1

Upper Mississippi River and Great Lakes Region Joint Venture

Technical Report No. 2014-1

Modelling Great Lakes Piping Plover Habitat Selection during the Breeding Period From Local

to Landscape Scales

Benjamin M. Kahler,

Upper Mississippi River and Great Lakes Region Joint Venture, U.S. Fish and Wildlife Service, 2651 Coo-

lidge Road, East Lansing, MI 48823

Vincent S. Cavalieri,

Ecological Services, U.S. Fish & Wildlife Service, 2651 Coolidge Road, East Lansing, MI 48823

INTRODUCTION

Effective planning, evaluation and delivery of conservation actions rely on an under-

standing of species’ ecology. In the absence of perfect knowledge, researchers and managers

should work collectively and use the best available information to develop habitat management

prescriptions in an adaptive management framework. Important decisions should be continual-

ly improved through evaluation addressing key knowledge gaps, particularly those factors per-

ceived to most limit population growth for a target species. Our understanding of species ecol-

ogy and life-history requirements drives the formulation of conceptual and inferential models

for bird habitat conservation (National Ecological Assessment Team 2006). Meaningful man-

agement objectives can be set by understanding the biological processes involved in controlling

the distribution of a species (Young and Hutto 2002). Furthermore, new information and a

more refined understanding of species ecology can increase the efficacy of habitat conservation

planning and delivery efforts (USFWS 2008).

Monitoring is essential to assess wildlife population status and trends of a species. Mon-

itoring data can also be used to inform understanding of species ecology including its distribu-

tion in time and space, and to assess species-habitat associations at multiple spatial scales. In-

creasingly the prediction of a species distribution from survey data is an important component

of conservation planning (Guisan and Zimmerman 2000, Scott et al. 2002, Johnson and Gilling-

ham 2005).

For example, distribution modeling is used to predict species occurrence in previously

unsampled sites by identifying biologically important variables (Young and Hutto 2002). Model-

ing the distribution of a species, also called an ecological or environmental niche, uses associa-

tions between species occurrence records and environmental variables to identify conditions in

2

which populations can be maintained (Austin 2002, Pearson 2007). Because there is no one

best method for modeling distribution, many studies have used a comparative approach (e.g.,

Moisen and Frescino 2002, Thuiller et al. 2003, Muñoz and Felicísimo 2004).

Ecological niche modeling methods can include those that use combinations of recorded

species presence, absence, and/or pseudo-absence (Austin 2002). Detailed descriptions of

these commonly used presence only, presence/pseudo-absence, and presence/absence meth-

ods have been previously described (Austin 2002, Guisan and Thuiller 2005, and Elith et al.

2006). Applying different modeling algorithms to the same survey data may lead to very differ-

ent predictions of a species’ distribution, mainly due to slight differences in the statistical struc-

ture and assumptions of each algorithm (Austin 2002). Brotons et al. (2004) found pres-

ence/absence models were more accurate than presence-only models, concluding that absence

data provides information that is useful and reliable in model calibration.

Many techniques have been developed to model the distribution of a species for con-

servation planning (Guisan and Thuiller 2005). Advances in quantitative methods, including ge-

ographic information systems (GIS) and remote sensing techniques, have enabled researchers

and managers to incorporate “landscape-level” measures into ecological research (Bissonette

1997, Klopatek and Gardner 1999, Turner et al. 2001) and to model species-habitat associations

at multiple spatial scales to predict species distributions (Scott et al. 2002). Predictive models

illustrate and infer the suitability of potential habitats when linked to a GIS. Many studies have

used GIS to analyze wildlife-habitat associations at multiple spatial scales (e.g., Naugle et al.

1999, Scott et al. 2002, and Elith et al. 2006).

The Piping Plover (Charadrius melodus) is a small species of shorebird endemic to

North America (Eliot-smith and Haig 2004, Wemmer et al. 2001). There are three recognized

breeding populations: the Northern Great Plains, Atlantic Coast and the Great Lakes (Eliot-

Smith and Haig 2004, USFWS 2003). While all three are imperiled, and were federally listed un-

der provisions of the Endangered Species Act

(ESA) in 1986, the Great Lakes population is by

far the smallest and most at risk and is listed as

endangered; the other two are listed as threat-

ened (Wemmer et al. 2001, USFWS 1985,

USFWS 2003). The Great Lakes Piping Plover

population was estimated to be between 492

and 682 breeding pairs in the late 1800s-early

1900s but only 17 pairs were recorded in the

entire Great Lakes basin at the time of listing

(Russell 1983, USFWS 1985).

V. Cavalieri

3

Habitat loss and degradation from development, as well as increased disturbance due to

an increase in recreational use of beaches, are believed to be among the primary causes leading

to the decline of the Great Lakes Piping Plover population, although other factors have also

contributed (Russell 1983, USFWS 1986, Wemmer et al. 2001, USFWS 2003, Haffner et al.

2009). Since listing, development of Great Lakes shoreline for residential, commercial and rec-

reational properties has continued to accelerate in some areas, resulting in reduced Piping

Plover nesting habitat at these sites (Wemmer et al. 2001). Conversely, fluctuating Great Lakes

water levels can significantly change coastal shorebird habitat (Potter et al. 2007), and the area

available to breeding Piping Plovers has likely expanded to relatively low Great Lakes water lev-

els since 1997. Protecting and monitoring as many Piping Plover nests as possible is very im-

portant for the recovery of this critically endangered species. Additionally, a better understand-

ing of Piping Plover habitat selection and use will provide managers with the tools they need to

be able to make important management decisions that will aid in the recovery of this very rare

shorebird.

Piping Plover research in the Great Lakes basin has enabled managers to determine

basic habitat characteristics for nesting locations. Typical nesting habitat consists of wide sand

or cobble beaches with sparse vegetation on Great Lakes shorelines (Powell and Cuthbert 1992,

Pike 1985, Wemmer et al. 2001, USFWS 2003). This understanding allowed for the designation

of Great Lakes Piping Plover critical habitat. Critical habitat is defined by the ESA as areas on

which have the physical or biological features (i.e., primary constituent elements) that are es-

sential to the conservation of the species and where there may be special management consid-

erations for protection (USFWS 2003). Only locations that have the primary constituent ele-

ments are considered critical habitat. The primary constituent elements for Great Lakes Piping

Plovers as defined in the critical habitat rule are “island and mainland shorelines that support

open, sparsely vegetated, sandy habitats, such as sand spits or sand beaches, that are associat-

ed with wide, unforested systems of dunes and inter-dune wetlands” (USFWS 2003). Additional

primary constituent elements include a total beach area of at least 2 ha, at least 50 m of beach

where beach width is greater than 7 m and a distance to tree line from the normal high water-

mark of more than 50 m. The location must also have low levels of disturbance from humans

and pets (USFWS 2003). While these primary constituent elements and associated critical habi-

V. Cavalieri

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tat have allowed for the protection of many Great Lakes Piping Plover habitats, the recent ad-

vancements in Geographic Information Systems and remote sensing techniques allow for a

broader examination of Piping Plover habitat across different spatial scales. We developed and

assessed spatially explicit models of Piping Plover presence and habitat use in Lakes Michigan,

Huron, and Superior. This allowed us expand efforts to predictively map Piping Plover habitat in

the Great Lakes region.

In addition to its federal status, the Piping Plover is a Joint Venture (JV) focal shorebird

species representing beach foraging habitats in the Upper Mississippi River and Great Lakes JV

region (Potter et al. 2007). Biological models for Piping Plovers were not developed in the 2007

JV Shorebird Habitat Conservation Strategy (Potter et al. 2007) due to a lack of adequate spatial

data and the dynamic nature of Piping Plover breeding and migration habitats. Nevertheless,

population estimates and goals for Piping Plover were translated into protection and restora-

tion objectives for beach habitat in the JV region (UMRGLR JV 2007).

The goal of this study was to use three analytical approaches to determine the land-

scape habitat features associated with the distribution of Piping Plovers in the U.S. Great Lakes

region. Our study is the first effort to evaluate landscape suitability for the Great Lakes Piping

Plover across the majority of its current geographic breeding extent in the U.S. Great Lakes re-

gion and our results will further JV planning efforts by updating understanding of quantifiable

habitat associations and assist in evaluating regional habitat requirements and objectives. In

addition, understanding the distribution of landscape suitability for Great Lakes Piping Plover

will enhance targeting of monitoring activities, understand what it may require to make areas

more suitable for Piping Plover through habitat restoration efforts, and provide a means to as-

sess areas designated as critical habitat for the Piping Plover. To achieve this goal, we asked two

questions.

1. What is the distribution of landscape suitability for Piping Plover across its current

breeding extent in Michigan, USA?

2. What are landscape metrics associated with Piping Plover nest locations in this re-

gion?

To address these questions we compare three analytical approaches to estimate landscape

suitability for Piping Plover across its geographic breeding extent in Michigan, USA (Figure 1).

This approach provides a suite of model predictions within a matrix of user familiarity and com-

prehension and statistical complexity and appropriateness. All models presented have utility in

understanding habitat selection by Piping Plover. By presenting and evaluating the performance

of different models we empower the user to choose which model(s), if any, have potential for

assessment in the field and/or the enhancement of population monitoring and habitat conser-

vation and restoration activities.

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Figure 1. Geographic extent of nest records and landscape modelling for

Piping Plovers in Michigan, USA.

METHODS

Nest locations

Monitoring efforts for Great Lakes Piping Plover have lacked systematic, unbiased col-

lection of data out of logistical and financial necessity. Biologists attempt to locate every Piping

Plover nest in the Great Lakes each breeding season (LeDee et al. 2010). Monitoring efforts are

largely targeted at locations where Piping Plovers have been previously recorded, particularly in

recent years (LeDee et al. 2010). Other locations having appropriate habitat conditions, but no

recent records, are checked more opportunistically. Each nest location is recorded with a GPS

unit and added to a nest location database. Piping Plovers exhibit strong breeding philopatry

(site fidelity; Haig and Oring 1988), nesting in close proximity to breeding territories from previ-

ous years for the duration of their adult life (believed to be ~5 years; Wilcox 1959, Elliot-Smith

and Haig 2004). In an effort to reduce pseudo-replication among nest locations in the analysis,

we used Piping Plover nest locations from recent years (2000—2010), separated by 5 years be-

tween time periods (further description below).

Predictor variable estimation

We hypothesized local and landscape variables (Table 1) that would predict presence of

Piping Plover nests during the breeding season based on current understanding of life-history

requirements, species-habitat associations, and expert opinion. These variables were surro-

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gates for local and landscape processes that influence habitat selection by Piping Plover either

directly or indirectly. We gathered spatial data from several sources (Table 1) and generated 30

m resolution raster coverages for each variable across the study area using ModelBuilder work-

flows in ArcGIS 10.0 (ESRI, Redlands, California, USA).

Analysis

We modeled the probability of Piping Plover nest occurrence using three modeling algo-

rithms: Generalized Additive Models (GAM; Hastie and Tibshirani, 1986, 1990, Yee and Mitchell

1991), Boosted Regression Trees (BRT; Elith et al. 2008), and Maximum Entropy models

(MAXENT; Phillips et al. 2006, Phillips and Dudík 2008). The first two algorithms are more wide-

ly understood and best suited for modeling species-habitat associations where systematic sam-

pling has led to recorded species presence and absence; two aspects absent in monitoring Pip-

ing Plover in the Great Lakes region. The third algorithm is lesser known and was developed to

study species-habitat associations and predict geographic distribution of species in the absence

of systematic sampling and known absence (e.g., museum specimens).

Each method required us to generate pseudo-absence or background locations to pair with

nest locations in analyses. We used generalized random-tessellation stratified (GRTS) design to

select pseudo-absence and background locations (Kincaid et al. 2008), and we used National

Land Cover Database (NLCD) from years most closely matching Piping Plover nest site data used

for model development.

We created separate sampling timeframes for the years 2001 and 2006 based on NLCD spa-

tial data. For GAM and BRT analyses, we paired nest locations from the year 2000 (n=34) with

spatial data from 2001 (Homer et al. 2007); paired nest locations from the years 2005 (n=57)

and 2010 (n=51) with NLCD spatial data from 2006 (Fry et al. 2011) (Table 2). We created coast-

line extents by buffering coastline derived from NLCD spatial data by 2.4 km for each time peri-

od. For GAM and BRT analyses we drew pseudo-absence locations only from areas within

coastal extents classified as barren cover. We drew unstratified, equal probability samples for

pseudo-absence locations at a 1:3 ratio (nests: pseudo-absence) for 2001 (n=102) and 2006

(n=324) coastal extents in R 2.15.1 (R Development Core Team 2012).

We combined nest records and pseudo-absence locations for GAM and BRT analyses and

divided them into separate training (70%) and testing (30%) sets using equal probability GRTS

sampling, stratifying the sample in proportion to nests in the year 2000 and nests in the years

2005 and 2010. For MAXENT analyses we paired nest locations (n=53) and spatial data from the

year 2006 (Table 2). We drew unstratified, equal probability samples for background locations

(n=5000) within the 2006 coastal zone extent in R. We extracted values of predictor variables

(i.e., local and landscape habitat characteristics) to nest and pseudo-absence/background loca-

tions.

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Table 1. Predictor variables used in analyses of Piping Plover nest occurrence in its recorded geographic breeding extent in Michigan, USA.

Scale

Type Abbreviation Description Local Landscape Unit Source

Non-anthropogenic BA100M Barren cover within 0.1 km radius X % National Land Cover Database

BA1KM Barren cover within 1 km radius X % "

WDY100M Woody cover within 0.1 km radius X % "

WDY1KM Woody cover within 1 km radius X % "

WDY10KM Woody cover within 10 km radius X % "

D2WDY Distance to woody cover X m "

D2RIV06 Distance to stream/river X m National Hydrography Dataset

Anthropogenic DVT100M Developed cover within 0.1 km radius X % National Land Cover Database

DVT1KM Developed cover within 1 km radius X % "

DVT10KM Developed cover within 10 km radius X % "

RD100M Road density within 0.1 k m radius X internal TIGER/Line roads

RD1KM Road density within 1 km radius X internal "

RD10KM Road density within 10 km radius X internal "

D2RD Distance to road X m "

D2DVT Distance to developed cover X m National Land Cover Database

Topographic PERSLOPE Slope X % x10 Digital Elevation Model

D2COAST Distance to coastline X m National Land Cover Database

Categorical SANDY Geomorphological shoreline classification X binary U.S. Army Corps of Engineers

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Modela MAXENT

Nest Year 2000 2005 2010 2006

NLCDb Year 2001 2006

Number of Piping Plover nests 34 57 51 53

Number of pseudo-absence samples 102

Number of background samples 4,603

Geographic domain of pseudo-absence

/ background points

Barren land within 2.4

km buffer of 2001

Great Lakes coastline

2.4 km buffer of

2006 Great

Lakes coastlineaBoosted Regression Trees, BRT; Generalized Additive Models, GAM; Maximum entropy, MAXENT

bLandscape metrics derived from National Land Cover Database (NLCD) 2001 Version 2 or 2006. Pseudo-

absense paired with nests from 2005 and 2010 were based on NLCD 2006.

Table 2. Pairings of Piping Plover nest records and pseudo-absence / background samples used to

estimate probability of Piping Plover nest occurrence in its recorded geographic breeding extent in

Michigan, USA

BRT and GAM

Barren land within 2.4

km buffer of 2006

Great Lakes coastline

2006

325

Generalized Additive Models:

A pairwise Spearman’s rank correlation matrix was generated for all continuous variables

(Appendix A). We created a suite of a priori candidate habitat models including alternative habi-

tat models that included combinations of 1) non-anthropogenic predictors, 2) anthropogenic

predictors, 3) topographic predictors, and 4) categorical descriptors of local habitat characteris-

tics for both local and landscape scales (see Table 1). We selected one predictor variable in

models where variable pairs were significantly correlated (r > 0.70), keeping the variable with

the most likely biological influence, or the variable at the smaller scale, when no clear ecological

distinction existed (e.g., WDY1M vs. WDY10KM). All candidate GAMs assumed a binomial error

distribution with logit link function. A null model was included in the candidate model set. Only

main effects were considered (i.e., interactions among predictor variables were not considered)

due to sample size considerations.

We partitioned these data into separate training (70%, n = 315) and test (30%, n = 135) sets

prior to model selection procedures using a spatially-balanced sampling procedure (GRTS; Kin-

caid et al. 2008). This approach ensured spatial distribution of species presence and pseudo-

absence across the study area in each of the sets.

We used a two-stage model ranking and improvement approach on the training data set to

select the best GAM among the suite of a priori models. First, model selection on a priori GAMs

proceeded on Akaike’s Information Criterion (AIC; Burnham and Anderson 2002). Best model(s)

were identified as those for which there was substantial empirical support (ΔAIC < 4; Burnham

and Anderson 2002). Model selection was conducted for GAMs using binomial logistic regres-

sion with logit link function. We added cubic spline smoothing terms to all continuous variables

in all GAMs with a maximum of 4 degrees of freedom and set gamma (a penalty term that is a

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multiplier for the model degrees of freedom and the AIC criteria) equal to 1.4. This reduces

overfitting of smoothing functions and produces increasingly smoothed models without much

degradation in prediction error performance (Wood 2006). Secondly, we sequentially removed

non-significant smoothing functions (effective degrees of freedom, edf= 1) and non-significant

(P > 0.075) variables among best models (ΔAIC < 4). GAM analyses were fit using the gam pack-

age (Hastie and Tibshirani 1996, Venables and Ripley 2002) in R.

Boosted Regression Trees:

Boosted regression trees (BRT), a relatively new technique used to model species distri-

butions (Elith et al. 2006) uses a combination of machine learning (ML) and statistics. Statistical

modelling approaches assume there is an appropriate model and that they estimate parame-

ters from the available data. Machine learning approaches, however, use an algorithm to learn

the relationships between the response and its predictors. Instead of focusing on questions re-

lated to model architecture (e.g., should the user include interaction terms, or are effects addi-

tive?), ML algorithms try to learn the response by learning from the relationships among the

response and parameter inputs by finding dominant patterns. BRT incorporates techniques

from these two approaches by combining the use of classification and regression tree models

with “boosting". Instead of producing a single “best” classification or regression tree model,

BRT uses a forward, stagewise procedure for improving model accuracy (i.e., boosting), which

combines many hundreds or thousands of simple tree models to adaptively optimize predictive

performance (Elith et al. 2008).

To create optimized BRT models for we fit an initial BRT model with a learning rate (con-

tribution of each tree to the final model) set between 0.001 and 0.01, a bag fraction (propor-

tion of data subsampled for each tree) to 0.50, and a tree complexity (number of interactions

among predictor variables) < 3 that achieved lowest mean predicted deviance and > 1,000

trees. The model was simplified by identifying and removing the least informative predictors

where the average change in predicted deviance exceeded its original standard error (Elith et

al. 2008), maintaining the constraints listed above. We determined the relative importance of

each predictor variable (% contribution to fitted model) and created partial dependence plots

(visualizations of fitted functions) for the most informative variables (up to 12) in fitted models.

Finally, we determined whether there were substantial two-way interactions among predictor

variables (Elith et al. 2008). Boosted Regression Trees were fit using the gbm package (Ridge-

way 2013) in R.

Maximum entropy models:

Maximum entropy (MAXENT) models are generally not well known among wildlife scien-

tists. However, this modelling technique has the benefit of not requiring systematic sampling to

identify occurrence locations. Therefore, it allows predictions from non-systematic survey data

such as targeted monitoring and museum specimens making it highly useful for estimating

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population distributions of species where adequate data may not be available. MAXENT is a

presence-only method that predicts landscape suitability by minimizing relative entropy be-

tween probability densities of species occurrences and background locations in covariate space

(Phillips et al. 2006; also see Elith et al. 2011 for a detailed explanation of the MAXENT model

with case study examples).

We used a two-stage procedure to eliminate variables that provided little to no benefit

to predictive performance in the final model. First, we ran a MAXENT model including all pre-

dictor variables except percent barren cover within 0.1 km (BA100M) which we assumed was a

nuisance variable in a coastal context (entire 2.4 km coastline buffer) given that Piping Plover

nests are only located in these areas. For each model run, twenty-five percent (25%) of nests

(n=13) were withheld for internal model testing. We eliminated variables for which univariate

jackknife estimates of area under the Receiver Operating Characteristic (ROC) curve (AUC, see

next section for description) on test data were < 0.6, indicating low information contribution to

overall model. A second MAXENT model was generated on the reduced parameter set. We de-

termined the relative importance of each predictor variable based on percent contribution to

the fitted model and resulting drop in training AUC normalized to percentages. We created de-

pendence plots - visualizations of fitted functions reflecting the dependence of predicted suita-

bility on the selected variable and on dependencies induced by correlations between the se-

lected variable and others - for the most informative variables (up to 12) in the final model.

MAXENT models were run with MAXENT version 3.3.k (Phillips et al. 2006;

http://www.cs.princeton.edu/~schapire/maxent/).

Model evaluation

Evaluation indices were calculated for the three final models using test data withheld

from GAM and BRT analyses (see explanation above). We used five global measures of map ac-

curacy (evaluation indices) to assess the predictive performance of final models: sensitivity,

specificity, overall prediction success (OPS), Kappa (Cohen 1960), and the area under a Receiver

Operating Characteristic curve (AUC). The first four of these indices were dependent on a pre-

determined threshold (Table 4). Threshold-dependent evaluation indices were derived from a

confusion matrix, a 2 x 2 classification table that describes the agreement between the ob-

served presence and absence (or pseudo-absence) of a species and the predicted presence and

absence (or pseudo-absence) of a species at a given threshold value. Model evaluation thresh-

olds were set equal to prevalence (proportion of sites with recorded presence among all sites)

of Piping Plover in the test data (Manel et al. 2001, Cramer 2003, Liu et al. 2005).

Sensitivity (true positive fraction) and specificity (true negative fraction) measured the

proportion of sites where the observations and the predictions were in agreement. Sensitivity

reflects a model’s ability to detect presence given that a species actually occurs at a location

(Fielding and Bell 1997). Specificity is the inverse of sensitivity and reflects a model’s ability to

predict an absence where a species does not exist. Overall prediction success (OPS), also known

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as correct classification rate, is a measure of the accuracy of predicting true presences and ab-

sences among all evaluation sites. Kappa measures the proportion of correctly predicted sites

after the probability of chance agreement has been removed (Moisen and Frescino 2002). Kap-

pa values of 0.0-0.4 indicate poor model performance, values of 0.4-0.75 good, and > 0.75 ex-

cellent (after Landis and Koch 1977). All threshold-dependent evaluation indices are sensitive to

species prevalence, although this is true to a lesser extent for Kappa (Manel et al. 2001).

The area under the ROC curve (AUC) provides a single measure of the overall model ac-

curacy by incorporating model performance indices across all threshold values (Pearce and Fer-

rier 2000). Values of AUC range from 0.5 to 1.0. The ROC plot for a poor model will lie near the

diagonal where the true positive rate equals the false positive rate for all thresholds, and has a

predictive ability equivalent to random assignment (AUC = 0.50). A good model will achieve a

high true positive rate (sensitivity) while the false positive rate (1-specificity) is still relatively

small, resulting in a ROC curve that rises steeply at the origin, then levels off at a value near the

maximum of 1 (see Figure 7 for example). Models with AUC values of 0.5-0.7 are considered to

have low discriminatory ability, while values of 0.7-0.9 indicate moderate, and > 0.90 indicate

excellent discriminatory ability (Swets 1988). Model evaluations were conducted using the

PresenceAbsence package (Freeman and Moisen 2008) in R.

Spatial prediction

Spatial prediction surfaces were generated in R using package raster (Hijmans and van

Etten 2012) and ArcGIS 10.0 (ESRI, Redlands, CA). Thirty meter (30 m) resolution surfaces were

mean-aggregated to 900 m and smoothed with a high pass filter for presentation in figures.

Prediction surfaces for each of the three modeling algorithms were averaged to create a “mosa-

ic model” representing mean correspondence (congruency) among models.

RESULTS

Generalized Additive Models

Models with combinations of anthropogenic, non-anthropogenic, and topographic vari-

ables tended to rank higher (higher empirical support) and models with only anthropogenic var-

iables tended to rank lower (lower empirical support) among the suite of a priori candidate

habitat models (Appendix B). Likewise, models with greater complexity (higher number of pre-

dictor variables) tended to rank higher than simpler models, suggesting variables chosen are

complementary to each other and each explains unique amounts of the variation in the data.

All a priori candidate habitat models were improvements over the null model.

The best supported model (∆AIC < 2) for probability of Piping Plover nest occurrence in-

cluded percent developed cover within 10 km radius (DVT10KM), percent barren and woody

cover within 1 km radius (BA1KM, WDY1KM), distances (m) to river mouth (D2RIV06), woody

cover (D2WDY), and coastline (D2COAST), and with sandy shoreline classification (SANDY) (Ta-

ble 3). Observers were 17.2 times (95% CI: 4.87-60.90) more likely to locate nests in areas with

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sandy shoreline classification (SANDY). Nest occurrence was more likely to occur in areas with <

60% barren cover within 1 km radius (BA1KM; Figure 2). Areas where BA1KM > 60% include in-

terior portions of large dune complexes (e.g., > 500 m from shoreline at Sleeping Bear Dunes).

Probability of nest occurrence decreased with higher percent developed cover within 10 km

radius (DVT10KM); odds of nest occurrence decreased by 42.3% (95% CI: 27.0-54.5) for every

1% increase in DVT10KM. Nests were more likely to occur at least 250 m from woody cover

(D2WDY; Figure 2). Probability of nest occurrence decreased with higher percent woody cover

within 1 km radius (WDY1KM); odds of nest occurrence decreased by 3.4 % (95% CI: -0.6-6.8)

for every 1% increase WDY1KM. Odds of nest occurrence also declined by 0.03% (95% CI: 0.0-

0.05) for every 1 m from river mouth (D2RIV06). Nest occurrence was more likely to occur with-

in 600 m of the coast (D2COAST; Figure 2)

Parameter Estimate (β)

Standard

error Wald's χ2

degrees of

freedom (df )

Effective

df

Relative

df p

Odds ratio

(eβ)

Linear predictor

(Intercept) -13.7246 6.4750 -2.12 1 0.034 NA

DVT10KM -0.5507 0.1199 -4.59 1 <0.001 0.58

WDY1KM -0.0349 0.0181 -1.93 1 0.054 0.97

D2RIV06 -0.0003 0.0001 -2.34 1 0.019 1.00

SANDY 2.8458 0.6430 4.43 1 <0.001 17.22

Non-linear predictor

D2WDY 22.80 2.15 2.53 <0.001

BA1KM 14.46 2.77 2.95 0.002

D2COAST 6.39 2.01 2.06 0.044

Table 3. Parameter estimates (untransformed logit link function) from final Generalized Additive Model for

Piping Plover nest occurrence across its recorded geographic breeding extent in Michigan, USA Parameter

descriptions are provided in Table 1.

See Figure 2

Figure 2. Partial dependence plots for non-linear predictors [distance (m) to woody cover, D2WDY; per-

cent barren cover within 1 km, BA1KM; distance (m) to coast, D2COAST] in final Generalized Additive

Model of the probability of Piping Plover nest occurrence in its recorded geographic breeding extent in

Michigan, USA. For each plot, there is a greater chance of nest occurrence than absence where y > 0 and

a greater chance of nest absence than presence when y < 0 holding all other variables at their mean val-

ues. Parameter descriptions are provided in Table 1.

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Boosted Regression Trees

The final model had a tree complexity of 3, a learning rate of 0.005, 14 predictor varia-

bles, and was fitted with 1900 trees. Cross-validated AUC from training data was 0.975

(SE=0.008), indicating excellent discriminatory ability on training data. Percent barren cover

within 0.1 km (BA100M) and 1 km (BA1KM) radii had the greatest contribution to the final

model (Table 4) and also had the highest interaction size among paired parameters (231.51).

Partial dependence plots from the final BRT model indicated Piping Plover nests occurrence was

more likely in areas characterized by higher percent barren cover within 0.1 km radius

(BA100M) and low to moderate percent barren cover within 1 km radius (BA1KM) and where

shoreline geomorphological classification (SANDY) suggests a distinct sandy component (Figure

3). Additionally, nest occurrence was more likely further from woody cover (D2WDY) and roads

(D2RD), where road density within 1 and 10 km radii (RD1KM and RD1M) was lower, closer to

river mouths (D2RIV06), where per-

cent woody cover in 1 km radius

(WDY1KM) was lower (Figure 3).

Permutation

importanceb

BRT MAXENT MAXENT

BA100M 20.2

BA1KM 38.9 49.8 18.9

D2COAST 1.5 23.1 41.8

D2DVT 1.4 1.6 0.3

D2RD 1.7 0.1 <0.1

D2RIV 2.4 3.0 0.8

D2WDY 14.1 0.4 0.6

DVT1KM 0.7 0.8

DVT10KM 1.4 0.8 0.5

RD1KM 6.0 < 0.1 0.1

RD10KM 2.3 0.7 1.0

SANDY 4.2 10.5 9.6

SLOPE 1.3

WDY100M 8.2 25.0

WDY1KM 2.8 0.5 0.5

WDY10KM 1.7 0.5 0.2

Percent

contribution (%)a

Variable

bThe drop in training AUC normalized to percentages

when training presence and background values are

randomly permutated.

Table 4. Variable importance in Boosted Regression

Tree (BRT) and Maximum entropy (MAXENT) model of

probability of Piping Plover nest occurrence in its

recorded geographic breeding extent in Michigan, USA.

Parameter descriptions are provided in Table 1.

aScaled measures (sum to 100) of the relative

contribution of the variable to the final model.

V. Cavalieri

14

Figure 3. Partial dependence plots for the most influential variables in the Boosted Regression

Tree model for Piping Plover nest occurrence in its recorded geographic breeding extent in

Michigan, USA. For explanation of variables and their units see Table 1. Variables are ordered

by increasing model contribution in parentheses and are highest in top left and lowest in bot-

tom right. Y-axes are on the logit scale and are centered to have zero mean over the data dis-

tribution. For each plot, there is a greater chance of species presence than absence where y > 0

and a greater chance of species absence than presence when y < 0 holding all other variables at

their mean values. Distance to development (D2DVT, 1.4%) and slope (1.3%) were omitted here

due to low model contribution.

Maximum entropy model

Within the coastal zone context, percent barren cover within 1 km radius (BA1KM), dis-

tance (m) to coastline (D2COAST), and shoreline geomorphological classification (SANDY) had

the greatest contribution to the final MAXENT model (Table 4). AUC value on training data

(0.994) and testing data (0.989, SD=0.003), indicated strong model discriminatory ability. De-

pendence plots from the final MAXENT model indicated Piping Plover nests were more likely to

occur in close proximity to coastline (D2COAST) in areas with low to moderate percent barren

cover within 1 km radius (BA1KM), in areas with a shoreline geomorphological classification

with a distinct sandy component (SANDY), in areas with low percent woody cover within 0.1 km

radius (WDY100M), and more distant to developed cover (D2DVT) (Figure 4).

15

Figu

re 4

. Pro

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16

Model evaluation:

We evaluated performance of the three final models using the locations of Piping Plover

nest occurrence and pseud-absence samples from the GAM and BRT test data set. Overall per-

formance of the three final models was good/moderate to excellent (Table 5) with performance

metrics lower for the final MAXENT model and higher for the final BRT model for all threshold-

dependent metrics. Distribution of predicted probabilities among sites with recorded presence

and pseudo-absence suggests moderate to high discriminatory ability for all models with great-

er ability among final GAM and BRT models (Figure 6). Final models had high overall prediction

success, sensitivity and specificity, and each can be classified as good based on values of Kappa

(Figure 7). Model discriminatory ability of final BRT and GAM models can be classified as excel-

lent based on values of AUC while MAXENT can be classified as moderate (after Swets 1988;

Table 5, Figure 8). Nevertheless, the MAXENT model had excellent discriminatory ability (AUC =

0.989) based on original test data.

Overall, MAXENT appears more conservative and BRT and GAM more liberal in predict-

ing landscape suitability for aggregated model predictions (Figure 8). Although Figure 8 shows

aggregated predictions only, it represents underlying processes at higher resolutions. Lacking a

single best model based solely on evaluation metrics, a mosaic model was created that incorpo-

rates all three together to provide average prediction among model sets and highlight congru-

ency among model predictions.

Table 5. Evaluation indices of model performance from final models of probability of Piping

Plover nest occurrence in its recorded geographic breeding extent in Michigan, USA. Threshold

indices [value (standard deviation); OPS, sensitivity, specificity, Kappa] were based on species

prevalence in test data.

Modela Prevalence OPSb Sensitivityc Specificityd Kappae AUCf

BRT 0.214 0.893 0.971 (0.029) 0.872 (0.030) 0.726 (0.061) 0.971 (0.011)

GAM 0.214 0.874 0.912 (0.049) 0.864 (0.031) 0.675 (0.066) 0.945 (0.018)

MAXENTg 0.214 0.805 0.794 (0.070) 0.808 (0.035) 0.509 (0.074) 0.820h (0.044) a Boosted Regression Tree (BRT), Generalized Additive Model (GAM), Maximum Entropy (MAXENT) b Proportion of all cases correctly predicted (OPS = Overall prediction success) c Proportion of true positives correctly predicted. d Proportion of true negatives correctly predicted. e Proportion of specific agreement. Model performance based on values 0.0-0.4 = poor, 0.4-0.75 = good,

> 0.75 = excellent (after Landis and Koch 1977). f Area under the Receiver Operating Characteristic Curve; Model discriminatory ability based on values

0.5-0.7 = low, 0.7-0.9 = moderate, > 0.9 = excellent (after Swets 1988).

g Evaluation indices for MAXENT were calculated from predicted values at the same nest and pseudo-

absence locations used to evaluate GAM and BRT models. h AUC value on original testing data = 0.989 (0.003), indicating excellent model discriminatory ability.

17

Figure 5. Distribution of predicted probabilities from three models (Generalized Additive Model, GAM;

Boosted Regression Tree, BRT; Maximum Entropy, MAXENT) of probability of Piping Plover nest occur-

rence in its recorded geographic breeding extent in Michigan, USA. For models with good discriminatory

ability, distribution of sites with recorded presence (black) will occur disproportionately at higher pre-

dicted probabilities and sites with recorded absence (grey) will occur disproportionately at lower pre-

dicted probabilities. Note: cross-hatched bars (number of pseudo-absence or background plots with low

predicted probability) are truncated.

Figure 6. Threshold-dependent evaluation indices (sensitivity, specificity, and Kappa) as a function of

threshold from three models (Generalized Additive, GAM; Boosted Regression Tree, BRT; Maximum

Entropy, MAXENT) of probability of Piping Plover nest occurrence in its recorded geographic breeding

extent in Michigan, USA. Model quality is better where Kappa reaches a maximum value and stays at a

higher value for a greater range of threshold values and where lines representing sensitivity and speci-

ficity cross at a higher value.

18

Figure 7. Receiver Operative Characteris-

tic (ROC) plots from models predicting the

probability of Piping Plover nest occur-

rence in its recorded geographic breeding

extent Michigan, USA. ROC plots and as-

sociated Area Under the Curve (AUC) val-

ues are reported for three algorithms

(Generalized Additive, GAM; Boosted Re-

gression Tree, BRT; Maximum Entropy,

MAXENT). Model discriminatory ability

based on AUC value 0.5-0.7 = low, 0.7-0.9

= moderate, > 0.9 = excellent.

V. Cavalieri

19

Figure 8. Probability of Piping Plover nest occurrence in its recorded geographic breeding extent in Michigan, USA, obtained with Generalized

Additive Model (GAM), Boosted Regression Tree (BRT), and Maximum Entropy (MAXENT) models. The mosaic model displays predicted probabil-

ities based on averaged model predictions.

20

Figure 8 (continued).

21

DISCUSSION

Model results point to a variety of factors, including anthropogenic, non-anthropogenic

and topographic variables that influence the selection of Great Lakes Piping Plover habitat. Like

previous work, these model results point to wide beaches on undeveloped Great Lakes shore-

line areas as being the best locations for Piping Plover nesting habitat. What this work does

however, is for the first time predicts the suitability of habitat across much of the state of Mich-

igan based on best fit models. Our analyses of landscapes associated with Great Lakes Piping

Plover nest sites provide a broader understanding of breeding habitat characteristics at multi-

ple scales. These results will help inform annual monitoring program efforts such as determin-

ing new survey locations and associated resource allocations. Additionally, models can contrib-

ute to important habitat management decisions, such as which locations might be most suita-

ble for habitat restoration efforts.

Although our understanding of potential factors limiting population growth throughout

the annual cycle is incomplete, effective habitat conservation and population monitoring for

the Great Lakes Piping Plover during the breeding period remains a critical management foci

(USFWS 2003, Haffner et al. 2009). As part of this effort, each season biologists attempt to lo-

cate every Great Lakes Piping Plover pair so each individual nest can be monitored and protect-

ed. Additionally, population demography has been studied through a long term banding effort,

with > 1100 color-banded Piping Plovers in the Great Lakes since 1993 (LeDee et al. 2010). Even

with high rates of annual banding and detection probability, each season adult Piping are ob-

served that are unmarked. Between 1993 and 2009 an average of 6 breeding adults per year in

the Great Lakes population was un-banded suggesting there may be areas in the Great Lakes

harboring Piping Plovers that remain unmonitored (LeDee et al. 2010). Model results can be

used to identify and prioritize additional suitable habitats to be surveyed for breeding pairs.

Once found new nesting areas can be assessed for protection and monitored to increase nest

success. Furthermore, population estimates (a measure of goal achievement) may be refined

for this Great Lakes cohort.

The Great Lakes Piping Plover population appears to be increasing slowly in recent

years, yet the only population viability analysis (PVA) completed on the Great Lakes segment of

the population suggests it will likely remain vulnerable to extirpation for decades as a result of

environmental and demographic factors (Wemmer et al. 2001). This PVA recommends many

conservation actions such as protecting as many physically suitable breeding sites as possible

and restoring marginally suitable areas to increase habitat quality for breeding Great Lakes Pip-

ing Plover (Wemmer et al. 2001). The PVA indicated that there is likely a shortage of habitat in

the Great Lakes where human disturbance is low enough for the successful breeding of Piping

Plovers and that an increase in permanent protected habitat is likely required for the long-term

recovery of the Great Lakes Piping Plover population (Wemmer et al. 2001). The amount by po-

tential nesting habitat for Piping Plover can now be estimated by combining predictions from

22

models presented here with information about area use during the breeding period (Haffner et

al. 2009).

This project has shown that there are many areas on the Michigan Great Lakes shoreline

where habitat for Plovers is available but perhaps marginal (Figure 9). Some of these areas may

be suitable locations for Great Lakes Piping Plover habitat restoration projects. The models also

suggest that habitat may not be the limiting factor for Piping Plover at this time. However our

methods may not have been able to assess human and domestic animal disturbance at sites or

other factors such as encroachment of vegetation on beaches. It is possible that variables cho-

sen as a proxy of disturbance, such as distance to roads, do not adequately measure true levels

of disturbance at some locations. It may be that many sites that appear suitable according to

these models may have high levels of disturbance making them unattractive locations for

breeding Piping Plovers or that plant succession has led to habitat conditions unsuitable for

Plovers. Future work should focus on including these factors into a similar analysis. Suggested

future actions include efforts to ground-truth model results using localized maps created with a

model layer (Figure 9). For example, biologists familiar with Piping Plover habitat requirements

should visit high likelihood of occurrence sites identified by the model but currently without

breeding plovers to evaluate model usefulness and accuracy. Biologists should also take meas-

urements of habitat variables known to be required by Piping Plovers or to validate model re-

sults or discover potential weaknesses in the model. Additionally, localized maps developed for

ground-truthing efforts should also be used to target locations for additional Piping Plover sur-

veys and ground-truthing results may also help select locations where habitat management can

be used to improve habitat conditions for Great Lakes Piping Plovers.

V. Cavalieri

23

Figure 9. Example of high resolution spatial prediction of Piping Plover nest occurrence two ar-

eas in the study area (bottom two images) based on average landscape suitability among three

algorithms (i.e., mosaic model). The two areas shown are intended to illustrate areas with rela-

tively high (bottom left) and relative low (bottom right) overall probability of nest occurrence.

Gray shading within model predictions (2.4 km coastline buffer) indicates minimal landscape

suitability (probability of Piping Plover nest occurrence = 0).

Model limitations:

An important distinction exists between geographic space and environmental space in

the context of distribution modeling. Ecological niche modeling relates spatially referenced oc-

currence records with environmental conditions (environmental space) to project modeled dis-

tributions onto geographic space (Figure 10). Hutchinson (1957) defined a fundamental niche as

the full range of abiotic conditions within which a species can persist. When plotted in geo-

graphic space, the fundamental niche is referred to as the potential distribution. The actual dis-

24

tribution of a species is the area within its fundamental niche that it truly occupies. When the

actual distribution is plotted in environmental space it is known as a species’ occupied niche

(Pearson 2007). The niche occupied by a species is the actual area where a species occurs and is

viable. However, most methods used to model ecological niches estimate a species’ realized

niche which is not the same as its occupied niche.

Figure 10. Illustration of the relationship between a hypothetical species’ distribution in

geographical space and environmental space. Adapted from Pearson (2007).

Implementing ecological niche modeling methods without accounting for population

demographic parameters results in a species’ realized niche (Dias 1996, Pearson 2007). The re-

alized niche includes the niche occupied by a species and other areas where it cannot persist

(i.e., non-habitat or habitat sinks). A species will occupy areas where it cannot persist locally,

also known as habitat sinks (Pulliam 1988, Pulliam and Danielson 1991). However, habitats may

fluctuate between being habitat sinks (λ < 1) and sources (λ > 1) depending on annual resource

fluctuations (e.g., water and food), predation, and conspecific competition (Pulliam and Dan-

ielson 1991, Dias 1996). Including all spatially referenced occurrence locations for a species in

geographic space in its occupied niche is of limited value in conservation planning without es-

timates of population demography (e.g., survival probability). Therefore, if ecological niche

modeling with species presence/absence data is applied without accounting for source/sink dy-

namics, results will include predictions of areas likely to serve as either population sources or

sinks.

25

ACKNOWLEDGEMENTS

We would like to thank Francesca Cuthbert, Jennifer Stucker and Sarah Saunders for da-

ta access, advice on study design and for reviewing the manuscript. Darin Simpkins, Christie

Deloria, Ted Koehler and Jack Dingledine were instrumental in developing the idea for this pro-

ject and for advice on study design and analysis, as well as manuscript review. We would also

like to thank Greg Soulliere and Rachel Pierce for additional manuscript reviews. Special thanks

to the dozens of plover monitors, grad students and volunteers who collected the Piping Plover

nesting data used in this analysis. Funding for this project came from the Coastal Program of

the U.S. Fish and Wildlife Service.

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29

Appendix A. Spearman rank (rs) correlation matrix of continuous variables considered in landscape distribution models for Piping

Plover in its recorded geographic breeding extent in Michigan, USA.

WDY100M WDY1KM WDY10KM SLOPE RD100M RD1KM RD10KM DVT100M DVT1KM DVT10KM D2WDY D2RIV D2RD D2DVT D2COAST BA100M BA1KM

WDY100M 1.00 0.40 0.09 0.20 0.19 0.14 -0.01 0.15 0.07 0.00 -0.88 0.04 -0.20 -0.15 0.04 -0.46 -0.05

WDY1KM 0.40 1.00 0.37 0.01 0.12 0.11 -0.09 0.14 0.00 -0.13 -0.52 -0.01 -0.18 -0.16 0.00 -0.21 -0.06

WDY10KM 0.09 0.37 1.00 -0.07 0.07 0.15 0.03 0.06 0.13 -0.05 -0.11 -0.22 -0.19 -0.18 -0.04 -0.09 -0.05

SLOPE 0.20 0.01 -0.07 1.00 0.14 0.17 0.28 0.05 0.12 0.20 -0.18 0.12 -0.12 -0.09 0.10 -0.02 0.08

RD100M 0.19 0.12 0.07 0.14 1.00 0.44 0.22 0.79 0.44 0.21 -0.22 -0.15 -0.75 -0.64 0.07 -0.23 -0.06

RD1KM 0.14 0.11 0.15 0.17 0.44 1.00 0.56 0.39 0.91 0.54 -0.15 -0.30 -0.77 -0.73 0.08 -0.26 -0.12

RD10KM -0.01 -0.09 0.03 0.28 0.22 0.56 1.00 0.17 0.58 0.93 0.03 -0.32 -0.45 -0.44 0.19 -0.01 0.06

DVT100M 0.15 0.14 0.06 0.05 0.79 0.39 0.17 1.00 0.44 0.18 -0.22 -0.20 -0.65 -0.73 0.07 -0.29 -0.17

DVT1KM 0.07 0.00 0.13 0.12 0.44 0.91 0.58 0.44 1.00 0.60 -0.08 -0.38 -0.75 -0.80 0.11 -0.24 -0.16

DVT10KM 0.00 -0.13 -0.05 0.20 0.21 0.54 0.93 0.18 0.60 1.00 0.02 -0.39 -0.44 -0.45 0.18 -0.05 0.08

D2WDY -0.88 -0.52 -0.11 -0.18 -0.22 -0.15 0.03 -0.22 -0.08 0.02 1.00 -0.01 0.22 0.19 0.03 0.45 0.08

D2RIV 0.04 -0.01 -0.22 0.12 -0.15 -0.30 -0.32 -0.20 -0.38 -0.39 -0.01 1.00 0.36 0.41 -0.02 0.10 0.18

D2RD -0.20 -0.18 -0.19 -0.12 -0.75 -0.77 -0.45 -0.65 -0.75 -0.44 0.22 0.36 1.00 0.91 -0.06 0.27 0.17

D2DVT -0.15 -0.16 -0.18 -0.09 -0.64 -0.73 -0.44 -0.73 -0.80 -0.45 0.19 0.41 0.91 1.00 -0.07 0.28 0.23

D2COAST 0.04 0.00 -0.04 0.10 0.07 0.08 0.19 0.07 0.11 0.18 0.03 -0.02 -0.06 -0.07 1.00 0.42 0.32

BA100M -0.46 -0.21 -0.09 -0.02 -0.23 -0.26 -0.01 -0.29 -0.24 -0.05 0.45 0.10 0.27 0.28 0.42 1.00 0.45

BA1KM -0.05 -0.06 -0.05 0.08 -0.06 -0.12 0.06 -0.17 -0.16 0.08 0.08 0.18 0.17 0.23 0.32 0.45 1.00

Appendix B. A priori candidate habitat models and null model estimating the effect of variables on the probability of Piping Plover

nest occurrence in its recorded geographic breeding extent in Michigan, USA. The evidence ratio (ωi) indicates the multiplicative

probability by which the best model is more likely than competing models, given the set of candidate models and the data. Parame-

ter descriptions are provided in Table 1.

Model typea Candidate Modelb-2 Log-

likelihoodKc AIC ∆AIC ωi

C π(DVT10KM + D2DVT + WDY1KM + D2RIV06 + D2WDY + BA1KM + SLOPE + D2COAST + SANDY) 131.71 26 161.9 0.0 0.990

C π(DVT10KM + RD1KM + D2DVT + WDY1KM + BA1KM + D2COAST + SANDY) 146.50 20 171.7 9.7 0.008

C π(DVT10KM + D2DVT + WDY1KM + D2WDY + BA1KM + D2COAST + SANDY) 150.96 20 174.0 12.1 0.002

C π(DVT1KM + WDY1KM + BA1KM + SLOPE + D2COAST + SANDY) 164.50 17 182.3 20.4 0.000

C π(DVT10KM + D2DVT + WDY1KM + D2RIV06 + BA1KM + D2COAST + SANDY) 159.33 20 186.6 24.7 0.000

N π(BA100M + BA1KM) 191.39 7 204.5 42.6 0.000

C π(DVT10KM + RD1KM + D2DVT + WDY10KM + BA1KM + SLOPE + D2COAST + SANDY) 183.65 23 209.2 47.3 0.000

N π(WDY1KM + D2WDY + BA1KM) 205.94 10 223.3 61.4 0.000

N π(D2RIV06 + D2WDY + BA1KM) 210.68 10 227.0 65.0 0.000

N π(WDY10KM + D2WDY + BA1KM) 218.01 10 235.0 73.1 0.000

N π(D2WDY + BA1KM) 225.93 7 237.5 75.5 0.000

N π(WDY1KM + BA1KM) 251.97 7 264.2 102.3 0.000

T π(SLOPE + D2COAST + SANDY) 334.67 8 344.4 182.5 0.000

N π(WDY1KM + BA100M) 354.44 7 367.8 205.9 0.000

T π(SLOPE + SANDY) 362.35 5 368.4 206.4 0.000

T π(D2COAST + SANDY) 371.73 5 379.5 217.5 0.000

A π(DVT10KM + RD1KM + D2DVT) 370.96 10 384.3 222.3 0.000

A π(DVT10KM + RD1KM) 397.51 7 403.8 241.8 0.000

A π(DVT10KM) 404.35 4 408.9 246.9 0.000

A π(DVT1KM + RD10KM) 408.44 7 414.4 252.5 0.000

N π(WDY1KM) 407.20 4 414.6 252.7 0.000

A π(DVT1KM) 426.30 4 430.4 268.5 0.000

π(.) 445.94 1 447.9 286.0 0.000

bNatural logarithm of the odds of detection as a function of area and water permanance categories.cK, number of parameters in model; AIC, Akaike's Information Criterion; ∆AIC, difference in AIC relative to top ranked model; w i , relative Akaike

weight

aModel derived from variables considered to be anthropogenic (A), non-anthropogenic or "natural" (N), topographic (T), or including

combinations of these three categorires (C)