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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: ethan.welty@colorado.edu1Present 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.

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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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