Louisiana Waterthrush Density and Productivity in
Hemlock-dominated Headwater Streams:
The Influence of Stream Morphology
Katie B. Barnes, Nicholas Ernst, Michael Allen, Terry Master, and Rabecca Lausch
Northeastern Naturalist, Volume 25, Issue 4 (2018): 587–598
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2018 NORTHEASTERN NATURALIST 25(4):587–598
Louisiana Waterthrush Density and Productivity in
Hemlock-dominated Headwater Streams:
The Influence of Stream Morphology
Katie B. Barnes1, Nicholas Ernst2, Michael Allen3, Terry Master 4,*, and
Rabecca Lausch5
Abstract - We assessed the density and productivity of Parkesia motacilla (Louisiana
Waterthrush) at 4 Tsuga canadensis (Eastern Hemlock)-dominated headwater streams representing
2 distinct stream morphologies: ravines, defined by steep banks and fast-flowing
water; and benches, characterized by braided streams meandering across a flat floodplain.
The Louisiana Waterthrush is an established bioindicator of headwater-stream ecological
integrity used to investigate overall habitat quality. We conducted the study from 2010 to
2013 in the Appalachian Highlands of northeastern Pennsylvania. Pair density and number
of fledglings produced per km of study stream were exceptionally high at the 2 bench sites
compared with the literature, and were significantly higher than in ravine sites, in part due
to significantly higher nest survival on benches (69%) compared to ravines (33%). Double
brooding was also significantly higher on benches. Differences in density, productivity, and
nest survivorship between ravines and benches in our limited study suggest that benches
may be of higher quality for this species. Our results have conservation and management
implications regarding threatened Eastern Hemlock ecosystems, and the topic warrants
further investigation.
Introduction
Determination of habitat quality for birds involves relating the habitat of
a species to its survival and reproduction, often referred to as habitat-fitness
potential (Beerens et al. 2015, Bock and Jones 2004, Wiens 1989). There are 2 approaches
to determining habitat quality: (1) measuring habitat attributes directly
and (2) using bird metrics to infer habitat quality (Johnson 2007). The latter, particularly
the use of reproductive metrics, is considered more effective although
often economically prohibitive (Johnson 2007). The use of measureable attributes
of birds as bioindicators of habitat quality has been well documented (Caro 2010,
Ormerod and Tyler 1993).
Obligate riparian passerine species, especially those confined to headwater
streams, are suitable bioindicators given their characteristic fidelity to the
1Birmingham Audubon Society, 118 North Royal Street, Suite 505, Mobile, AL 36602.
2Rhode Island National Wildlife Refuge, 50 Bend Road, Charlestown, RI, 02813. 3Department
of Ecology, Evolution, and Natural Resources, Rutgers University, New Brunswick,
NJ 08901. 4Department of Biological Sciences, East Stroudsburg University of Pennsylvania,
200 Prospect Street, East Stroudsburg, PA 18301. 5Department of Biological
Sciences, Northern Arizona University, Flagstaff, AZ 86011. *Corresponding author -
tmaster@esu.edu.
Manuscript Editor: Jeremy Kirchman
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immediate stream vicinity and dependence on stream resources for food and nesting
habitat (Buckton and Ormerod 2008, George 2004, Master et al. 2005). These species
possess the hallmark of good bioindicators: they exhibit measurable variations
in behavior and demography that reflect changes in their habitat, and by extension,
differences in habitat quality. Nevertheless, extensive documentation of their suitability
as bioindicators has been limited to relatively few species, in particular
Cinclus cinclus L. (White-throated Dipper) in Eurasia (O’Halloran et al. 1990,
Ormerod and Tyler 1991, Tyler and Ormerod 1994) and Parkesia motacilla Vieillot
(Louisiana Waterthrush), the only obligate stream passerine in the eastern US and
a robust bioindicator of headwater stream integrity (Mattsson and Cooper 2006,
Mulvihill et al. 2008, O’Connell et al. 2003).
In northeastern Pennsylvania, and throughout much of the Appalachian Highlands,
the Louisiana Waterthrush commonly inhabits Tsuga canadensis (L.) Carr.
(Eastern Hemlock, hereafter Hemlock)-dominated headwater streams (Barnes
2014, Ernst 2012, Mattsson and Cooper 2006). These habitats have unique environmental
and biological features, including dense foliage almost to ground level,
deep shade, highly tannic litter, and characteristic aquatic and terrestrial animal
communities (Ross et al. 2004, Snyder et al. 2002). They are currently threatened
by the introduced Adelges tsugae Annand (Hemlock Woolly Adelgid) with potentially
dramatic consequences for associated fauna (Ellison et al. 2005, Evans 2004,
Foster et al. 2014, Toenies 2017).
Preferred aquatic macroinvertebrate prey from the orders Ephemeroptera,
Plecoptera, and Trichoptera (EPT) are commonly associated with these streams
(Barnes 2014, Muenz et al. 2006), but Louisiana Waterthrushes consume a wide
variety of both aquatic and terrestrial organisms (Mattsson et al. 2009, Mulvihill et
al. 2008), thus serving as a link between both ecosystems and enhancing their value
as a bioindicator (Baxter et al. 2005). They are also recognized as a forest interior
species sensitive to habitat fragmentation, which further enhances their suitability
as a bioindicator across spatial scales from breeding territory to the entire watershed
(O’Connell et al. 2003).
To better understand the linkage between reproductive success and habitat
quality, we intensively studied Louisiana Waterthrush abundance and productivity
at 4 streams dominated by Hemlock stands moderately impacted by adelgid infestations
in eastern Pennsylvania, representing 2 distinct morphologies: ravines
and benches. Ravines are characterized by high-gradient, fast-flowing streams
confined between steep banks, whereas benches, underlain by harder bedrock, are
characterized by braided streams that meander across a relatively wide, flat floodplain.
In general, benches in this region have higher avian species richness and
density than ravines (Ross et al. 2004), and their Hemlocks are in somewhat better
condition (Napoli 2015). Our results will contribute to understanding whether
intrinsic differences exist between benches and ravines by using the density and
productivity metrics of Louisiana Waterthrush to compare habitat quality between
the 2 stream morphologies.
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Methods
Study sites
We studied Louisiana Waterthrush pairs on 4 Hemlock-dominated headwater
streams in Pike County, PA, within the Appalachian Plateaus Physiographic Province
from 2010 to 2013 (Fig. 1). Hornbeck’s Creek (41º11'22.19''N, 74º53'15.78''W) and
Tumbling Waters (41º9'19.98''N, 74º55'7.03'W) are ravines in the Delaware Water
Gap National Recreation Area characterized by shale cliffs, waterfalls, rock/cobble
substrates on bedrock and exposed root overhangs along steep stream embankments.
Saw Creek (41º10' 41.99''N, 75º4'29.03''W) and Spruce Run (41º10'1.96''N,
75º7'32.68''W) are benches in nearby Delaware State Forest. Bench sites have an
abundance of overturned trees with exposed root mats, moss-covered rocks, woody
debris, isolated pools, and gravel/mud substrates on harder bedrock interlaced with
moss-covered, exposed roots.
Study-stream reaches varied in length from 1.7 km to 2.8 km (Table 1). Ravine
and bench lengths differed because we made an effort to keep reaches on public/
protected land to limit access and disturbance issues. All streams are located within
an extensively forested landscape dissected by paved and unpaved roads, and a few
scattered houses/cabins. The 2 sites with the most fragmentation (and potential
edge effects) include both a ravine and a bench site: Tumbling Waters (ravine) has
a paved road at its southern end and an abandoned house along a paved road within
67 m of its upper boundary. Saw Creek (bench) is surrounded by roads, both paved
Figure 1. Map of study sites in northeastern Pennsylvania. Hornbeck’s Creek and Tumbling
Waters are ravines located in the Delaware Water Gap National Recreation Area. Saw Creek
and Spruce Run are benches located in Delaware State Forest. All sites are located in Pike
County, PA. High-resolution aerial orthoimages from 2003 to 2006 are from Pennsylvania
Spatial Data Access (http://pasda.psu.edu).
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and unpaved, and a power-line cut 290 m from the stream. A narrow dirt road with
several sporadically used cabins also crosses this stream. Hornbeck’s Creek (ravine)
and Spruce Run (bench) are minimally impacted by 1 perpendicular (500 m)
and parallel (240–950 m) road, respectively. Direct human impact is minimal on all
4 streams and largely confined to a few hikers and fishermen using trails that parallel
each stream.
All sites are dominated by Hemlock stands that may be nearly pure, as is
characteristic of this species, or mixed sparingly with Acer spp. (maple), Carya
spp. (hickory), Betula spp. (birch), Quercus spp. (oak ), Fagus grandifolia Ehrh.
(American Beech), and Tilia americana L. (American Basswood) (Napoli 2015).
Understory and groundcover is generally limited by shading from the Hemlock canopy,
but areas exist where fallen Hemlocks and adelgid-induced defoliation have
created canopy gaps, resulting in denser understory growth, consisting largely of
Rhododendron maximum L. (Great Rhododendron), Hamamelis virginiana, Gronov
ex L. (Witch-hazel), Lindera benzoin Boerth. ex Schaef (Spicebush), Acer rubrum
L. (Red Maple), and, especially, Betula lenta L. (Black Birch) (Napoli 2015).
Banding
Throughout the study, we banded virtually all male Louisiana Waterthrushes
on study streams with USFWS aluminum bands and a unique color sequence of
up to 3 celluloid color bands (Avinet®, Portland, ME). Males responded readily
to song playback and were easily captured before or shortly after pair formation.
Females were less responsive to song playback making them more difficult to capture.
Whenever possible, incubating females were captured off nests and uniquely
marked in similar fashion to males. This allowed us to determine site fidelity, track
individual movements, delineate territories, and document nest ownership as well
as instances of double brooding.
Pairing success, pair density, and productivity
Accumulation of GPS coordinates (Garmin 60CSX®, Garmin Ltd., Olathe, KS)
of singing males allowed us to determine movements and delineate territories of
all males along study streams over the length of the breeding season from 1 April
through 31 July each year. We visited study streams daily, alternating visits between
sites. The number of waypoints, when downloaded onto maps using ArcGIS 10®
Table 1. Pair density and productivity measures from 2010 to 2013.
# double # failed
Reach # # broods/total nests/ Daily nest
length pairs/ fledglings/ successful total Exposure survival
Stream Habitat (km) km km nests monitored days rate (%)*
Hornbeck’s Creek Ravine 2.7 1.9 ± 0.3 6.1 ± 2.4 0/14 6/17 154.5 96.2 ± 1.1
Tumbling Waters Ravine 2.8 1.8 ± 0.1 5.3 ± 1.1 1/14 6/19 158.5
Spruce Run Bench 1.7 3.1 ± 0.4 12.2 ± 1.2 4 /18 7/24 472.5 98.7 ± 0.4
Saw Creek Bench 1.7 3.1 ± 0.4 14.3 ± 2.4 5/13 2/16 218.5
*Corresponds to 33% (ravines) and 69% (benches) overall success over the 28-d nest cycle.
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software (ESRI, Redlands, CA) clearly defined individual territories as well as
segments of streams unoccupied by either paired or unpaired males. We employed
100% minimal convex polygons to determine territory area, and thus, length, which
provided a clear delineation of pairs along streams necessary for nest monitoring,
and determining pair density and fledgling production, as measured per km of
study-stream reach, as well as extent of double brooding and nest survival. A few
males never paired, and those individuals often continued to sing throughout the
season within defended territories but were not included in pair-density calculations.
If males paired with different females within their territories to raise second
broods, we considered them the same pair for density-estimation purposes.
Nest survival
We conducted nest searches and subsequent nest monitoring on each study
stream. We located, recorded, and mapped nests with GPS by observing adult
behaviors within each territory. We monitored active nests to check the status of
eggs and nestlings every 3–4 d throughout incubation and chick rearing to limit
disturbance and predation risk. We recorded clutch initiation, fledging, hatching,
and nest-failure dates for all nests. If nests were found after clutch completion or
hatching, then we estimated clutch initiation and hatching dates by back-calculation,
using the average 13-d incubation period (beginning with last egg laid) and
10-d nestling period (Mattsson et al. 2009; Mulvihill et al. 2008, 2009). We added
in a 5-d egg-laying period for a total next cycle of 28 days when calculating the
daily nest survival rates. Nests with too little data were not included in Mayfield
calculations but if the ultimate fate was known, they were included in the nest success
analysis. We considered a nest successful if at least 1 nestling fledged at the
age of 10 d, the typical number of days between hatching and fledging (Mattsson
et al. 2009, Mulvihill et al. 2008), and depredated if contents were missing before
the expected fledge date or if dependent fledglings were not observed with adults
during subsequent visits (N. Ernst, unpubl. data).
Statistical analyses
For presentation of pair density and productivity results, we first computed
means by site (across years) and then used these values to compute means and
standard errors for all 4 sites, and for bench and ravine sites separately. To test for
differences by habitat type, we used repeated measures analysis of variance (RMANOVA)
on the annual data because this method accounts for non-independence
of repeated measurements nested within sites. We used the lme4 package in R to
conduct this analysis (Bates et al. 2014, R Core Team 2017) and included a fixed
effect of habitat (bench or ravine) and a random effect of year nested within site
(after Bates et al. 2014). Models were estimated with restricted maximum likelihood
(REML) and fixed effects were evaluated based on Type II Wald chi-square
tests. More complex models, including fixed effects of year and year x habitat
interaction, were excluded iteratively using likelihood ratio tests (i.e., sequential
decomposition; Bates et al. 2014).
We calculated overall nest survival, as well as estimates by habitat type, based
on daily survival rates (Mayfield 1961, 1975) with 95% confidence intervals
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(Johnson 1979), and extrapolated to the full nest cycle of 28 d (Mattsson et al.
2009). We eliminated from analysis nests lacking information (found late, unknown
fate) (n = 20). We performed a z-test to evaluate the differences in daily nest survival
rate for the 2 habitat types. We employed the Fisher exact test to compare
double-brooding rates (proportion of males that raised a second brood). We analyzed
territory size and unoccupied stream-length comparisons with t-tests. We set
an alpha level of 0.05 for all tests.
Results
Pair density
Mean pair density across all 4 sites was 2.5 ± 0.4 (SE) pairs/km, with higher
values at bench sites (3.1 ± 0.01; n = 2) than ravine sites (1.8 ± 0.05; n = 2; RMANOVA,
χ2 = 31.8, df = 1, P < 0.001; see Table 1; Fig. 2). Territory length averaged
279 m ± 43 m on benches (n = 36 territories) and 301 m ± 59 m on ravines (n = 41).
Territory area averaged 1.35 ha ± 0.98 ha on benches (n = 36) and 1.12 ha ± 0.92
ha on ravines (n = 41). We detected no statistically significant differences in territory
length or area between ravines and benches (t-tests). We estimated the length
of unoccupied stream reaches (no territories of either pairs or unpaired males) from
our territory maps,which averaged 0.41 km ± 0.35 km on benches (n = 10) and
Figure 2. Summary of major differences in reproductive metrics between Hemlock benches
and ravines.
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0.35 km ± 0.17 km on ravines (n = 14); there was no significant difference (t-test).
We did not measure the degree of territory overlap throughout the study, although
Ernst (2012) reported that mean length of overlap was 181 m for 8 bench territorial
boundaries and 112 m for 7 ravine territories.
Nest survival
Pooled Mayfield nest-survival estimates were as follows: 55% across all sites
(95% CI = 43%, 71%; n = 76 nests; 1004 exposure days), 33% at ravine sites (CI
= 18%, 62%; n = 36 nests, 313 exposure days), and 69% at bench sites (CI = 54%,
88%, n = 40 nests, 691 exposure days). The difference between ravine and bench
sites was statistically significant (z-score for difference in daily survival rates =
2.17, P = 0.030). Of the 36 nests of known fate at ravine sites, 24 fledged, 11 were
depredated, and 1 was abandoned. Of the 40 nests at bench sites, 31 fledged, 8
were depredated, and 1 was abandoned.
Productivity and double brooding
Mean productivity (fledglings produced per km of stream reach per year) across
all sites was 9.5 ± 2.2 (SE; n = 4), with higher productivity at bench (13.1 ± 1.0; n = 2)
vs. ravine sites (5.7 ± 0.4; n = 2; RM-ANOVA, χ2 = 28.6, df = 1, P < 0.001) (Table 1,
Fig. 2). Overall, 17% of pairs double brooded, with a significantly higher percentage
of bench pairs (29% [9 of 31]) raising double broods compared to ravine pairs (4%
[1 of 28]) from 2010–2013 (Fisher’s exact test; χ2 = 0.038, P = 0.036) (Fig. 2).
Discussion
Density and productivity metrics are particularly important in evaluating habitat-
quality differences (Johnson 2007). We found that pair density was significantly
higher on 2 benches (3.1 ± 0.7 pairs/km) compared to 2 ravines (1.8 ± 0.4 pairs/
km) in our Pennsylvania study area from 2010–2013. Our density data for benches
is the highest reported for focused population studies (Mattsson et al. 2009, Mulvihill
et al. 2008, O’Connell et al. 2003; Fig. 2). Territories were stacked end to
end in linear fashion on both stream types even though bench habitat is generally
greater in width than ravine habitat. Potential causes of differences in pair densities,
including disparities in territory length, degree of territory overlap, and the
length of unoccupied portions of the stream reach, were not significantly different.
Thus, higher densities on benches may be due to other factors such as increased
nesting substrate and/or food-resource availability, but more research is needed to
determine the causes of high density on benches.
Ross et al. (2004) is the only published study that distinguished differences regarding
habitat and avian characteristics between Hemlock ravines and benches.
Prior to their study, Louisiana Waterthrush population metrics were largely investigated
on ravine or ravine-like streams or in studies where stream types were
not distinguished (Craig 1985, Mattsson and Cooper 2006, Mulvihill et al. 2008).
Ross et al. (2004) reported significantly more territories of Hemlock-associated
species, including Empidonax virescens Vieillot (Acadian Flycatcher), Setophaga
fusca Müller (Blackburnian Warbler), Setophaga virens Gmelin (Black-throated
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Green Warbler), and Vireo solitarius Gmelin (Blue-headed Vireo), on Hemlock
benches but found Louisiana Waterthrush to have a higher affinity for ravines.
Previous studies on Pennsylvania streams reported Louisiana Waterthrush pair
densities of 2.3 pairs/km of stream reach in eastern Pennsylvania, 1.1 pairs/
km in central Pennsylvania, and 1.8 pairs/km in western Pennsylvania, all very
similar to ravine pair densities reported here (O’Connell et al. 2003). Mulvihill
et al. (2008) reported pair densities of 2.6 ± 0.2 (SE) territories/km on pH circumneutral
streams (n = 4) compared to 1.0 ± 0.1 territories/km (range = 0.5–1.8)
on acidified streams (n = 4) in western Pennsylvania, demonstrating that habitat
quality impacts pair density. High pair-densities, such as those found on benches,
indicate streams with a higher percentage of EPT, the favored insect prey of Louisiana
Waterthrushes (Master et al. 2005, Mattsson and Cooper 2006).
Bench sites also produced significantly more fledglings per kilometer of stream
reach due to a combination of higher pair densities, higher nest-survival rates, and
higher rates of double brooding (Fig. 2). The number of fledglings produced per
kilometer of study-stream reach was 13.1 on benches, more than double the 5.7 on
ravines. The number of young fledged per kilometer of stream reach on circumneutral
streams (5.0 ± 0.4 fledglings/km) was significantly higher compared to 2.6 ±
0.4 (SE) on acidified streams in southwestern Pennsylvania because of the reduced
number of territories on the latter (Mulvihill et al. 2008). Twenty-nine percent of
bench pairs raised a second brood, while only 3.6% of ravine pairs double brooded.
This finding compares with 4.8% (4 of 83 pairs) in Georgia (Mattsson and Cooper
2006) and 5.6% (8 of 143 pairs) in southwestern Pennsylvania (Mulvihill et al.
2009). On ravines, the lone second nest was successful producing 6 fledglings,
while on benches, 7 of 9 second nests successfully produced 20 fledglings. Thus,
bench pairs in our study area engaged in double brooding much more frequently
than previously reported for Louisiana Waterthrush. Bench pairs are apparently
more successful at overcoming documented constraints limiting the occurrence of
double brooding in passerine species including length of nesting season on temperate
breeding grounds (Holmes et al. 1996, Monroe et al. 2008, Mulvihill et al. 2009)
and food availability (Holmes et al. 1992; Nagy and Holmes 2005a, b; Rodenhouse
and Holmes 1992). Based on banding information, at least 1 member of double
brooding pairs was an experienced adult more than 1 y old. Older individuals in
many songbird species often settle in more productive habitats and initiate nesting
earlier, both characteristics that make double brooding more likely (Mahoney et al.
2001, Ortega 2006). Time is also a critical factor in the ability to double brood. The
nest-initiation date was on average 8 May for ravines and 12 May for benches from
2010 to 2012 (Ernst 2012) and 3 May for both benches and ravines from 2013 to
2014 (Barnes 2014). Median fledging date for nests included in Mayfield calculations
was 9 June for ravines (23 May–27 June) and 11 June for benches (23 May–30
June). Median nest-failure date was 3 June (17 May–16 June) on ravines compared
to 30 May on benches (11 May–18 June). Thus, it appears there is no obvious influence
of nesting chronology responsible for the higher incidence of double brooding
on benches; a more likely explanation may be higher habitat-qua lity on benches.
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Predation was the predominant cause of nest failure on both stream types. From
2010 to 2013, the nest-predation rate for nests in ravine sites was 28% compared to
19% on bench sites. The results are comparable to other studies where nest predation
caused the loss of 30% of all nests across Pennsylvania (O’Connell et al. 2003).
Fledglings, attending adults, and/or nest contents are susceptible to predation by
many predators including Corvids, snakes, and many species of mammals (Mattsson
and Cooper 2009, Robinson 1987). We documented no brood parasitism by
Molothrus ater Boddaert (Brown-headed Cowbird), which is similar to other Pennsylvania
studies that found low incidence (O’Connell et al. 2003), but contrasts with
other regional studies (Bent 1953, Eaton 1958).
Predators may find it easier to discover active nests in the eroded and exposed
root overhangs used by Louisiana Waterthrushes for nest sites on ravine embankments
while traveling a narrow, linear corridor bounded by high streambanks
and steep inclines (Baker 1978, Ernst 2012). Benches lack the confining nature
of ravines because they have braided side-channels paralleling the main channel,
perhaps producing less of a funneling effect of predator movements. Louisiana
Waterthrushes on benches nest almost exclusively in the root overturns of naturally
fallen trees. These sites appear more randomly located across a wide floodplain than
are more predictably placed root overhangs on ravines, whose locations correspond
to the more regular spacing of sinuous and eroding curves characterizing these
headwater streams (Mattingly 2016). Nests on benches were sometimes located
relatively far from the main channel (>20 m), while on ravines virtually all nests
were located immediately adjacent to or within root overhangs protruding from the
stream bank (Mattingly 2016). Reduced predation pressure on benches is a contributing
factor to higher nesting success and productivity on benches. Differences in
edge effects on predation rates among the 4 stream reaches cannot be ruled out as a
contributing cause of observed predation patterns even though streams within each
type appear relatively evenly matched in this regard.
The Louisiana Waterthrush is a robust bioindicator whose density, reproductive
metrics, and susceptibility to nest predation reflect the quality of its
headwater stream habitat (Holmes et al. 1996, Mulvihill et al. 2008, O’Connell
et al. 2003). Johnson (2007) stated that bird metrics, as opposed to habitat characteristics,
better reflect habitat quality. For example, Bock and Jones (2004)
demonstrated that density was correlated with habitat quality for birds in general.
Pidgeon et al. (2006) cautioned that individual-level metrics, such as nest success
or fecundity, and population-level metrics, like fledglings produced per unit area,
often classify habitats differently with respect to quality. The combined individual
and population-level metrics used here support the differences found between
the 4 ravine and bench streams. Our sample size was small, and thus even though
study duration was relatively long, our results should be interpreted with caution
as it will take additional effort to better resolve differences in habitat quality between
Hemlock benches and ravines. Thus, the Louisiana Waterthrush may serve
as an effective surrogate species capable of distinguishing differences in habitat
quality important to a range of organisms living in Hemlock-dominated habitats,
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especially regarding management strategies, including prioritization of treatments
implemented to combat adelgid infestations.
Acknowledgments
The Department of Biological Sciences at East Stroudsburg University of Pennsylvania
deserves thanks for its support, both financial and otherwise, during the course of this
project. Funding was provided by the Faculty Development and Research Committee. J.
Shreiner and C. Vorhees were instrumental in obtaining permits and permissions to conduct
our research in the Delaware Water Gap National Recreation Area and Delaware State Forest,
respectively. Megan Napoli provided much expert assistance in the field at a time when
she was busy conducting her own research on Acadian Flycatchers on Hemlock ravines and
benches. The manuscript benefited substantially from the comments and suggestions of 2
anonymous reviewers.
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