Estimation of Atlantic salmon smolt carrying capacity of rivers ...

ICES Journal of Marine Science, 62: 708e722 (2005)doi:10.1016/j.icesjms.2005.02.005

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Estimation of Atlantic salmon smolt carrying capacityof rivers using expert knowledge

Laura Uusitalo, Sakari Kuikka, and Atso Romakkaniemi

Uusitalo, L., Kuikka, S., and Romakkaniemi, A. 2005. Estimation of Atlantic salmon smoltcarrying capacity of rivers using expert knowledge. e ICES Journal of Marine Science, 62:708e722.

A mixed salmon fishery with both natural wild salmon stocks and reared salmon exists inthe Baltic Sea. The agreed-upon goal of management is to safeguard the wild stocks, andthe practical management objectives have been agreed to attain at least a 50% maximumsalmon production capacity in each river. This natural production capacity is, however,largely unknown. Here, a new approach has been used to estimate the salmon maximumproduction capacity of northern Baltic Sea rivers. A probabilistic salmon productioncapacity model was built entirely upon expert knowledge. The model describes the externalphysical and biological factors of the rivers and the juvenile salmon stocks’ response tothese factors. We found that the experts estimated the carrying capacity to be considerablyhigher than former estimates. A very high uncertainty was, however, connected with theseestimates. We also found considerable disagreement over the general carrying capacitylevel among the experts; the major uncertainty emerged from the conflicting views of theexperts. The result implies that perhaps operational management objectives other than thosebased on maximal smolt production levels should be considered to decrease the uncertaintyconnected with evaluation of management success.

� 2005 International Council for the Exploration of the Sea. Published by Elsevier Ltd. All rights reserved.

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.

L. Uusitalo and S. Kuikka: Department of Biological and Environmental Sciences,University of Helsinki, PO Box 65, FI-00014 University of Helsinki, Finland.A. Romakkaniemi: Finnish Game and Fisheries Research Institute, Oulu Game and FisheriesResearch, Tutkijantie 2 A, FI-90570 Oulu, Finland. Correspondence to L. Uusitalo: tel:C358 9 191 58992; fax: C358 9 191 58257; e-mail: [email protected].

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Introduction

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).

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; Stahl, 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.

1054-3139/$30.00 � 2005 International Cou

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 themechanisms

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

ncil for the Exploration of the Sea. Published by Elsevier Ltd. All rights reserved.

mailto:[email protected]

709Atlantic salmon smolt carrying capacity of rivers

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North

ESTONIA

FINLAND

RUSSIA

POLAND

SWEDEN

LATVIA

LITHUANIA

12

11

10

RUSSIA

Gulf of Bothniawild salmon rivers

1. Simo2. Tornio3. Kalix4. Råne5. Pite6. Åby7. Byske8. Rickle9. Sävar10. Vindel11. Öre12. Lögde13. Ljungan

8

9

13

1

2

3

5

4

7

6

Figure 1. The Baltic Sea, showing the Gulf of Bothnia (referred to herein as northern Baltic Sea). Rivers 1 to 13 are those studied.

(i) the Simojoki (hereafter referred to as the Simo) in

Finland, (ii) Tornionjoki (Tornio) on the Finnish-Swedish

border, and (iii) Kalix alv (Kalix), (iv) Rane alv (Rane), (v)

Pite alv (Pite), (vi) Aby alv (Aby), (vii) Byske alv (Byske),

(viii) Ricklean (Rickle), (ix) Savaran (Savar), (x) Ume/

Vindelalven (Vindel), (xi) Ore alv (Ore), (xii) Logde alv

(Logde), 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

710 L.Uusitalo et al.

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a poor state for decades (Jutila, 1992; Pruuki, 1993;

Karlsson and Karlstrom, 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 pro-

duction 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 pro-

duction. 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 Karlstrom, 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-re-

cruitment 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 objec-

tives 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 esti-

mates, 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 manage-

ment.

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 (Karlstrom, 1977; Jutila and

Pruuki, 1988; Kemppainen et al., 1995), which corresponds

to 0.3e1.5 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 in-

formative 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,


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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 method-

ology 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).

Methods

Bayesian statistics

Bayesian statistics are based on Reverend Thomas Bayes’

(1702e1762) 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 relation-

ships 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 in-

troduction 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. 163e164) 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

Karlstrom, 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 compat-

ible 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


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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.

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 northernBaltic 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 1C 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

Chance for successfulspawning

Mortalityduringmigration,

Size of productionarea

Parr density capacity

Pre-smoltdensity capacity

Smolt production capacity

River Expert

Habitatquality of parr area

Smoltificationage

Figure 2. Model structure. The solid rectangular nodes denote

river-specific characteristics which are estimated for each river

separately by each expert; the elliptical nodes denote conditional

estimates on related input arcs, e.g. smolt production capacity

depends on pre-smolt density capacity, mortality during migration,

and the size of production area. The dashed nodes denote the

auxiliary variables. The variables that are children of river are

estimated separately for each river; the variables that are children

of ‘‘expert’’ include separate estimates from each expert.

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! 5! 5Z 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:

SPCZ

�100�M

100

�!PSDC!SoPA!100

where SPC is the smolt production capacity (number of

smolts produced), M the mortality during migration (%),

PSDC the pre-smolt density capacity (number of smolts per

100 m2), and SoPA is the size of production areas (ha).

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

Pera, 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 3e5 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


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Table 1. Description of the model variables.

Name Description Relevant factors

Chance of successful

spawning

Opportunity for salmon spawning in the river,

including: dispersion of spawners to spawning

grounds, laying the eggs in nests, incubation and

hatching of the eggs, dispersion of the fry to all

parr habitats

Obstacles to migration, quality of the

bottom gravel and water, predation

directed at the fry

Habitat quality

of parr area

The quality of the areas the parr occupy,

including physical, chemical, and biological

habitat characteristics, as well as the occurrence

of periods of physical or chemical ‘‘bottlenecks’’,

and human impacts

Bottom substrate, velocities and depths,

prevalent water quality, predation and

competition; droughts, frazil/anchor ice,

extremely high water temperature, and

short-term low pH; effluents, ditches,

channel modifications

Smoltification age The age at which most parr become smolts

Size of production areas The area (in hectares) of suitable reproduction

grounds, i.e. the area over which parr and pre-

smolts are dispersed.

Mortality during migration The proportion of smolts that die during

migration down the river

The length of in-river migration, presence

of predators

Parr density capacity The maximum amount of salmon parr that can

occupy a unit of production area at the same

time, expressed here as the density of older

(1C and older) parr per 100 m2

Pre-smolt density capacity The amount of pre-smolts (parr that transform to

smolts during the same year) that can be

produced by a unit of production area yearly,

expressed as the number of pre-smolts per 100 m2

Smolt production capacity The absolute number of smolts leaving the river

per year

River Auxiliary variable; permits handling all rivers in

the same model

Expert Auxiliary variable; permits combining the expert

judgements

/674638 by guest on 29 July 2022

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 distribu-

tions 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 distribu-

tions 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! 5Z 25

distributions to estimate. Pre-smolt density capacity given

the values of smoltification age and parr density capacity

included 4! 14Z 56 probability distributions. These


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Table 2. Structure of the model.

Variable Discretized levels Role Conditional on

Chance of successful

spawning

Very poor,

poor, OK, good,

very good

River specific Expert, river

Habitat quality

of parr area

Very poor,

poor, OK, good,

very good


Smoltification age 2,3,4,5 River specific Expert, river

Size of production

areas (ha)

49 classes,

ranging from 0 to 12 000 ha


Mortality during

migration (%)

0e5, 5e10, 10e20, 20e30,

30e40, 40e50, 50e60,

60e70, 70e80, 80e90, 90e100


Parr density

capacity

(number of 1C

and older parr per 100 m2)

0e1, 1e2, 2e3, 3e4, 4e6, 6e8,8e12, 12e16, 16e24, 24e32, 32e48,

48e64, 64e96, 96e128

Response to

river-specific conditions

Expert, chance

of successful spawning,

habitat quality of parr area

Pre-smolt density

capacity

(number of pre-smolts

per 100 m2)

0e0.5, 0.5e1, 1e2, 2e3, 3e4, 4e6,6e8, 8e12, 12e24, 24e48

Response to


Expert, parr

density capacity,

smoltification age

Smolt production

capacity (smolts per 1000

individuals)

0e1, 1e5, 5e10, 10e25, 25e50, 50e75,

75e100, 100e250, 250e500,

500e750, 750e1 000, 1 000e5 000,

5 000e10 000, 10 000e57 600

Response to


Pre-smolt density

capacity, mortality

during migration, size

of production areas

River Tornio, Simo, Kalix, Ore, Vindel,

Ljungan, Logde, Savar,

Rickle, Byske, Aby, Pite, Rane

Auxiliary None

Expert Expert 1, expert 2, expert 3, expert 4, expert 5 Auxiliary None

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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 judge-

ments (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 symmet-

rically (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 justifica-

tions 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 correspond-

ing former point estimates.

Results

Controversy between experts

Estimates of both the river characteristics and conditional

connections varied widely among the experts, and this


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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 0.5e2

pre-smolts per 100 m2 by one expert and 8e12 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).

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

Expert 2

Expert 1

0.00.10.20.30.4

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Expert 3

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Joint distribution for all experts

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Pre-smolt density capacity, ind. per 100 m2

Prob

abili

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Figure 3. Pre-smolt density capacity aggregated over all rivers,

estimated by the different experts. Note that the x-axis is not linear.

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 24e48 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 Logde

and Rickle Rivers (Figure 5). These estimates were

considered to be very uncertain.

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,

40e80% 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).

The greatest SPC was estimated for the Tornio River, the

probability distribution peaking strongly at 1e5 million

smolts per year (Figure 6). The Kalix River also had high

smolt run values, having the highest probability density in

1e5 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

0

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Parr density capacity, ind. per 100m2

Prob

abili

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Figure 4. Probability distribution for the variable parr density

capacity aggregated over all rivers and experts. Note that the x-axis

is not linear.


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Råne

0

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Pre-smolt density capacity, ind. per 100m2

Figure 5. Probability distributions for Pre-smolt density capacity for each river aggregated over all experts. Note that the x-axis is not

linear.


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0.6

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Pite

no. of smolts, in thousands

Figure 6. Probability distributions for smolt production capacities in northern Baltic Sea wild salmon rivers. Numbers of smolts in

thousands. Solid arrows indicate previously estimated SPC (as per column 2, Table 2), and dashed arrows indicate smolt production in

2001 (as per column 4, Table 2). Aggregated over all experts. Note that the x-axis is not linear.

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


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Table 3. Comparison between the present model, previous estimates of smolt production potential (ICES, 2001b), and present smolt

production rates, with probabilities of attaining the new target.

River

Previous estimate

of SPC

Probability mass

above the previous estimate

Smolt production

in 2001

Probability mass

above the 2001

production value

Probability that 2001 production

attains the new goal

(50% of the SPC)

Tornio 500 000 0.82 620 000 0.77 0.41

Simo 75 000 0.51 47 300 0.72 0.59

Kalix 250 000 0.85 287 000 0.81 0.37

Ore 20 000 0.49 900 0.98 0.04

Vindel 200 000 0.6 75 000 0.93 0.3

Ljungan 20 000 0.11 10 000 0.28 0.89

Logde 20 000 0.71 4 100 0.97 0.1

Savar 4 000 0.52 1 500 0.84 0.45

Rickle 5 000 0.66 900 0.97 0.09

Byske 80 000 0.8 106 000 0.74 0.52

Aby 16 000 0.59 16 300 0.58 0.67

Pite 33 000 0.71 18 000 0.87 0.32

Rane 20 000 0.82 8 800 0.96 0.14

Average 95 615 0.63 91 985 0.80 0.38

p.com/icesjm

s/article/62/4/708/6746

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).

These probabilities varied widely from 4% in the Ore

River to 89% in the Ljungan River (Table 3). The Simo,

Ljungan, Aby, and Byske Rivers were the only ones having

over 50% probability of achieving target production. The

Tornio and Savar Rivers are close to this stage, having

probabilities higher than 40% (Table 3). The situation

appears to be the most unfavourable in the Ore, Logde,

Rane, 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

38 by guest on 29 July 2022

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Smolt production target, no. of smolts (in thousands)

Prob

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Figure 7. Example of the usage of smolt production targets expressed as a probability distribution. The distribution presented is the

probabilistic smolt production target of River Pite and the arrow indicates the estimated smolt production in River Pite in 2001 (18 000

smolts; Table 3). The probabilities up to the 18 000 smolts point (the dark columns) sum up to 32%; thus, the probability that River Pite has

reached the target production is 32%.


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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 pre-

cautionary approach is adopted, the probability of achiev-

ing 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.

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 Savar 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

Ore 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 Savar

Rivers, the change is only about C5%, but in the Tornio

River the change is as great as C274% (Table 4).

Discussion

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

Table 4. Comparison between new and previous point estimates of

smolt production targets in northern Baltic Sea rivers.

Previous smolt

production target

Revised point

estimate of smolt

production target

Relative

change (%)

Tornio 250 000 936 000 C274

Simo 37 500 39 000 C4

Kalix 125 000 365 000 C192

Ore 10 000 9 800 �2

Vindel 100 000 128 000 C28

Ljungan 10 000 3 000 �70

Logde 10 000 20 000 C100

Savar 2 000 2 200 C10

Rickle 2 500 3 700 C48

Byske 40 000 102 000 C155

Aby 8 000 10 000 C25

Pite 17 500 26 000 C49

Rane 10 000 31 000 C210

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 uncertain-

ties 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 manag-

ers 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 impor-

tant? 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


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intuitive and almost entirely familiar to the experts, and the

dissimilarity in the results is thus unlikely due to mis-

interpretation 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 causeeeffect 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

1C and older parr densities have varied 0.5e5.2 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

1C 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 1e3.5 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 (Romak-

kaniemi 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 1e2 and

2e3 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 Aby 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).

Conclusions

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 un-

certainty 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.

Acknowledgements

The present study was supported by the EU Commission

study contract Nr. 99/064 and the Finnish Biological


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Interactions Graduate School. We thank Lars Karlsson,

Ingemar Pera, 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 Mantyniemi

provided useful comments. We are grateful to the reviewers

for many valuable comments and suggestions on this

manuscript.

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