Author Correction: Large-scale variation in density of an aquatic ecosystem indicator species

An amendment to this paper has been published and can be accessed via a link at the top of the paper.


Results
In 2013, 138.10 km and 152.64 km of waterway were surveyed in the Hudson River and Mohawk River, respectively. In 2014, 540.22 km and 571.23 km of waterway were surveyed in the Hudson River and Mohawk River, respectively (Table 1) Table S1). Transect and scat summaries are provided in Table 1.
Selecting the Detection Probability Model. Of the 32 candidate encounter models, those that relaxed the Euclidean assumption of circular and stationary space use (ecological distance models from here, see Methods), were systematically favored over the Euclidean distance models based on AIC (Supplementary  Table S2, Fig. S7). Ecological distance models received a cumulative model weight of ω + = 1.00 compared to ω + = 0.00 for the Euclidean distance models. A model allowing the baseline detection probability (p 0 : probability of encounter when distance is 0) to vary by session was overwhelmingly preferred (ω + = 0.91) to models with detection varying by river (ω + = 0.02) or by year (ω + = 0.04, Fig. 1). There was some support for sex difference in baseline detection probability (ω + = 0.33), and complete support for sex-specific space use parameter, σ (ω + = 1.00, Fig. 1 In summary, ecological distance models that allowed for visit-specific detectability and sex-specific σ were preferred (Supplementary Table S2). Although there was support for models with and without sex differences (ω + = 0.32 and 0.68, respectively), sex-specificity is biologically important and of interest. So as not to overly constrain the estimation of the detection function, we proceeded to analyze the 58 density models using both detection model structures: p(visit + session + sex) and p(visit + session), resulting in a total of 116 density models.
Inference about Detection and Density. No single density model received overwhelming AIC support (Supplementary Table S1), so we used model averaging to account for model uncertainty 29 . The full model  selection table is provided in the supplemental material (Supplementary Table S3) and, for clarity, we provide a reduced model selection table containing only models for which the 85% confidence intervals for all density covariates do not overlap zero 30 (Table 2).   The effects of 'Visit' and 'Session' on detection were present in every model and had full model support (i.e., ω + = 1, Table 3). The effect of sex, however, was present in only half of the models and had a relatively low RVI value (ω + = 0.33, Table 3). This suggests that, although there is non-zero support for differences in baseline detection probabilities between sexes, the differences are likely to be small or that we did not have sufficient power to detect the differences ( Table 3, Supplementary Fig. S8).
As expected, detectability was highest during the initial visit, the period with most accumulation time and before scat removal, lower during the second visit (p 0,visit2 = −0.20 [95% CI −0.02-−0.38]), and lowest during the third visit (p 0,visit3 = −0.31 [95% CI −0.09 −0.53]). In addition to visit-specific variation, detectability varied by session (i.e., by unique river-year combinations). Baseline detection probability was similar in the Hudson River in 2014 and the Mohawk River in 2013 and 2014, ranging from 0.08 to 0.15, but was markedly lower in the Hudson River in 2013, ranging from 0.03 to 0.05 ( Supplementary Fig. S8). Estimates of σ were σ ♂ = 0.34 (95% CI: 0.29-0.39) and σ ♀ = 0.20 (95% CI: 0.18-0.23) for males and females respectively (Table 3), suggesting scatting area of male mink is larger than that of females. The estimate of the cost parameter determining how movement is influenced by riparian/non-riparian habitat was α = − . 1 23 2 [95% CI: −1.44-−1.02], which means that, for our binary cost surface (riparian = 0, non-riparian pixel = 1), the effective distance between two points on the landscape is closer when separated by non-riparian habitat (out-of-network) than by 'within-network' riparian habitat (see Discussion).

Discussion
Our results provide compelling evidence that the density of American mink is significantly lower in the Hudson River than in the Mohawk River in both years (Fig. 2). Specifically, estimated mink density in the Hudson River was 1.64 and 1.67 times lower than the Mohawk River in 2013 and 2014, respectively. We found very little support  for within-river spatial variation in density using vegetation cover, distance from urban areas and distance from the main stem as potential density predictors. Our objective was not to attribute variation explicitly to PCB contamination, but rather, investigate whether patterns of density were consistent with the hypothesis that extensive contamination has resulted in adverse effects on mink. So, whether the mechanism resulting in reduced densities in the Hudson are the result of direct impacts, e.g., on mink survival and/or fecundity, or indirect effects, e.g., on the riparian prey community, the fact remains that mink density varies substantially, and consistently, between two rivers that are similar in most ways other than the major difference in PCB contamination levels.
As expected, detectability decreased with successive surveys (Supplement Fig. S8). Scat encounter probability was highest in the occasion with the longest potential scat accumulation time, whereas after removal, and with on average 25 days between visits, scat detectability decreased. Detection was similar in all sampling sessions apart from in the Hudson River in 2013 (Supplement Fig. S8), the river-year sampling session with fewest scat samples collected, which may have been due to the extreme rainfall and flooding in 2013, although it is not clear whether this should have affected detectability in the Hudson more than in the Mohawk. Regardless of the fact that the source of this variability may not be clear, the session-by-visit structure of the detection model is flexible enough to account for these unknown sources of session-specific variation that density is estimated reliably with respect to the specification of the detection model.  Table 2). On the right of each session, red points are model averaged predictions of session-specific density holding all continuous covariates, that had very little support and coefficient estimates not significantly different from 0, at their mean value (i.e., 0 because covariates were standardized). Bold black lines are unconditional standard errors of the predictions and the thin grey lines are the unconditional 95% confidence intervals. Using the ecological distance formulation of the SCR model 31,32 we were able to account for spatial asymmetry in expected encounter probabilities around an activity center that was explicitly related to the riparian landscape. Mink movement is typically assumed to have a higher degree of association with water networks or riparian corridors than areas away from water or non-riparian habitats 10,33,34 . Yet, contrary to expectation, we found that space use is more frequent between two points when separated by non-riparian habitat than the points separated by the same Euclidean distance along the water network (α = − . 1 23 2 , SE = 0.11). This result is in contrast to the positive resistance value reported in Fuller et al. 35 which was based on a much smaller spatial extent than considered here (388 km 2 vs. 1315 km 2 ), and substantially fewer individuals detected at multiple traps (15 vs. 145). It is likely that these differences are scale-dependent and arise from the specific characteristics of the river network in the localized area considered in Fuller et al. 35 . In our study, the large spatial coverage and number of individuals is likely to remove such sensitivity to scale.
While counterintuitive, this makes sense biologically: although mink are unlikely to have symmetric (circular) home ranges, they are equally unlikely to have strictly linear home ranges. Instead, mink home ranges conceivably encompass multiple river sections that are in close proximity, and hence, when unconnected waterways separated by apparently unsuitable non-riparian habitat fall within an individual's home range, movement between these locations may be more frequent than expected under the Euclidean assumption. In a sense, a stream acts as an attractant to a mink whose home range is located on a different but nearby stream. The estimated negative resistance parameter likely reflects that movement occurs more frequently across the non-riparian matrix to access resources within a territory that is not linear, as is often assumed, but rather that can encompass multiple disconnected waterways. We note that it is possible that some within-river spatial variation in density exists that is related to prey availability (e.g. 36 ). Measuring prey availability across the (large) spatial scales investigated here however, is prohibitively time intensive and was beyond the scope of this study. Two observations are noteworthy in this regard. First, the two river systems are very similar in terms of their hydrology and land use compositions (see methods), and second, the diets of mink in both rivers systems are similar both in terms of species composition and the proportional species make-up 37 .
The debate surrounding the use of focal species as indicators is largely focused on whether or not the chosen species adequately reflects the conditions of the system 3,4 . Thus, when adequately justified, certain species are viable indicators (e.g., diamondback terrapins 38 clapper rails 39 ). During the process of the Hudson River natural resource damage assessment, several independent conclusions provide such justification for using mink as an indicator species. First, PCB contamination levels greatly exceed that expected naturally 40 . Second, PCB burdens in aquatic species, including mink, are positively correlated with environmental levels 18,19 . Third, aquatic species make up the majority of mink diet 12,37 . And finally, experimental evidence shows that elevated PCB burdens cause direct physical damage, reduced survival, and reproductive impairment 23 . Thus, given the exposure history of individual mink to PCBs, and the fact that individual variation in vital rates has the potential to influence spatio-temporal population dynamics 22 , monitoring American mink is useful for understanding the potential impacts of PCB contamination on mink populations as well as on the aquatic ecosystem. In fact, American mink are an ideal candidate species for aquatic ecosystem assessment in general 8 .
Once an indicator species is selected, the challenge that remains is that the state of the focal species should be estimated precisely and over an area large enough to be considered representative of the ecosystem. We demonstrated how this can be achieved by combining three tools for monitoring rare, elusive or otherwise difficult to observe species: scat detection dogs to locate genetic material for species of interest, non-invasive genetic methods for identifying individuals, and spatial capture-recapture methods for inference from the resulting individual encounter history data. Doing so, we obtained large-scale spatially explicit estimates of American mink density in the Hudson River, a river system exposed to high levels of long-term PCB contamination, and the Mohawk River, a hydrologically independent river system. Estimated mink density in the Hudson River was lower than in the Mohawk River, consistent with the hypothesis that sustained contamination of aquatic ecosystems has had a negative impact on the species occupying those niches. The integration of spatial and genetic sampling and spatially explicit density estimation methods is now commonly adopted in ecological monitoring, and, as we have demonstrated, should be considered when conducting ecosystem assessments using indicator species.

Methods
The Hudson and Mohawk River Systems. This study focused on a 620 km 2 area within a 5 km buffer centered on a 65.21 km section of the main stem of the Hudson River extending downstream of the known point source of the PCB contamination ( Supplementary Fig. S1). As a reference, we selected a 695 km 2 area within a 5 km buffer centered on a 71.53 km section of the main stem of the Mohawk River, a geographically close river system within the Hudson River drainage basin, but hydrologically independent from the influence of Hudson River plant PCB discharges (Supplementary Fig. S2). Both rivers have similar environmental characteristics, receive approximately 10 cm of rain per month during the May-July survey period, have a relative elevation change of approximately 35 m, are heavily managed water bodies with canal systems consisting of dams and locks, and have comparable land use and land cover (Supplementary Fig. S3). Recorded environmental PCB levels and mink PCB burdens are, however, markedly different between the two rivers: PCB levels are lower in the Mohawk River than in the Hudson River 18 . For example, it was estimated that the Hudson River contributed 90% of the PCB loadings south of where the rivers meet 41 . The Mohawk River thus provides a reasonable reference study area for comparing estimates of mink density. Land Cover Database 42 , 2) they did not have landowner access permission, or 3) on direct inspection, were either deemed unsafe for dogs and/or humans to survey, or had no surface water. This resulted in 506 and 567 potential sampling sites in the Hudson and Mohawk Rivers, respectively. Sites located within 1 km of each other were grouped into 'clusters' to reduce travel time between sites and to expose individual mink to detection at multiple locations. Sites with no neighboring sites within 1 km, were removed.
Using a swapping algorithm (Chapter 10 in 43 ), and based on two survey teams sampling over 10-weeks in 2013, we selected 74 and 68 sites in the Hudson and Mohawk River study areas, respectively. In 2014, three survey teams sampled over the same 10-week period which allowed for additional sites to be surveyed and for transect lengths to extended (Table 1). Of the sites sampled in 2013, 69 and 65 sites were sampled in 2014 in the Hudson and Mohawk areas, respectively. All remaining accessible and suitable sites were then ranked based on the optimization procedure and, based on available effort, an additional 7 sites in the Hudson and 11 sites in the Mohawk were selected resulting in 76 sites in both rivers in 2014 (Table 1, Supplementary Figs S1 and S2). Sampling in both years was conducted between the end of the breeding season in April 44 , and the onset of juvenile dispersal in late July 10,45 . In both years, each site was visited three times between May 2 and July 15. Transect lengths, and the number of days between surveys are provided in Table 1.
Scat Surveys and Individual Identification. Scat surveys were conducted by scat detection dogs, a handler and a data recorder surveying both banks of the river along the transects. Dogs wore GPS collars and searched off-leash and in-sight of the handler. When the scat was located by a dog, the exact location was recorded (see 35 ). Fewer scat samples were found in 2013 compared to 2014 (1059 and 3005 respectively, Table 1), and in both years fewer scat samples were found in the Hudson River study area than in the Mohawk (Table 1) (Table 1). Scat samples were identified to individual level using 11 microsatellites using the methods described in detail in Fuller et al. 35 . In total there were 316 genetically identified mink (Table 1). Fewer mink were detected in the Hudson River study area in both years: 30 and 78 individuals in 2013 and 2014 respectively, compared to 85 and 123 in the Mohawk River (Table 1). Individual spatial encounter histories were constructed using the genetic identity, location, and sample occasion of each scat sample. Effective "traps" were created by converting GPS track lines from the dogs to 50 m × 50 m grid cells (Supplementary Fig. S4). This resulted in 817 and 1,857 trap locations in the Hudson in 2013 and 2014, respectively, and 805 and 1,854 in the Mohawk in the two years, respectively. Density Estimation. We used the standard SCR model assuming that y ijk , the observation of an individual (i) at a trap (j) during an occasion (k), are binomial random variables where the probability of y = 1 is a function of the distance, d(x j , s i ), between an individual's activity center, s i and the location of the trap, x j : where p 0 is the baseline encounter probability, which could vary by individual, trap, and/or occasion attributes using a logit-link, logit(p0 i,j,k ) = a0 i,j,k , and α 1 = 1/(2σ 2 ) controls the shape of the function. d(x j , s i ) is the Euclidean distance between a trap and an individual activity center. Parameters α 0 and α 1 are parameters to be estimated.
To account for the unknown accumulation time in the first visit and the subsequent clearing of samples, we were interested in accounting for occasion-specific variation in detection probability. This is easily accommodated in SCR by modeling p 0 as a function of a time-varying trap level covariate 'visit' . Because accumulation times differed from visit one to visits two and three, a 'visit' effect was included in all models. We also tested for sex-specific variation in both the baseline detection probability and the spatial scale parameter, and allowed detection to vary by session, i.e., by year and river, by river only, and by year only. To accommodate the fact that sex determination was not made for all identified individuals, we applied a discrete 2-class mixture model to estimate the parameter ψ, the probability that an individual in the population is male 46 . All combinations of these effects produced a candidate set of 16 encounter models.
American mink are riparian habitat specialists and their movements are known to be closely associated with, but not necessarily restricted to, waterways 33,34 . This behavior potentially violates the Euclidean assumption that the detection kernel is symmetric and stationary (e.g. 32,35 ). We adopted the 'Ecological distance model' 31,32 that allows explicit estimation of landscape resistance, and can therefore accommodate movement patterns that deviate from the circular assumption. For mink, a riparian specialist, we generated a 100 m 2 resolution binary riparian cost surface where pixels that did not contain water were classified as non-riparian and had a value of 1, and pixels containing water were classified as riparian and were given a value of 0 ( Supplementary Figs S4 and S5). This model represents an alternative, competing model to the Euclidean distance model with a single additional parameter, α 2 , determining the strength of the effect of landscape structure on space use. We fit an ecological distance analogue of each of the encounter models described above resulting in 32 detection models in total.
A point process model describes the distribution of individual activity centers across the landscape (i.e., density 43,47 ). In addition to the standard uniform density model, spatial variation in density can be modeled using spatially varying covariates. For statistical convenience, the state space of the point process, S, is a discrete representation of the landscape described by pixel centroids. We use the standard log-linear model for μ(s, β), the per-pixel density, which can accommodate spatial covariates (C): The resolution of the state-space, and the scale at which all spatially explicit density covariates were computed, was 210 m × 210 m ( Supplementary Figs S5 and S6). This resolution was considered fine enough to approximate a continuous landscape for mink while maintaining computational tractability and parameter insensitivity 43 . The state-space must be an area large enough to include all plausible activity centers of all detected individuals and, following recommendations by Sollmann et al. 48 , and based on the results from a pilot study 35 , we defined  as all pixels within a conservative 4.5 km of any trap. Because mink are semi-aquatic riparian specialists, mink activity centers, e.g., denning sites 49 , are likely to be located along the water network. For example, all denning sites of 13 telemetered individuals were within 50 m from water 50 , and in the Hudson River, almost all mink resting sites were located within 10 m of water 51 . As such, we created a biologically realistic state space that included only riparian areas. It is important to note that, while activity centers are restricted to the riparian corridors, space use is not restricted to the waterway but rather is affected by the waterway according to the ecological distance model.
We expected the distribution of mink to be influenced by proximity to urban areas 52 , and vegetative cover 53 . Distance to the nearest urban area, D d2urban , was calculated as the distance to the edge of the nearest area of high intensity urbanization, (≥10 ha contiguous 50-100% impervious surface based on the NLCD landcover data). Percent vegetation cover, D cover , was calculated as the percentage of overstory (deciduous, coniferous, and mixedwood trees >5 m tall) and/or understory (shrub/scrub <5 m tall) vegetation within each state-space pixel ( Supplementary Figs S5 and S6).
We hypothesized that based on proximity to the pollutant source, densities in areas closer to the main stem of the Hudson River may be lower 18,19,23,24 . Therefore, we included a continuous 'distance to main stem' covariate, D d2stem , computed as the Euclidean distance from the center of each pixel to the main stem (Figs S4 and S5). We expected this gradient to differ between the contaminated Hudson River and the reference Mohawk River, so we included a river-distance interaction term that allows the effect of distance to vary between the two rivers.
Finally, our primary interest was to compare river-specific estimates of density while also accounting for potential variation in density across years. Therefore, we allowed density to vary by river but fixed across years, by year but fixed across rivers, and also by session (each unique river-year combination). All combinations of these density covariate models, including the uniform density model, resulted in a total of 58 candidate density models.
Testing all combinations of the detection and density models would result in a prohibitively large number of possible model combinations (≈2, 000), and instead, we adopted a two-step model fitting approach 54,55 . First, we fitted all 32 encounter models using a flexible session specific density model. Using AIC-based model selection 29 , we selected the most supported detection model structure(s) to proceed with the second modeling stage. Using the most supported detection model(s) we fitted and compared all 58 density models. Inference was based on this final model set which we ranked, weighted, and if necessary, averaged using AIC 29 . We calculated relative variable importance (RVI or ω+) for each covariate by summing the AIC model weights across each model in which the covariate was present. All models were fitted using the R package oSCR 56,57 , a package designed specifically for fitting multi-session sex-structured SCR models.
The data analysed and the code to conduct the analysis are available here 58 .