 000 km2. The Gulf of Bothnia, referred to hereafter as the northern Baltic Sea, is the northernmost arm of the Baltic Sea, and has the highest amount of run-off: 12 dm3 s–1 km–2 (Ehlin, 1981).
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The salmon population in the Baltic Sea belongs to the Atlantic salmon species, Salmo salar L., but is genetically isolated from those populations living in the Atlantic (Ryman, 1983; Ståhl, 1987). Tagged Baltic salmon are very rarely reported outside the Baltic area (Christensen and Larsson, 1979; Christensen et al., 1994). Baltic rivers were strongly modified during the 19th and 20th centuries by regulation for hydroelectric power production, logging, pollution, etc., and these operations have reduced the number of rivers available for salmon reproduction.
The Baltic Sea salmon fishery relied heavily upon wild populations in the early 20th century (Lindroth, 1974; Christensen et al., 1994). Attempts have been made to counteract the threats of river modifications to the salmon fishery. Sweden initiated a program of releasing hatchery-reared salmon fry into rivers as early as in the 1860s, and in 1987 the total rearing in the Baltic Sea exceeded 5.5 million smolts (Ackefors et al., 1991). Constant intensive stocking promotes the salmon fishery but also provides a potential threat to wild salmon stocks, because it enables high fishing pressure without risking recruitment collapse of reared stock. Thus, the rearing system has removed one of the mechanisms that usually restrict interest in increasing fishing pressure. The Baltic salmon fishery consists mostly of a typical mixed-stock fishery, in which reared salmon cannot be harvested without also harvesting wild salmon to some extent.
Wild salmon stocks are present in 13 rivers discharging into the northern Baltic Sea (Figure 1). These rivers include (i) the Simojoki (hereafter referred to as the Simo) in Finland, (ii) Tornionjoki (Tornio) on the Finnish-Swedish border, and (iii) Kalix älv (Kalix), (iv) Råne älv (Råne), (v) Pite älv (Pite), (vi) Åby älv (Åby), (vii) Byske älv (Byske), (viii) Rickleån (Rickle), (ix) Sävarån (Sävar), (x) Ume/Vindelälven (Vindel), (xi) Öre älv (Öre), (xii) Lögde älv (Lögde), and (xiii) Ljungan (Ljungan) rivers in Sweden. In addition, salmon smolts have been released into 15 rivers draining into the northern Baltic Sea (IBSFC and HELCOM, 1999). Most wild salmon stocks have been in a poor state for decades (Jutila, 1992; Pruuki, 1993; Karlsson and Karlström, 1994), and hatchery-reared juvenile salmon have been released into eight of these rivers in order to support wild stocks. In 2001, wild stock production was about 20% of total smolt production in the northern Baltic Sea (ICES, 2002).
It is generally accepted that freshwater salmon production must be limited to a certain river-specific level due to the territorial behaviour of salmon parr together with the finite space available in a river (Symons, 1979; Solomon, 1985), and this complex phenomenon is encapsulated in stock-recruitment curves (Symons, 1979; Solomon, 1985; Kennedy and Crozier, 1993; Chaput et al., 1998). In cases where a maximum of the stock-recruit curve can be indicated, it represents potential maximum smolt production. This level is determined by the physical, chemical, and biological characteristics of the river environment. It is generally accepted that the wild Baltic salmon stocks have not reached this level during the last decades owing to the poor state of the stocks (Karlsson and Karlström, 1994; ICES, 2001a).
North Atlantic salmon stocks have been managed by establishing egg deposition and spawning stock reference points based on stock-recruitment relationships, in which the potential productivity of the rivers naturally plays a major role (CAFSAC, 1991; ICES, 2000; Potter, 2001). There are numerous options for stating the principles and objectives for deriving reference points from stock-recruitment curves (Potter, 2001). In Atlantic Canada, for instance, the reference points aim at optimizing the number of spawners so that the fullest sustainable advantage is derived from the salmon resource, and the resource is maintained (CAFSAC, 1991). These principles and objectives are then given operational management objectives, like river-specific spawning stock targets or limits.
The International Baltic Sea Fishery Commission (IBSFC), which manages the Baltic salmon fishery, has the specific goal of "safeguarding of wild salmon stocks". The corresponding operational management objective is to increase the natural production of wild Baltic salmon to at least 50% of the natural smolt production capacity (SPC) of each river by 2010, while retaining the catches at as high a level as possible (IBSFC, 1995). To support the IBSFC's goal of increasing smolt production, SPC estimates are needed for each river. These estimates bear a direct link to the required management actions, and therefore this information plays a very important role in the overall assessment of salmon stocks.
No stock-recruitment curves have been established for Baltic salmon (Romakkaniemi et al., 1995), and only for a limited range of index rivers for North Atlantic salmon (ICES, 2000). Attempts have been made to estimate the SPC of northern Baltic rivers over the course of decades, the main methods of which are described by ICES (1999), and the most regularly referred estimates have been used as reference points in the assessment and management of Baltic salmon. However, the bases of these estimates are shaky and the recent increase in Baltic salmon populations (Romakkaniemi et al., 2003) indicates that some of the proposed "maximum values" are clearly underestimates. Furthermore, the earlier estimates have been point estimates, and risk-averse fisheries management, such as the precautionary approach, should be based on uncertainty estimates. Furthermore, we argue that the uncertainty of the operational objectives should be considered in management.
Opinions differ among salmon biologists in Sweden over the SPC in northern Baltic Sea rivers (L. Karlsson, National Board of Fisheries, Sweden, pers. comm.). Former estimates of SPC have varied between 1 and 3.5 smolts per 100 m2 of nursery area (Karlström, 1977; Jutila and Pruuki, 1988; Kemppainen et al., 1995), which corresponds to 0.3–1.5 smolts per 100 m2 of total fluvial habitat (i.e. not only nursery areas, which are suitable habitat for salmon parr) accessible to salmon (Romakkaniemi et al., 1995). In Atlantic Canadian rivers, the SPC of 3 smolts per 100 m2 of total fluvial habitat is considered average and in Atlantic European rivers even this value has been considered too low (ICES, 1994). This has led a group of salmon biologists to believe that the earlier Baltic estimates for SPC are far too low.
Salmon production in the Baltic has never been measured under conditions enabling maximum production; thus this controversy remains unresolved. It is likely that the available Baltic stock information cannot be very informative about maximum production rates, since the exploitation rate has been fairly high over the years for which data are available. However, the Baltic salmon is currently studied extensively by a large repertoire of methods at varying stages of its life cycle (Romakkaniemi et al., 2003). We believe that these studies lay an adequate basis for indirect reassessment of the SPC provided that the various pieces of information can be sensibly combined. This reassessment could later on be updated by data-based probabilistic models by setting the expert opinions as priors.
In the natural sciences, the role of subjective expert knowledge does not play an essential role in decision making. In some cases it is even considered to be a negative element. However, it is obvious that in most applied questions data cannot cover all the elements of required knowledge. Subjective knowledge must then be used, e.g. in model selection, parameter assumptions (such as natural mortality), risk attitude, etc., and it would be useful to apply tools that enable the systematic use of subjective expert knowledge. Our view is that applied science should not avoid the use of subjective expert knowledge, but it is the duty of the scientists to demonstrate the impact of subjectivity on the scientific results.
The present analysis is not the first Bayesian treatment of this type of problem. For instance, Kuikka and Varis (1997) applied networks to watershed analysis (see also Reckhow, 1999), and Varis and Kuikka (1997) analysed adult Baltic salmon populations with a probabilistic VPA model. Lee and Rieman (1997) and Shepard et al. (1997) applied belief networks to other salmonid populations, Kuikka et al. (1999) to cod management analysis, and Hammond and O'Brien (2001) applied networks to assessment of model uncertainty.
The present paper has two major goals: to present probabilistic estimates of the SPC of wild salmon rivers in the northern Baltic Sea area and to demonstrate a methodology for deriving prior probability distribution that is based on expert knowledge of a complicated system. We apply Bayesian belief network methodology, which is considered to be an important tool in applied ecological analysis (Edwards, 1996; Ellison, 1996, 2004) and in fisheries management (Punt and Hilborn, 1997; McAllister and Kirkwood, 1998).
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Methods |
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Bayesian statistics
Bayesian statistics are based on Reverend Thomas Bayes' (1702–1762) theory of probability. The core of Bayesian statistics is the use of probability as a measure of uncertainty. Beliefs about variable values are expressed as probability distributions, and the higher the uncertainty of the real value, the wider is the probability distribution. As information accumulates, knowledge of the true value of the variable usually becomes enhanced, i.e. uncertainty of the value diminishes and the probability distribution grows narrower (Gelman et al., 1995; Sivia, 1996).
The basic idea of Bayesian models is to analyse the uncertainties of the variables by means of probability distributions and to examine the interdependencies of the variables by means of conditional probabilities. In Bayesian networks, each variable is represented by a node in the network and causal relationships are represented as arcs between these variables (which are often called parents and children; Jensen, 2001). Each of the variables has one or several probability distributions related to it. If the variable does not have any parents, i.e. is not dependent on any other variables (in the model universe), it has one probability distribution stating the probabilities of its possible values. If the variable has parents, it has several probability distributions, one related to every possible combination of the values of its parents. The Bayes' Theorem can then be used to compute all other probabilities. The graphical network comprises a description of probabilistic relationships among the variables, and allows for the computation of any desired probabilities.
For example, assume a three-variable model in which A is the parent of B and C. Initially, we have probability distributions for A, B given A, and C given A. Using Bayes' rule, we can compute probability distributions for A given B, A and B given C, etc. After introducing probabilistic observations to some part of the model (one or several variables), the probability distributions in other parts of the model are updated according to their mutual dependencies. Jensen (2001) gives a comprehensive introduction to Bayesian networks.
Bayesian methods are increasingly used in modelling of complex environmental interactions (Reckhow, 1999; Marcot et al., 2001; Borsuk et al., 2004). They have also been found to be a good way to formalize expert opinion and combine expert knowledge and experience with existing data (Marcot et al., 2001). Clemen and Winkler (1999) noted that expert judgements have been used informally for many years, but that consulting several experts more formally in forecasting and risk analysis situations increased after World War II.
Use of a model that divides the problem into a set of smaller problems hints at which quantities are the most uncertain, or spark the most disagreement among experts, and aids in tracking the roots of the controversy regarding the maximal SPCs. Furthermore, Morgan and Henrion (1990, pp. 163–164) noted that experts may have cognitive difficulty in estimating probability distributions over many dimensions. Structuring the problem into subproblems reduces the dimensionality of the problem and thus helps the experts to give the required probability distributions reasonably.
Smolt production capacity model
Our model summarizes the current expert knowledge of SPCs of northern Baltic salmon rivers. The model was constructed in cooperation with salmon experts and aims to describe all the noteworthy factors that affect salmon smolt production, while striving to remain as simple as possible. The variables of the model were chosen so that they adhered to concepts familiar to the experts. Many of the variables in the model are those that are also commonly studied today, such as density of older parr, smolt production, and size of production areas (Karlsson and Karlström, 1994; Romakkaniemi et al., 2003). These monitoring data serve as valuable background information for the experts without modification. These variables correspond to the concepts that experts use when dealing with salmon reproduction. The model aims to be compatible with experts' lines of reasoning rather than to describe the actual relationships of the nature in a detailed manner. Thus it describes a probabilistic justification for the expert views of salmon smolt production.
The model consists of 10 variables (Figure 2, Tables 1 and 2), five of which (chance of successful spawning, habitat quality of parr area, smoltification age, mortality during migration, and size of production areas) describe or reflect the external factors, physical and biological, to which salmon reproduction is exposed in the reproduction rivers. Three variables (parr density capacity, pre-smolt density capacity, and smolt production capacity) describe the juvenile salmon stocks' response to the external factors. The remaining variables, expert and river, are auxiliary variables that enable handling of all the estimates in the same model.
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The first two variables have five discrete classes (Table 2). The lowest class (i.e. very poor) is fixed to describe the situation in the poorest river in the northern Baltic Sea area, and the highest class (i.e. very good) the best salmon production river in the northern Baltic Sea. This relative scale is based on the fact that some part of the required knowledge is related to the intuitive understanding of experts who have spent most of their careers in studying these populations. Current knowledge is based on several small pieces of information, and the model here permits the experts to quantify this knowledge as probabilities.
The variable smoltification age does not aim to reflect a distribution for the smoltification age, i.e. the percentage of parr that smoltify at each age, but the modal smoltification age and uncertainty connected with it. The minimum age of wild smolts in the rivers concerned is 2 years, which means that all salmon juveniles contribute to the densities of older parr (age 1+ and older) prior to smoltification.
Dependencies between the variables (Table 2, Figure 2) are described by conditional probabilities. For example, there is a table that contains the probability distribution of parr density capacity as a function of chance of successful spawning, habitat quality of parr area, and expert. It states the probability distribution, i.e. the probabilities of every possible value, of parr density capacity, given that e.g. the value of chance of successful spawning is "very good" and the value of habitat quality of parr area is "good" and expert is "Expert 1". A probability distribution exists stating the probabilities of different values of parr density capacity for every combination of values of the parent variables, in this case chance of successful spawning, habitat quality of parr area, and expert. Since there are 5 experts, 5 possible values of chance of successful spawning, and 5 possible values of habitat quality of parr area, there are a total of 5 x 5 x 5 = 125 conditional probability distributions in parr density capacity. There are conditional probability distributions of the same kind related to every variable.
The conditional probability tables of the variable smolt production capacity are calculated using the equation:
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The model contains all the expert estimations for all the rivers included in the estimation. A river of interest can be selected from the variable river by giving it a probability of 1. This input updates the probability distributions of the variables that are conditional on river. The changes in probability distributions of these variables in turn affect the probability distributions of parr density capacity and pre-smolt density capacity, and finally that of smolt production capacity.
Expert estimation
Five experienced salmon experts (Lars Karlsson, Ingemar Perä, Ulf Carlsson, Eero Jutila, and Atso Romakkaniemi) from the northern Baltic Sea area assembled for 2 days for the estimation process. The experts represented different views in the controversy over the SPC. Clemen and Winkler (1999) noted that experts who are very similar in philosophy and modelling style tend to provide redundant information, and heterogeneity among experts is thus desirable. The marginal utility of information decreases as the number of experts increases, and using 3–5 experts is suggested (Makridakis and Winkler, 1983; Clemen and Winkler, 1985; Ferrell, 1985).
All the participating experts had access to the same data sets regarding the population dynamics of Baltic salmon. It must be noted, however, that no actual data were used in the estimation except to serve as background knowledge for the experts. This approach was chosen because data on the values for the model variables come from the current situation, not from maximal production levels, and include no estimates of uncertainty.
The first day was used for discussions on the model structure and assumptions, and for ironing out any possible differences in definitions of the parameters. Clemen and Winkler (1999) pointed out that great effort may be required to reach this goal. For successful combination of the estimations it is vital that experts agree on what is to be estimated and on the definitions regarding the model. The experts agreed on the definitions of the variables and on the semantics of the model during these discussions.
The experts together conducted a "warm up-exercise", going through the estimation using as an example a southern Swedish salmon river not included in the analysis. This was intended to help the experts become familiar with the practice of probabilistic estimation in this specific context (Morgan and Henrion, 1990, p. 158). The probability distributions and conditional distributions were also explained in detail to ensure that they were understood in the same way by all experts.
Finally, the experts estimated the probability distributions of the river-specific variables and conditional distributions that link these environmental factors to salmon reproduction. All these distributions were discretized. Each expert did this alone via a questionnaire form, with the possibility to hold discussions with the analyst, if desired. This arrangement was made to ensure that nobody's opinions and interpretations would affect the judgements of others, but that every expert would give the estimates in accordance with his own judgement. Hints also exist that interaction between experts at this stage may increase overconfidence and thus produce poorer results (Morgan and Henrion, 1990, p. 165).
The experts first estimated the probability distributions for the river-specific variables (the solid rectangular nodes in Figure 2) by filling in a questionnaire that included the discretized ranges of the 5 river-specific variables for each river separately. They gave their estimates in the form of probability distributions so that the probabilities assigned to different values of the same variable summed to 1. At this stage, the experts had to estimate the probability distributions of 5 variables in 13 rivers, altogether 65 distributions. The next step was to estimate the conditional probabilities: parr density capacity given chance of successful spawning and habitat quality of parr area included 5 x 5 = 25 distributions to estimate. Pre-smolt density capacity given the values of smoltification age and parr density capacity included 4 x 14 = 56 probability distributions. These distributions encompassed all possible combinations of the parent variables, also those that are very uncommon in the nature.
The probability distributions of the experts were combined by simple average since there is evidence that simple combinational methods outperform group judgements (Gigone and Hastie, 1997) compared with more complex combinational rules (Clemen and Winkler, 1999). The experts were also considered exchangeable in the sense that their probabilities were treated equally and symmetrically (Clemen and Winkler, 1999).
Earlier SPC estimates of Baltic rivers have been based on expert estimates (i.e. there have been few hard facts serving as a starting point augmented by numerous subjective judgements or assumptions), but without detailed justifications or uncertainty estimates.
Comparison with the former estimates
The former Baltic point estimates of the maximal smolt production capacity are results from a varying degree of biological assumptions, calculations based on data and expert judgement (ICES, 1999). Thus, it is at least very difficult if not impossible to infer what type of estimates they are, i.e. do they represent modal values, expected values (mean), median values, or something else with respect to the obvious uncertainty hidden behind them.
As some degree of comparison with the former estimates and the estimates obtained in this study is interesting, we attempted to demonstrate the issue in various ways. The safest way of comparison is to study the amount of probability mass of the new estimates above or below the former point estimates. For demonstrating implications of varying smolt production capacity estimates for the Baltic salmon management objectives we also derived new point estimates by choosing the median (50% chance) values from the corresponding probability distributions, and compared them with the former point estimates of the target smolt production. This effectively means that we assume median values to be comparable to the corresponding former point estimates.
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Controversy between experts
Estimates of both the river characteristics and conditional connections varied widely among the experts, and this caused the peak of the probability mass to be assigned on different values by the various experts. The conflicting views of the experts thus introduced a large degree of uncertainty into the model results.
For example, the highest probabilities of pre-smolt density capacity were estimated to be at values of 0.5–2 pre-smolts per 100 m2 by one expert and 8–12 pre-smolts per 100 m2 by another (Figure 3). The other experts lay somewhere in between, so that no single expert deviated markedly from the opinion of others, but the experts formed a continuum of views (Figure 3).
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The experts were all coherent and logical in their estimations, and there were no inner conflicts in any single expert's assessment. Some of the experts were more certain of their assessments than others in the sense that they gave probability distributions with smaller uncertainty than the others (Figure 3); this was especially the case regarding the conditional probabilities.
Parr and pre-smolt density capacities
The probability distribution of parr density capacity aggregated over all the rivers was smooth, with highest probabilities in values between 4 and 24 parr per 100 m2 and the mean of 12 parr per 100 m2 of nursery area (Figure 4). The probability distribution for pre-smolt density capacity varied as a function of its parent variables (river, expert, chance for successful spawning, habitat quality of parr area). Generally, the distributions were smooth, depicting a high degree of uncertainty in pre-smolt density capacities. The mean pre-smolt density capacity for all rivers and experts was approximately 4.5 pre-smolts per 100 m2 (Figure 3). However, a very high degree of uncertainty is connected with this value, and pre-smolt densities as high as 24–48 pre-smolts per 100 m2 were possible (Figure 3). The pre-smolt density capacities varied between rivers, the mean value ranging from 2 pre-smolts per 100 m2 in the Pite River to more than 6 in the Lögde and Rickle Rivers (Figure 5). These estimates were considered to be very uncertain.
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Smolt production capacities
The resulting probability distributions of smolt production capacity showed higher estimates of the potential smolt production than the previous point estimates. In most cases, 40–80% of the probability mass was assigned higher values than previous estimates of the potential production level (Figure 6, Table 3). However, in the case of the Ljungan River, the probabilistic estimation surprisingly indicated a lower SPC than earlier estimates; almost 90% of the probability mass was assigned values lower than the point estimate proposed earlier (Table 3).
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The greatest SPC was estimated for the Tornio River, the probability distribution peaking strongly at 1–5 million smolts per year (Figure 6). The Kalix River also had high smolt run values, having the highest probability density in 1–5 million smolts. Generally, the probability distributions were rather wide, reflecting high uncertainty in the potential smolt run. This derives naturally from the fact that the pre-smolt density capacities also showed a high degree of uncertainty. ICES (2001a) gave point estimates of wild smolt runs in Baltic rivers in 2001. Some of these estimated that smolt runs even exceeded the previously estimated potential production levels. These values were compared with the SPC estimates created in this study (Table 3).
We have chosen to express the SPC as a probability distribution to explain the uncertainty related to it. The smolt production target is a function of the SPC, and thus it is reasonable to express the target set by the IBSFC as a probability distribution, and to examine how well these targets were achieved. For example, in the case of Pite River, 32% of the probability mass of the target production probability distribution is assigned lower values of smolt production than is the estimate for year 2001. We thus argue that there is 32% probability that the target production was reached (Figure 7), given the expert knowledge available. Probabilities that smolt productions in 2001 achieved the smolt production target of 50% of the potential were calculated (Table 3).
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These probabilities varied widely from 4% in the Öre River to 89% in the Ljungan River (Table 3). The Simo, Ljungan, Åby, and Byske Rivers were the only ones having over 50% probability of achieving target production. The Tornio and Sävar Rivers are close to this stage, having probabilities higher than 40% (Table 3). The situation appears to be the most unfavourable in the Öre, Lögde, Råne, and Rickle Rivers, where the probability is 14% or less. On average, the rivers had 38% probability of achieving the target production level in 2001 (Table 3).
A reasonable management strategy could be to strive toward a situation in which there is at least a 50% probability that the average smolt run for each river achieves the target production. This approach gives new point estimates for the smolt production target (Table 4). As estimates of the potential production become more accurate, the uncertainty in the target production value diminishes. This process may also change the point estimates of target production. Naturally, if a truly precautionary approach is adopted, the probability of achieving the production target should be higher than 50%. The IBSFC objective states that the production of wild Baltic salmon needs to reach 50% of the smolt production capacity by 2010. This would mean that the probability of reaching 50% of the smolt production capacity would need to be 100% (ICES, 2004a). This issue clearly needs further discussions between managers and scientists.
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The revised point estimates for the smolt production targets based on this study are generally somewhat higher than the old estimates, varying between 2200 smolts per year in the Sävar River to almost 1 million smolts per year in the Tornio River (Table 4). Differences between previous and proposed smolt production targets varied widely between rivers (Table 4). In the Ljungan River, the new production target is only 30% of the old target, and in the Öre River the new target is slightly smaller than the old target. In all the other rivers, however, the new production targets are higher than the old target. In the Simo and Sävar Rivers, the change is only about +5%, but in the Tornio River the change is as great as +274% (Table 4).
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Discussion |
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The SPC estimates presented here indicate much higher levels of potential smolt production than do former estimates for Baltic salmon. The parr densities observed recently in many northern Baltic salmon rivers are higher than what has previously been considered realistic (Romakkaniemi et al., 2003), which further supports our findings. However, former point estimates occur within the probability distributions found in this study. These new estimates include not only the inconsistency between the expert opinions, but also the uncertainty associated with each component of the inference needed. These uncertainties are described by individual probability distributions.
ICES used the revised estimates obtained here in its advice for Baltic salmon stocks (ICES, 2002, 2004b), providing essential justification for the advice that managers should reconsider their use of current objectives, using instead operational objectives that are easier to assess. Since there is uncertainty both in the actual smolt production estimates and in the SPC, the comparison of these two very uncertain figures does not constitute a very reliable guidance system. All the experts have been working with northern Baltic Sea and salmon issues for years, and their expertise is likely to be the best available in this field. To improve these estimates through the use of new fieldwork would be too laborious a task. Therefore, a better solution would be to consider more informative operational objectives, even though the fundamental aim of management (to safeguard wild salmon stocks and their genetic diversity) would remain the same.
The diverging views of the experts raise critical questions regarding the plausibility of the study. Morgan and Henrion (1990, p. 164) listed the following questions that should be considered in this situation and they were used to assess the plausibility of our study: "Are there different disciplinary perspectives involved? Do different experts interpret the world with different theoretical models? Are there disagreements about the validity of various experiments or data sets? Have some experts ignored evidence that other experts consider very important? Are motivational biases operating? Are some (or all) of the experts just not very ‘expert’? Are the questions posed simply impossible for human experts to answer?"
The matter most strongly influencing the results is probably the unresolved scientific controversy over the maximal pre-smolt densities. This is a highly relevant issue in Baltic salmon reproduction biology, and since it has not been resolved it is important to take both views into consideration. In contrast, the dissimilar views of the experts probably are very beneficial to the model, since they clearly indicate that there is no "true" knowledge of the subject in question. They thus aid in avoiding overconfidence regarding the model and regarding the subject in general.
The theoretical model of salmon smolt production was readily accepted by the experts. The model structure was designed to represent the relevant parts of the physical features of the river system, from the point of view of salmon productivity. The model does not take into account the dynamics of the spawning stock, since this is outside the scope of the present study. The model structure was intuitive and almost entirely familiar to the experts, and the dissimilarity in the results is thus unlikely due to misinterpretation of either the model structure or the parameters, or the difficulty of the questions posed. Each of our experts applied the same model structure in the estimation task. Kuikka and Varis (1997) allowed each expert to develop his own model structures when modelling impacts of climatic change, and their approach was therefore more focused on the structural uncertainties, i.e. on the plausible cause–effect chains. Presently we have no basis for judging which approach is more justified and further studies are needed in this area.
The potential levels of parr density have seldom been estimated, since many studies estimate the egg-to-smolt ratio without explicitly estimating the parr density capacity. Parr densities have, however, been monitored in many Baltic rivers using electrofishing. In the Tornio River, age 1+ and older parr densities have varied 0.5–5.2 parr per 100 m2 from the early 1990s until 1998, but in 1999 and 2000 the densities have risen to 12 parr per 100 m2 (ICES, 2001a; Romakkaniemi et al., 2003). Parr densities have also been high in the other large Baltic rivers in recent years (ICES, 2002; Romakkaniemi et al., 2003). Parr densities in the Kalix River were 12.5 parr per 100 m2 in 1997 (ICES, 2001a). These numbers support the view that the density of 1+ and older parr can achieve higher values than those previously estimated.
The mean density capacity of 4.5 pre-smolts per 100 m2 of nursery area found in this study is noticeably higher than the former estimates of 1–3.5 smolts per 100 m2, even when a reasonable amount of mortality is assumed to occur between the pre-smolt and smolt stages. This pre-smolt density corresponds to approximately 2 smolts per 100 m2 of the whole fluvial habitat accessible to salmon (Romakkaniemi et al., 1995), which is still lower than the mean value of 3 smolts per 100 m2 of fluvial habitat estimated for Atlantic Canadian rivers. Moreover, the two categories, which were given the highest probabilities, were 1–2 and 2–3 pre-smolts per 100 m2, i.e. the same level of density as that indicated by former estimates was thought to be most probable in our study.
Some of the latest river-specific smolt run estimates support our findings that the smolt production potential is higher than assumed so far. The smolt runs in 2001 exceeded the previously estimated potential production values in the Tornio, Kalix, Byske, and Åby Rivers (Table 3, Figure 6). The wild smolt production in 2001 was 620 000 smolts in the Tornio River (Table 3, ICES, 2001b), which is 124% of the previously estimated potential. The present study indicates, however, that this production is still below 50% of the potential value (Table 4). The estimated actual smolt production in the Byske River in 2001 is 132% of the previous estimate of potential production. We propose, however, that the estimated 2001 smolt production in the Byske River is just 26% of the potential and thus 52% of the new target (Table 3).
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Conclusions |
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The present study strongly suggests that previous expert estimates of maximum production have been too low and shows that the experts are now willing to update their estimates, based on better understanding of the possible production rates. The Baltic salmon populations have been depleted for such a long period that the maximum capacity may not be easily elicited from historical data, but instead from knowledge of river characteristics and general features of Atlantic salmon populations. Due to the major uncertainty inherent in the estimates, the probabilistic approach is the most useful.
The higher estimates for SPC proposed here naturally lead to increased requirements for the spawning stock sizes to achieve the IBSFC goal of having a smolt production of at least 50% of the SPC. Our results suggest that restrictive management actions are still needed to improve the status of the salmon to attain the agreed objectives.
The SPC estimates for the wild salmon rivers of the northern Baltic Sea include a large degree of uncertainty. There were notable differences in the estimates developed by different experts, and this increased the overall uncertainty related to the estimates. In the expert estimation literature, the use of multiple experts is recommended to avoid overconfidence. The differing views of the experts indicate that there is great uncertainty related to potential salmon smolt production in the Baltic Sea, and this should be accounted for in fisheries management to improve the status of wild salmon stocks.
The estimates proposed here can be used as background (prior) information in further studies and be updated by field observations and further data-based modelling, as demonstrated by Michielsens (2003). Thus, we want to stress the usability of our results as priors for any analysis, which could further shed light on the smolt production capacity or stock-recruit relationship in general in the Baltic region. This approach would gradually lead to more certain estimates of the production capacity, as the accumulating data update prior information.
Our experiences in this and previous studies suggest that Bayesian belief networks are useful tools when expert knowledge is the most important part of the knowledge available for some part of the management problem. Up-to-date software applications also permit the updating of probabilities in those parts of the problem where data exist. The core of the Bayesian inference, i.e. learning from earlier experiences, is therefore well supported by belief networks.
The model file, in Hugin net file format, can be acquired from the corresponding author upon request.
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The present study was supported by the EU Commission study contract Nr. 99/064 and the Finnish Biological Interactions Graduate School. We thank Lars Karlsson, Ingemar Perä, Ulf Carlsson, and Eero Jutila for producing the estimates. Tapani Pakarinen from the Finnish Game and Fisheries Research Institute and Kimmo Valtonen from the University of Helsinki Complex Systems Computation Group provided help during the process. Samu Mäntyniemi provided useful comments. We are grateful to the reviewers for many valuable comments and suggestions on this manuscript.
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