Assessing the decline of brown trout (Salmo trutta) in Swiss rivers using a Bayesian probability network

Ecological Modelling 192 (2006) 224–244

Assessing the decline of brown trout (Salmo trutta) in Swiss rivers using a Bayesian probability network Mark E. Borsuk a,∗ , Peter Reichert a,b , Armin Peter c , Eva Schager c , Patricia Burkhardt-Holm d a

Department of Systems Analysis, Integrated Assessment, and Modelling, Swiss Federal Institute of Aquatic Science and Technology (Eawag), P.O. Box 611, 8600 D¨ubendorf, Switzerland b Department of Environmental Sciences, Swiss Federal Institute of Technology (ETH), Z¨ urich, Switzerland c Department of Applied Aquatic Ecology, Eawag, D¨ ubendorf, Switzerland d Program for Humans, Society, and the Environment, University of Basel, Basel, Switzerland Received 10 September 2004; received in revised form 8 June 2005; accepted 6 July 2005 Available online 9 September 2005

Abstract A Bayesian probability network has been developed to integrate the various scientific findings of an interdisciplinary research project on brown trout and their habitat in Switzerland. The network is based on a dynamic, age-structured population model, which is extended to include the effect of natural and anthropogenic influence factors. These include gravel bed conditions, water quality, disease rates, water temperature, habitat conditions, stocking practices, angler catch and flood frequency. Effect strength and associated uncertainty are described by conditional probability distributions. These conditional probabilities were developed using experimental and field data, literature reports, and the elicited judgment of involved scientists. The model was applied to brown trout populations at 12 locations in four river basins. Model testing consisted of comparing predictions of juvenile and adult density under current conditions to the results of recent population surveys. The relative importance of the various influence factors was then assessed by comparing various model scenarios, including a hypothetical reference condition. A measure of causal strength was developed based on this comparison, and the major stress factors were analyzed according to this measure for each location. We found that suboptimal habitat conditions are the most important and ubiquitous stress factor and have impacts of sufficient magnitude to explain the reduced fish populations observed in recent years. However, other factors likely contribute to the declines, depending on local conditions. The model developed in this study can be used to provide these site-specific assessments and predict the effect of candidate management measures. © 2005 Elsevier B.V. All rights reserved. Keywords: Integrated modelling; Causal assessment; Population viability; Anthropogenic stressors; Ecological risk

∗

Corresponding author. Tel.: +41 1 823 5082; fax: +41 1 823 5375. E-mail address: [email protected] (M.E. Borsuk).

0304-3800/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2005.07.006

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1. Introduction Several indications over recent years have suggested that brown trout (Salmo trutta) populations in Switzerland are at risk. Angler records indicate a decrease in catch of up to 50% since the 1980s (Friedl, 1999). These declines are especially strong in the more anthropogenically impacted midlands and northern regions of the country (Frick et al., 1998). In parallel with the indications of decreasing catch, health monitoring since the 1980s has yielded evidence of an impaired health status. Brown trout with both macroscopic lesions and histopathological tissue alterations have been observed in a number of Swiss streams (Bernet et al., 2000; Schmidt-Posthaus et al., 2001). The causes of the widespread health problems and decreased catch are not readily apparent. Possibilities that have been suggested include poor water quality, altered habitat, increased fine sediment inputs, infectious disease, and increased water temperature (Burkhardt-Holm et al., 2002). In 1998, a nationwide research effort named “Fischnetz” (Netzwerk Fischr¨uckgang Schweiz) was organized to evaluate the problem (Burkhardt-Holm et al., 2002). A variety of field and laboratory studies were funded over a period of 5 years to investigate the various possible causal factors and consider opportunities for improvement. With the recent completion of these studies (Fischnetz, 2004), a method is now required to integrate the results in a manner useful for causal assessment and management support. We have developed a Bayesian probability network as a means for summarizing both the qualitative and quantitative information resulting from the Fischnetz research projects. Probability networks have the advantage of making causal assumptions explicit and facilitating uncertainty analysis (Pearl, 2000; Jensen, 2001). As with other attempts to model fish populations (e.g. Lee and Rieman, 1997; Nickelson and Lawson, 1998; Gouraud et al., 2001; Todd et al., 2004), the core of our network model is a dynamic representation of the organism’s life cycle. This is characterized by population parameters, such as growth, survival, and reproductive rates. These parameters are then linked to external indicators of habitat quality and anthropogenic influence using the results of the Fischnetz studies. In a probability network, these links take the form of conditional probability distributions which capture the

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expected response of parameters to their immediate influences, including uncertainty and natural variability (Pearl, 2000; Jensen, 2001). While other authors have provided qualitative guidance on selecting appropriate parameter values for their models under various conditions (e.g. Shepard et al., 1997), our method is an attempt to formalize this procedure, making the scientific knowledge (and uncertainty) arising from recent studies on the link between fish and their environment an integral part of the model. For a given set of model inputs, these conditional probabilities are then propagated to model endpoints, giving users an indication of the degree of uncertainty present in final model predictions. The incorporation of uncertainties into population models and management decision-making has been recognized as a key fisheries research challenge (Milner et al., 2003). The model we developed was applied to specific brown trout populations in Switzerland to assess the relative importance of different local stress factors in limiting fish density. In this study, we used four river basins with varying characteristics to represent the range of conditions found in the Swiss midlands. Model results corresponding to current conditions are compared to recent population surveys to assess the ability of the model to reproduce observed population variation across locations. The relative importance of stress factors is then estimated by comparing various model scenarios, including a hypothetical, pre-impact “reference” condition. A measure of causal strength is developed based on this comparison, and the major stress factors are assessed according to this measure for each location. Results give an indication of the type of management actions that would be most effective in protecting or restoring brown trout populations, and model predictions of the expected consequences of these actions are presented. These results should help managers to determine the most appropriate activities to pursue in the respective river basins.

2. Methods 2.1. Approach Bayesian probability (or belief) networks have been used in a variety of settings to compile information from various sources to generate probabilistic predic-

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tions (e.g. Haas et al., 1994; Varis, 1995; Sahely and Bagley, 2001; Borsuk et al., 2004). A key element in their use is a graphical representation of the causal relationships described by the model. In this graph, nodes represent important system variables (inputs, outputs, or intermediate variables), and arrows between nodes indicate a dependent relationship between the corresponding variables. Such arrows can be drawn using conventional notions of cause-and-effect (Pearl, 2000). The interesting feature that is made explicit by the graph is the conditional independence implied by the absence of connecting arrows between some nodes. These independences allow the complex network of interactions from primary cause to final effect to be broken down into sets of relations which can each be characterized independently (Pearl, 2000). This aspect of belief networks significantly facilitates their use for representing the results of multi-team, multidisciplinary research projects such as Fischnetz. Characterization of the relationships in a belief network consists of constructing conditional probability distributions that reflect the aggregate response of each variable to changes in its immediate “up-arrow” predecessors, together with the uncertainty in that response. Conditional probability relationships may be based on any available information, including experimental or field results, process-based models, or the carefully elicited judgment of scientists. Observational field data that consist of precise measurements of the variable or relationship of interest are likely to be the most useful and least controversial form of information. Unfortunately, appropriate and sufficient field data may not always exist. Experimental evidence may fill this gap, but concerns may arise regarding the applicability of this information to the natural, uncontrolled system, and appropriate experimental data may also be limited. As a consequence, the elicited judgment of scientific experts may be required to quantify some of the probabilistic relationships. This approach is consistent with the Bayesian perspective on statistical inference and decision, which states that probabilities are a useful way of expressing one’s degree of knowledge (Berger, 1980). Established techniques exist for performing such elicitations (Morgan and Henrion, 1990; Meyer and Booker, 1991) and help to assure accurate and honest assessments. Once all relationships in a network are quantified, probabilistic predictions of model endpoints can be

generated conditional on values (or distributions) of any “up-arrow” causal variables. These predicted endpoint probabilities, and the relative change in probabilities between alternative scenarios, convey the magnitude of expected system response to historical changes or proposed management while accounting for predictive uncertainties. The scenarios investigated in this study can all be represented by alternative specifications of the primary input nodes. 2.2. Brown trout life cycle Resident, stream-dwelling brown trout in Switzerland deposit their eggs during late autumn or early winter. The eggs incubate over winter, hatch in early spring, and the alevins emerge from the gravel around March or April. Soon after gravel emergence, fry disperse locally and establish territories, which they defend vigorously against other fry, and from which they gather their food (Elliott, 1994). The availability of territories is believed to be an important factor limiting populations, and evidence of density dependence is most frequently observed at this stage. After about 2–3 years, depending on growth rate, juvenile trout become reproductively mature and begin to spawn. Brown trout in Switzerland rarely live longer than 5–7 years (Fischnetz, 2004). The natural range of brown trout can be estimated according to the fish zone designations of Huet (1959) and Illies (1978). Such designation systems use characteristics such as slope, flow, substrate size, and temperature to estimate the naturally dominant fish species for a stream reach. In addition to designated trout zones in areas of high slope and low temperature, other species zone designations in Switzerland include grayling, barbel, and bream. 2.3. Model A graphical belief network representing the key factors influencing brown trout density was drawn in collaboration with the 12 members of the Fischnetz project leadership committee through a series of individual and group meetings (see www.fischnetz.ch for project participants). The members of the committee have been responsible for overseeing 77 research projects covering all major aspects of the brown trout and its environment in Switzerland (Burkhardt-Holm et al., 2002). At the heart of the resulting graph (Fig. 1) is a represen-

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Fig. 1. Graphical representation of probability network. Shaded nodes represent model inputs to be determined from site-specific data. Rounded bold nodes represent submodels which contain multiple additional nodes (e.g. different cohorts within the same life stage). Dynamic variables, in addition to those representing the various life stages, are indicated by small arrowheads on the left side of the node. The influence of adult density on egg density in the next year is shown as a dashed arrow. PKD: proliferative kidney disease.

tation of the trout’s life cycle with five major stages: eggs, emergent fry (age 0), late summer fry (age 0+), immature juveniles, and spawning adults. The distinction between emergent and late summer fry was made to delineate the period of greatest density dependence (see details below). The number of individuals in each life stage is influenced by the number in the previous life stage, as well as relevant population parameters, such as survival and reproductive rates. These parameters are influenced, in turn, by intermediate variables, such as body size and growth rate, or by external controls, including habitat conditions, temperature, water

quality, stocking practices, angling, prey resources, and competing species. With the basic structure of the model determined, the next step was to develop the conditional probabilities characterizing the dependences among the variables. These relationships must be sufficiently general so that they can be applied to the range of conditions found in Swiss midland streams. A dynamic, age-structured population model is used to relate the nodes representing the various life stages and population parameters. However, these parameters must still be related to the environmental and anthropogenic factors that represent

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the root causes of population change and which may differ across locations. This is where the recent data and experience resulting from the Fischnetz projects were most valuable. The development of the relations leading to each life stage is described in the following sections. 2.3.1. Eggs The number of viable eggs deposited in the gravel in autumn depends on the total number produced by females and the joint deposition and fertilization success rate (referred to here as a combined spawning rate). The total number of eggs produced is the product of average fecundity and the number of mature females. Females were assumed to comprise half of the simulated adults. Fecundity values reported in the literature for female brown trout in Switzerland range from 100 to 2200 eggs per individual (Peter, 1987). Much of this variability can be explained by differences in female body size, and Swiss data (Fischnetz, 2004) can be used to derive the following relationship, F = 6.26 × W 0.89

(1)

where F is fecundity (eggs/female) and W is weight (g). The spawning rate, combining egg deposition and fertilization success, is expressed as a proportion of produced eggs. Spawning success, as measured by presence and density of redds, has been found to depend primarily on the availability of suitable substrate (Beard and Carline, 1991; Kondolf and Wolman, 1993; Fischnetz, 2004). If suitable substrate is available, then high spawning rates can be expected. On the other hand, streams that have a clogged gravel bed or a high percentage of fines can be expected to have lower spawning success. The relation between spawning rate and fines/ clogging was elicited independently from three experts involved in the Fischnetz project who based their answers on their research experience and the literature. A fines/clogging variable was first defined as “low”, “medium”, or “high,” depending on either the results of an informal “kick test” (Sch¨alchli, 1993) or a measured percentage of fine particles (<5 mm diameter)(Olsson and Persson, 1988). If the percentage of fine particles in a local area is less than 10%, then the classification is “low”; if it is 10–20%, then “medium”; if it is >20%, then “high.” The classification level of a stream seg-

Fig. 2. Results of the expert elicitation concerning the relation between spawning success rate and sediment fines/clogging.

ment supporting a trout population is the level assigned to the majority of the streambed area. The experts stated the most likely value of spawning rate conditional on each of these levels, as well as upper and lower bounds. All three experts agreed that spawning rate decreases with increased levels of fines/clogging (Fig. 2). However, there was some disagreement over the “baseline” spawning rate (i.e. under “low” fines) as well as the magnitude of the substrate effect. Additionally, the different experts had different levels of uncertainty, as represented by the difference between their upper and lower estimates. As there is currently no reason to distinguish between the judgments provided by the three qualified experts, the results were combined. This was done by averaging the values stated by each expert to be the “most likely” for each level of fines. These were then used as the mode (i.e. point of maximum probability) of triangular distributions with upper and lower limits given by the average of the upper and lower limits of the three experts (see Fig. 2). 2.3.2. Emergent fry The number of emergent fry is the product of the number of deposited eggs and the average survival rate in the gravel. Referred to as incubation survival, this rate includes the incubation, hatching, and gravel emergence processes. Substrate composition is the most commonly cited factor influencing the rate of incubation survival. The composition of the substrate determines the permeability, which, in turn, influences

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Fig. 3. Results from the literature (Olsson and Persson, 1988) and expert elicitation concerning the relation between incubation survival and sediment fines/clogging. Sediments fines were expressed as a discrete variable (low, medium, and high) for the expert elicitation and as a continuous percent in the literature.

the interstitial water flow and oxygen concentration (Rubin and Glims¨ater, 1996). Additionally, poor substrate composition can hinder the successful emergence of hatched fry (Chapman, 1988). In most published studies, these two effects are not distinguished and the total effect of substrate on survival is estimated. Relationships between incubation survival and percent fines

CN =

conducted as part of the Fischnetz project have not shown evidence of reduced egg survival prior to hatching at polluted sites (Kobler, 2004). It may be that embryos are sufficiently protected by their eggs during the incubation stage. However, during and after hatching, in-gravel alevins seem to be more susceptible to poor water quality. Kobler (2004) found a strong increase in mortality immediately after hatching at polluted sites. This pattern was also observed in other early life stage tests on brown trout (Luckenbach et al., 2001). We used the results of 14-egg incubation experiments performed in situ with brown trout eggs at various locations in Switzerland (Bernet, 2004) as the basis for the relationship between water quality and incubation survival. The proportion of eggs surviving through the alevin stage was related to the mean annual concentration of total nitrogen, used as a surrogate for water quality. Zobrist and Reichert (submitted for publication) found that total nitrogen, nitrate, phosphate, chloride, and potassium varied in parallel across the Swiss basins they studied, and mean annual concentrations could be accurately predicted from basin land use and population size. Intensive agriculture was found to be the most important contributing land use for these substances, and, using a simplified form of their model, mean annual total nitrogen concentration CN (g m−3 ) can be estimated as,

[(4.29 ± 0.83) (g/m2 y)Aagr + (0.83 ± 0.36) (g/m2 y)Aother + (2180 ± 580) (g/inhabitant y)n] Q

have been reported in the literature for brown trout (Witzel and Maccrimmon, 1983; Olsson and Persson, 1988). To evaluate the applicability of these results to Swiss streams, an independent expert elicitation was performed with two Fischnetz experts. Results (Fig. 3) are generally in good agreement, so the results of all sources were combined. This was done by using the average of the values stated to be the “most likely” as the mode of triangular distributions with upper and lower limits given by the upper and lower limits across all three sources (see Fig. 3). In addition to substrate composition, water quality has been reported to have an effect on survival during incubation (Brooks et al., 1997). Exposure to nitrogen compounds may be of particular concern (Constable et al., 2003). However, egg incubation experiments

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(2)

where Aagr and Aother are the areas (m2 ) of intensive agricultural and all other land use, respectively, n is the number of river basin inhabitants, and Q is the median annual flow (m3 /y). The model coefficient values given in parentheses (including standard errors) are the result of a Bayesian parameter estimation by Zobrist and Reichert (submitted for publication). The 14 measured in situ incubation survival rates show a strong relation to the mean annual total nitrogen concentration estimated for each location using Eq. (2) (Fig. 4). A logistic curve was fit to these data and was used, together with uncertainty estimates, to characterize the effects of water quality on incubation survival in the model. The hydrologic regime may also have an important influence on incubation survival. High flows during

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Fig. 4. A logistic curve relating incubation survival to water quality (indicated by estimated annual mean total nitrogen concentration). The solid line shows the best-fit curve and the dashed lines represent 90% predictive intervals. Points represent observed values.

the intra-gravel period can cause egg pocket scouring (Montgomery et al., 1996). For a particular streambed, the flow magnitude at which egg scour occurs (Qs ) can be estimated using river width, bed slope, and gravel size (Chang, 2002). The extent of scour can then be expected to increase with higher flows (Cattaneo et al., 2002). For example, in a Canadian river using typical egg burial depths of 10–15 cm, Lapointe et al. (2000) estimated the probability of egg scour due to flows with a 10-year recurrence interval to be 5% and with a 100year recurrence interval to be 20%. Therefore, in the model, the flood frequency (defined as flows greater than Qs ) during the intra-gravel phase is used as a site-specific input. Estimation of egg scour is then based upon the assumption that scour does not occur at flow values below Qs , but increases linearly in magnitude for flows above this value, reaching 20% scour at a flow value of 2.5Qs , consistent with the results of Lapointe et al. (2000). 2.3.3. Late summer fry After emerging from the gravel substrate, the first year of life for brown trout can be divided into two distinct periods which are most clearly distinguished from survivorship curves. The first period, often termed the “critical period,” generally lasts 33–70 days after emergence and is marked by high mortality rates associated with the initiation of feeding (Elliott, 1989a). The second begins in mid to late summer, when the population density is substantially reduced and the mortality rate decreases (DeAngelis et al., 1993). In addition to the

magnitude of the mortality rate, the relative dependence of mortality on the population density differs between the two periods. Elliott (1994) found density dependent mortality only during the critical period from emergence to the end of the first summer. After this time, mortality was fairly constant with respect to density. The substantial differences between the two periods of early trout development with regard to mortality rate and density dependence have been observed by other researchers as well (DeAngelis et al., 1993; Crozier and Kennedy, 1995) and suggest separate handling in the model. The first period covers the density dependent transition from emergent fry to late summer fry, and the second covers the transition from late summer fry to 1-year-old juveniles. The relationship between mortality and population density observed by Elliott (1994) during the critical period was found to be consistent with the Ricker model of density dependence (Ricker, 1954). According to the Ricker model, the relationship between stock (S) and recruitment (R) (in this case, emergent fry and late summer fry, respectively) is described by the functional form: R = aSe−bS

(3)

which yields a dome-shaped curve between R and S, allowing for the possibility of overcompensation (Fig. 5). The Ricker model is generally appropriate for populations which are subject to factors which increase the time it takes for young fish to grow through a vulnerable size range (Jonsson et al., 1998).

Fig. 5. Example of a Ricker curve, indicating the two parameters, low density survival and maximum capacity.

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The specification of the parameters a and b of the stock-recruitment curve, as well as how these parameters depend on local stream conditions, is recognized to be a difficult task (Rose et al., 1996) and an important area of research (Elliott, 1989b). This task can be facilitated by expressing the two parameters of Eq. (3) in terms of more easily measured variables. It can be shown that the parameters a and b of the Ricker curve can be derived from the following two features: (1) the slope of the curve at the origin, i.e. the survival rate of fry at low population density (rf = a), and (2) the maximum of the curve, i.e. the maximum capacity of the stream for late summer fry (Kf = 0.3679a/b). These features will be described in the following two sections. 2.3.4. Fry survival at low density (rf ) Estimates reported in the literature for fry survival at low initial density (<10 ind/m2 ) range from 0.08 to 0.10 (Peter, 1987; Elliott, 1989a; Crisp, 1993). We therefore used a symmetric triangular distribution with these values as limits for all modeled populations. 2.3.5. Maximum capacity (Kf ) The maximum recruitment capacity Kf of a population is generally believed to be limited by the availability of consumable habitat resources, such as space, cover, and food availability (Hayes et al., 1996). This is because the amount of these resources available per fish decreases with fish abundance. For example, the amount of suitable habitat accessible to a fish depends on the utilization of available locations by other fish. With increasing fish density, habitat becomes more limiting, thus resulting in lower survival (Hayes et al., 1996). To our knowledge there have not been any studies relating maximum recruitment capacity of brown trout to habitat quality or food availability. Therefore, a method developed previously to assess the total production potential of rivers in Switzerland was adapted for this purpose (Vuille, 1997). Vuille proposed that maximum production per unit area will be proportional to the abundance of prey, an index of habitat quality, a temperature coefficient, and a width correction factor. This relationship, when considered as an upper limit, has been supported by electrofishing and angler catch data

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in rivers throughout the Swiss canton of Bern (Vuille, 1997). If it is assumed that the limits imposed by these resources are primarily manifest during the critical period, then the maximum recruitment capacity of late summer fry can also be assumed to show such a proportionality. Unfortunately, reliable estimates of prey density are not available for most rivers in Switzerland outside of Bern, making this unsuitable as a continuous input variable. Therefore, in the model, maximum capacity, Kf (ind/ha) is estimated using the following equation, Kf = c × K

(4)

where c is an empirical scaling factor (ind/ha), and K is a dimensionless capacity score, defined as:
 1m (5) K = (khab × kzone × ktemp × kprey ) × w In Eq. (5), khab is a habitat quality score (ranging from 0 to 1) indicating the presence of important habitat features including depth and width variation, a diverse bank structure, shade, appropriate substrate, and a high percent riffles (calculated as the arithmetic mean of the scores obtained for each of these six criteria; Table 1), kzone is a correction factor (0–1) introduced to account for competition with other species for food in nontrout designated waters (Table 2), ktemp is a water temperature adjustment factor (0.75–1.75) accounting for greater productivity in warmer waters (Table 3), kprey is a factor set equal to 0.5 under known conditions of low prey density (<25 g m−2 ) and 1.0 otherwise, and w is average river width (m). The width scaling term ((1 m)/w) is included to account for the fact that the stream margins on which fry depend comprise proportionally less of the overall area in a wider channel. The value of c in Eq. (4) was estimated using data from surveys of habitat and late summer fry density at 97 locations in Switzerland, conducted as part of the Fischnetz project (Schager and Peter, 2001, 2002). A quantile regression was performed on the data to estimate the 90th percentile of density as a linear function of the dimensionless capacity score K defined by Eq. (5). Quantile regression is the appropriate statistical tool for using density data to estimate the effect of factors expected to set maximum limits on a population (Terrell et al., 1996). Results (Fig. 6) yield a value for c of 38950 (±2700) ind/ha and show that observed

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232 Table 1 Habitat quality scoring method

Habitat quality score

%Riffles Depth variability Width variability Shade Dominant substrate size Stream-bank connectivity

Poor 0.2

Good 0.6

Excellent 1

None or very few (<10%) Low (CV <25%) Low (CV <10%) Low (<10%) <0.2 cm or >20 cm or artificial stream bed Very low connectivity, straight shoreline

Some (10–30%) Medium (CV 25–50%) Medium (CV 10–40%) Medium (10–50%) 0.2–2 cm or 6.3–20 cm Medium connectivity, some inlets

Many (>30%) High (CV > 50%) High (CV > 40%) High (>50%) 2–6.3 cm High connectivity, many inlets

The overall score, khab , is calculated as the arithmetic mean of the scores obtained for each of the six criteria. Measurement methods can be found in Schager and Peter (2003). CV = coefficient of variation (standard deviation/mean).

densities substantially less than the maximum capacity can generally be attributed to factors, such as substrate fines/clogging and proliferative kidney disease (PKD), that are not accounted for in the capacity score because they either cause mortality at earlier life stages or are density-independent. Eqs. (4) and (5) are used in the model to estimate site-specific values of Kf . 2.3.6. Disease Proliferative kidney disease is a serious parasitic infection of salmonids and is the most common disease affecting brown trout in Switzerland (Wahli et al., 2002). Young-of-year fish are especially vulner-

able to PKD when they are exposed to the parasite for the first time (Wahli et al., 2002). An interviewed Fischnetz expert believed that mortality of fry due to PKD would typically be between 0 and 20% in rivers in which the PKD parasite is present. However, if water temperature exceeds 15 ◦ C for more than 2 weeks and PKD is present, then mortality is expected to increase to between 10 and 70%. These assessments were based on both the expert’s personal findings and those reported in the literature (Hedrick et al., 1993; El-Matbouli and

Table 2 Values for the correction factor accounting for competition in nontrout designated waters Species designation

kzone

Trout Grayling Barbel Bream

1.0 0.5 0.25 0.0

Table 3 Values for the temperature correction factor ktemp for given ranges of the temperature statistic Tk temp Tk temp = Tmin × (Tmax − Tmin )

ktemp

<25 25–45 45–70 70–80 >80

0.75 1.0 1.25 1.5 1.75

Tmax and Tmin are the annual maximum and minimum daily average water temperatures for the river reach of interest (from Vuille, 1997).

Fig. 6. Measured late summer fry density plotted against capacity score, K . Triangles indicate populations with proliferative kidney disease (PKD), squares indicate populations subject to high gravel bed clogging, crosses indicate populations with both PKD and clogging, and circles indicate populations with neither. The curve represents the estimated 90th percentile of all data. Note that the horizontal axis is on a logarithmic scale for ease of presentation; the 90th percentile curve is linear in the natural scale with a slope of c = 38950 ind/ha.

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Hoffman, 2002; Wahli et al., 2002) and were used as the limits for uniform probability distributions for the effect of PKD mortality on late summer fry in the model. This mortality is assumed to occur after the density dependent stage, and so cannot be compensated. 2.3.7. Juveniles After the critical period, the survival rate increases and is no longer density dependent (Elliott, 1989a). However, over the first winter, mortality may be higher than for later life stages. In the model, it is assumed that the annual mortality rate at this age is twice that for adults. However, because the period is only 6 months long (October–March), the total winter survival for the transition from late summer fry to juveniles, Sw , is equal in value to the annual natural survival of adults, Sa . Annual juvenile survival in subsequent years, Sj , is also assumed to equal the natural survival of adults. Juveniles are subdivided into discrete age classes from 1 to m − 1, where m is the age of first maturity. 2.3.8. Adults Many female brown trout in Switzerland are reproductively mature by their third year (age 2+) and almost all are mature by their fourth year (age 3+) (Gouraud et al., 2001; Kobler, 2004), although there is some variation. This variation may depend on genetic factors, but it is generally observed that early maturity is associated with higher growth rates (Mangel, 1996; Hutchings and Jones, 1998; Kobler, 2004). The researchers in Fischnetz studying this aspect of the life cycle provided assessments of the proportion of a population that is expected to be reproductively mature given the average size at age 2+ (Table 4). These assessments of mature age were used directly in the model. The natural survival rate of juvenile and adult brown trout is commonly estimated at 0.3–0.5 per year (Geiger, 1962; Maisse and Bagliniere, 1990; Sabaton Table 4 Results of an expert elicitation concerning the probability of maturity at ages 2+ and 3+, given average growth rate/size-at-age Age of maturity

Growth rate Slow (<26 cm at age 2+) (%)

Fast (>26 cm at age 2+) (%)

2+ 3+

25 75

50 50

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et al., 1998; Gouraud et al., 2001), but may be lower in streams with poor habitat structure (Armstrong et al., 2003). Therefore, we use a symmetric triangular distribution contained within these bounds as the maximum natural survival rate. Survival is then reduced in proportion to the habitat quality score for the stream section, khab , reaching a minimum value represented by a symmetric triangular distribution bounded by the values 0.15 and 0.35. This rate is assumed to apply to juvenile and adult fish, not including the effects of angler removal. As with juveniles, adults are also divided into discrete age classes from m to m + 9. 2.3.9. Individual growth To determine growth/size at each age, we used the brown trout growth model developed by Elliott et al. (1995) in which the specific growth rate GW is expressed as a function of weight at time t, Wt , and water temperature T according to, GW = gWt−h

(T − TLIM ) (TM − TLIM )

(6)

where TLIM = TL if T ≤ TM or TLIM = TU if T > TM . The parameter TM is the temperature of optimal growth, and TL and TU are lower and upper temperatures at which growth rate is zero. The exponent h is an empirical transformation of weight W, and g is the growth rate of a 1 g trout at optimum temperature. We added an asymptotic size term, W∞ , to the model of Elliott et al. (1995) to avoid infinite size. With this new term, fish weight at time t + 1 is expressed as a function of weight at time t and temperature as,  1/ h Wth + hg(1 − Wt /W∞ )(T − TLIM )t Wt+1 = (7) {100(TM − TLIM )} Values for the parameters of Eq. (7) come from Elliott et al. (1995) and Staub (1985) (Table 5). Other factors in addition to temperature, such as food availability and water pollution, may also influence growth. However, sufficiently detailed historical data to relate these factors to growth using results from the literature are not available for most rivers in Switzerland. Specific Fischnetz studies have revealed how aggregate descriptors of these factors influence other aspects of the trout life cycle, such as maximum capacity and incubation survival, but detailed studies of

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Table 5 Parameter values used in the growth model, with standard errors given in parentheses (from Elliott et al. (1995) and Staub (1985)) Parameter

Value (std. error)

TL TM TU h g W∞

3.56 (0.04) 13.11 (0.03) 19.48 (0.04) 0.308 (0.002) 2.80 (0.02) 1250 (250)

growth were not undertaken. Therefore, water temperature was used as the only controlling factor on growth. 2.3.10. Stocking In Switzerland, brown trout are often stocked in rivers popular with anglers. Stocking of 0+ fry is most common, but may occur in either the spring or autumn. As these periods are before and after the critical period of density dependence, respectively, they are handled separately in the model. Fry stocked before the critical period (early stocking) are simply added to the number of newly emergent fry for the year in which they are stocked, thus contributing to density-dependent mortality. Fry stocked after the critical period (late stocking) are assumed to initiate a new phase of density dependent mortality, which follows a “hockey stick” shape (Barrowman and Myers, 2000), with a low-density survival equal to the juvenile survival rate, Sj , and a maximum capacity, Kj , equal to the maximum capacity for late summer fry, Kf , multiplied by the juvenile survival rate, Sj . Additionally, because a larger fraction of the stream width is available as habitat for juveniles than for fry, a width correction factor that has previously been employed for adult fish (Vuille, 1997) is used. This correction assumes that streams less than eight meters wide provide fully suitable habitat, while the center channel of wider streams provides habitat that is only half as suitable. After multiplying by the width, w, to offset the width correction employed in Eq. (5), this leads to the following expression for juvenile capacity,  if w < 8.0 m  Sj Kf w Kj = 8.0 m+0.5 (w−8.0 m)  Sj Kf w else w (8) The hockey stick shape was chosen rather than the Ricker curve for this phase of density dependence because, while habitat may still set the upper limit to the

population, there are no theoretical reasons to expect overcompensation, such as an extended period of high vulnerability (Jonsson et al., 1998). 2.3.11. Angler catch Anglers in Switzerland are required to record and submit to the appropriate canton the number, size, location, and date of all fish caught and retained. However, the number of unsuccessful trips and the duration of trips are not generally recorded, making calculations of total effort and catch per unit effort impossible. Fish that are caught and released are also not recorded. Therefore, only total angler removal per year is calculated for specific stream reaches of interest and can be used as an input to the model. Size limits in Switzerland are reach-specific and are set at a level that should allow fish at least one opportunity to spawn. Therefore, in the model, the total recorded catch is simply removed from the adult population at the end of each year, proportional to the relative abundance of each age class more than 1 year beyond spawning. 2.4. Simulations The model described in the previous section was implemented using Analytica, a commercially available software program for evaluating graphical probability models (Lumina, 1997). Other, non-commercial software packages are also available. We chose Analytica because it allows for the use of continuous or discrete variables related by any functional expression. Conditional probabilities can be represented by a wide variety of distributions and are propagated through the network using random or Latin hypercube sampling. Bayesian belief networks are required to be acyclic. However, the population model requires a cycle linking adults back to eggs. This was handled in Analytica by creating dynamic nodes for the variables representing the various life stages. The values of these variables at one time step then depend on the values of other, down-arrow variables at a previous time step. In this way, cycles are avoided (Haas et al., 1994). Five hundred simulations were performed for each scenario to represent the effects of uncertainty on results. The Latin hypercube sampling method was used to draw random samples from all probability distributions. Each simulation consisted of 120 years, with only the last 100 years used for analysis. The variables

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Fig. 7. A set of five typical simulations, illustrating annual variability in density.

average fecundity, spawning rate, incubation survival, PKD mortality, fry survival, natural survival, and egg scour, were modelled as dynamic variables, with new values drawn in each year. The other variables, which are interpreted as average values, differed across simulations but were assumed to have constant values for all years of a simulation. Water temperature variables, including the term used to estimate maximum recruitment capacity and the probability of more than 2 weeks greater than 15 ◦ C, were calculated from sinusoidal curves describing seasonal variation, with site specific estimates of mean and amplitude. Model results represent the density of the various life stages of a particular brown trout population given values for the different primary influence factors. The predicted density is a long-term summary for that location, and significant annual variability may underlie this summary, depending on annual conditions (Fig. 7). Regular fluctuations can also be an inherent property of populations controlled by the Ricker function (Levin and Goodyear, 1980). To capture this variability and oscillation, our results include estimates of the variability across years, expressed as statistics of the distribution of predictions. 2.4.1. Case study locations Four river basins, the Emme, Lichtenstein Binnenkanal (LBK), Necker, and Venoge were chosen to represent the range of conditions in Switzerland (Fig. 8). These four basins served as case studies for other parts of the Fischnetz project, and so more extensive data exist here than for other locations. These basins were selected for study because they each show

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Fig. 8. Map of Switzerland indicating the four river basins investigated in this study.

a considerable decline in brown trout catch over the last 10–20 years. In addition, they are typical in that they exhibit a multitude of potential causal factors. In each basin, three spatially distinct brown trout populations were studied. In the Emme, Necker, and upper Venoge, these populations were either separated by barriers or the distance between them was great enough that migration was considered negligible. In the lower Venoge and LBK, there may be some potential for inter-population movement. The angler associations and cantonal administrations voluntarily discontinued stocking in the reaches for the 2 years in which population surveys were performed. The Emme River is in a steep pre-alpine region considerably influenced by spring snowmelt and seasonal flow fluctuation. Downstream, historically high occurrence of floods prompted intense river management activities in the nineteenth and twentieth centuries. The construction of small dams and weirs has resulted in isolation of tributaries, poor riparian conditions, and high water extraction (primarily for agriculture). Natural trout habitats are mostly found in the upper reach. Primary land use in the Emme basin (963 km2 ) consists of 35% intensive agriculture (mostly downstream) and 40% forest. Two large wastewater treatment plants (WWTPs) discharge into the downstream Emme, while a number of smaller WWTPs discharge into the river’s tributaries. Catch of brown trout has declined approximately 50% since 1990. The Liechtenstein Binnenkanal (LBK) is a channel constructed in the 1930s for flood protection and land

Numbering of the sites corresponds to relative position: 1 = downstream, 2 = midstream, 3 = upstream. The 90% confidence interval of the estimated maximum fry capacity, Kf , is also given for reference, although it is not a direct model input.

38 55 76 5 0 0 28 90 9 150 150 170 150 178 136 1954 1954 1954 0 0 0 803 803 0 0 331 987 0 0 0 7303 4753 2418 1437 1437 8114 154–247 282–424 1360–1708 1289–2074 2006–2543 5358–6795 863–1413 1485–2374 1850–2357 414–632 413–594 5853–8682 Grayling Trout Trout Trout Trout Trout Grayling Trout Trout Barbel Barbel Trout 0.53 0.53 0.73 0.4 0.27 0.53 0.73 0.8 0.8 0.47 0.67 0.93 23.6 32 11.7 8.5 4.9 3.9 13.3 15.4 5.7 11.8 14 6.1 6.4 5.5 6.6 1.8 2.1 3.3 7.0 6.9 5.5 6.2 5.9 5.1 9.6 9.1 6.6 8.7 9.8 8.5 8.8 8.7 6.6 10.9 10.5 8.8 Yes Yes No No No No No No No Yes Yes Yes Low Low Low High High 50% Med, 50% High Low 50% Low, 50% Med Low 50% Med, 50% High 50% Med, 50% High 66% Low, 34% Med Emme 1: B¨atterkinden Emme 2: Burgdorf Emme 3: Bumbach LBK 1: Schaan LBK 2: Triesen LBK 3: Balzers Necker 1: Letzi Necker 2: Aachs¨age Necker 3: Hemberg Venoge 1: Ecublens Venoge 2: Bussigny Venoge 3: Montricher

5.69 3.87 2.54 1.13 1.18 1.08 2.88 2.77 1.20 8.96 7.76 5.16

Late stocking (ind/ha) Early stocking (ind/ha) Max. fry capacity 90% C.I. (ind/ha) Species zone Habitat quality khab River width (m) Temperature amplitude (◦ C) Temperature mean (◦ C) PKD Water quality (as predicted mean CN , mg/l) Level of fines/clogging

2.4.2. Model testing To assess the ability of the model to reproduce observed population patterns, model results were first generated for current conditions at the 12 survey sites (Table 6) and compared to population surveys taken in 2002 and 2003 (Schager and Peter, 2003). From two to five surveys were conducted at each site, depending on population density, flow conditions, and personnel availability. For stocking and angler catch, the annual average values for the period 1996–2000 were used in simulations for predicting adult population densities. However, for juveniles, stocked fish were not counted in the model predictions because stocking was discontinued for the 2 years of the surveys. Mean model predictions with 90% uncertainty intervals were compared against the mean, minimum, and maximum of the observed values over the five survey dates for the

Location

conversion. The flow is rather constant, and the only prominent barrier, at the mouth of the channel, was removed in 2000. Restrictions of natural habitat are mainly due to longitudinal constructions leading to low variability in width and a regulated flow. This situation has resulted in high levels of sediment fines and stream bed clogging. One WWTP serving about 4500 people discharges into the LBK. The LBK basin (138 km2 ) is dominated by forest (50%) with only 18% intensive agriculture. Catch levels of brown trout have declined by more than 90% since the mid 1980s. The Necker is a pre-alpine river with natural, seasonally fluctuating flow. River morphology is only mildly disturbed, providing varied habitat for all life stages of brown trout. Primary land use in the basin (123 km2 ) consists of 35% intensive agriculture and 38% forest. Little wastewater is discharged into the Necker, but input of fines and gravel clogging may be a problem. Angler catch has decreased by more than half since the mid 1980s. The Venoge is located in the west midlands of Switzerland and flows into Lake Geneva. Habitat quality seems adequate in the upper reaches but somewhat worse in the lower section. The area of the basin is 231 km2 and land use includes 50% intensive agriculture and 34% forest. Twenty, mostly small, WWTPs discharge to the Venoge or its tributaries. Catch of brown trout in the Venoge has decreased less than in the other studied rivers (approximately 15% since the late 1980s).

Angler catch (ind/ha)

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Table 6 Summary of model input values representing current conditions at the survey locations

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237

Necker and LBK and Emme 3 populations, four dates for Venoge 1 and 2, three dates for Venoge 3 and Emme 2, and two dates for Emme 1. These represent all the data available for each site. 2.4.3. Causal assessment The potential for the various stress factors to limit the population of brown trout was assessed by examining the midstream Necker site in more detail. This site was one of the most accurately predicted by the model and is currently relatively unimpaired. Model predictions were generated for hypothetical situations in which the population is exposed to each major stress factor individually to assess its impact on adult density. To assess the current relative impact of each major stress factor at each survey site, a quantitative measure of causal strength was developed. This was defined as the change in adult density that would result if that stress factor were the only one present at that location, divided by the predicted adult density in the absence of any of the selected stress factors. This was calculated one by one for each major stress factor. Negative values indicate the percentage reduction in density and positive values indicate an increase. Because the measure depends on the other site-specific characteristics, such as width, temperature, and fish species zone designation, it can be used as an indication of the relative importance at a particular site but should not be quantitatively compared across different sites. 2.4.4. Effects of management To consider the effect of management measures to improve conditions, model predictions were generated assuming the removal of the two most important stressors at each site. As PKD eradication is not considered to be a feasible option, removal of the PKD effect was not considered. Other site-specific conditions, such as temperature, width, and fish zone were maintained at the current values. The recent historical levels of stocking were also maintained.

3. Results 3.1. Model testing Model predictions show a reasonable correspondence with observations for juveniles, when uncer-

Fig. 9. A comparison of mean model predictions and observations for (a) juvenile and (b) adult density at the case study locations. Vertical error bars for the predictions represent the 10 and 90% predictive limits, indicating the effects of uncertainty and variability. For the observations, error bars represent the minimum and maximum of the sampling dates in 2002–2003. Numbering of the sites corresponds to relative position: 1 = downstream, 2 = midstream, 3 = upstream.

tainty and variability are taken into account (Fig. 9a). Both predictions and observations show clear upstream to downstream trends in brown trout density in all four rivers. The upstream LBK and Venoge locations (site #3) seem to provide the most favorable conditions, but there is particularly high uncertainty in the model predictions at these two sites. This is primarily due to uncertainty in the actual gravel bed conditions. The level of fines and clogging were found to vary across habitat survey dates and this was reflected by using uncertain model inputs (see Table 6). Further, PKD has been identified at the upstream Venoge site, but the water temperature is relatively low compared to other PKD locations (see Table 6). The result is that summer water temperatures do not always exceed the threshold for PKD-induced mortality of 2 weeks greater than 15 ◦ C, leading to high year-to-year population vari-

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ability. The model predicts near extinction of the local populations at the two downstream Venoge sites, which have high levels of clogging, poor water quality, PKD, high water temperature, high angler catch, and high competition with other fish species. Despite all this, however, population surveys have found a reasonable number of juvenile brown trout. Stocking is fairly high at these locations and, although discontinued for the years of the survey, may still contribute to the density of 2+ or late maturing 3+ juveniles. There is less correspondence between predictions and observations for adults (Fig. 9b). The LBK populations are especially overpredicted. However, this was not the case for juveniles, suggesting that some cause for loss of adult fish may have been neglected. The LBK is known to support rainbow trout in addition to brown trout, and this competition, which was not accounted for by our model, could be a factor explaining lower observed brown trout densities (Bassi et al., 2001). Bird predation, unrecorded angler catch, or emigration may also lead to disproportionate losses of adult fish. Such losses may also account for the overprediction at the upstream Necker site. With data available for only 2 years, it is difficult to distinguish whether mismatches between predictions and observations are due to model weaknesses or natural variability. What can be concluded is that the main differences in population density across rivers and across locations within a river can be reasonably well represented by the model. 3.2. Causal assessment Detailed predictions for the midstream Necker population show that, given the current level of angler catch (90 fish/ha/y), if the population were exposed to either high clogging, PKD, or worsened habitat quality (khab = 0.4), further declines would result (Fig. 10, white bars). A worsening of water quality, as represented by a hypothetical doubling in river basin inhabitants and doubling of agricultural area, may also result in declines. However, as shown by the error bars, the uncertainty in this prediction is relatively high. Even if angler catch were reduced to 30 fish/ha/y (the level of the downstream Necker 1 site), high gravel bed clogging would still limit the population, as would poor habitat quality (Fig. 10, grey bars). Marginal, but uncertain, decreases would result from poor water

Fig. 10. The predicted effect of individual stress factors at the midstream Necker 2 location. Vertical bars represent the mean predictions and error bars represent the 10 and 90% predictive limits. White bars assume current angler catch of 90 fish/ha/y; shaded bars assume reduced angler catch of 30 fish/ha/y.

quality, and PKD would also reduce the population. However, the cooler temperatures at this site may limit PKD-induced mortality, causing high population variability in this case. Causal strength estimates show that the relative impact of the different causal factors differs by location (Fig. 11). Habitat degradation is very important at nearly all sites, potentially responsible for reductions (relative to optimal conditions) of over 50% in nine of the populations. PKD is also fairly important at sites where it occurs, causing reductions over 25% in most cases. Angler catch is important at some locations, such as all the sites in the Emme and downstream sites in the Venoge, and may be responsible for reductions as high as 50%. The effects of gravel bed clogging and water quality are much more ambiguous, potentially causing both large reductions or large increases and being very uncertain in any case. This is because, unlike the other stress factors, these exert their effect prior to the period of density dependence at the end of the first summer. This means that if a population would otherwise produce too many fry relative to the maximum capacity of the habitat, reductions in newly emergent fry caused by a clogged gravel bed or poor water quality may actually increase the number of fry at the end of the summer by reducing competitive losses (see Fig. 5). Therefore, especially for locations with relatively poor habitat (such as most of the downstream locations), factors that cause early life stage mortality may lead to adult population density increases. Total reductions

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Fig. 11. The estimated causal strength of the five most important stress factors at each test area. Relative causal strength for a particular stress factor is defined as the change in adult density that would result if that stress factor were the only one present at a location, divided by the predicted adult density in the absence of any of the five stress factors. If a bar is not shown for a location, then the stressor is not present. Stress factors are shown in the order (from top to bottom) of the life stage in which they have their primary effect.

caused by all of the stress factors together are at least as great as the observed declines in angler catch over the last 10–15 years. This suggests that there is at least the potential to explain the declines by a degradation in conditions.

3.3. Effects of management The predicted effects of removing the two most important stressors at each site (Table 7) indicate that significant improvements can be expected for some of

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Table 7 Management measures considered for each location Location

Management measures

Emme 1: B¨atterkinden Emme 2: Burgdorf Emme 3: Bumbach LBK 1: Schaan LBK 2: Triesen LBK 3: Balzers Necker 1: Letzi Necker 2: Aachs¨age Necker 3: Hemberg Venoge 1: Ecublens Venoge 2:Bussigny Venoge 3: Montricher

Improve habitat quality to 0.8 Improve habitat quality to 0.8 Improve habitat quality to 0.8 Improve habitat quality to 0.8 Improve habitat quality to 0.8 Improve habitat quality to 0.8 Improve habitat quality to 0.8 Improve habitat quality to 0.8 None Improve habitat quality to 0.8 Improve habitat quality to 0.8 Eliminate intensive agriculture

the populations (Fig. 12). The LBK populations would benefit greatly from an improvement in habitat and a reduction in angler catch. The upstream Emme and midstream Necker population would also benefit from such changes. The population at the upstream Venoge site could double if water quality were improved. The adult density of other populations would not increase substantially, even if the major stress factors other than PKD could be removed. The two downstream Emme sites, for example, are limited by the presence of PKD and, potentially, poor water quality. The most downstream Emme, the downstream Necker, and the two downstream Venoge sites cannot be expected to support high brown trout densities because of their classification as grayling or barbel zones. The most upstream

Fig. 12. The predicted effect of management measures to eliminate the major stress factors at each location (see Table 7). Bars represent mean model predicted adult density under current and improved conditions. Vertical error bars represent the 10 and 90% predictive limits.

Reduce angler catch by half Reduce angler catch by half Reduce angler catch by half Reduction of clogging to low Reduction of clogging to low Reduction of clogging to low Reduce angler catch by half Reduce angler catch by half None Reduce angler catch by half Reduce angler catch by half Eliminate wastewater inputs

Necker site does not currently appear to be subject to any major stress factors, so no management measures were tested. 4. Discussion Compared to previous efforts to model fish populations using Bayesian networks (e.g. Lee and Rieman, 1997; Shepard et al., 1997), ours has some advantages. Variables in our model are represented as continuous, rather than discrete, quantities, thus conveying more detailed information in both inputs and outputs and avoiding artificial error expansions that can occur when uncertainty is propagated through discretized variables. We also incorporate the representation of population dynamics directly into the model, rather than using the network to simulate the results of an externally controlled population model (as is done by Lee and Rieman, 1997). This improves model accuracy and the ease of future updating. Finally, we explicitly link population parameters to external influences as part of the model. While this has been done in other frameworks, such as individual-based (Van Winkle et al., 1998), Leslie matrix-type (Charles et al., 2000) and dynamic (Jessup, 1998) models, it has not been previously implemented in Bayesian networks. As mentioned earlier, Bayesian networks have the advantages of: (1) a readily understandable, graphical causal structure that facilitates decomposition into separate submodels, (2) the ability to use information obtained from field or experimental results, other models, or expert judgment to formulate the submodels, and (3) the explicit consid-

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eration of variability and uncertainty in model inputs and relationships. The predictions of our model seem to capture the variability observed across the 12 studied locations. However, mismatches at some locations suggest that factors not included in the model may be important. These may include competition, bird predation, unrecorded angler catch, or immigration and emigration. While these could conceivably be included in the model, we do not have any information on their values for specific populations. Further the effects of the latter three of these factors are essentially interchangeable, making explicit inclusion of these unknowns superfluous with regard to causal assessment. On the other hand, mismatches could simply be due to natural population variability. Data from more years are required to better assess the long-term average density and yearto-year variability. Many of the populations in the study locations are exposed to more than one stress factor. Our causal assessment showed that, in most cases, even if only one of the important stress factors were present, it could still be the cause for a low population density (see Figs. 10 and 11). This implies that if multiple factors are present, then all of them would have to be eliminated to achieve a significant recovery. This result was confirmed by the predicted response of the populations to management measures (see Fig. 12): locations with PKD and warm water temperatures, for example, did not generally show a very large improvement upon removal of other stressors. While many factors may be contributing to trout declines, suboptimal habitat seems to be a strong causal factor at most of the locations studied. In part, this is because of the way we defined causal strength; any habitat that is less than optimal (a habitat quality score of 1.0) will be assigned some causal responsibility. This is true whether the deficiency is anthropogenic or entirely natural. Some rivers, for example, may never have had suitable spawning substrate or a complex morphology. More insight could be gained by comparing current conditions to those that existed when trout populations were apparently larger. Unfortunately, historical habitat surveys are generally not available. The quantitative results of our causal strength assessment can be expected to be sensitive to the choice of a function describing density dependent survival in

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the first year. We chose the Ricker curve because it has been conceptually and empirically supported for brown trout populations (Elliott, 1994; Jonsson et al., 1998), however, it has the distinctive feature that decreasing stock densities can lead to a higher number of resulting recruits. Another recruitment curve without this property, such as the Beverton–Holt curve (Beverton and Holt, 1957) which approaches the carrying capacity asymptotically, would not lead to the potentially positive population impacts of gravel bed clogging or poor water quality observed in the present study for the Ricker curve. Density dependence in a population can lead to sustained oscillations or even chaotic fluctuations in density with time (Levin and Goodyear, 1980). In our model, such behavior was not readily apparent in the results because many controlling parameters were also assumed to vary with time (see Fig. 1). Therefore, to gain further insight into the natural dynamics of the 12 modeled populations, we eliminated all uncertainty and variability in model parameters, setting each to its mean value. Results then indicated that the populations at Emme 1, Emme 2, LBK 1, LBK 2, LBK 3, Venoge 1, and Venoge 2 would approach stable equilibria of 0, 0, 222, 256, 590, 33, and 35 ind/ha, respectively. The others would display regular, approximately 8year oscillations, with the most severe being at Venoge 3, which would fluctuate between adult densities of 7 and 550 ind/ha. It is beyond the scope of this study to further investigate this aspect of population behavior, especially because the dynamic nature of controlling factors is likely to make such deterministic behavior in natural populations irrelevant. However, it is useful to bear in mind that a certain amount of temporal variability may be inherent. The present modeling study, and the Fischnetz project in general, were initiated primarily in response to a historical decline in angler catch. Unfortunately, simultaneous historical fish population survey data do not exist for most rivers. Therefore, the relation between stock and catch cannot be accurately assessed, and it cannot be known whether actual population declines have occurred or angler behavior has simply changed. Other studies have investigated this question and the results are equivocal (Staub et al., 2003). However, from the investigated study sites, we can conclude that a number of potential stress factors have population level effects that are sufficiently strong to lead to

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declines of a magnitude similar to those observed in catch records. The conditions observed at the 12 study sites are common throughout the midlands of Switzerland. Sediment clogging, agricultural runoff, wastewater inputs, PKD, and poor habitat are common problems (Schmidt-Posthaus et al., 2001; Burkhardt-Holm et al., 2002; Wahli et al., 2002). Therefore, the results of our modeling study can be expected to be generally applicable. However, the response of a population to the introduction or removal of a particular stressor will depend highly on existing conditions, including the presence of other stressors and angling effort. The model developed in this study can be used to provide these site-specific assessments.

Acknowledgements We thank all the members of the Fischnetz project leadership committee for applying their diverse expertise to this effort. Helmut Segner and Heinz Renz should be specifically acknowledged for their extended contributions of time and knowledge. Daniel Bernet kindly provided data used in this study, and Renat Hari, Rosi Siber, and Karin Scheurer provided critical support in data handling and analysis. Danny Lee provided his model and code, which were used to develop preliminary versions of our model. Productive and stimulating discussions were had with Thomas Vuille, Danny Lee, Bernd Kobler, Maria Roos, John Malcolm Elliott, and Steffen Schweizer. Roger Koenker provided the quantile regression package. Funding was provided by the Fischnetz project which was supported by the Swiss Federal Institute for Environmental Science and Technology, the Swiss Agency for the Environment, Forests and Landscape, all 26 cantons of Switzerland, the principality of Lichtenstein, the Swiss Society of Chemical Industries, the Swiss Fishery Federation, the Center for Fish and Wildlife Medicine of the University of Bern, and the University of Basel.

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