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Johan Spens, Department of Wildlife, Fish, and Environmental Studies, Swedish University of Agricultural Sciences, SE-901 83 Umeå, Sweden (fax: +46 (0) 90 7868162; e-mail: firstname.lastname@example.org).
1The keystone piscivore northern pike Esox lucius can structure fish communities, and models predicting pike-focused connectivity will be important for management of many waters.
2We explored the ability of pike to colonize upstream locations and modelled presence–absence in lakes based on landscape features derived from maps. An upstream connectivity model (UC model) was generated using data from 87 lakes. We validated the UC model with retrospective whole-lake experiments involving introductions (n = 49) and extirpations (by rotenone) of pike (n = 96), as well as with the natural distribution of pike in lakes (n = 1365) within 26 drainage basin networks in northern Sweden.
3The UC model predicted the incidence of pike in lakes with stream-connections with 95·4% accuracy, based mainly on a single variable, SV5max, that measures the minimum distance found between 5 m elevation intervals (= maximum stream slope) along watercourses from nearest downstream source of potential immigrants. Recolonizations of pike in rotenone lakes generated a near-identical classification tree, as in the UC model. The classification accuracy of pike presence in the external validation procedure ranged from 88·7 to 98·7% between different drainage basins. Predictions of pike absence were not as accurate, due possibly to undetected introductions, but still lead to 86·6% overall accuracy of the external validation. Most lakes lacking pike, but misclassified as having pike based on low SV5max, were isolated from downstream sources of pike by subsurface streamflow through bouldery areas (SSB).
4Synthesis and applications. The variable SV5max provide managers with a tool for revealing the location and severity of natural dispersal barriers to pike (and logically also barriers to other species with equivalent or less dispersal capacity). Because presented models only require map-based information, and have high predictive power, they may have the potential to be of fundamental use in predicting distribution of freshwater fish. These predictions may provide the means for prioritizing in risk assessment and control programmes to combat pike invasions, as well as contribute to determining a reference state of species incidence in specific lakes. Our results also point towards a possibility that, even where stream slope is low, long-term effective barriers may be designed that mimic natural SSB.
The ability to determine the past, present and potential distributions of species would facilitate effective management and conservation of ecosystems. Comprehensive field surveys are time-consuming with both logistic and financial difficulties involved. With the rise of new and powerful statistical techniques, geographical information system (GIS) tools and electronic access to databases with species occurrences, the development of predictive distribution models in ecology is increasing rapidly (Guisan & Zimmermann 2000; Elith et al. 2006; Ferrier & Guisan 2006). A common approach to model building is to develop the habitat requirements of a species from presence–absence data. When using this approach, it is important to recognize that a species may simply lack sufficient access to some suitable habitats where they now are absent (Guisan & Zimmermann 2000). Dispersal barriers can thus reduce the utility of habitat assessment measures as species indicators (Olden, Jackson & Peres-Neto 2001). In these instances, integrating measures of accessibility into models of species distributions should result in more useful tools. Given the linear nature of freshwater ecosystems, it is expected that community compositions are structured fundamentally by drainage network connectivity (e.g. Snodgrass et al. 1996; Matthews & Robison 1998; Hershey et al. 1999). This is demonstrated clearly by the frequent success of intentional or unintentional introductions of species that circumvent the role played by natural barriers, leading to invasions of translocated fish species world-wide (Hawaii and Florida: Lachner, Robins & Courtenay 1970; Great Lakes: Mills et al. 1993; New Zealand: Townsend 1996; Japan: Yuma, Hosoya & Nagata 1998; world-wide: Rahel 2002; Norway: Hesthagen & Sandlund 2004; Africa: Mbabazi et al. 2004). Accordingly, we expect that relevant measures of connectivity will increase our ability to describe accurately past and present distributions of freshwater species and potentially to predict their future invasions.
Understanding fish habitat connectivity is related directly to the needs of conservation and management of freshwater fish species. Parameters extracted easily from topographic maps will enable larger-scale studies to be undertaken with significantly less effort. Several studies have identified measures of the degree of isolation between lakes that are associated with fish community composition, e.g. presence of lake inlets and outlets, mean stream slope, altitude, land distance and watercourse distance (Robinson & Tonn 1989; Tonn et al. 1990; Olden et al. 2001). However, many of these measures are not particularly specific regarding the location and degree of difficulties to dispersal anticipated within a specific watercourse. One of our goals is to examine whether a finer resolution of topography can resolve some of these difficulties. As dispersal ability, and therefore connectivity, is species-specific, our strategy is to construct and validate a model with a single species and its connectivity-related variables.
We use the northern pike Esox lucius (hereafter pike), as a case study to explore the ability of connectivity-related variables to predict colonization in lakes from presumed sources downstream. Pike is a keystone predator responsible for determining the structure of certain fish community assemblages (Robinson & Tonn 1989; Findlay, Bert & Zheng 2000; Spens 2007), and predicting its colonization potential may be important, especially where E. lucius is already altering ecosystems or even local economies (e.g. Ireland: Went 1957; Toner 1959; Spain: Rincon et al. 1990; North-western United States: McMahon & Bennett 1996; California: Moyle 2002; South-central Alaska: Dalton 2002).
Our main objective in this study was to create a model that anticipates the presence or absence of E. lucius in individual lakes within watersheds with interconnecting lotic and limnetic networks. We tested relationships between the incidence of E. lucius and variables that we considered to be most probable candidates for describing access to lakes by fish species. The results led us to propose an upstream connectivity model (UC) that is based primarily upon the minimum distance found between 5 m elevation intervals (= maximum stream slope) along watercourses from the nearest potential downstream sources of immigrants.
To validate the model and gain further insight into causality of any correlative associations, we used the empirical results of pike introductions into pike-free lakes to demonstrate that the pike distribution is not determined primarily by within-lake factors. The model is validated using patterns of recolonization where E. lucius was first eradicated from certain lakes with rotenone. Finally, we demonstrated the portability of the UC model with an extensive external validation for more than 1000 lakes located within a number of separate drainage basin networks.
Materials and methods
The study area covered 671 000 hectares in the northern boreal region of Sweden (Fig. 1). The landscapes range from coastal to inland, including upland as well as flatter productive forest land, to low slope wetlands and agricultural areas. This investigation included 1365 lakes in 23 complete (e.g. Moälven, Nätraån, Husån, Idbyån, Näskeån, Strömsån) and three partial river drainage basins (Gideälven, Lögdeälven, Dockstaån), each terminating in the Baltic Sea. This lake district is a result of deglaciation 9600 years ago and subsequent isostatic rebound (currently 8 mm year−1) of the land from the sea. The lakes range in elevation from 0·1 to 515 m. They range from clear to dystrophic, mainly oligotrophic to mesotrophic, although there are some eutrophic lakes in cultivated areas. The average air temperature (1921–2005) is estimated to range from 3 °C at sea-level to 0 °C at 500 m. Most lakes (99%) are situated within 5 km from present or historical human settlements.
Detailed face-to-face interviews with representatives of local fishery management organizations (FMO) or other well-informed individuals were conducted from 1985 to 2003 to collect information on current species distributions, introductions and extinctions in all lakes (see Spens 2007 for details). Data were sought from at least two corroborating sources when evaluating the presence–absence of fish species based on interviews. Interviews that defined clearly each informant's knowledge and allowed for collection of data relevant to their expertise were utilized to generate more reliable data. Historical documents on fish species distribution and stocking from the years 1552–2000 were obtained from three major forest companies, county administrations, municipality administrations, FMOs, the National Board of Fisheries and other sources. Two hundred and seventy-seven lakes had been surveyed with multimesh-sized gillnets according to Appelberg (2000), or with a slightly modified sampling stratification. In addition, most lakes (n = 753) were surveyed with other methods which helped to verify the archival and the interview data. Our quality control confirmed that pooled test-fishing surveys (multimesh-sized gillnets with a catchability of 90·8%, complemented by single mesh-sized nets, trapping and hooks) were in close agreement with pooled interviews and historical documents, differing in less than 1·3% of all lakes.
Several potential fish migration barriers between lakes were identified during extensive field surveys, e.g. absence of outlet stream (LakeOUTLET(–)), stream restricted to subsurface flow through bouldery areas (SSB), steep slopes and vertical falls associated with bedrock or boulders. These observations were used to validate barriers identified by GIS data. Maximum depth was determined in 503 lakes and water chemistry data was measured in 648 lakes (see Tables S1 & S2 in Supplementary material). Relationships between pike occurrence, altitude, latitude, longitude, water chemistry and lake morphometry were examined with partial least-square analysis (PLS) (Wold 1998). PLS allowed for an initial exploration of a large number of related habitat variables while eliminating any concerns of collinearity.
A migration barrier indicator (SV5max) was constructed to increase the resolution when characterizing upstream dispersal difficulties. It provides a measure of steepness in relation to 5 m (vertical) contour intervals, rather than the traditional measure of rise over a fixed, and typically long, distance (e.g. 100–200 m or whole stream (Fig. 2, Table 1). A prehistoric stocking indicator (AOA = adjoining open areas) was constructed to identify lakes that were more likely to have had introductions, but for which no archival data exist. We used a conservative measure of historical human presence by determining the amount of open areas such as pasture, old fields and agricultural land adjoining the shoreline (Table 1). In order to determine if AOA reflected the effects of land use disturbance, e.g. eutrophication, potentially confounding this variable, we compared the median total phosphorus levels among lake types. In that respect average lakes, 9·5 µg/L, n = 352, did not differ from those classified as pike lakes merely by AOA: 9·5 µg/L, n = 35 (t-test, P = 0·278).
Table 1. Description of connectivity related measures used in the CART analysis of presence absence of pike in the Huså basin and acronyms used in this paper
Total area of lake minus area of islands
Adjoining open areas
Historic persistent human presence. Surface area of predominantly older culturally distinct areas such as pasture, old fields and agricultural land with any part of edge within lake shore (shore = 100 m buffer around lake). Neighbouring AOA-polygons were merged into one combined shape if less than 100 m apart, without adding more area
Lake drainage area
Land area draining into lake plus lake area.
Average annual flow
Mean discharge from lake outlet (DRA × mean annual specific run-off)
Distance to source
Stream distance from lake to nearest connected potential downstream sources of immigrants
Elevation above source
Elevation above nearest potential downstream sources of immigrants. When stream is lacking, the temporary or theoretical watercourse is followed downstream to source
Lake elevation above sea level
Below highest post-glacial coastline
Was the lake under sea level since last ice age?
Maximum stream slope (fixed vertical drop)
Maximum stream slope (= minimum distance found between 5 m elevation contours) along watercourses from lake to nearest potential downstream sources of immigrants = (5 m/minimum segment length) × 100 (see Fig. 2)
SL50max or SL100max
Maximum stream slope (fixed longitudinal length)
Maximum stream slope between 50 m or 100 m stream segments from lake to nearest potential downstream sources of immigrants = (maximum vertical drop/50 m or 100 m) × 100
Mean stream slope
Mean stream slope from lake to nearest potential downstream sources of immigrants = (total vertical drop/total stream length) × 100
Presence of outlet
Outlet stream marked on map continuously from lakes down to nearest potential downstream sources of immigrants (categorical)
Ten additional GIS-derived, connectivity-related variables (Table 1) were developed in the hope of improving the pike lake classification scheme. These variables or those similar to them have appeared in the fish habitat/distribution literature (e.g. Tonn et al. 1990; Bain & Stevenson 1999; Olden et al. 2001)
upstream connectivity model
An upstream connectivity model (UC model) was constructed to distinguish lakes with pike from those without pike based on landscape characteristics. Upstream-directed connectivity is the colonization or potential colonization of a lake by pike from lakes located downstream, as revealed by studying lakes that were not exposed to colonization from pike lakes located upstream. Thus we extracted connectivity measures for (a) streams connecting a pike lake downstream with a pike-free lake upstream, assuming that such a stream had a dispersal barrier, and for (b) streams connecting a downstream lake with pike with an upstream lake with pike that was not subjected to colonization by pike living further upstream, and assuming that such a stream did not have any dispersal barriers. The procedure is illustrated in Fig. 2. One extreme slope was a result of an error on the topographic map. It was corrected from field measurements obtained with a laser.
Lakes in one drainage area, Husån, were used to build the UC model, saving the other drainage areas for model validation. Classification trees were used to build separate predictive trees; one for lakes with a continuous (i.e. unbroken line from lake to lake or sea) outlet stream marked on topographic maps and one for lakes without a continuous outlet stream. Hereafter, the two types of lakes are denoted as LakesOUTLET(+) and LakesOUTLET(–). Lakes were split into these two groups as stream-related variables such as SV5max could not be extracted for LakesOUTLET(–).
Classification trees (CART) are nonparametric techniques that split data sets into new mutually exclusive dichotomous subgroups, selecting splits that minimize misclassification, until there is no significant decrease in the misclassification rate. CART allowed us to examine relationships among pike occurrence and a large number of closely related and collinear connectivity variables (Table 1), where we anticipated nonlinear threshold effects (e.g. barriers). We used the phi coefficient as splitting method using the systat (version 10·2) tree-module. It produced hierarchical decision trees from the set of GIS-based predictor variables. The phi coefficient is χ2/n for a (2 × k) table formed by the split on k categories of the dependent variable (Wilkinson 2002). We also generated alternative linear models with stepwise discriminant function analysis (DA) to contrast the performance of classification trees. For the sake of simplicity and anticipated nonlinearity, only CART-derived models were used in the subsequent validations. In lakes with known introduction or those with rotenone-induced extirpation of pike, only the pre-intervention situation was modelled.
validation of uc model using retrospective experiments
Addition of pike – revealed habitat requirements
Historical records of introductions of pike into 49 formerly pike-free (and isolated) locations provided an opportunity to evaluate the ability of pike to establish self-sustaining populations within wide ranges of chemical, physical and biological conditions. The success of pike introductions was determined from interviews with individuals working for fishery management organizations. The results were validated by test fishing in 28 of these lakes. Ninety-three per cent of these interventions have histories longer than 30 years.
Subtraction of pike – revealed recolonization within 0–48 years
Systematic eradication of pike with rotenone was carried out in 96 lakes that varied in their chemical, physical and biological makeup. These retrospective whole-lake experiments presented an opportunity to evaluate spontaneous long-term recolonization of pike from 9 to 48 years ago (mean year: 1964, mode: 1961). The effects were revealed by considering historical knowledge of the pretreatment distribution of pike, along with post-rotenone interviews, examination of historical documents and verification by test fishing with multimesh-sized gillnets in 49 lakes and sampling with other fishing methods in another 47 lakes. The result of treatments with rotenone was then used to assess the potential of connectivity measures to correctly classify recolonization results. Five of the treated lakes were excluded because impassable highway culverts or the construction of timber floatways precluded any natural spontaneous recolonization.
Predicting pike distribution in whole drainage networks
We performed the analysis in the following manner in order to demonstrate a practical procedure to predict large sets of lakes in whole drainage networks. Predicting species distribution in whole drainage basin networks using connectivity analysis requires starting-points from assumed or known present or past sources, e.g. stocked lakes or glacial relict populations. As a first step, an estimate of the highest post-glacial coastline was reconstructed as lakes that formed below this line from isostatic rebound provided historical access to pike. However, not all lakes below the highest post-glacial coastline are current sources of pike. As species persistence is a function of lake size (e.g. Tonn et al. 1990), a larger-scale survey within the Baltic drainage basin was conducted to assess lake area–pike presence relationships below the highest post-glacial coastline. To determine the maximum size of pike-free lakes below the highest post-glacial coastline we used a national database (ntot = 2296 lakes) of postal inquiries collected in 1996 by the Institute of Freshwater Research, Drottningholm, Sweden. Pike is always present in lakes larger than 100 ha and located below the highest post-glacial coastline. These lakes were treated as sources of pike (SP), i.e. conservative starting points in the validation. Other potential sources were defined as possible surrogates for unregistered stocking activity (AOA), generated in the UC model.
In applying the UC model (Table 2), the predictor in the first splitting rule (SV5max) was measured throughout whole drainage networks starting from SP. A second splitting rule (AOA) was used to produce additional starting points in the networks of lakes, and the classification procedure according to the first split was repeated. This procedure was applied to more than 1000 lakes within a number of separate drainage networks: Husån (n = 136), Gideälven (n = 413), Moälven (n = 468), Nätraån (n = 176) and 22 smaller basins (n = 172), all of which terminate in the Baltic Sea. The number of correctly and incorrectly classified lakes were counted.
Table 2. Components used when predicting presence (P+) and absence (P–) of pike in drainage networks. *Consistent downstream colonization (CDC)
Components (resulting from)
SP (external inquiry)
Classified as P+ if lake below highest post-glacial coastline and area > 100 ha
CDC* (rejected hypothesis of limiting habitat requirements)
Classified as P+ if receiving stream from P+ lake
Migration barrier indicator (UC model)
Classified as P+ if SV5max < 6·6% in stream connecting to nearest classified P+ downstream. Classified as P– if LakesOUTLET(–)
Prehistoric stocking indicator (UC model)
Classified as P+ if AOA ≥ 3 ha and steps 2 and 3 reperformed. Residual unclassified lakes were classified as P–
The historical and contemporary distributions of pike are in complete agreement, except where lakes were treated with rotenone. Thus, no extinctions of pike populations occurred as a result of acidification or anthropogenic barriers. In addition, pike distribution was extended somewhat by anthropogenic introductions into new waters, exceeding the number of permanent extinctions. The comprehensive surveys showed that pike were found in 717 (52·5%) of 1365 lakes studied. Pike lakes seem scattered in a near-random manner within the study area (Fig. 1) and neither altitude, latitude, longitude, water chemistry, drainage area nor lake morphometry (Tables S1 and S2, see Supplementary material), explained much variation in pike incidence: PLS (R2 = 0·26, 0·26 by cross-validation, i.e. Q2).
upstream connectivity model
Nevertheless, by generating classification trees from connectivity-related variables, pike distribution in the Husån basin was predictable (Fig. 3). Pike were absent from 13 of 14 lakes lacking stream connections. The incidence of pike was determined correctly in 91·8% of lakes with stream connections according to the migration barrier indicator, SV5max. In all but two cases, pike was present in a lake when the outlet stream had a maximum slope SV5max < 6·6% to a downstream source lake. The PRE (similar to R2 for a regression model) for the whole tree was 0·80 (94·5% accuracy). Minor improvement in classification (PRE = 0·11) was achieved with a measure of historical human presence (AOA). No variables other than SV5max and AOA appeared in the classification tree. Alternative models were more complex and had lower predictive ability than CART-derived models: DA (four variables; 87·7% accuracy, 85·0% by jack-knifed classification). However, selection of only SV5max and AOA as predictors; instead of all four predictors (excluding area and altitude) generated from stepwise selection, resulted in a discriminant function with improved accuracy (89·0%, 88·0% by jack-knifed classification).
validation of uc model
Addition of pike – revealed habitat requirements
Introductions persisted in 47 of 49 lakes. Ninety-six per cent of lakes where E. lucius had been introduced had SV5max = 7·0%, so it appears that connectivity rather than habitat limits the distribution of pike in these lakes. Introductions of pike to six headwater lakes led to downstream colonization in 10 formerly pike-free lakes. In each case self-sustaining populations of pike became established in each lake, producing a continuous distribution of pike from the headwaters downstream to where lakes with resident pike occurred. This consistent downstream colonization pattern (CDC) provides further support for the idea that connectivity is more important than in-lake habitat characteristics in determining pike distribution.
Subtraction of pike – revealed recolonization within 0–48 years
The CART-analysis of spontaneous recolonizations of pike to rotenone-treated lakes produced nearly identical classification trees as the UC model (Fig. 4). Ninety-one per cent of lakes with stream connections were recolonized by pike where SV5max < 7·0%. The PRE for this model was 0·61. All but one lake lacking a stream connection [OUTLET(–)] were classified correctly according to its elevation from potential source populations (WC-elev, PRE = 0·74). This splitting rule fitted all but one OUTLET(–) lake in Husån (the UC model) as well. No other connectivity variables were included in the model generated by CART.
A temporal analysis of recolonization was not possible because the exact dates of recolonization of most lakes were difficult to determine. Many lakes with lower values of SV5max were recolonized soon after treatment with rotenone, but seven lakes with SV5max = 6·7% were observed to have pike only after 36–39 years. Five lakes were misclassified, in that they had not yet been recolonized, even though SV5max values were low. These lakes were isolated by other natural barriers (e.g. SSB) that were identified during field visits. In addition, a non-existent stream that appeared on maps was corrected, which changed the classification from LakeOUTLET(+) to a LakeOUTLET(–).
Predicting pike distribution in whole drainage networks
To identify starting points when applying the UC model, 52 lakes > 100 ha situated below the highest coastline were used. As more than three-quarters of these lakes were currently isolated from the Baltic Sea by observable natural barriers as well as SV5max > 6·6%, it is reasonable to view them as relict populations. This view is supported by 94% of these lakes also having either glacial relict crustaceans, e.g. Mysis relicta and Pallasea quadrospinosa, or landlocked populations of fishes with similar post-glacial origins (native populations restricted to areas once covered by the Baltic sea, rarely above), e.g. Coregonus albula and Osmerus eperlanus (Ekman 1922). Lakes located downstream of predicted starting point lakes were predicted as P+ and also used as starting points, as the hypothesis of limiting habitat requirements was refuted.
We found that these starting points, when used in sequence with the components from the UC model as outlined in Table 2, performed well in determining the incidence of pike (Fig. 5). The model determined correctly the incidence of pike for 86·6% of the 1365 lakes located within 26 separate drainage basin networks. Predictions of starting points and CDC lakes were 100% correct, meaning that pike were found in every lake with upstream connections to another lake with pike. Pike were not found in 90% of seepage lakes. This analysis of connectivity between lakes in whole networks had an accuracy ranging from 88·7 to 98·7% in predicting pike presence between main drainage basins. The validation was not particularly sensitive to an alternate selection of starting points. Classifications changed among 0·8% of all individual lakes when we used lakes > 50, instead of > 100 ha, as starting points. However, such an alternate selection of starting points was less reliable since many had not retained any other relict species and some even lacked pike.
Barriers formed by subsurface flow through bouldery areas (SSB) were found downstream of nearly all lakes (80%) that were misclassified as P+ by low values of SV5max. We were able to discriminate a second, but smaller group of P+ lakes with 82·1% accuracy using the prehistoric stocking indicator (AOA) (Fig. 5). Residual lakes were classified as P– with an accuracy ranging from 75·0% to 93·2% in the different drainage basins. Graphic charts visualizing patterns of connectivity between lakes and pike incidence in the Nätraån drainage basin network is presented in Fig. 6.
The high proportion of successful introductions of pike as well as their general distribution demonstrates that the species tolerates a wide variety of biotic and abiotic conditions. Our finding that the incidence of pike in a lake is generally not a function of the lake's habitat, within the range of habitats considered, is an important and useful result. One implication is that a consistent downstream colonization pattern (CDC) should be anticipated, i.e. pike should be found in every lake downstream from a source population. A second implication is that upstream-directed connectivity also controls the distribution of pike among lakes, i.e. every lake with adequate connections to a dispersal source situated downstream is expected to have pike. Our results also reveal that at least 50% of all lakes in this boreal landscape are isolated by dispersal barriers to pike (and logically also to other species with equal or less dispersal capacity). Thus, one part of the explanation for the high predictive power of the UC model is that in-lake habitat factors generally do not limit the distribution of pike, even where wide variation in of physical, chemical and biological conditions are known to occur. Secondly, SV5max has higher resolution than many measures used in earlier studies. For example, a sharp 5 m vertical drop may not be detected when stream slope is measured at a scale of 100 m segments. High values of SV5max represent an increased probability of fish to encounter barriers, hence it is still possible that some lakes are misclassified due to limited resolution, even at this scale. In the future, more precise topographical measurements will be available as digital elevation models (DEMs) based on airborne light detection and ranging (LIDAR) measurements in decimetres become more available (Toyra et al. 2003).
Another factor that contributes to these highly predictable patterns is that the behaviour of pike is inherently dispersive. This explains why distance from sources are unimportant to the distribution of pike among lakes, at least within the scales considered in this study. Other studies have shown that pike can disperse rapidly (16 km in 22 h, Carbine & Applegate 1946; 240 km in 75 days, Moen & Henegar 1971; 16 km upstream in 18 days, Ovidio & Philippart 2002). Thus, we do not anticipate clear-cut patterns of isolation by distance at the scales considered here.
Upstream colonization patterns could be discriminated from downstream patterns simply by selecting every lake that lacks an upstream source within a drainage network. Using this novel approach, it was possible to eliminate interference from colonizations originating potentially from upstream sources. However, this study also demonstrates that a synthesis of both dispersal processes, i.e. the UC model and downstream colonization patterns must be considered when predicting presence–absence of pike in a specific lake.
predicting species distribution from network connectivity
Based on our approach, managers can now predict the whole drainage network distribution of pike in lakes, by deriving map data, starting from assumed (predictions from other models, historic stocking activities or glacial relict patterns) or confirmed sources (cases of survey data) of pike. Connectivity charts (Fig. 6) offer straightforward predictions, overviews and understanding of species incidence in hundreds of individual lakes at a glance. The charts facilitate the identification of predictors by emphasizing barriers and sources, and by discarding of irrelevant information, e.g. (in the case of pike) water surface shapes and distances between lakes. Our UC model is designed for pike, but should be of use for predicting other species, e.g. salmonids, as they are often completely excluded by pike in lakes (Maitland & Campbell 1992; Spens 2007). As natural connectivity seems to be the primary predictor of this keystone predator, more so than, for example, water quality, managers should consider SV5max as an integral part of lake characterization in drainage networks where pike occur. When connectivity is the decisive factor, the key to understanding the incidence of a species is not found normally in the lake itself, but somewhere up- or downstream. The European Water Framework Directive requires member states to report ‘the hydromorphological elements supporting the biological elements’ in lakes and rivers in a map format (EU 2000). Clearly, connectivity charts could contribute to meet that requirement.
estimating undocumented introductions
The European Water Framework Directive also requires that member states produce river basin management plans that cover the ‘identification of reference conditions’ for lakes. This study has shown a method whereby managers can identify the reference state of a species’ distribution using connectivity to estimate natural distributions and distinguish them from human-mediated introductions. Similar to AOA, Whittier, Halliwell & Paulsen 1997) measured human disturbance along shorelines in north-eastern United States and concluded that, as human activity at a lake increases, so does the likelihood that humans will introduce predators. With the prehistoric stocking indicator (AOA) we attempted to predict historical human behaviour, but not with absolute precision. That allegedly stocked pike lakes were classified as having pike by this criterion with 82·1% total mean accuracy seems reasonable, considering that prediction of human behaviour is hardly expected to be precise. Prediction errors possibly reflect unregistered stocking activity that our model was unable to capture. Although classified incorrectly as pike absence lakes, the measurements of low connectivity to these lakes may well be of essential value to management because they indicate present isolation, as shown in the recolonization model (no post-rotenone recolonization when SV5max > 7%). Thus, our explanation is that unexplained populations in clearly isolated lakes probably originate from stocking. We generated model estimates of stocking activity above the highest post-glacial coastline from map-derived variables. If AOA essentially describes stocking activity, then at least 11·0% of all pike populations above the highest post-glacial coastline are the result of unregistered introductions. AOA was also useful for predicting pike incidence in lakes below the highest post-glacial coastline (where pike once had access) as well, although we cannot exclude the possibility that some of these lakes are relict populations.
a previously undescribed type of dispersal barrier (ssb)
A novel term – ‘subsurface streamflow through bouldery areas’ (SSB) was introduced to complement other widely recognized natural dispersal barriers such as waterfalls, cascades and bedrock chutes. SSBs are found downstream most lakes, where pike presence is not predicted correctly with the UC model (lakes connected by streams with maximum slope SV5max < 6·6%). SSB provides a possible explanation for how reaches with low slopes can inhibit upstream invasion even in the long term. It also remains to be tested if SSB also functions as a downstream dispersal barrier due to the restricted interstitial space for fish passage. In comparison, vertical barriers are classified and recognized more readily as barriers by fish biologists (Powers & Orsborn 1985). Modern maps cannot be expected to identify all barriers to pike dispersal as streams flowing through SSBs are often represented as continuous unbroken lines on maps.
As pike are large keystone piscivores that are important in ‘top-down’ predatory regulation of the fish community (Casselman & Lewis 1996), are a considerable predator of waterfowl (Solman 1945), and have been known to extirpate other fish taxa such as salmonids (Maitland & Campbell 1992; Spens 2007), it follows that SSB is probably a fundamental structuring factor for many freshwater species communities. Managers must be made aware of the consequences of removing SSBs (e.g. for channelling purposes, timber floatways or stream restoration), as SSBs can be impediments to upstream spreading of this keystone predator, with the potential to alter irreversibly an upstream ecosystem. In cases where managers need to prevent invasions of pike in stream networks with low SV5max, we suggest that effective barriers can be constructed that mimic natural SSBs. Consideration must, of course, be taken for other migrating species. Our study also suggests that natural bypass channels with SV5max > 7% (plus a reasonable safety margin) may provide for differential species passage, but only for species with dispersal abilities that are superior to those of pike.
recolonization/invasive potential and setting ecologically appropriate management units
Generally, when restoring lake habitat by liming programmes or pollution control, for example, managers often need to assess the intrinsic potential for natural recovery of eradicated species. In the case with fishes, managers can estimate connectivity as demonstrated in this study to predict which habitats will be recolonized from natural populations. For example, the eradications examined in our study show that many extirpations of pike are reversible, and that no reintroduction is necessary, provided that connectivity is sufficient. The UC model worked well even without taking anthropogenic barriers (such as impassable road culverts) into account, when pike were not limited by in-lake habitat. This may be because the model incorporates the historical (e.g. preculvert) access that pike had already used to colonize lakes, and that pike are capable of completing their whole life-cycle within a lake. However if in-lake habitat becomes unsuitable and leads to extinction (e.g. in our specific case, eliminated by rotenone), contemporary connectivity would then be crucial for recolonization, in which case anthropogenic barriers must also be taken into account.
SV5max or related measurements of natural connectivity (i.e. SVimax, where the fixed vertical interval Vi can be set anywhere from less than a metre up to many metres) should be a useful tool to estimate natural connectivity for different species. With this new tool, managers will be able to estimate the potential for introductions to affect new lakes and streams as well as classify objectively areas more resistant to invasion. Mapping of connectivity in drainage networks can indicate pro-active priorities needed for managers to protect communities vulnerable to future invasions that risk damaging local economies and ecosystems. There is also an obvious need for managers to master methods to measure natural connectivity in order to help define the ecological importance of adding or removing anthropogenic barriers at specific locations, considering the effects of existing natural barriers. Just as drainage-divides are now used widely as management boundaries (e.g. ‘river basin districts’ in the European Water Framework Directive), connectivity related variables such as SVimax should also be useful in certain cases for setting ecologically appropriate aquatic management units in subbasins. This is because high SVimax between two waterbodies can indicate isolation and separate species populations, needing separate management. We also suggest that the emerging field of landscape genetics (Manel et al. 2003) may benefit by taking connectivity variables such as SVimax into consideration. For example, Castric, Bonney & Bernatchez (2001) uses ‘the sum of altitude differences as a surrogate for the number of impassable falls and thus for the intensity of physical isolation’ to test for genetic patterns. Our study suggests that measures of slope in relation to a fixed interval of smaller rises in elevation will provide managers with substantially higher resolution when judging fish passage possibilities.
The municipality of Örnsköldsvik, together with FMOs, provided parts of data. The completion of this study (May 2003– April 2005) was supported by grants from the Centre for Environmental Research (CMF) to J. S. and from the Swedish Research Council for Environment, Agricultural Sciences and Spatial planning (FORMAS, no. 217-2004-2192) and CMF to G. E.