Supporting Information
Appendix S1. Broad-scale habitat data and variable selection
More than 300 enduring (i.e., variables resistant to anthropogenic influences, such as bedrock geology, landscape slope, stream order,
etc.) habitat characteristics indicating influence from the stream reach scale to total watershed scale were attributed to each
confluence-to-confluence stream reach within the 1:100,000 scale National Hydrography Database (NHD) (McKenna et al. 2006).
Land cover was also included to provide a general indicator of human activity, but other anthropogenically sensitive conditions were
excluded. The five scales of mean habitat condition were those associated with the channel (C), the riparian zone for each stream
reach (R), the local watershed draining to each stream reach (W), the entire upstream riparian zone for each stream reach (RT), and the
entire upstream watershed for each stream reach (WT) (McKenna et al., 2010). Previous research (McKenna et al., 2006) used a series
of multivariate analyses to eliminate highly correlated variables and identify the most influential of these habitat variables within the
Great Lakes-Allegheny portion of New York. In this study, the 10 - 23 habitat variables most influential to the rare darters or the
species assemblage were used to develop each NN model (Table 1). While the fish observations were limited to New York State,
habitat attributes were available for all stream reaches within the Allegheny watershed downstream to the confluence of French Creek
with the Allegheny River in Pennsylvania.
Appendix S2. Assemblage identification and model development methods details
The Great Lakes-Allegheny Modelling Unit is a large region of NY (including the Allegheny and all the New York Great
Lakes watersheds) and contains a wide range of habitats. Each field sample was considered a replicate representative of the fish
assemblage found within the stream reach from which it was collected. The Bray-Curtis similarity index and the UPGMA linkage
method were used with 1,000 bootstrap samples to test the significance of each cluster linkage at the α = 0.05 level. All sample
assemblages identified by the cluster analysis as a particular type were averaged to determine the fractional component of total fish
abundance contributed by each species, including rare darters. While the rare darter species in this study are limited to the Allegheny
drainage, they were identified as parts of assemblages whose more common species are also found elsewhere in the region.
We used the simplest backpropagation NN architecture with a single layer of hidden neurons, each hidden neuron applying a logistic
activation function (McKenna & Castiglione, 2010; McKenna & Johnson, 2011). The number of input neurons in the first layer was
equal to the number of habitat variables used and each applied a linear scaling function [-1, 1]. Species-specific models had a single
output neuron (with logistic activation function), while assemblage models had one output for each of the assemblage types that
contained a rare darter and the most heavily weighted output neuron determined the assemblage type predicted to occupy the stream
reach. During development of each model, 20% of the data (randomly selected) was held out (i.e., not used in training) to validate the
results and to prevent over-learning (Olden et al., 2002; McKenna 2005; McKenna & Castiglione 2010; McKenna et al., 2010). Each
test set was examined to ensure that some records of the species’ presence were included. Neural network training continued until 107
learning events had occurred without improved accuracy in prediction of test set values. Learning (0.1) and inertia (0.1) rates were
implemented to ensure global, rather than local, convergence during training. Each species-specific NN was trained to predict the midpoint of the observed abundance class values for that species. Raw predictions are real numbers from which the mean squared error
(MSE) and Coefficient of Determination (R2) were computed to measure the amount of variability explained by the model. The NN
configurations were selected because they were the simplest sufficient to achieve R2 ≥ 0.8. Those raw predictions were then classified
into the log-scale abundance classes (0 = class 0, > 0 – 1.5 = class 1, and > 1.5 = class 2 – 10). Omission (i.e., predictions of absence
where the species was known to be present) and commission error rates (i.e., false positives) were then computed to measure the NN’s
ability to correctly predict presence or absence. Cohen’s Kappa was also computed (using only samples from the Allegheny watershed
in New York), because it is a commonly used index combining omission and commission error (Manel et al., 2001, Allouche et al.,
2006). However, commission error, is not emphasized here because there are many collection effectiveness and habitat modification
issues that might explain the absence of a species from a suitable location (e.g., poor collection methods or efficiency, misidentification, local acute pollution, restricted access and opportunities to invade, etc.), but that are not a reflection of model
performance; this is especially true with rare species. The magnitude and direction of weights of each habitat variable input to each
NN model were determined by tracing the changes in weight of each variable through the neural network. This is the best method for
determining weights and direction of effect (i.e., positive or negative) (Olden et al., 2004; McKenna, 2005; McKenna et al., 2010).
Appendix S3. Exclusive model predictions for (a) spotted darter and (b) variegate darter in the vicinity of collection sites through 2002
(pre-2003) and post-2002. Line shade and thickness indicate predicted darter abundance within each stream reach.
a.
b.
Lake Erie
New York
Appendix S4. Neural network input weights for (a) species-specific (the left ordinate indicates weights for the variegate darter models
and the right ordinate indicates weights for the spotted darter model) and (b) assemblages-based models. Definitions of habitat
variables are given in Table 1. The ordinates indicate the relative weight that the NN places on each input variable and the direction of
the effect.
8
1
6
0.8
0.6
Relative Weight
4
0.4
2
0.2
0
0
-0.2
-2
-0.4
-4
-0.6
-6
-0.8
-8
-1
Longhead Darter
Variegate Darter
Spotted Darter
Relative Weight (SPDT)
a.
b.
Appendix S5. Interpretation of neural network input variable weights
The longhead darter model emphasized high values of July precipitation and non-row crop agriculture and low values of local
watershed July air temperature, forest cover, and landscape slope (See Appendix S4 in Supporting Information, Figure a). Local forest
cover, watershed-wide landscape slope and growing degree-days (GDD), and riparian agriculture were positively weighted in the
spotted darter model; a suite of climate, land use, and landscape configuration variables were negatively weighted. Local watershed
influences dominated the variables emphasized in the variegate darter model. Watershed size (Down Length), summer climate
variables, and forest cover had the strongest positive weights, while local watershed landscape slope and GDD had the strongest
negative influence.
The proportion of agriculture within the total riparian corridor had the strongest positive influence on occurrence of
Assemblage 17 (See Appendix S4 in Supporting Information, Figure b). Assemblage 19 was associated with a positive effect of Down
Length, local watershed slope, and proportion of agriculture in the total riparian corridor. The strongest negative influences were local
watershed GDD and proportion of total watershed forest cover. The occurrence of assemblage 26 was associated with high values of
mean annual air temperature and low values of July air temperature within the local watershed and GDD throughout the watershed.
Assemblage 31 was predicted to occur where Down Length and Down Order were large and predicted water temperature was low.
Assemblage 36 was the rarest type predicted and was expected to occur where predicted water temperature and local watershed slope
were high.
Appendix S6. Predicted vs. observed habitat conditions for spotted darter and variegate darter.
High abundances of variegate darter were expected in areas of somewhat steeper riparian slopes and more extensive forest cover than
the average collection site (Figure a). Streams predicted to contain marginal variegate darter habitat were smaller and in higher
elevation areas with steeper landscape slopes and more extensive forest cover than collection sites. Habitat conditions in the single
stream reach where spotted darter were found deviated in magnitude, and sometimes direction, from those of the set of stream reaches
where the Exclusive model predicted the fish could occur (Figure b). Comparisons with fish samples collected after 2002 showed that
predicted optimal variegate darter habitat was expected in areas with cooler water temperatures and somewhat flatter local watershed
slope than at recent collection sites (Figure a). Marginal variegate darter habitats were expected to be in smaller, higher elevation
streams, with less extensive forest.
Figures show habitat signatures for field collections within each time period (pre-2003 and post-2002) and model predictions by
abundance class (marginal habitat or optimal); the spotted darter occurred in only one class of abundance. The left ordinate indicates
average values of habitat conditions at sites where (a) variegate darter and (b) spotted darter were collected relative to the mean of
values for all stream reaches in the Allegheny watershed. The right ordinate indicates average values of habitat conditions in stream
reaches where the exclusive model predicted the species to occur relative to the mean of values for all stream reaches in the Allegheny
watershed.
a.
1.5
1.2
1
0.7
0.5
0.2
0
-0.3
-0.5
-0.8
-1.3
-1
-1.8
-1.5
<2003
b.
>2002
Optimal
Marginal
Deviation (Predicted)
Deviation (Observed)
1.7
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
1.5
1
0.5
0
-0.5
-1
-1.5
-2
Observed
Predicted
References:
Allouche, O., Tsoar, A. & Kadmon, R. (2006) Assessing the accuracy of species distribution models: prevalence, kappa
and the true skill statistic. Journal of Applied Ecology, 43, 7 1223–1232.
Manel, S., Williams, H.C. & Ormerod, S.J. (2001) Evaluating presence-absence models in ecology: the need to account
9 for prevalence. Journal of Applied Ecology, 38, 921–931.
Olden, J.D., Jackson, D.A. & Peres-Neto, P.R. (2002) Predictive models of fish species distributions: a note on proper
validation and chance predictions. Transactions of the American Fisheries Society, 131, 329–336.
Olden, J.D., Joy, M.K. & Death, R.G. (2004) An accurate comparison of methods for quantifying variable importance in artificial neural networks using simulated data. Ecological Modelling, 178, 389–397.
Deviation (Predicted)
Deviation (Observed)
2