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North American Journal of Fisheries Management
ISSN: 0275-5947 (Print) 1548-8675 (Online) Journal homepage: http://www.tandfonline.com/loi/ujfm20
Multiscale Analysis of River Networks using the RPackage linbin
Ethan Z. Welty, Christian E. Torgersen, Samuel J. Brenkman, Jeffrey J. Duda &Jonathan B. Armstrong
To cite this article: Ethan Z. Welty, Christian E. Torgersen, Samuel J. Brenkman, Jeffrey J.Duda & Jonathan B. Armstrong (2015) Multiscale Analysis of River Networks using the RPackage linbin , North American Journal of Fisheries Management, 35:4, 802-809, DOI:10.1080/02755947.2015.1044764
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MANAGEMENT BRIEF
Multiscale Analysis of River Networks usingthe R Package linbin
Ethan Z. Welty*1 and Christian E. TorgersenU.S. Geological Survey, Forest and Rangeland Ecosystem Science Center, Cascadia Field Station,
School of Environmental and Forest Sciences, University of Washington, Box 352100, Seattle,
Washington 98195, USA
Samuel J. BrenkmanU.S. National Park Service, Olympic National Park, 600 East Park Avenue, Port Angeles,
Washington 98362, USA
Jeffrey J. DudaU.S. Geological Survey, Western Fisheries Research Center, 6505 Northeast 65th Street, Seattle,
Washington 98115, USA
Jonathan B. ArmstrongWyoming Cooperative Fish and Wildlife Unit, University of Wyoming, 1000 East University Avenue,
Laramie, Wyoming 82071, USA
AbstractAnalytical tools are needed in riverine science and manage-
ment to bridge the gap between GIS and statistical packages thatwere not designed for the directional and dendritic structure ofstreams. We introduce linbin, an R package developed for theanalysis of riverscapes at multiple scales. With this software, riv-erine data on aquatic habitat and species distribution can bescaled and plotted automatically with respect to their position inthe stream network or—in the case of temporal data—their posi-tion in time. The linbin package aggregates data into bins of dif-ferent sizes as specified by the user. We provide case studiesillustrating the use of the software for (1) exploring patterns atdifferent scales by aggregating variables at a range of bin sizes,(2) comparing repeat observations by aggregating surveys intobins of common coverage, and (3) tailoring analysis to data withcustom bin designs. Furthermore, we demonstrate the utility oflinbin for summarizing patterns throughout an entire stream net-work, and we analyze the diel and seasonal movements of taggedfish past a stationary receiver to illustrate how linbin can be usedwith temporal data. In short, linbin enables more rapid analysisof complex data sets by fisheries managers and stream ecologistsand can reveal underlying spatial and temporal patterns of fishdistribution and habitat throughout a riverscape.
Ecological patterns and processes occur at multiple spatial
and temporal scales within a river network (Levin 1992;
Fausch et al. 2002), and this complexity is increasingly being
examined in fisheries and water resources management
(Arthington et al. 2010; Wheaton et al. 2010; Nakagawa
2014). The riverscape approach to investigating and managing
stream fishes emphasizes the importance of considering the
many spatial scales that are relevant to the diverse life histories
of fish and the objectives of fisheries managers (Fausch et al.
2002). However, despite considerable advancements during
the last decade, existing tools do not allow analysts to nimbly
toggle between scales during stream analysis and modeling
(Burnett et al. 2007; Brenkman et al. 2012; Carbonneau et al.
2012; Lawrence et al. 2012; Klett et al. 2013; McMillan et al.
2013). Although better tools have been developed to bridge
the gap between spatial data in a GIS and statistical packages
(Benda et al. 2007; Isaak et al. 2014; Peterson and Ver Hoef
2014; Ver Hoef et al. 2014), none of these tools allows users
to quickly and easily evaluate the influence of scale on patterns
of species distribution and aquatic habitat.
*Corresponding author: [email protected] address: Institute of Arctic and Alpine Research, University of Colorado, Campus Box 450, Boulder, Colorado 80309, USA.Received November 13, 2014; accepted April 14, 2015
802
North American Journal of Fisheries Management 35:802–809, 2015
� American Fisheries Society 2015
ISSN: 0275-5947 print / 1548-8675 online
DOI: 10.1080/02755947.2015.1044764
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Analysis of riverscape data first requires that geographi-
cally referenced variables be extracted from a GIS and plotted
as a function of river distance. We define these plots of biotic
and abiotic variables (y-axis) versus distance along the river
channel (x-axis) as longitudinal profiles. Creating such profiles
from complex riverine data sets (e.g., with braided channels,
gaps in sampling effort, and irregular sampling intervals) is
difficult and time consuming. Hence, these analyses may be
beyond the reach of many stream ecologists and fisheries man-
agers who use fish distribution, habitat, and water quality data
collected in elaborate spatial and temporal arrangements. The
need to analyze the associations between fish species and their
habitat at multiple scales led to the development of flexible
and automated routines for longitudinal data aggregation and
plotting. Used by Brenkman et al. (2012), Lamperth (2012),
Lawrence et al. (2012), Klett et al. (2013), and Fullerton et al.
(in press), these functions have now been formalized in the R
package linbin (“linear binning”; Welty 2015) and published
as open-source code on the Comprehensive R Archive Net-
work (CRAN; R Development Core Team 2014). In this paper,
we describe how linbin works, and we provide examples of its
applications.
LINBIN: A TOOL FOR MULTISCALE ANALYSIS OFRIVERSCAPES
The R package linbin was originally conceived for the anal-
ysis of detailed, spatially continuous riverscape data (e.g.,
Torgersen et al. 2006) and has been used by the U.S. Geologi-
cal Survey, the U.S. National Park Service, and other investi-
gators studying spatial patterns in riverine landscapes (e.g.,
Brenkman et al. 2012; Lamperth 2012; Lawrence et al. 2012).
It is now actively maintained and available as free, open-
source code on GitHub (github.com) and in the CRAN pack-
age repository (Welty 2015).
Linbin Workflow and Core Functions
The linbin package contains a suite of functions to perform
multiscale analysis. Steps include (1) creating, converting, and
reading input data from a file (events, as_events, and read_e-
vents); (2) designing the “bins”—that is, the intervals over
which the data are summarized (e.g., event_range, event_
coverage, and seq_events); (3) assigning data to the bins (sam-
ple_events); and (4) creating sets of bar plots from the binned
data to visualize longitudinal profiles of riverscapes at multiple
scales (plot_events; see Figure 1 for an example).
Linearly Referenced Input Data
The linbin package is broadly conceived for any data that
are arranged along a single dimension, whether the dimension
is spatial (e.g., distance upriver), temporal (e.g., time elapsed),
or neither (e.g., a sum or percentage variable). As an example
of how riverscape data are reduced to one dimension for linbin,
Figure 2a shows riverine habitat mapped in a GIS as a series of
adjacent units (Radko 1997; ESRI 2003, 2010). In such spatial
data, position can be expressed as distance upstream measured
from a downstream reference point (e.g., river mouth or conflu-
ence), equivalent to the “river mile” or “river kilometer” used
in cartography. In GIS science, this technique of expressing
geographic positions as measurements along a line is known as
linear referencing. The line measures are used to locate
“events” along the line: either (1) point events (e.g., salmon
redds, logjams, and road crossings) with one measure or (2)
line events with two endpoint measures (e.g., the habitat units
of Figure 2a). The linbin package stores linearly referenced
data in an “event table,” wherein each row includes a point
event or a line event and the values of any variables (e.g.,
water depth or number of fish) associated with that event.
Designing the Bins
An important concept for bin design in linbin is event
“coverage,” or the intervals over which the data contain no
gaps (see Figure 2b). Groups of sequential bins can be gener-
ated automatically from the event coverage with the function
seq_events by using one of three strategies (illustrated in
Figure 3): (1) a fixed number of bins (if the data contain gaps,
then the bin endpoints are adjusted so that each bin contains
an equal share of the total event coverage); (2) a fixed bin
length (the bin endpoints are adjusted so that each bin contains
the specified length of coverage; when bin length does not
evenly divide the total coverage, a bin with the remainder is
added to the end of the sequence); and (3) an adaptive bin
length (bin lengths are varied about the specified length such
that a whole number of bins fits within each interval of cover-
age, thereby preserving gaps and minimizing edge effects). By
choosing to preserve breaks between adjacent or overlapping
units (Figure 2b) or inserting custom breaks in the coverage
(e.g., with the cut_events function), the third strategy can also
ensure that the bin sequence corresponds to hydrologic or geo-
morphic features (e.g., stream reaches or tributary confluences).
Assigning Data to the Bins
The binning function sample_events can process event varia-
bles of all types (numeric, logical, character, etc.) since it allows
the use of all functions that compute a single value from one or
more vectors of values. Functions that are commonly used on
single numeric variables include sum (e.g., channel length or
fish counts), mean (e.g., depth, wetted width, or percent sub-
strate), and min and max (e.g., minimum or maximum depth). A
function that is commonly used on multiple variables is
weighted.mean (e.g., mean depth weighted by channel unit
length). Categorical variables, such as channel unit type (e.g.,
pool or riffle), can be applied as filters to any computation (e.g.,
the mean depth of pools or the sum of fish in riffles).
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Binning begins by cutting events at bin endpoints via the
cut_events function (Figure 2c). When events are cut, any
user-specified variables (typically sums) can be scaled to the
relative lengths of the resulting events (i.e., an assumption of
uniform distribution); all other variables remain unchanged.
Finally, the variables are computed according to the specified
sampling functions from the (cut) events that fall within each
bin (example 1 in Figure 2c).
In cases where data are collected in braided stream chan-
nels, overlapping events can be merged together in a prelimi-
nary binning step (example 2 in Figure 2c). In this way, for
example, contributions of parallel channels to a bin mean can
be weighted by their width, while contributions from adjacent
units can be weighted by their length.
Plotting the Binned Data
The plotting function plot_events produces a grid of bar
plots for all variables and groups of bins. Batch processing
and plotting in linbin make it possible to explore patterns in
riverine data at multiple scales without needing to laboriously
compute and plot individual longitudinal profiles. To incorpo-
rate information on sampling effort, bins with no data are not
shown, whereas bins with a value of zero are drawn as a thin
black line.
APPLICATIONS IN RIVERINE MANAGEMENTAND RESEARCH
To illustrate the applications of linbin to riverscape science,
we provide examples from rivers and streams in Washington
and Alaska. We demonstrate the utility of linbin for examining
spatial patterns in long river sections or throughout an entire
stream network and for analyzing temporal patterns of fish
movement. The data for these case studies are included in the
linbin package; the code is provided in the package documen-
tation (Welty 2015).
A 53-km, spatially continuous snorkel survey of the Qui-
nault River, Washington (August 2009), illustrates how lin-
bin can be used to quantify multiscale patterns. Figure 1
FIGURE 1. Longitudinal profiles of trout abundance throughout the Quinault River, Washington, plotted at multiple spatial scales indicated as bin lengths. The
formatting of the bars, axes, ticks, and tick labels illustrates the default plotting output of the linbin package.
804 WELTY ET AL.
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depicts trout abundance (from visual counts) at a range of
bin sizes from 100 to 25,600 m. The scales at which fish
counts are binned can be specified by the user to reveal
different patterns attributable to a hierarchy of ecological
processes (Frissell et al. 1986; Turner et al. 1989; Levin
1992).
Events
Coverage
Coverage
Range
River
Measuredlength (m)
Bins
Example 14 4
44
2
621
(40 * 4 + 20 * 2 + 50 * 2 + 80 * 2) / 10 (80 * 2 + 10 * 4) / 6
40% 20%80%
10%20%80%
80%40%
33%46%
%01%05%02 80%
Example 2
4 46
4 2 2 4
4
0101
421
4
20
(b)
(a)
(c)
unsurveyed rapid
side channel
0 2 4 6 8 10 12 14 16 18 20
Events are cut at event endpoints and averaged, then cut at bin endpoints
and averaged.
Events are cut at bin endpoints and summed.
with endpoints of adja-cent and overlapping
events both discarded.
with endpoints of adja-cent and overlapping
events both preserved.
FIGURE 2. Illustration of riverine habitat mapped as (a) adjacent units on a hypothetical river main stem and (b) as events, with example event table metrics
from the linbin package. The labels correspond to the length of each interval, represented by dark gray bars. Note that the side channel is located by its intersec-
tions with the main stem (at 6 and 12 m), along which it is assigned a length of 6 m. (c) The data are binned in two ways: (1) by summing all events (cut at bin
endpoints) that fall into each bin (i.e., total stream length per bin); and (2) by computing the mean of overlapping events (cut at event endpoints) and then comput-
ing the length-weighted mean of the resulting events (cut at bin endpoints) that fall within each bin (i.e., a percentage as a function of position along the main
stem, averaged per bin).
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Similar riverscape surveys were conducted throughout
65 km of the Elwha River, Washington, during summer low
flow in August 2007 and August–September 2008 (Brenkman
et al. 2012). These surveys had differing spatial gaps where no
data were collected due to high water velocities in canyon sec-
tions that were unsafe for snorkeling. Furthermore, long
reaches were sampled more coarsely in 2007 than in 2008.
The linbin package facilitated the spatially explicit compari-
son of fish abundance between years by aggregating the data
from both surveys into bins corresponding to their largest com-
mon intervals of coverage. Despite differences in hydrology
between the two study years, the patterns in adult fish abun-
dance were similar (Brenkman et al. 2012). During the 2008
survey, physical habitat variables were collected concurrently
with fish counts; linbin was used to resample variables (e.g.,
Original data (a)
0
56
0
56
0
56
0
56
Equal length bins (1.99 km) (b)
Equal coverage bins (2.05 km) (c)
Variable length bins (d)
0 65.7Distance upstream (km)
Wet
ted
wid
th (m
)
FIGURE 3. Longitudinal profiles of mean wetted width throughout the
Elwha River, Washington, in 2008, illustrating the different strategies for auto-
matic bin generation in the linbin package. Resampling of (a) the original sur-
vey data is illustrated as follows: (b) equal-length bins (ignoring gaps),
(c) equal-coverage bins (straddling gaps), and (d) variable-length bins locally
adapted to fit the coverage of the data (preserving gaps). The latter strategy
was used by Brenkman et al. (2012). The conventional solid line on the x-axis
is not displayed in order to reveal gaps in the data. The formatting of the bars,
axes, ticks, and tick labels illustrates the default plotting output of linbin.
FIGURE 4. (a) The river network of the Dungeness River, Washington, from
NetMap (www.terrainworks.com/netmap-demo-tools-download); and exam-
ples of longitudinal profiles for NetMap variables (in distance upstream from
the river mouth) for (b) the main stem (5.57-km bins containing 5.57 km of
stream) and (c) the entire river network (5.62-km bins containing 14–404 km
of stream). The variables were binned as means weighted by stream length and
include intrinsic potential (IP; a modeled estimate of the likelihood of
fish occurrence, as defined by Burnett et al. 2007) for Chinook Salmon
(IP_CHINOOK), Coho Salmon (IP_COHO), and steelhead (IP_STEELHD);
the fraction of favorable habitat for North American beaver (BeavHab); and
mean channel depth (DEPTH_M).
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mean wetted width) by using bins that were adapted to the sur-
vey coverage so as to preserve gaps and minimize edge effects
(Figure 3).
The linbin package can also be used to produce longitudinal
profiles for entire stream networks. NetMap (Benda et al.
2007; www.terrainworks.com) employs digital elevation mod-
els to generate detailed river networks and to compute bio-
physical variables for spatially continuous hydrologic units
(Figure 2a) throughout the networks. Figure 4 depicts longitu-
dinal profiles that were computed by linbin from NetMap out-
put for both the main-stem and the entire network of the
Dungeness River, Washington. For Coho Salmon Oncorhyn-
chus kisutch, Chinook Salmon O. tshawytscha, and steelhead
O. mykiss, the mean intrinsic potential (a modeled predictor of
species occurrence developed by Burnett et al. 2007) declined
rapidly with distance upstream in the tributaries—from a near-
power-law decline for Chinook Salmon to a near-linear
decline for steelhead. In contrast, for distance upstream in the
main stem, intrinsic potential declined more slowly (for Coho
Salmon and Chinook Salmon) or even increased (for steel-
head). Similarly, the majority of habitat for the North Ameri-
can beaver Castor canadensis occurred in tributaries just
upstream from the river mouth (Figure 4), a pattern that a
main-stem-only analysis failed to reveal.
The linbin package can process temporal data in a manner
similar to the processing of spatial data. For example, rather
than locating fish counts on a river based on distance
upstream, the time elapsed can be used to locate the fish in
time. This approach can be helpful for identifying popula-
tion-level trends from individual-level movement data. Here,
we use linbin to visualize cyclic habitat use by juvenile Coho
Salmon in a thermally heterogeneous stream. In Bear Creek,
southwest Alaska, Coho Salmon prey on the eggs of Sockeye
Salmon O. nerka, which spawn only in cold, groundwater-
dominated habitats in the lower 1 km of the stream. Antenna
arrays revealed that many PIT-tagged Coho Salmon gorged
on eggs during the night and then moved upstream 500 m or
more, where warmer temperatures accelerated digestion
(Armstrong et al. 2013). Computation of fish abundance from
individual residence time intervals with linbin revealed super-
imposed diel and seasonal patterns of Coho Salmon abun-
dance in the stream region where Sockeye Salmon spawned
(Figure 5). The high-frequency pattern reflected cyclic feed-
ing movements at night, while the positive trend indicated an
accumulation of nonmoving fish as the Sockeye Salmon run
declined through mid-August. This may reflect a reduction in
postfeeding movements as (1) the abundance of Sockeye
Salmon eggs declines and (2) Coho Salmon, which have to
spend more time foraging, are less likely to be digestively
constrained.
In conclusion, we have demonstrated that linbin can be
used to analyze complex data sets and reveal underlying pat-
terns by generating multiscale summaries of variables col-
lected throughout a riverscape. A key advantage to using
linbin for multiscale analysis is that it includes a flexible and
automated bin generation routine; although the provided
examples are either spatial or temporal, linbin can process any
data that are arranged along one dimension. It accounts for
overlaps and gaps in sampling and is thus especially well-
suited for the dendritic structure of streams. Furthermore, by
FIGURE 5. Temporal abundance patterns of tagged Coho Salmon in the downstream 1 km of Bear Creek, Alaska, from July 29 to August 19, 2008 (Armstrong
et al. 2013), normalized by the studywide abundance of Coho Salmon that were first tagged in this river reach. The vertical gray lines mark the start of each day
(0000 hours [midnight] in local time).
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reducing such complex data to longitudinal profiles, linbin
facilitates direct interpretation and analysis by conventional
plotting, smoothing, and modeling routines (e.g., locally
weighted scatterplot smoothing). Once linbin has been used to
summarize fish occurrence and potential explanatory variables
(e.g., habitat structure) in a stream network, statistical tools
can be used to model the probability of fish occurrence within
each bin. The same analysis can be repeated for a range of bin
lengths; in this manner, hypotheses can be tested regarding the
relative influences of explanatory variables on fish distribution
at different spatial scales (see Bult et al. 1998).
The linbin package can also be used in conjunction with
other geospatial hydrologic tools, such as the National
Hydrography Dataset (U.S. Geological Survey; nhd.usgs.gov/
tools.html) and Arc Hydro (ESRI 2011), to explore longitudi-
nal patterns in modeled watershed attributes. Furthermore,
the use of linbin with other R packages that implement spa-
tial statistical analysis (e.g., Ver Hoef et al. 2014) will make
it possible, for example, to assess spatial autocorrelation in
stream networks, to develop appropriately scaled covariates
for use in predictive spatial statistical models (e.g., Peterson
et al. 2013; Isaak et al. 2014), and to plot and analyze model
output.
ACKNOWLEDGMENTS
We thank Jeremy M. Cram, Katherine J. C. Klett, David J.
Lawrence, and other early adopters of the code for their testing
and useful feature suggestions, and we thank Katherine Beirne
for preparing the Quinault River data for analysis. We are
grateful to the Working Group on Dam Removal at the U.S.
Geological Survey’s John Wesley Powell Center for Analysis
and Synthesis for contributing to the ideas behind this work;
and the U.S. National Park Service, the U.S. Geological
Survey’s Ecosystems Mission Area, and the U.S. Fish and
Wildlife Service for contributing financially. We appreciate
Nathaniel P. Hitt, Daniel J. Daugherty, and two anonymous
reviewers for their assistance and comments on earlier drafts
of the manuscript. Any use of trade, product, or firm names is
for descriptive purposes only and does not imply endorsement
by the U.S. Government.
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