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North American Journal of Fisheries Management 26:960–975, 2006 Ó Copyright by the American Fisheries Society 2006 DOI: 10.1577/M04-187.1

[Article]

A Logistic Regression Model for Predicting the Upstream Extent of Fish Occurrence Based on Geographical Information Systems Data BRIAN R. FRANSEN,* STEVEN D. DUKE, L. GUY MCWETHY, JASON K. WALTER, AND ROBERT E. BILBY Weyerhaeuser Company, Post Office Box 9777, Federal Way, Washington 98063-9777, USA Abstract.—Regulations governing human activities in streams and riparian zones frequently differ depending on whether or not a stream reach supports fish. Fish presence or absence is usually determined by sampling or by assuming the presence of fish if the stream exhibits certain physical characteristics. Field surveys of fish occurrence in streams are time consuming and expensive. Inference of fish presence from simple thresholds of physical attributes, such as gradient or channel width alone, is inaccurate. We attempted to improve the accuracy and efficiency of this determination by developing a geographical information systems (GIS)-based predictive model. A 10-m digital elevation model incorporated field data on fish distribution from 517 streams in western Washington State and GIS-derived representations of the physical characteristics of stream networks. A model predicting the upstream extent of fish occurrence was derived using logistic regression models coupled with a heuristic ‘‘stopping rule.’’ Candidate variables included stream gradient, upstream basin area, elevation, and mean annual precipitation. When assessed against independent survey data, 91.9% of the occupied fish habitat was correctly classified by the model. Errors were generally small, but occasional large errors did occur and were most frequently associated with barriers to fish movement. Smaller errors occurred in marginal habitats, streams of low topographic relief, and streams that originated from headwater ponds. Use of this type of model, coupled with targeted field survey in areas most likely to be associated with model error, would greatly improve the efficiency and accuracy of current classification schemes.

The presence of fish influences the type and intensity of land uses that are permitted in and adjacent to streams in many western states and provinces. Many of the forestry regulations in this region specify larger riparian buffers along fish-bearing streams, and road crossings over fish-bearing streams are required to provide for fish passage (Ellefson et al. 1995; Moore and Bull 2004). Many municipalities have enacted more restrictive policies governing development along fish-bearing streams than along streams that do not support fish (e.g., Fish Protection Act 2001; Snohomish County [Washington] 2003). Rules governing the application of chemicals also are more restrictive in areas adjacent to fish-bearing streams (U.S. District Court 2002). Therefore, a thorough knowledge of the distribution of fishes in a drainage network is often needed to provide the required level of protection to aquatic habitats. Whether or not the upstream extent of fish use is an appropriate ecological break on which to base regulations is subject to debate. One could certainly argue that management of aquatic systems for benefit * Corresponding author: [email protected] Received November 1, 2004; accepted April 12, 2006 Published online November 30, 2006

to fish should occur with consideration of ecological function across the entire stream network because of the connectivity of stream networks from headwaters to the terminus of large rivers (Fausch et al. 2002). Transport of sediment, nutrients, large wood, and other materials from fishless streams to downstream fishbearing streams is an important component of productive fish habitat (Wipfli and Gregovich 2002). In some cases, however, the distinction in regulatory requirements does have a rational basis. For example, unrestricted passage for fish at road crossings is only a consideration in stream reaches occupied by fish. Regardless of the underlying factors influencing regulations, many jurisdictions currently distinguish between fish- and non-fish-bearing streams by focusing specific regulatory requirements only on streams supporting or presumed to support fish. Application of regulations based on fish presence requires accurate delineation of fish distribution. Because fish are mobile and often hard to sample, their use as a regulatory indicator has proven to be a challenge. Determination of the fish distribution is most commonly conducted by directly sampling the stream reaches in question. Surveys usually are conducted with electrofishing equipment, a very effective method of capturing fish. However, this

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technique involves a considerable amount of field effort, is expensive, and runs the risk of injury to the sampled fish (Dalbey et al. 1996; Schreer et al. 2004). Fish occurrence in some streams may vary temporally. Fishes may migrate annually into low-gradient, ephemeral stream reaches during wet times of the year and move downstream as flow diminishes (Erman and Hawthorn 1976; Brown and Hartman 1988). A single survey of a stream may therefore not accurately identify the upstream extent of occupied habitat. Droughts, debris torrents or other disturbances may temporarily compress fish distribution over the course of one or more years. The information generated by single-visit surveys of fish occurrence cannot account for intra-annual or interannual variation in the upstream extent of fish distribution. Some streams cannot be sampled reliably during periods of high flow or turbidity. Concerns about seasonal use of habitats and sampling efficiency problems have prompted some jurisdictions to develop guidelines restricting the time of year that field surveys demonstrating fish absence can be conducted (Washington Forest Practices Board 2002; Oregon Department of Forestry and Oregon Department of Fish and Wildlife, no date). Because of the potential for spatial and temporal variation in fish distribution and the effort and expense required to perform direct sampling, some regulatory programs provide physical standards and thresholds based on simple physical attributes of streams (e.g., width or gradient) to indicate probable fish presence or absence (e.g., British Columbia Ministry of Forests and Range 1998; Washington Forest Practices Board 2002). This method of estimating the upstream extent of fish habitat also presents difficulties. Inference of fish use from a few physical habitat factors assumes a relationship between certain habitat conditions and fish use, usually with little or no empirical evidence of such a relationship. Simple physical criteria can therefore be highly inaccurate and may bias estimates of the upstream extent of fish use. The shortcomings in both of these methods indicate the need for exploring more reliable and efficient approaches to delineating fish distribution. The increasing availability and sophistication of spatial data may enable the development of a system that would address some of the shortcomings in the approaches currently being employed. Ideally, such a system would be able to rapidly and accurately delineate the extent of fish-bearing streams for large drainage networks with accuracy comparable to on-ground surveys. If sufficient accuracy cannot be achieved on all streams, the capability to identify areas most likely to be inaccurately classified could provide a way to concentrate field survey efforts on areas that are most

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likely to improve overall stream classification. To be useful in a management context, such a system would need to be inexpensive and easy to implement across large areas. Other researchers have predicted fish presence or absence using models based on field-measured or mapderived physical criteria (Kruse et al. 1997; Porter et al. 2000; Latterell et al. 2003). Recent advances in geographical information systems (GIS) technology present an opportunity to expand this approach to empirically derived landscape-scale models that have a capability to rapidly and consistently delineate the extent of fish-bearing streams across large geographic areas. Such an approach will be most successful if the upstream distribution of fishes is determined by a relatively few factors, all of which can be reliably generated from available GIS data sources. In our study, we sought to develop a model to predict the upstream extent of fish distribution via a logistic regression coupled with a heuristic stopping rule. The model was based on data from a large empirical database on fish distribution in western Washington State and GIS coverages available for the entire state. Variables included basin area, elevation, mean annual precipitation, average basin slope, and channel gradient. The development of our model involved three steps: (1) characterization of conditions at locations with known fish presence or absence using field data of fish distribution and available GIS coverages and tools, (2) use of these data to develop a logistic regression that computes an index of the likelihood of fish presence at points (based on their GIS-derived characteristics) evenly spaced along a channel network, and (3) development of a stopping rule to resolve ambiguities in the habitat index values along a stream reach and subsequently identify a single-point prediction of the upper extent of fish occurrence. The accuracy of the model predictions were assessed by comparing model predictions against actual fish distribution for a large basin in southwestern Washington. Methods Field data collection.—The upstream extent of fish occurrence was determined by electrofishing 517 streams in western Washington between 1997 and 2002. Surveyed sites were located within forested watersheds and distributed across a broad area (Figure 1). Sites were selected in response to anticipated timber harvest, correction of fish passage blockages, verification of existing stream classification, or other management-related activity in or adjacent to streams requiring a regulatory permit. We based our survey protocol on the state-specified methodology for surveys on forest

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FIGURE 2.—Schematic diagram of lateral versus terminal upstream limits of fish occurrence (ULO) within streams. The black bar indicates the location of the ULO.

FIGURE 1.—Study sites in western Washington State used in modeling predictions of the upstream limits of fish occurrence, as designated by the black dots. County names and boundaries are provided for reference. At one watershed, Stillman Creek (gray outline and cross-hatching), a complete field inventory of fish occurrence was conducted to provide an independent assessment of model performance.

land in Washington (Washington Forest Practices Board 2002), which requires a single-visit, electrofishing survey to determine the upstream extent of fish occurrence. All surveys followed a standard protocol. Sampling was performed with a backpack electroshocker (Smith-Root model 12-A) between March 1 and July 15 of each year, which coincided with periods of moderate to low streamflow; sampling during elevated flows would have reduced sampling reliability. We employed a two-person crew on each survey; one operated the electroshocker, and the other followed with a large dip net to restrict downstream fish movement and assist in the observation of fish presence. Upstream movement by fish was not restricted. Surveys were initiated in a stream reach verified as fish bearing and continued upstream to a location where one or more of three criteria were met: (1) no fish were encountered within a minimum continuous survey distance of 400 m upstream of the last captured fish, (2) stream gradient increased to and remained above 20%, or (3) no fish were encountered between the uppermost fish identified and a location

where continuous absence of surface flow upstream occurred. The location of the uppermost fish captured was then defined as the upstream limit of occurrence (ULO). Surveys were continued after meeting one or more of the minimum survey criteria at many locations to ensure that they accurately defined an end to fish occurrence. In no cases were fish found above the location where one of the three criteria was met. After the ULO was determined, a heavy plastic plaque nailed to the nearest tree was used as a monument and the location was marked on a 1:1,000-scale base map. The ULOs were divided into two categories: terminal and lateral (Figure 2). Terminal ULOs were defined as sites where fish occurrence terminates within a continuous reach of stream or at the junction of two or more fishless streams. Lateral ULOs occur at sites where a small stream without fish intersected a fish-bearing stream reach with fish both upstream and downstream of the junction with the fishless stream. Lateral ULOs often represent extreme changes in stream size and gradient and provide fewer opportunities to examine a gradual change of physical conditions near the observed end of fish occurrence. We intentionally focused survey effort in the terminal sites because they represent the ULO and provide the best opportunity to assess and characterize the channel features associated with the end of fish use. During our surveys, we collected data to characterize the physical features and fishes associated with the ULO. Fish present in the stream reach (reach boundaries defined by changes in gradient or tributary junctions) immediately below the ULO were identified. We identified salmonids captured at all terminal ULOs to species. Sculpins Cottus spp. captured at these sites were not identified to species because of the difficulty of distinguishing species in the field. Species present below lateral ULOs could not always be reliably assessed, as the stream channels associated with these sites were often main-stem rivers that were too large or


deep to reliably determine all species present, although these reaches were always known to support fish or verified as fish bearing during the survey. Additionally, because lateral ULOs can occur anywhere along a fishbearing stream between the headwaters and estuary, the fish communities immediately downstream from a lateral ULO do not necessarily reflect fish communities representative of those found at the ULO. Gradient immediately above and below the ULO was measured with a hand-held clinometer along the channel thalweg. In addition, any physical features at the ULO that may have restricted the upstream occurrence of fish were noted. This determination required a subjective assessment of those channel features that could present an impediment to fish passage (i.e., we had no precise definition of what constituted a blockage because the range of blockage situations varied widely). Channel features that were included as possible passage barriers included waterfalls, dramatic increases in stream gradient, cessation of perennial flow, or other abrupt changes in habitat character that were likely to restrict fish movement. Surveyors identified both permanent and transitory migration barriers. Permanent barriers included waterfalls or other abrupt increases in stream gradient caused by geologic features at a ULO. Transitory barriers included presumed temporary fish blockages (e.g., beaver dams, log jams, landslide deposits, or other natural features) that may preclude upstream movement at the time of survey but would probably be breached over a period of years or decades. Surveyors assigned a gradient break classification to sites where a continuous change in stream gradient of 5% or more occurred at the ULO. Small stream size was assigned to the ULO when the streamflow became intermittent in close proximity to the ULO, where a defined channel ended, or where the stream was judged to contain insufficient flow or depth to provide areas capable of supporting fish. A stream junction classification was assigned where the confluence of one or more non-fish-bearing tributaries was associated with the ULO. If no obvious change in channel character corresponded with the ULO, ‘‘no change’’ was noted. In recognition of potential error associated with single-visit surveys arising from temporal variability in the ULO, we repeated surveys on a subset of streams to assess intra-annual and interannual fish use. These resurveyed streams were randomly drawn from the previously surveyed pool of candidate streams meeting our criteria. We assessed intra-annual variability by resurveying 37 streams in January and February of the winter after their original surveys (May–July 2001). To examine interannual variability, we resurveyed 40 streams 2 years after their original surveys in March–

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July 1997. We focused the sampling in both assessments on areas that were most likely to allow for fish movement upstream or downstream by limiting our sampling to terminal ULOs and by excluding sites with upstream gradients greater than 20% or sites with natural barriers to migration. A complete field inventory of fish occurrence was also conducted in one watershed, Stillman Creek, to provide an independent assessment of model performance. This 11,960-ha basin is centrally located within the area where the surveys were conducted and exhibits a range of elevation, geology, and topography that is representative of conditions generally found within the other sampled areas. Development of GIS platform.—We developed a GIS platform to characterize the physical attributes of stream networks for those western Washington basins where our surveys were conducted (McWethy et al., in press). Watersheds ranged in area from 2,584 to 38,990 ha. The primary input data sets were the U.S. Geological Survey 10-m digital elevation model (DEM) data for western Washington and average annual precipitation isopleths and 1:24,000-scale hydrology stream vectors (Washington Department of Natural Resources, unpublished data). The DEM data were hydrologically corrected to ensure water flow across each basin using the function TOPOGRID (ESRI 1998), which modifies the DEM in areas under hydrology stream vectors to force downstream flow. We derived three grids for each watershed from the modified elevation and the annual precipitation data: a flow direction grid, a flow accumulation grid, and a basin-weighted average annual precipitation grid. Vectors delineating streams were created from the accumulated flow grid, assuming a minimum basin area of 1.5 ha to generate a channel. We then created stream points approximately every 10 m along each stream vector, assigning each point a unique identifier. Average stream gradients along the channel, both 100 m above and 100 m below each stream point, were calculated. We then assigned elevation, average precipitation, basin area, upstream gradient, and downstream gradient to all stream points within the GIS stream networks derived for the basins where our field surveys were performed. The locations of ULOs from all field surveys were digitized on the GIS-derived stream network from the 1:1,000-scale field base maps. Field-identified features, such as stream junctions and gradient breaks, were used to ensure correct placement of ULOs on the GIS stream network. We were able to digitize 492 of the 517 ULOs determined during the field surveys across 52 basins. Twenty-five ULOs were not included because inconsistencies between conditions observed

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on the ground and those represented on the GISderived stream network prevented accurate digitization of these points. Additional ULOs were excluded because they were caused by manmade obstructions. Because our objective was to predict the upstream extent of fish distribution under natural conditions, these ULOs were considered inappropriate for model development. We retained 417 digitized ULOs in 50 watershed area units for model development. We assigned a response variable to all the GISderived stream points along the channel network above and below the ULO indicating the presence or absence of fish. Stream points on reaches not related to a fieldverified ULO were coded as unknown. Modeling data consisted of GIS-derived stream points with known fish presence or absence spaced at 100 m along the stream network. Model development.—We used logistic regression (Hosmer and Lemeshow 2000) to develop a model for predicting the likelihood of fish presence from the data generated with the GIS platform. Logistic regression is a type of generalized linear model (Myers et al. 2002) that fits a binary response (fish/no fish) via either continuous or discrete predictors. One of the challenges in fitting this model was that our data failed to meet one of the primary assumptions of logistic regression, that a binary response is observed on a set of independent units (Myers et al. 2002). Unfortunately, GIS-derived points on the stream network are not independent. Because the GIS-derived points are only 100 m apart, nearby stream points are more likely to have the same response value than are widely separated stream points. The main effects of this lack of independence are to understate and invalidate standard error estimates and P-values (Stokes et al. 2000). A possible approach to this problem is the method of generalized estimating equations (Myers et al. 2002), which explicitly model the dependencies in the data. The structure of a stream network, where dependencies are not related simply to distance, and the large amount of data associated with the landscape scale of this model made this approach unfeasible for us, but it is a promising approach for future work. Although the lack of independence in the stream network points hampers the estimation of standard errors and P-values, it does not affect the final prediction equation. Interpreting the predicted value as a probability is not justified. Used as an index, however, the predicted value is a useful way to combine several physical variables into a single value that indicates the relative likelihood of fish presence or absence. The index has values ranging from 0 to 1; values approaching 1 suggest a greater likelihood of

fish presence, and values approaching 0 suggest a greater likelihood of fish absence. Given the independence problem and its potential effect on P-values, we took an information-theoretical approach to model building (Burnham and Anderson 1998; Anderson et al. 2000) and de-emphasized the more usual model-building process involving sequential variable selection (e.g., Manly et al. 1993; Hosmer and Lemeshow 2000; Harrell 2001). The information theory approach starts with a set of candidate models, which are then evaluated and ranked with Akaike’s information criterion (AIC) (Burnham and Anderson 1998). Because the AIC values are relative, we followed the convention of scaling them by subtracting the smallest AIC from each value (Burnham and Anderson 1998). We focused our attention on five variables related to physical channel characteristics that the field surveys and previous research (e.g., Kruse et al. 1997; Porter et al. 2000) had suggested were related to the likelihood of fish presence. These variables were (1) basin area above each GIS-derived stream point, scaled by taking the base-10 logarithm (logba), (2) channel gradient for 100 m upstream of each stream point (gu), (3) channel gradient for 100 m downstream of each stream point (gd), (4) weighted average precipitation for the area draining to the stream point (precip), and (5) elevation (el). Apart from elevation, each of these variables is related either to stream size, and thus permanence of flow, or gradient, affecting accessibility to fish. In forming our set of candidate models, we considered combinations of the five variables with some restrictions. First, we only considered models that included basin area and at least one gradient variable, ensuring that some aspect of flow permanence and accessibility were included. Second, we favored simple models over more complex ones because we believed the independence problem could make us more vulnerable to overfitting. Therefore, we did not include models involving cross-product terms. All logistic regression models were fit using the LOGISTIC procedure in the Statistical Analysis System (SAS) version 8.2 (SAS Institute, Inc. 1999). Although AIC was our main model-building tool, we also computed and considered other statistics as a check on the process. We computed the variable Pvalues by using a significance standard of 0.05, to see what model would result from a variable-elimination fitting process, and we computed a generalized version of R2 (Nagelkerke 1991) that is scaled to fall in the usual range (0, 1). As a general lack-of-fit test, we used the Hosmer–Lemeshow test (Hosmer and Lemeshow 2000). Although this test has known deficiencies (Hosmer et al. 1997; Harrell 2001), we believed it


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FIGURE 3.—Index of fish presence values for an example stream profile plotted against distance from stream origin. Based on a cut point of 0.5, the index suggests that fish will be present far downstream and absent far upstream. However, index values fluctuate above and below the cut point value for a distance of approximately 1.6 km. The ‘‘stopping rule’’ was developed to address this area of ambiguity and to enable an exact location of the ULO to be predicted.

would be adequate for our purposes. To measure the model’s ability to discriminate between fish presence and fish absence, we computed the area under the receiver operating characteristic (ROC) curve (Hosmer and Lemeshow 2000). This statistic, which has a value between 0 and 1, is interpreted as the likelihood that a stream point where fish are present will have a greater index value than a stream point where fish are absent. Because the objective for the logistic model was the indication of fish presence or absence, we were interested in its ability to classify stream points as fish bearing or non-fish bearing. We used SAS to compute three rates of correct classification, corrected for the bias of using the model to classify the same data with which it was built (SAS Institute, Inc., 1999). A cut point of 0.5 was used, which means that if a stream point’s index value of fish presence is 0.5 or more, the point is classified as fish bearing,; otherwise, it is classified as non-fish bearing. The percent correct classification of fish-bearing stream points (also called ‘‘sensitivity’’) is the number of correctly classified fishbearing points divided by the total number of fishbearing points. The percent correct classification of non-fish-bearing points (also called ‘‘specificity’’) is the number of correctly classified non-fish-bearing points divided by the total number of non-fish-bearing points. Finally, the overall percent correct is the number of

correctly classified points divided by the total number of stream points. Developing the stopping rule.—Logistic regression index values near the upstream extent of fish distribution in some streams displayed regions of ambiguity in which the index value varied above and below a cut point along a stream reach (Figure 3). This most commonly occurs on a small channel where a high-gradient reach is followed by a reach of lower gradient further upstream and the index value displays a corresponding increase. The occurrence of one stream point with an index value below the cut point may not accurately predict the upstream extent of fish distribution, especially if a large area above this point had index values above the cut point. We developed a heuristic stopping rule to determine whether to include or exclude upstream habitat in the fish presence prediction where areas of ambiguity occurred. The stopping rule has three parameters: (1) the cut point, (2) the trigger size, and (3) the upstream block size. The cut point is the index value selected to indicate the absence of fish. We evaluated cut point values from 0.0 to 1.0 in increments of 0.01. The trigger size is some number of consecutive stream points with index values less than the cut point. We tested trigger values of 1 to 11. The upstream block size indicates the relative abundance of fish-bearing stream points upstream from the trigger point. We

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evaluated two measures of upstream block size. First, we simply characterized the fish habitat block as a count of consecutive stream points above the cut point. We also used the sum of index values for consecutive predicted fish-bearing points above the cut point. This second approach provides an indication of the relative quality of the habitat in the block. In the end we found that the two measures gave essentially the same results, but the second definition was selected for use in the final stopping rule. We tested values in the range of 5– 500. Subsets of the GIS data called ‘‘profiles’’ were used for fitting the stopping rule. There was one profile for each of the 417 surveyed ULOs. A profile is a linear string of stream points consisting of the main-stem stream points downstream from the ULO and the upstream points following the branch with the largest basin area at each fork and stopping when the basin area reaches 6.8 ha. To give better resolution for determining the predicted ULOs, we used GIS-derived stream points spaced at 10 m for the profiles (Figure 3). We determined values of the stopping rule parameters that minimized the mean absolute error distance of the predicted ULOs. Because each of the three parameters is discrete, the optimization method we used for identifying the most accurate stopping rule was a simple grid search. We started with a coarse grid, followed by a fine grid once the general optimal region was located. For each tested combination of values for the three parameters, we first applied the resulting stopping rule to each of the 417 stream profiles with known fish presence and absence in our modeling data and then evaluated the objective function for the resulting set of errors. Although a grid search is computationally intensive, it is simple to implement and proved satisfactory. We used graphics to identify the general optimal region. Results were then sorted and examined to determine the optimal parameters. This simple approach to finding the optimal stopping rule was possible because of the discrete parameter values. In all cases we examined, the optimal region is rather flat, particularly for the upstream habitat block variable. Our convention was to choose the smallest value of each parameter that gave the optimal value of the objective function. Application of the stopping rule is fairly straightforward. We start downstream where the habitat index is consistently above the derived cut point and continue upstream until reaching an index trigger that indicates we have reached a potential ULO prediction. Points on the stream network above this trigger point are evaluated. If there is a reach upstream with consecutive index values above the cut point, the index values for this reach are summed. If the sum exceeds the

threshold value for upstream block size, we ignore the initial trigger and move upstream of the reach with values above the cut point to the next trigger. If there is no sufficiently large upstream block above a trigger point, the predicted ULO is set at the GIS-derived stream point immediately downstream of the trigger. A benefit of fitting the stopping rule is that it gave us an objective way of selecting a cut point. When logistic regression is used for classification, a cut point is required to convert the predicted probability into an actual prediction. A cut point of 0.5 is commonly used by default. In our case, where the predicted values are not legitimate probabilities, there is no obvious best value to use as a cut point, although 0.5 is still intuitively appealing. However, development of the stopping rule enabled us to identify the cut point that provided the greatest accuracy. Along with the optimal stopping rule, we considered two benchmark stopping rules. These benchmarks amount to stopping at either end of the reach with fluctuating index values. The first benchmark is to stop just before the first predicted non-fish bearing point (using cut point ¼ 0.5). The second benchmark is to stop at the last predicted fish-bearing point (using cut point ¼ 0.5). Model validation.—Validating a model typically involves applying the model to data that has been withheld from the model-fitting process to avoid bias. A number of methods have been developed for handling validation (Harrell 2001). Our approach was to withhold a complete basin, Stillman Creek, from the modeling process. As noted earlier, Stillman Creek is located in southwestern Washington, central to the area from which the data used in constructing the model were collected. All streams in the Stillman Creek watershed were surveyed to determine the ULOs. There were several reasons why we chose to use a single watershed for validation rather than randomly distributing the withheld data across the entire data set. Stillman Creek exhibited proportions of terminal and lateral ULOs more likely to be representative of the landscape. Our survey data contained a higher proportion of terminal ULOs because our survey effort was focused on stream reaches containing the upstream limit of fish distribution. Terminal sites provided the best opportunity to assess the size and slope of streams at the extremes of fish use. Lateral ULOs were therefore known to be underrepresented in the survey data. Simply withholding a randomly selected subset of the data from model building for the purpose of validation would have biased the error estimation. Also, by conducting the validation in a single geography, we had the ability to graphically display the distribution of error across this landscape and

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TABLE 1.—Species present within the stream reaches immediately below the terminal upper limits of occurrence among streams in western Washington State. More than one species was identified in some sites.

TABLE 2.—Physical features associated with the upper limit of fish occurrence among 517 streams in western Washington State. More than one feature was identified at many sites. Sites where present

Sites where present Species

Percent

Number

Cutthroat trout Oncorhynchus clarkii Sculpin Cottus spp. Coho salmon Oncorhynchus kisutch Rainbow trout Oncorhynchus mykiss Brook trout Salvelinus fontinalis Threespine stickleback Gasterosteus aculeatus

88.9 10.4 5.2 2.8 2.1 0.3

256 30 15 8 6 1

illustrate the accuracy of the model. It would be ideal to have several randomly selected basins with complete fish surveys to use for validation. However, the time and resources required to complete a survey of a basin prevented us from considering this approach. Under the circumstances, having one complete, independent basin was better than any available alternative. Model error was calculated by measuring the distance along the DEM-derived stream network between each surveyed ULO and the modeled ULO. If the stream section in error extended up several branching tributaries, the total unduplicated adjacent error distance was summed across all the associated tributaries and reported as a single error length. To avoid inflating the number of zero-error predictions assigned to small lateral streams that could not reasonably be expected to contain fish, we applied a minimum basin area value for predictions that count for assessing model error distance. Perennial streams generally represent the areas where resident fish are reasonably likely to occur. Within the Stillman Creek basin, the upstream extent of perennial flow was surveyed on 21 streams at summer low-flow conditions. Median basin area associated with the upstream extent of perennial flow was 6.8 ha, so we excluded lateral streams smaller than 6.8 ha from the calculation of error distances. Results Fish Distribution Species of fishes found at the ULO varied depending on the type of ULO and the characteristics of the channel. A single species of fish, most frequently a salmonid, was associated with terminal ULOs in 92.3% of the terminal sites surveyed; two species were observed at 7.0% of the sites, and three species were observed at 1.4% of the sites. We did not encounter more than three species at any terminal ULO. In the small, often steep streams typically associated with terminal ULOs, anadromous species or life history

Physical feature

Percent

Number

Stream junction Small stream size Gradient change .5% Permanent natural barrier Culvert Transient natural barrier None identified

53.6 31.5 30.8 23.6 4.4 3.5 6.2

277 163 159 122 23 18 32

types were rare because natural barriers to fish passage typically occurred well below the ULO. Coastal cutthroat trout Oncorhynchus clarkii clarkii occupied habitat immediately below the ULO in 88.9% of the terminal sites (Table 1). Sculpins were found at the terminal ULO at 10.4% of the sites, usually in relatively low-elevation streams with low gradient. Fish community composition was more complex below lateral ULOs than below terminal ULOs, because the small lateral tributaries typically entered larger channels that tended to support a more complex fish community (often including anadromous species) than that found in the small headwater channels of terminal ULOs. However, effective sampling of large streams below lateral ULOs was difficult, and thus a reliable inventory of all species present was not possible. Only rarely did ULOs occur without any associated change in habitat character or apparent barrier to upstream movement. We identified one or more physical features associated with the ULOs at 93.8% of sites surveyed (Table 2). An abrupt change in stream size due to a tributary junction was most frequently associated with the ULO; all lateral ULOs are in this category. Gradient-related features of various types were also a common factor that appeared to restrict upstream occurrence. Abrupt gradient changes and vertical barriers to fish movement were associated with over 60% of the ULOs. Changes related to the diminishing size of the stream, such as loss of continuous surface flow, lack of sufficient depth, or disappearance of a defined channel, were also commonly identified by surveyors. Features unrelated to fixed physical characteristics of streams, such as culverts, debris jams, beaver dams, and landslide deposits, were identified at a relatively small proportion of the ULOs. Temporal Variability in Fish Occurrence Seasonal and interannual change in ULOs were observed, although the changes were generally small.

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FIGURE 4.—Seasonal (summer versus winter) change in the location of the upstream limit of occurrence (ULO) of fish in selected streams of western Washington State. The ‘‘0’’ on the x-axis indicates the location of the ULO during the initial survey. Assessment of seasonal movement was restricted to terminal ULOs where there was no impediment to upstream movement of fish (we assumed that movement was not impeded at channel gradients , 20% ).

FIGURE 5.—Interannual (1997–1999) change in surveyed location of the upstream limit of occurrence (ULO) of fish in selected streams of western Washington State. The ‘‘0’’ on the x-axis indicates the location of the ULO during the initial survey. Assessment of interannual movement was restricted to terminal ULOs where there was no impediment to upstream movement of fish (we assumed that movement was not impeded at channel gradients , 20%).

Resurvey of summer survey sites in winter revealed both upstream and downstream changes in ULOs (Figure 4). Average movement for all 37 sites was 14 m upstream but extended as far as 340 m upstream and 175 m downstream. No changes in ULOs were observed at 17 of the surveyed streams. We found 10 sites with upstream movements and 10 with downstream movements. Interannual variability in fish occurrence also revealed both upstream and downstream changes in ULOs (Figure 5). Average movement at all sites was 41 m upstream but extended to 355 m upstream and 215 m downstream. No changes in ULOs were observed at 15 of the 40 sites. A downstream change was observed at 8 sites, and an upstream change was observed at 17 sites.

candidate models had generalized R2 values (Nagelkerke 1991) between 0.90 and 0.92. The Hosmer– Lemeshow test (Hosmer and Lemeshow 2000) gave Pvalues less than 0.03 for all the models, indicating poor fit. Finally, the area under the ROC curve was greater than 0.9 for all the models, indicating outstanding discrimination (Hosmer and Lemeshow 2000). As Hosmer and Lemeshow (2000) noted, a model that fits poorly according to a goodness-of-fit test may still have good discrimination (Hosmer and Lemeshow 2000), and discrimination is precisely the characteristic needed for our purpose. We selected model 9 as the basis for our prediction tool. In addition to having the minimum AIC, model 9 is simple, uses predictors that are consistent with the features we observed to be associated with the ULOs in the field surveys, and has parameters with intuitively correct signs. A case could also be made for model 12, which includes precipitation along with the variables in model 9. The precipitation coefficient was not significant in model 12, however. Although precipitation has a substantial effect on channel size at any

Modeling Results Changes in either stream gradient or stream size were associated with most ULOs (Table 2). The GIS data generated from ULO locations clearly reflected the difference in these two factors between fish- and nonfish-bearing stream reaches (Table 3). However, there is considerable overlap in both gradient and basin area between fish- and non-fish-bearing reaches, making predictions of fish presence based on only one of these attributes inaccurate. Logistic regression enabled us greatly to improve predictive power. When we fit the candidate logistic regression models to these data (Table 4), the models were quite similar in some respects but were well differentiated by AIC. Model 9 had the best AIC results. Variable selection using P-values would have identified the same final model as did AIC. All of the

TABLE 3.—Means (standard deviations in parentheses) for the variables used in logistic regression models, disaggregated by the presence or absence of fish. There were 15,022 stream points with fish present and 8,371 with fish absent. Variable Log10(basin area [ha]) Downstream gradient (%) Upstream gradient (%) Precipitation (cm) Elevation (m)

Symbol logba gd gu precip el

Fish present 3.58 1.95 3.03 211.23 195.04

Fish absent

(0.85) 1.06 (0.54) (3.72) 17.10 (10.79) (11.11) 18.63 (11.60) (35.26) 216.99 (32.87) (159.51) 535.95 (247.93)

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TABLE 4.—Candidate logistic regression models and their fit statistics used in estimating the upstream limit of fish occurrence (ULD) in streams of western Washington State. Variables evaluated included basin area (ha; logba), gradient (%) upstream of the ULO (gu), gradient (%) downstream of the ULO (gd), precipitation (cm; precip), and elevation (m; el). Model 9, with the smallest Akaike’s information criterion (AIC), was the preferred model. The prediction equation for model 9 is h ¼ 1/[1 þ exp(u)], where u ¼ 4.7655 þ 3.7628(logba) 0.0140(gu) 0.0988(gd) 0.00389(el). Percent correct Model number (variables)

AIC

Fish

Nonfish

Overall

9 (logba, gu, gd, el) 12 (logba, gu, gd, precip, el) 7 (logba, gd, el) 11 (logba, gd, precip, el) 5 (logba, gu, el) 10 (logba, gu, precip, el) 8 (logba, gu, gd, precip) 6 (logba, gd, precip) 3 (logba, gu, gd) 2 (logba, gd) 4 (logba, gu, precip) 1 (logba, gu)

0.000 1.33 2.68 4.29 218.11 219.44 357.59 369.04 404.63 422.04 756.28 905.58

96.4 96.4 96.4 96.5 96.3 96.4 96.3 96.2 96.1 96.1 96.0 95.7

94.3 94.3 94.3 94.3 94.0 94.0 93.8 93.8 93.6 93.6 93.6 93.3

95.7 95.7 95.7 95.7 95.5 95.5 95.4 95.3 95.2 95.2 95.1 94.8

given basin area, the range of precipitation in our data are not great, which suggests that our model could reasonably fail to include it, even though it would probably be important in a model with broader geographical scope. The predicted value from the logistic regression equation (h) is a value between 0 and 1, which we interpret as an index of the likelihood of a fish occupying a site. Based on a cut point of 0.5 (i.e., assuming that h 0.5 indicates fish presence), model 9 correctly classified 96% of the GIS-generated stream points (i.e., those with known fish presence or absence) we used in developing the regression equation (Table 5). We fit the stopping rule using the 417 profiles derived from the modeling data. The optimal values derived from the evaluation of various combinations of the parameters were a cut point of 0.36, a trigger size of 1, and an upstream habitat block size of 184. Error distances when the model and this stopping rule were applied to the modeling profiles were generally small

Nonsignificant terms precip (P ¼ 0.41) precip (P ¼ 0.53) precip (P ¼ 0.41)

(Figure 6). Although the distribution was skewed and had several large errors, it was centered at zero and included many zero errors. The optimal stopping rule had considerably lower error distances than did either of the benchmark stopping rules we assessed (Table 6). The optimal rule also produced the lowest number of underpredictions but had a higher incidence of overpredictions than the two benchmark rules. By our convention, overpredictions occur where the predicted ULO is upstream from the true ULO and underpredictions occur where the predicted ULO is downstream from the true ULO. The previous results on modeling stream points and profiles pertain to how well the logistic regression model and optimal stopping rule fit the modeling data. A more realistic picture of prediction accuracy was

TABLE 5.—The bias-corrected result of classifying the modeling data using the final logistic regression model (model 9; see Table 4) and a cut point of 0.5 in the estimation of upstream limits of fish occurrence in streams of western Washington State. Actual Predicted

Fish present

Fish absent

Total

Fish present Fish absent Total

14,487 535 15,022

474 7,897 8,371

14,961 8,432 23,393

FIGURE 6.—Histogram of error distances for the optimal stopping rule, as applied to the modeling profiles of the upstream limit of occurrence (ULO) of fish in selected streams of western Washington State.

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TABLE 6.—Results when the optimal stopping rule and two benchmark rules are applied to the modeling profiles used in estimating upstream limits of fish occurrence in streams of western Washington State. Note that the benchmark rules use a cut point of 0.5. Absolute error (m)

Prediction error (%)

Model and stopping rule

Mean

Median

Under

Exact

Over

Model 9 and optimal stopping rule Model 9 and benchmark stopping rule: first nonfish index value Model 9 and benchmark stopping rule: last-fish index value

226.3 581.8 281.5

58.7 74.7 75.7

40.8 50.6 44.1

36.6 35.7 37.9

22.5 13.7 18.0

obtained by using the model and stopping rule to predict the ULOs in the Stillman Creek basin (Figure 7) data, which were not used in constructing the model or stopping rule. The model exactly predicted 53% of the ULOs (Table 7). Overpredictions were more common than underpredictions. Compared with a total stream length in the basin of 278.0 km, the total underprediction error was 8.4 km (3.0%), and the total overprediction error was 17.0 km (6.1%). Of the total 103 km of fish-bearing streams occurring in Stillman Creek, 91.9% were correctly classified by the model. The improvement in predictive accuracy for Stillman Creek (Table 7) relative to the modeling data (Table 6) is due to the fact that the Stillman Creek data contains a higher and more representative proportion of the easierto-predict lateral ULOs. The Stillman Creek validation assessment is probably a more accurate portrayal of the performance of the model and stopping rule than is the classification of the modeling data. Discussion Species Present The species occurring at the upstream limit of fish distribution appears to be influenced by the physical characteristics of the channel and the species present in a particular basin. Coastal cutthroat trout were the prevalent species we found at the upstream limit of fish distribution. The presence of this species at most ULOs is probably a product of their wide distribution in western Washington and their tolerance of small and steep headwater streams typical of the upstream limits of occupied fish habitat (Wydoski and Whitney 2003). Rainbow trout, juvenile steelhead (anadromous rainTABLE 7.—Summary statistics for the errors produced by predicting the upper limit of fish occurrence at 253 sites in Stillman Creek in western Washington State. FIGURE 7.—Map of Stillman Creek basin in western Washington State, showing the results of predicting upstream limits of fish occurrence (ULOs) with logistic regression model 9 and the optimal stopping rule. Predicted ULOs (open circles) without gray (underpredictions) or black (overpredictions) shading to indicate error distance are locations where the model and actual fish distribution coincided exactly.

Error type

Statistic

Mean absolute error distance (m) Median absolute error distance (m) Underpredictions (%) Exact predictions (%) Overpredictions (%)

100.1 0 11.9 53.0 35.2


bow trout), and brook trout exhibit similar habitat preferences. However, relative to cutthroat trout, resident populations of rainbow trout and brook trout are rare in this region; upstream distribution by juvenile steelhead is limited by the need for access to and from the ocean (i.e., steelhead or other anadromous fishes would be absent above any passage barrier). Fishes such as coho salmon, sculpins, and threespine sticklebacks were found almost exclusively at lowgradient, low-elevation ULOs, reflecting their lower tolerance of the physical conditions typical of steep headwater streams. However, in some low-gradient channel networks, these species were found in very small stream channels above the uppermost observation of cutthroat trout, particularly in streams in close proximity to a much larger stream. Factors Influencing Upstream Occurrence of Fishes A number of factors contribute to limiting the upstream occurrence of fishes in a channel network. The key role of physical barriers, both natural and manmade, to movement has long been recognized. Often fish populations are not found above such barriers even when seemingly appropriate habitat is present, perhaps reflecting historical lack of access to these locations or extirpation of these populations by some rare climatic or disturbance event (Swanson et al. 1987) that limited opportunity for recolonization. Diminishing channel size and water availability also are important factors. All fishes in our study area require year-round availability of surface water. Therefore, the upstream distribution of fish may be heavily influenced by periods of drought that temporarily render some stream segments unsuitable for fish. If barriers or areas of high channel gradient occur downstream of these periodically dry segments, recolonization after droughts may be difficult, whereas in systems with lower gradients recolonization of displaced populations may be very rapid. The interaction between stream size and gradient and the effect these attributes have on fish presence are clearly indicated in our data showing fish to be generally found in smaller channels within lowgradient reaches than in steeper reaches. Because our surveys were conducted during wetter periods of the year, it may be that some of the ULOs we observed on small, low-gradient channels reflected some of the seasonal fish movement. Despite the fact that multiple, interacting processes likely play a role in dictating the upstream extent of fish distribution, the results of our field surveys and the subsequent modeling results clearly indicate that the upstream extent of fish distribution in western Washington is very heavily

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influenced by stream size, channel gradient, and access to suitable habitat. In addition to these physical features of the stream channel, elevation was found to be a significant variable in our best-performing models. This result is consistent with the findings of other researchers (Kruse et al. 1997; Dunham et al. 1999). It is possible that elevation indirectly captures the influences of other landscape-scale factors influencing the likelihood of fish presence. Streams at higher elevations tend to be steeper and therefore may contain more barriers to upstream fish movement than streams at lower elevations. High-elevation streams also may tend to be associated with harsher climates and cooler temperatures, contributing to less-productive habitats for fish (Bozek and Hubert 1992). Inclusion of elevation in our models may indirectly incorporate a variety of broad influences on habitat suitability and the likelihood of fish use. Sampling Efficiency and Variability in ULO Location We are confident that our identification ULO locations was quite accurate. Although we did not directly assess the efficiency of our electrofishing sampling method, there are several factors that strongly suggest that our sampling efficiency was as high as or higher than many published values would suggest (Peterson et al. 2004; Peterson and Cederholm 1984). Nearly all of the ULOs were in very small channels, which limited the ability of fish to elude the charge field produced by the electroshocker. In an assessment of single-pass survey reliability in very small channels in eastern Washington, surveys were repeated four consecutive times during a single site visit to estimate the frequency with which fish were missed during the first sampling pass (Cole et al. 2006). No additional fish were detected after the first pass at 27 of 28 sites. Another important difference between our surveys and those typically employed to evaluate capture efficiency is that visual observation of a fish alone is sufficient to demonstrate fish presence; the fish does not have to be captured. Thus, our sampling efficiency would be higher than that reported for cases where sampling efficiency is based on the likelihood of capturing a fish. We found the upper extent of fish occurrence to vary temporally at nearly 60% of the resurveyed terminal ULOs lacking barriers to movement. Our assessments of intra-annual and interannual variability yielded similar lengths and frequencies of upstream and downstream movement. In both cases, the temporal variation in the location of the ULO was generally small: about 14 m for intra-annual changes and 40 m for interannual changes. Although these resurvey assessments were not

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replicated in time, they were conducted at 77 of the previously located ULOs and thus do provide a basis for assessing the utility of single-visit surveys for ULOs. Fish movements we observed lacked any trend related to season, year, or direction of movement; approximately equal numbers of sites exhibited upstream movement as downstream movement. These data suggest that some ULOs may be more precisely described as a zone used by fish intermittently rather than as a fixed point, which is typically presumed in the regulatory context. Recognition of this intermittent zone during the development of regulations and survey protocols may lead to more effective management of fish populations and their habitats. Therefore, singlevisit surveys provide some indication of where this zone of intermittent fish use is located but cannot always provide an indication of the extent of this zone. However, information on the relationship between habitat attributes and fish occurrence derived from data collected at many locations, as in our model, can provide an average location of ULOs, potentially offering more consistency in ULO designation than the single-survey method. Further research on this topic may enable identification of relationships between stream characteristics and fish movement, and thereby providing a basis for not only predicting average ULO location but also indicating the spatial extent of this zone of intermittent fish use. Accurate definition of this zone might provide a much more biologically meaningful foundation for regulations than the current single-site approach. Predicting Upstream Fish Distribution Our ability to construct an accurate model to predict the upstream extent of fish distribution was facilitated by our finding that the location of the ULOs was heavily influenced by gradient and stream size, parameters that can easily be derived from existing GIS data sources. Our field surveys indicated that there was often an easily identifiable change in one or both of these factors at the ULO (Table 2). These types of abrupt changes were usually detectable using the 10-m DEM and the GIS platform we used to build the model. The best logistic regression model with a 0.50 cut point was able to correctly classify about 96% of the stream points used to construct the model, which emphasizes the overriding importance of the physical setting in dictating ULOs. For a small number of sites, we could not associate the ULO with a change in physical habitat. The ULO locations at these sites may simply represent a temporary absence of fish from normally occupied habitats on the date of our single survey. However, biological factors also may play a role in determining

the upstream limit of fish use and might have contributed to the ULO location at these anomalous sites. We did not characterize the quality of habitat at our survey sites but low availability and quality of habitat might have precluded fish from occupying locations that were accessible and of sufficient size. Poor quality habitat, especially in small channels, may expose fish to increased predation, particularly during extreme low-flow conditions. It also is possible that trophic productivity of some small headwater streams may be insufficient to support enough fish to enable long-term persistence of a population. Metabolic demands on fish may be particularly severe in the steep channels typical of many ULOs, exacerbating the problem of limited food availability. The limitation of trophic support for fish at the upstream limit of fish distribution is indicated by the relatively small fish size and low abundance typical at these sites. However, given our observations in the field and the demonstrated ability to predict fish presence based solely on physical characteristics, the number of streams where biological factors alone restrict fish distribution appears to be limited. Most predictions occurred in close proximity to the surveyed ULO, and many predictions were exactly right based on coincidence of a predicted and actual ULO with a stream junction or barrier identified both in the field survey and the GIS-derived stream network. The accuracy of the model can be attributed to several factors. The ULOs with very little or no model error tended to occur at lateral sites and terminal sites where stream gradient increased or watershed area decreased dramatically. Thus, the habitat index values produced by the model tended to change rapidly from near 1.0 (very high certainty of fish presence) to values well below the cut point (indicating fish absence) over relatively short lengths of stream channel. Long stream reaches with intermediate habitat index values, indicating areas of predictive uncertainty, occurred relatively rarely. Lateral sites and terminal sites with very distinct changes in index values accounted for a high proportion of the ULOs within our study area and are largely responsible for the high model accuracy. The accuracy of the model was further improved through the development of the stopping rule. The procedure used to develop the stopping rule enabled the determination of the most accurate cut point. The stopping rule also provided a mechanism to deal with those reaches where the index value fluctuated above and below the cut point. Gradient-related barriers with a potential of fish use farther upstream (i.e., when the index value declines below the cut point and then increases farther upstream) also are addressed by the


stopping rule, further enhancing the accuracy of the model predictions. The largest model errors can all be attributed to incorrect predictions of fish presence or absence above barriers. Our field surveys suggested that the probability of fish presence above barriers increased where a large area of suitable fish habitat was found above the barrier. This observation was incorporated into the stopping rule by extending a prediction of fish presence above barriers and high-gradient reaches in cases where some minimum amount of suitable habitat (i.e., sites with index values above the cut point) occurred upstream. Many ULOs associated with barriers were correctly identified by the stopping rule, although some relatively large errors did occur. Therefore, the presence or absence of fish above barriers was not entirely explained by the amount of suitable habitat. In some cases, large areas of habitat above barriers that had relatively high index values were found to be devoid of fish. Fish occupying marginal habitat above barriers also was observed at some sites. The inconsistencies associated with sites above barriers may be caused by several factors. Relatively long underprediction errors occasionally occurred in streams originating in a headwater pond. In these cases, small or steep streams with index values consistently below the cut point did support fish farther upstream. In many cases, the presence of fish in these headwater ponds was probably a product of stocking. Stocking of fish above barriers, in streams with and without ponds, has been widespread within the study area but has not affected all streams. Records of such stocking are very limited; therefore, stocking could not be incorporated into our model. Catastrophic disturbances, such as debris torrents, may account for some cases of overprediction if these events were severe enough to eliminate entire populations above barriers. Recolonization rates of areas impacted by such events could vary widely, depending on the proximity of colonists and the frequency and size of any barriers. Many stream reaches above pronounced natural barriers may never have supported fish. The presence of headwater ponds, stocking, and absence of fish due to restricted access or periodic elimination of fish populations by disturbance events probably contributed to the error associated with stream reaches above barriers. Smaller overprediction and underprediction errors could often be attributed to the inability of the 10-m DEM to accurately represent features of some stream channels. The DEM generally proved unable to detect small permanent or transient barriers. As a result, the gradient data input to the model for these sites was incorrect and led to an inaccurate index value and,

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potentially, an incorrect prediction of the ULO. However, we found that faulty input data associated with the inability of the 10-m DEM to detect small barriers typically did not result in large model errors. Within areas of very low topographic relief, the DEM was sometimes incapable of accurately representing the location of streams, the connectivity among streams, and watershed boundaries. As a result, watershed area values input to the model from the GIS platform were often in error and produced inaccurate predictions of ULOs. This type of problem was particularly acute in streams on floodplains or in large wetlands. In addition, low-relief areas typically had a higher probability of anthropogenic modification to the stream network, which also can affect both fish distribution and the reliability of the DEM in correctly characterizing the stream network. Higher resolution and more current topographic information would help correct this problem and improve the predictive precision of the model. In locations where high-resolution topographic information is available, such as lidar coverage (Elmqvist 2002), it may be possible to greatly reduce this source of model error. Management Application If a model for predicting the extent of fish-bearing streams is to be considered an option for improving stream classification, then topographic and other potential data layers must be available across the entire area to be modeled. We were able to easily obtain topographic and precipitation layers representing conditions across our study area. The utility of a model as a management tool is also dependent upon the level of precision demanded of the stream classification system. The model in its current form does predict the extent of fish occurrence with relatively high precision, particularly in the lateral tributary streams. However, relying solely on the model to classify streams used by fish could result in occasional large prediction errors in some specific situations. As noted above, many of these error problems might be alleviated with more detailed and accurate topographic information. If resulting error is considered unacceptable for a particular management objective, a model such as ours could also be used to efficiently target field surveys to locations where error is most likely to occur. The model was highly reliable at predicting ULOs on lateral sites. Survey efforts at these locations could be minimized. Model predictions occurring at terminal locations were responsible for the vast majority of model error. For these terminal sites, the model can identify stream reaches containing intermediate model index values and potential barriers to fish where suitable habitat for fish use occurs upstream. Headwa-

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ter ponds or anthropogenic alterations of stream channels cannot be identified by the model, but these features are often discernable on aerial photographs and could be used to further refine the list of locations where field surveys would be most appropriate. Stream reaches that are most likely to be associated with model error could therefore be identified in a variety of ways. Targeting supplemental field surveys in such areas could greatly improve the overall classification accuracy of the fish-bearing stream network and simultaneously minimize survey effort. Because areas of high model certainty might not require further field evaluation, this approach could greatly reduce the amount of field survey effort required yet could still achieve a very high level of accuracy in the classification of streams used by fish. The parameters of the stopping rule could also be adjusted to make the model predictions of ULOs more or less conservative. We attempted to develop a stopping rule that minimized total error. An alternative stopping rule could be developed to meet any desired target for classification of fish habitat, although deviation from our approach would increase overall model error. For example, in some instances a very conservative estimate of ULO might be desired (e.g., where there is little opportunity for field verification of the model predictions and where a high level of protection for fish habitat is considered appropriate). Adjustments in the stopping rule, including a lower cut point, a higher trigger point, or a smaller block size, would provide ULO predictions that more frequently overpredict than underpredict. Acknowledgments We greatly appreciate the field support of Storm Beech, Ernie McKenzie, Graham MacKenzie, and John Heffner. Scott Needham and Vickie Kim were instrumental in developing the required GIS tools. This project could not have been completed without the support and encouragement of Peter Farnum, Christine Dean, and Cassie Phillips. References Anderson, D. R., K. P. Burnham, and W. L Thompson. 2000. Null hypothesis testing: problems, prevalence, and an alternative. Journal of Wildlife Management 64:912–923. Bozek, M. A., and W. A. Hubert. 1992. Segregation of resident trout in streams as predicted by three habitat dimensions. Canadian Journal of Zoology 70:886–890. Brown, T. G., and G. F. Hartman. 1988. Contribution of seasonally flooded lands and minor tributaries to the production of coho salmon in Carnation Creek, British Columbia. Transactions of the American Fisheries Society 117:546–551. British Columbia Ministry of Forests and Range. 1998. Forest

practices code of British Columbia. Fish-stream identification guidebook, 2nd edition, version 2.1. ISBN 07726-3664-8. British Columbia Ministry of Forests and Range. Burnham, K. P., and D. R Anderson. 1998. Model selection and inference: a practical information–theoretic approach. Springer-Verlag, New York. Cole, M. B., D. M. Price, and B. R. Fransen. 2006. Change in the upper extent of fish distribution in eastern Washington streams between 2001 and 2002. Transactions of the American Fisheries Society 135:634–642. Dalbey, S. R., T. E. McMahon, and W. Fredenburg. 1996. Effect of electrofishing pulse shape and electrofishinginduced spinal injury on long-term growth and survival of wild rainbow trout. North American Journal of Fisheries Management 16:560–569. Dunham, J. B., M. M. Peacock, B. E. Reiman, R. E. Schroeter, and G. L. Vinyard. 1999. Local and geographic variability in the distribution of stream-living Lahontan cutthroat trout. Transactions of the American Fisheries Society 128:875–889. Ellefson, P. V., A. S. Cheng, and R. J. Moulton. 1995. Regulation of private forestry practices by state governments. Minnesota Agricultural Experiment Station, Bulletin 605-1995. University of Minnesota, St. Paul. Elmqvist, M. 2002. Ground surface estimation from airborne laser scanner data using active shape models. Pages 114– 118 in Proceedings of the Commission III Symposium, Photogrammetric Computer Vision, Graz, Austria, September 9–13, 2002. International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences, volume XXXIV, part 3A/B, ISSN 1682– 1750. International Society for Photogrammetry and Remote Sensing. Erman, D. C., and V. M. Hawthorn. 1976. The quantitative importance of an intermittent stream in the spawning of rainbow trout. Transactions of the American Fisheries Society 6:675–681. ESRI (Environmental Systems Research Institute, Inc.). 1998. ArcInfo Workstation, ArcDoc, version 7.2.1. ESRI, Redlands, California. Fausch, K. D., C. E. Torgerson, C. V. Baxter, and H. W. Li. 2002. Landscapes to riverscapes: bridging the gap between research and conservation of stream fishes. BioScience 52:483–498. Fish Protection Act. 2001. The revised statutes and consolidated regulations of British Columbia, British Columbia regulation number 10/2001, order in council number 34/ 2001. (19 January 2001). Harrell, F. E., Jr. 2001. Regression modeling strategies with applications to linear models, logistic regression, and survival analysis. Springer-Verlag, New York. Hosmer, D. W., and S. Lemeshow. 2000. Applied logistic regression, 2nd edition. Wiley, New York. Hosmer, D. W., T. Hosmer, S. Le Cessie, and S. Lemeshow. 1997. A comparison of goodness-of-fit tests for the logistic regression model. Statistics in Medicine 16:965– 980. Kruse, C. G., W. A. Hubert, and F. J. Rahel. 1997. Geomorphic influences on the distribution of Yellowstone cutthroat trout in the Absaroka Mountains,


Wyoming. Transactions of the American Fisheries Society 126:418–427. Latterell, J. J., R. J. Naiman, B. R. Fransen, and P. A. Bisson. 2003. Physical constraints on trout (Oncorhynchus spp.) distribution in the Cascade Mountains: a comparison of logged and unlogged streams. Canadian Journal of Fisheries and Aquatic Sciences 60:1007–1017. Manly, B. F. J., L. L. McDonald, and D. L. Thomas. 1993. Resource selection by animals. Chapman and Hall, London. McWethy, L. G., S. D. Duke, and B. R. Fransen. In press. GIS methodology used in the creation of a fish habitat model for western Washington. Weyerhaeuser Technical Report. Weyerhaeuser Library, Federal Way, Washington. Moore, K., and G. Bull. 2004. Guidelines, codes, and legislation. Pages 715–723 in T.G. Northcote and G.F. Hartman, editors. Fishes and forestry: worldwide watershed interactions and management. Blackwell Scientific Publications, Oxford, UK. Myers, R. H., D. C. Montgomery, and G. G. Vining. 2002. Generalized linear models with applications in engineering and the sciences. Wiley, New York. Nagelkerke, N. J. D. 1991. A note on a general definition of the coefficient of determination. Biometrika 78:691–692. Oregon Department of Forestry and Oregon Department of Fish and Wildlife. No date. Surveying forest streams for fish use. http://www.odf.state.or.us/pcf/Pub/fp/ FishPresncSurveyProtocol.pdf. (September 2006). Peterson, N. P., and C. J. Cederholm. 1984. A comparison of the removal and mark-recapture methods of population estimation for juvenile coho salmon in a small stream. North American Journal of Fisheries Management 4:99– 102. Peterson, J. T., R. F. Thurow, and J. W. Guzevich. 2004. An evaluation of multipass electrofishing for estimating the abundance of stream-dwelling salmonids. Transactions of the American Fisheries Society 133:462–475.

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Porter, M. S., J. Rosenfeld, and E. A. Parkinson. 2000. Predictive models of fish species distribution in the Blackwater Drainage, British Columbia. North American Journal of Fisheries Management 20:349–359. SAS Institute, Inc. 1999. SAS/STAT user’s guide, version 8. SAS Institute, Inc., Cary, North Carolina. Schreer, J. F., S. J. Cook, and K. B Connors. 2004. Electrofishing-induced cardiac disturbance and injury in rainbow trout. Journal of Fish Biology 64:996–1014. Snohomish County (Washington). 2003. Snohomish county code, chapter 30.62.300, classification of streams and wetlands. Stokes, M. E., C. S. Davis, and G. G. Koch. 2000. Categorical data analysis using the SAS System, 2nd edition. SAS Institute, Inc., Cary, North Carolina. Swanson, F. J., L. E. Benda, S. H. Duncan, G. E. Grant, W. F. Megahan, L.M. Reid, and R. R. Zimmer. 1987. Mass failures and other processes of sediment production in Pacific Northwest landscapes. Pages 9–38 in E. O. Salo and T. W. Cundy, editors. Streamside management: forestry and fishery interactions. Institute of Forest Resources, University of Washington, Seattle. U.S. District Court. 2002. Washington Toxics Coalition et al. v. Environmental Protection Agency, case number C01132C in the United States District Court for the Western District of Washington, Seattle and Tacoma. Washington Forest Practices Board. 2002. Forest practices board manual, section 13. Washington Forest Practices Board, Olympia. Wipfli, M. S., and D. P. Gregovich. 2002. Invertebrates and detritus export from fishless headwater streams in southeast Alaska: implications for downstream salmonid production. Freshwater Biology 47:957–970. Wydoski, R. S., and R. L. Whitney. 2003. Inland fishes of Washington, 2nd edition. University of Washington Press, Seattle.