Habitat characterization and species distribution model of the only large‐lake population of the endangered Silver Chub (Macrhybopsis storeriana, Kirtland 1844)

Abstract The endangered Silver Chub (Macrhybopsis storeriana, Kirtland 1844) is native to North America and primarily riverine, with the only known large‐lake population in Lake Erie. Once a major component of the Lake Erie fish community, it declined and became nearly extirpated in the mid‐1900s. Recent collections in western Lake Erie suggest that Silver Chub may be able to recover, but their habitat and distribution are poorly known. A recent work showed an extensive area of western Lake Erie with the potential to support large numbers of Silver Chub, but was based on a geographically limited dataset. We developed a neural network‐based species distribution model for the Silver Chub in western Lake Erie, improved by new synoptic data and using habitat variables resistant to anthropogenic activities. The Potential model predictions were compared with a model that included anthropogenic‐sensitive variables. The Potential model used 10 habitat variables and performed well, explaining > 99% of data variation and had generally low error rates. Predictions indicated that a large area of the waters approximately 2–9 m deep contained Appropriate habitat and the highest abundances should be supported by habitat in a wide arc through the western end of the basin. The model indicated that Appropriate Silver Chub habitat was associated with relatively deep water, near coastal wetlands, where effective fetch is less than average. Disturbance model predictions were similar, but predicted poorer Silver Chub habitat in more areas than that predicted by the Potential model. Our Potential model reveals Appropriate habitat conditions for Silver Chub and its spatial distribution, indicating that extensive areas of western Lake Erie could support Silver Chub. Comparisons with Disturbance model predictions demonstrate that Potential model predictions may be used in conjunction with analyses of degrading conditions in the system to better conserve and manage for this endangered species.


| INTRODUC TI ON
The Silver Chub (Macrhybopsis storeriana) is a minnow native to central North America (Kinney, 1954;McCulloch et al., 2013). Most of its distribution is within riverine habitat of the Mississippi watershed but a large-lake population also exists in Lake Erie (FishBase, 2014;McCulloch et al., 2013;ODNR, 2014;Page & Burr, 2011). Where it occurs, Silver Chub is consumed by piscivores (Hoover et al., 2007) and may historically have been a substantial component of the Lake Erie ecosystem. Kinney (1954) estimated that until the 1950s there were 8-80 Silver Chub/ha in western Lake Erie. This is similar to present densities of mimic shiners (Notropis volucellus) (USGS, 2018).
However, the Lake Erie population declined severely in the late 1950s, possibly due to habitat degradation or reduced food availability (Kinney, 1954), and never recovered to its prior abundance (COSEWIC, 2012;Parker et al., 1987). After the 2012 Committee on the Status of Endangered Wildlife in Canada (COSEWIC) assessment, Silver Chub was designated as endangered in the Great Lakes-St. Lawrence unit (COSEWIC, 2012). This species is also listed as endangered and is extirpated from New York waters of Lake Erie, listed as special concern [Critically Imperiled] in Michigan (Kočovský, 2019), and has not been collected in Pennsylvania waters of Lake Erie since the 1970s.
The first Silver Chub species distribution model (SDM) for western Lake Erie showed extensive areas of the basin with the potential to support large populations (McKenna & Castiglione, 2014).
However, data were limited to collections before 2003 and did not include samples from Canadian waters. As a result, predictions for much of the habitat in western Lake Erie were based on extrapolation into areas that were not well represented within their dataset.
McKenna and Castiglione (2014) also included some explanatory variables that are sensitive to human activities, which may reflect status appropriate to the time frame of the dataset, but is not as effective at providing the best benchmark of the habitat's potential to support Silver Chub.
Higher resolution data can improve the Silver Chub distribution model and enhance conservation of this species. We redeveloped the SDM for Silver Chub in western Lake Erie using a temporally and spatially more extensive dataset than was available to McKenna and Castiglione (2014) and restricted the explanatory variables to those least influenced by human activity. This allows for the best estimation of the potential for the lake's habitats to support Silver Chub, if human influence was minimized. This benchmark of potential (i.e., the highest Silver Chub abundance that can be expected) is critical to focus conservation on habitats that are the best candidates for protection or restoration, when predictions are compared with present-day conditions (e.g., observations (McKenna & Johnson, 2011) or disturbance model predictions), and may guide scientific sampling efforts and population monitoring.
Our objectives in this study were to (a) train an artificial neural network model (NN) with the best available standardized trawl data and matching broadscale habitat conditions to predict Silver Chub abundances, (b) apply that model to predict the potential distribution of Silver Chub throughout western Lake Erie, (c) describe the habitat conditions associated with various qualities of Silver Chub habitat, and (d) contrast predictions with a model that includes disturbances and discuss some of the conservation implications of this improved model.

| ME THODS
Data on fish collected in western Lake Erie by trawling programs in Ohio and Ontario were provided by the Ontario Ministry of Natural Resources and Forestry (OMNRF), Lake Erie Management Unit, and the Ohio Department of Natural Resources (ODNR), Division of Wildlife, Lake Erie Fisheries Unit. These trawl data are fishery-independent and included summer catches of Silver Chub, as well as the absences of the species and information about the location, gear, and fishing effort. Silver Chub catches were standardized to catch per unit effort (CPUE) in units of fish/1,000 m 2 (assuming 100% catchability) and then categorized into a log-scale of abundance classes, following the methods of McKenna and Castiglione (2014). The finest scale of the spatial framework used for this study is the 90-m cell (McKenna & Castiglione, 2010, 2017. Habitat variable values and fish observation data were assigned to the spatial cells within which those data were collected. Coarser-scale units are available in this spatial framework, including Aquatic Habitat Areas (AHA). All 90-m cells within an AHA have similar basic fish habitat conditions, namely effective fetch (energy), distance from the nearest large river (i.e., Strahler ≥ 5 at the mouth) (material and water source), predicted presence of substantial submerged aquatic vegetation (SAV) (threedimensional structure), and water depth (habitat volume). Variability of fish abundance data was high due to the rarity of this species in the lake. Thus, individual CPUE values were averaged within the slightly coarser AHA spatial units. Classification of CPUE into the log-scale classes (1, 2-10, >10) was based on these averages; we considered "Appropriate" conditions those that supported at least 2 fish/1,000 m 2 . A suite of lakescape data was provided at the 90-m resolution for all spatial cells within the entire Western Lake Erie Aquatic Lake Unit (ALU) (a coarse-scale spatial unit based on largescale circulation patterns) by the Great Lakes Regional Aquatic Gap Analysis Coastal Project (McKenna & Castiglione, 2010, 2014, 2017 (Table 1, Figure S1a-j and Figure S2a-i). While some data for variables such as water temperature and shoreline modification were available, we chose to use only variables that are not affected by human activity over ecological time scales (decades to centuries) to provide the best predictions of the potential that each habitat unit has to support Silver Chub.

| Model of potential
We used a principal components analysis (PCA) on the habitat data to identify the variables most likely to influence the distribution and abundance of Silver Chub in Lake Erie. The influence of each variable was ranked based on the length of its vector in the plane of the first two axes. Decrease in the relative weight of ranked variables along the first two PCA axes suggested that 10 variables would explain most variation. Those  a 100-km radius circle from each spatial cell on a per km 2 basis and multiplied by 106 to produce integer values for the raster representation of the data in the geographic information system. b Hillyer (1996)

| Disturbance Model and Contrasts
While our primary goal was to develop the model of best potential habitat conditions (hereafter Potential model) for Silver Chub throughout western Lake Erie, model predictions that incorporate some level of disturbance (Disturbance model) provide useful contrasts and help to illustrate the value of benchmark predictions provided by the Potential model. Many possible disturbances to Silver Chub habitat conditions exist in Lake Erie. However, only two classes of anthropogenically influenced variables were available to us for this study, surface water temperatures and artificial shoreline modification. Also, little information exists on the sensitivity of Silver Chub to various potentially degrading environmental factors (but see, Britt, 1955;Kinney, 1954;Krumholtz & Minckley, 1964).
We are assuming that unnatural shoreline conditions and nonoptimal temperatures would adversely affect the Silver Chub distribution and would be reflected in habitat distributions. Mean surface water temperatures (°C) and their coefficients of variation (CV) were available in each 90-m spatial cell of the study area for each month from May through October (Table S1). There was high autocorrelation among these variables, and only two temperature and two CV variables were required to represent those data and their variability (

| RE SULTS
Catches from 2,066 ODNR and OMNRF trawl samples from 1987 to 2014 collected 9,414 Silver Chub and were standardized and assigned to the appropriate log-scale abundance classes. Silver Chub were collected in 676 samples and CPUE ranged from 0.32 to 503/1,000 m 2 but was less than 4/1,000 m 2 in 76% of the samples where Silver Chub was present. There was no trend in Silver Chub CPUE during the sampling time period. The catches were widely distributed throughout the western basin of Lake Erie and were usually in the same areas where they were absent from previous, subsequent, or adjacent trawls; the highest abundances occurred in the southwestern end of the lake in approximately 5.5-7.0 m of water ( Figure 1). More than 99% of Silver Chub were collected in waters > 2.5 m deep.
The first two axes of the PCA explained 30.1% of variation in the data. Among the 29 anthropogenically resistant habitat variables available, the 10 most influential variables included representation of system energy, distance to major rivers and wetlands, coastal geomorphology, SAV, and habitat volume (Table 1, Appendix S1).

| Model performance
The NN model of Potential used the 10 most influential habitat variables as inputs and 46 neurons in the hidden layer. The model performed well, explaining 99.5% of variation (R 2 adj = 0.995, MSE = 0.64). Correct predictions of abundance classes were high (96%) ( Table 2). On an overall presence-absence basis, the commission error rate was high (53%), but only a single omission error occurred. Cohen's Kappa shows that error rates for the model, both on the basis of presence-absence and for predictions of any given abundance class, were substantially lower than expected by chance and indicate a strong model. Visually, the match between observed abundance values and that predicted by the model was good (Figure 1).

| Model predictions
The Potential model predicted a mosaic of habitats throughout the western basin of Lake Erie capable of supporting various abundances of Silver Chub (Figure 1). Appropriate habitat (i.e., the two largest abundance classes, Optimal (>10/1,000 m 2 ) and Moderate (2-10/1,000 m 2 )) was predicted to occupy > 50% of the Western Lake Erie Aquatic Lake Unit area, of which only 10% was expected to support Optimal densities. Optimal habitat conditions were predicted to generally occur in a band from the Marblehead Peninsula to the mouth of the Detroit River, in waters about 6.5 m deep. Most of the study area was encompassed by habitat predicted to have the potential to support Moderate abundance of Silver Chub, which occupied western, central, and northern portions of the lake unit, plus Sandusky Bay. Nearly 1/3 of the study area was predicted to support Marginal abundances (1/1,000 m 2 ) of Silver Chub, and only 17% of the area was predicted to be Unsuitable. Most of the Marginal and Unsuitable habitats were located in the central and eastern portions of the lake unit. A complex mosaic of habitat patches existed around the archipelago that roughly separate the western and central basins of Lake Erie and along the southeastern coast of the western basin.
The Detroit River Delta in the northwestern portion of the lake is the primary conduit of water entering Lake Erie and was predicted to be largely Unsuitable.
The Silver Chub abundance classes increase in size as abundance increases, and the model provides only broad relative abundance estimates. Model predictions could be used to provide a range for the potential Silver Chub population size within the western Lake Erie Omissions are in bold, and commissions are in italics. Cohan's Kappa (K) and prevalence are also shown for each model and abundance class.
Aquatic Lake Unit (Table 3). While such an estimate would be similar to Kinney's original estimate (Kinney, 1954), capture variability and other uncertainties make such an estimate highly speculative.

| Habitat characteristics
Appropriate Silver Chub habitat may be described by environmental

| Prediction evaluations
Simple correlations between independent test data (OH data and USGS data) and predicted abundance classes were low for both datasets (OH: r = .10, USGS: r = .24). There were mixed results with goodness-of-fit tests (

| Model performance
The Disturbance model used the 10 habitat variables from the Potential model, plus the four temperature metrics and five shoreline modification variables as inputs and 55 hidden layer neurons. Model weightings were generally similar to those of the Potential model, except for distances to delta-type wetlands and nearest larger river ( Figure S3). The model performed well, explaining 99.9% of variation (R 2 adj = 0.999, MSE = 0.05). Correct predictions of abundance classes were high (98%) ( Table 2), and on an overall presence-absence basis, the commission error rate was relatively low (34%); only a single omission error occurred.
Cohen's Kappa showed that error rates for the model, both on the basis of presence-absence and for predictions of any given abundance class, were substantially lower than expected by chance, indicating a strong model. Visually, the match between observed abundance values and model predicted values was good (Figure 4).

TA B L E 3
The number of 90-m spatial cells (Potential model allocation), areal extent, and percentage of the study area predicted by the Potential or Disturbance models to support each class of Silver Chub habitat quality Note: Total Potential model predicted silver chub population range for the western Lake Erie Aquatic Lake Unit (ALU). Error estimates around population totals are based on the root mean squared error estimate from fit of the neural network model.

| Model comparisons
There were strong similarities between the Potential and Disturbance model predictions. Half (50.1%) of the study area was predicted to have the same Silver Chub habitat quality by both models (

F I G U R E 3 Ontario MNRF and Ohio DNR trawl collection samples used in model development (centered circles), spring and fall samples from the USGS (circles and triangles) and
Ohio DNR (squares and stars), and Potential model predictions (polygons) of silver chub abundance (number/1,000 m 2 ) in Western Lake Erie. Abundance classes equate to Optimal (11-100/1,000 m 2 ), Moderate (2-10/1,000 m 2 ), Marginal abundances (1/1,000 m 2 ), and unsuitable (0/1,000 m 2 ). Note that the symbols for the highest abundance classes for each group are stacked on top of numerous lower abundance symbols in some locations Areas predicted by the Disturbance model to have lesser quality Silver Chub habitat than that predicted by the Potential model may have been associated with higher temperatures in May and higher water temperature variability (CVs) in August and September, but slightly lower water temperatures in September (Table 5, Figure S4a-d). Those areas also may have been associated with more extensive areas of major (70%-100%) or minor (15%-40%) shoreline modification ( Figure S4e,g). However, values of each "disturbance" variable showed wide variability within classes of difference between the Potential model and Disturbance model. Means and medians of areas differing between model predictions were rarely more extreme than that associated with areas predicted to be the same quality by both models ( Figure S4). Chub occupy riverine habitat throughout most of their range, but are known to use low energy habitats within those lotic systems (e.g., Pflieger, 1975;Ross, 2001); whether the Lake Erie Silver Chub population is genetically distinct from riverine populations or would have different behaviors is unknown (but see Ahmad, 2017). Model predictions indicate that the majority of Lake Erie habitats have the potential to provide Appropriate or at least Marginal conditions for Silver Chub.

| Performance of potential model
The more extensive dataset used here, particularly with representation from Canadian waters, allowed for improvement over the model developed by McKenna and Castiglione (2014). The metrics of model performance were all better than they report for their model, and the new model shows finer spatial detail, particularly in the northern part of the lake unit, which was strictly extrapolation in the previous model. The result is a more accurate description of the potential spatial distribution and extent of high-and low-quality habitats with respect to the needs of Silver Chub within the lake unit and a better tool to support Silver Chub conservation efforts. However, differences in trawling vessels, when and where trawls occurred, and different catchabilities may affect prediction accuracy.
Our Potential model, like all models, has its limitations and, in addition to data changes, differs in a number of ways from the previous Silver Chub SDM for western Lake Erie

| Model interpretation
The Potential model was designed to predict the best potential for any given habitat unit to support Silver Chub, and anthropogenic influences were explicitly excluded as inputs to provide that benchmark.
The model relies on the large dataset to separate the signal of Silver Chub abundances matched to "natural" habitat conditions from the noise imposed by anthropogenic influences and other environmental and ecological factors (e.g., seasonal and other natural variation in the data and biological factors). To assist the model with this separation of signal from noise, we used averages of abundances and habitat conditions within AHAs, which helps to more clearly separate the array of habitat conditions associated with a particular class of Silver Chub abundance, but also reduces the resolution of predictions. Despite this generalization, we believe the model predictions are appropriate for most conservation efforts. In fact, they may be more appropriate than numerically specific predictions; one does not usually need to know if there are 7 versus 12 fish in a given area but rather are the fish rare, uncommon, common, or abundant-these qualitative classes match the TA B L E 6 Habitat fragmentation metrics for each habitat quality type comparing the predictions of the Potential (10 variable) and Disturbed (19 variables) Silver Chub models Note: Mean distance is the mean Euclidean distance (m) to the nearest neighboring patch of the same type, based on shortest edge-to-edge distance. Aggregation Index is basically the ratio of the number of like adjacencies to the maximum possible like adjacencies (see McGarigal & Marks, 1995).
model's quantitative abundance classes. The model predicts a temporal snapshot of Silver Chub habitat potential and does not explicitly capture seasonal or long-term temporal dynamics, although no seasonal or long-term trends were evident in the data (Figure 3).

| Model comparisons
Habitat conditions may be driving differences in the extent of and locations that could support high or low Silver Chub abundances, and>¼ of the study area (27%) was predicted to support poorer conditions when effects of disturbance variables were included.
However, direct relationships between independent variables and model predictions are difficult to make. We provide a cursory analysis of the associations of individual disturbance variables with differences in predictions between the two models ( Figure S4 Spatial distributions of any habitat type may be consolidated or fragmented. Fragmentation is often associated with degraded ecological conditions in terrestrial systems (Saunders et al., 1991;Turner, 1989;Wilcox & Murphy, 1985), but has rarely been examined quantitatively in aquatic systems (Jacobus & Webb, 2005).
Subtle differences in the synergies within the two models can also affect predicted fine-scale spatial distributions. Predictions of the Disturbance and Potential models were generally similar but with slightly different spatial distributions of the Optimal and Moderate habitat classes, resulting in nearly the same amount of Appropriate Silver Chub habitat in both models. Differences in fragmentation of model predictions, based on the selected metrics, were equivocal. The Disturbance model predicted fewer good-quality and more poor-quality habitats (which were more aggregated) and greater distance between good-quality habitats, but greater overall patch diversity and larger good-quality patches. As mentioned above, most habitat was predicted to be of equal or lesser quality by the Disturbance model than by the Potential model, but a minority of habitat was predicted to support higher quality Silver Chub habitat when the "disturbance" variables were included. The reasons for these predictions of improvements are not clear, but several factors should be considered with our example. It is possible that addition of the disturbance variables to the anthropogenically resistant variables of the Potential model revealed some higher quality conditions than what was detected by the learning process of the Potential model. However, some of these differences may be explained by minor geographic discrepancies between predictions, where one model predicted a certain quality condition to occur in a particular habitat patch, but the other model predicted that same habitat quality to occur in an adjacent location. This can be seen among the fragmented habitats around the islands. Another important factor is that some of the "disturbance" variables, like extent of unmodified shoreline, might be expected to indicate high-quality (with large values) rather than low-quality conditions. Finally, ecology and physiology of this rare species are poorly known, as are responses of Silver Chub to the disturbance variables used here (Kinney, 1954;Krumholtz & Minkley, 1964). For example, Silver Chub could prefer warmer water temperatures or higher variability in temperatures at certain times of the year, which would only be reflected in Disturbance model predictions. There is a large suite of stressors that degrade aquatic habitat in western Lake Erie (Hartig et al., 2009), and fragmentation associated with disturbances may become more evident with a more thorough representation than the two types included in our Disturbance model.  suggesting that rehabilitation of those habitats might benefit Silver Chub ( Figure 5). In contrast, if an area predicted by the Potential model to be Unsuitable for Silver Chub is degraded, it makes no F I G U R E 5 Differences in Potential and Disturbance model predictions of Silver Chub habitat in western Lake Erie. Differences are shown as changes from the habitat quality class predicted by the Potential model to that predicted by the Disturbance model. Red patches indicated the most negative difference between the Potential model and the Disturbance model, and darkest green indicates the most positive differences. Note that only shoreline modifications and water temperature variables represent disturbance effects sense to expend resources to rehabilitate that area, with regard to conservation of Silver Chub.

| CON CLUS IONS
Our improved Silver Chub model predictions help to address the need in the Canadian species recovery strategy for knowledge and a map of the current distribution and extent of suitable Silver Chub habitat to support conservation and future targeted sampling efforts for this species (McCulloch et al., 2013). Our benchmark predictions within the multiscale spatial framework give a better sense of the potential for this species under the best of circumstances than the previous model and provide for accounting of habitat quality and spatial distribution from fine-to coarse-scale (McKenna & Castiglione, 2010). While comparisons of Potential and Disturbance model predictions help identify the degree of degradation in any habitat unit, additional models that include the broader array of disturbance variables and more accurately represent present-day conditions can be developed and compared with benchmark (and Disturbance model) predictions developed in this study. Our empirically based modeling approach statistically describes the best conditions that might be achievable to support Silver Chub. This approach may also be applied to any other species, and multiple species comparisons could enhance conservation planning. Clearly, more research is needed on Silver Chub tolerances and the effects of other disturbance factors, and achieving remediation of degrading factors in Lake Erie is a high challenge. Neither model considers all habitat-degrading factors, biological impediments, or socio-political concerns, but they may be used with other tools and data to conduct triage and establish priorities for conservation of Silver Chub. Application of our predictions requires field validation and careful consideration of the factors not included in the models that may significantly affect Silver Chub abundance.

ACK N OWLED G M ENTS
We are grateful to the Ontario Ministry of Natural Resources and Forestry, Lake Erie Management Unit, Ohio Department of Natural Resources, Division of Wildlife, Lake Erie Fisheries Unit, the USGS Lake Erie Biological Station, and the USGS Aquatic Gap Analysis Program, Great Lakes Regional Aquatic Gap Analysis Project for providing the data that made this project possible. We also thank C. Castiglione, M. Slattery, and R. Alexander for their assistance with data and mapping of results. We appreciate the advice and manuscript reviews provided by B. Widel and N. Mandrak. We are also grateful to journal reviewers for their efforts to improve this paper. This work was conducted and supported by the US Geological Survey. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

CO N FLI C T S O F I NTE R E S T
The authors declare no conflicts of interest.