Effects of Fish Size, Habitat, Flow, and Density on Capture

Probabilities of Age-0 Rainbow Trout Estimated from

Electrofishing at Discrete Sites in a Large River

JOSH KORMAN*

Ecometric Research, Inc., and Department of Zoology, University of British Columbia,

3560 West 22nd Avenue, Vancouver, British Columbia V6S 1J3, Canada

MIKE YARD

EcoNatura, 1920 Crescent Drive, Flagstaff, Arizona 86001, USA

CARL WALTERS

Fisheries Centre, Aquatic Ecosystems Research Laboratory, University of British Columbia,

2202 Main Mall, Vancouver, British Columbia V6T 1Z4, Canada

LEWIS G. COGGINS

U.S. Geological Survey, Grand Canyon Monitoring and Research Center,

2255 North Gemini Drive, Flagstaff, Arizona 86001, USA

Abstract.—We estimated size-specific capture probabilities of age-0 rainbow trout Oncorhynchus mykiss in

the Lee’s Ferry Reach of the Colorado River, Arizona, by backpack and boat electrofishing at discrete

shoreline sites using both depletion and mark–recapture experiments. Our objectives were to evaluate the

feasibility of estimating capture probability for juvenile fish in larger rivers; to determine how it is influenced

by fish size, habitat, flow, density, and recovery period; and to test population closure assumptions. There was

no mortality among the 351 rainbow trout that were captured by electrofishing, marked, and held for 24 h. Of

a total of 2,966 fish that were marked and released, only 0.61% were captured outside of mark–recapture sites,

and total emigration from mark–recapture sites was 2.2–2.6%. These data strongly suggest that populations

within discrete sites can be treated as effectively closed for the 24-h period between marking and recapture.

Eighty percent of capture probability estimates from 66 depletion experiments and 42 mark–recapture

experiments ranged from 0.28 to 0.75 and from 0.17 to 0.45, respectively, and the average coefficient of

variation of estimates was 0.26. There was strong support for a fish size–capture probability relationship that

accounted for the differences in vulnerability across habitat types. Smaller fish were less vulnerable in highangle shorelines that were sampled by boat electrofishing. There was little support for capture probability

models that accounted for within-day and across-month variation in flow. The effects of fish density on

capture probability were challenging to discern, variable among habitat types and estimation methodologies,

and confounded with the effect of fish size. As capture probability estimates were generally precise and the

closure assumption was met, our results demonstrate that electrofishing-based mark–recapture experiments at

discrete sites can be used to estimate the abundance of juvenile fish in large rivers.

Catch information has a variety of uses in the study

of animal populations, but all require an understanding

of the dynamics of capture probability, which is the

proportion of a population that is captured per sampling

event (Williams et al. 2002). For example, in

commercial or recreational fisheries, changes in catch

per effort over time can be used to assess trends in

abundance under the assumption that capture probability has remained stable or, alternatively, that

temporal changes in capture probability can be

estimated (Hilborn and Walters 1992). In scientific

surveys of stream-dwelling fishes, differences in catch

rates among habitat types can be used to evaluate the

relative importance of those habitats, but only if the

capture probabilities in these habitats are known.

Studies conducted over a period in which fish are

growing and undergoing ontogenetic habitat shifts

must account for the effects of both changes in fish size

and habitat use on capture probability. Efforts targeted

at improving the status of freshwater fish populations,

such as increasing minimum stream flows in regulated

rivers, are sometimes assessed by comparing catch

rates before and after flow changes. In this situation, it

is important to understand how persistent environmen-

* Corresponding author: jkorman@ecometric.com

Received February 7, 2008; accepted July 25, 2008

Published online February 5, 2009

58

Transactions of the American Fisheries Society 138:58–75, 2009

Copyright by the American Fisheries Society 2009

DOI: 10.1577/T08-025.1

[Article]
tal changes, such as flow, potentially alter capture

probability. A common assumption required in all such

studies is that catch rates are proportional to abundance; in other words, that capture probability is

independent of density.

Electrofishing is a commonly used means of

sampling stream-dwelling juvenile salmonids and other

fishes. A variety of studies have investigated the effects

of electrofishing on movement (Dunham et al. 2002;

Young and Schmetterling 2004) and behavior (Cross

and Stott 1975; Mesa and Schreck 1989; Ainslie et al.

1998), and how capture probability is influenced by

habitat and environmental variables (Bayley and

Austen 2002; Peterson et al. 2004; Rosenberger and

Dunham 2005), fish size (Borgstrom and Skaala 1993;

Anderson 1995), and density (Bayley and Austen

2002). The vast majority of studies have been

conducted in small streams and lakes or in very small

artificial systems. Very few have been undertaken in

medium- to large-sized rivers. Speas et al. (2004) found

that capture probability for adult rainbow Oncorhynchus mykiss and brown trout Salmo trutta in the

Colorado River (mean annual discharge [MAD] 1⁄4 385

m3

/s) varied with turbidity, and was density-independent and density-dependent for rainbow trout and

brown trout, respectively. Mitro and Zale (2002) used

mark–recapture to estimate capture probability for age0 rainbow trout in a tributary of the Snake River (MAD

1⁄4 24 m3

/s). They found that capture probabilities at

discrete sites tended to be low (average 1⁄4 0.17), and

that sites could be treated as effectively closed because

emigration rates of marked fish were relatively low

(16%). To our knowledge, there have been no attempts

to estimate capture probabilities at discrete sites for

juvenile fish in large rivers using depletion or mark–

recapture experiments, or other methods. This represents a significant limitation in our ability to estimate

the abundance, distribution, growth, and survival of

juvenile fish in these environments, which is critical for

understanding effects of habitat enhancement and other

management efforts.

The objective of this paper is to evaluate the

feasibility of estimating capture probabilities for

juvenile fish populations in larger rivers. We define

capture probability as the proportion of a population

within a discrete shoreline site that is removed by a

single-pass of electrofishing effort. The assumption

that populations within sites can be treated as closed is

evaluated based on the recovery rates of marked fish

outside of mark–recapture sites and by 24-h holding

experiments to determine the potential mortality of fish

between the release and recovery periods. We compare

capture probabilities estimated by depletion and mark–

recapture experiments, and examine how capture

probabilities vary with fish size, habitat, flow, recovery

period, and density. The results from this investigation

should be of interest to researchers wishing to study the

population dynamics of small or juvenile fish in large

river environments.

Methods

Study area.—This study was conducted in the Lee’s

Ferry reach of the Colorado River, Arizona, which

begins at Glen Canyon Dam below Lake Powell and

extends 26 km downstream to the confluence with the

Paria River (latitude 1⁄4 36.86638; longitude 1⁄4

111.58638). The average flow during months when

the study was conducted in 2006 (July–November) and

2007 (June–November) was 325 and 339 m3

/s,

respectively (U.S. Geological Survey [USGS] gauge

09380000). Although located in a canyon, the reach is

broad, shallow, and low gradient. The average wetted

width, depth, and gradient at 325 m3

/s are 144 m, 5.2

m, and 0.25 m/km, respectively (Randle and Pemberton 1987). There are no significant tributary inputs to

the reach, and water quality is determined by the

hypolimnetic release from Glen Canyon Dam. The

annual range of main-stem water temperatures recorded

at the downstream end of the reach since 2003 has

ranged from 9–158C (Voichick and Wright 2007), and

Secchi depths have consistently ranged from 6 to 7 m

(Vernieu et al. 2005). The fish fauna in the Lee’s Ferry

reach is almost exclusively comprised of a large, selfsustaining population of nonnative rainbow trout

(McKinney et al. 2001).

Flow from Glen Canyon Dam normally fluctuates on

a diel cycle that is driven by power demand but

controlled through regulation of the maximum daily

flow range (141–227 m3

/s), minimum (141 m3/s) and

maximum (708 m3

/s) flows, and maximum downramp

(42 m3

/s  h) and upramp (113 m3/s  h) rates. There is

little variation in flow during the low- and high-flow

periods within a day. Flow was very similar within

months across years during the study period (Table 1),

being relatively high with large daily flow variation

during summer months (June–August), and low with

less daily variation during fall (September–November).

Field methods.—Depletion and mark–recapture

methods were used to estimate capture probability

and population size for age-0 rainbow trout at discrete

sites within the Lee’s Ferry reach. Both these methods

rely on the assumption that a population within a site

can be treated as effectively closed; in other words, that

the number of fish that migrate from or into the site, or

that die over the period when the site is sampled, is

negligible. Shoreline habitat in the reach has been

classified into the following five strata based on lowlevel aerial photographs: cobble bars, vegetated sand

CAPTURE PROBABILITIES IN A LARGE RIVER 59
bars, debris fans, talus (large angular boulders), and

cliffs (Mietz 2003). In total, there are 96 shoreline

habitat units summing to 56.5 km. The total shoreline

length is slightly greater than twice the total length of

the river because it includes both banks and the

shorelines are more sinuous than the centerline of the

channel. We reclassified the five original habitat strata

into low- (cobble and vegetated sand bars and debris

fans summing to 27.8 km of shore length) and highangle (talus slopes summing to 21.5 km of shore

length) shoreline habitat types that could be sampled by

backpack and boat electrofishing, respectively. Cliff

habitat was excluded because it comprises only 12% of

the total shoreline length and because pilot sampling

showed it was very rarely utilized by age-0 rainbow

trout. The sites at which the depletion or mark–

recapture experiments were conducted were randomly

selected units from low- and high-angle habitat strata.

All sampling was conducted after dark between

midnight and 0600 hours when sampling at the daily

minimum flow and between 2100 and 2300 hours

when sampling at the daily maximum flow. Electrofishing sites extended 3–4 m from shore, were not

enclosed by block nets, and were fished very

methodically in upstream (backpack electrofishing) or

downstream (boat electrofishing) directions. The effects of daylight and flow on the distribution of age-0

rainbow trout within the immediate shoreline areas that

were electrofished are explored in a companion paper

(Korman and Campana 2009, this issue). Backpack and

boat electrofishing were conducted by a two-person

crew operating Smith-Root Type 12b and Coffelt CPS

electrofishers, respectively. A single pass of electrofishing required an average of 10 s of electrofishing

effort per meter of shoreline sampled. Boat electrofishing was conducted from a shallow-draw, 5.3-m

aluminum boat (50-hp [1 hp 1⁄4 746 W] outboard motor

with power trim). The combination of boat design,

highly experienced operators, and slow shoreline water

velocities allowed fine control of anode position and

very thorough coverage of the immediate shoreline

area relative to typical boat electrofishing operations.

After electrofishing, fish were anesthetized with clove

oil, and fork lengths were measured to the nearest

millimeter.

In 2006, 66 depletion experiments (n 1⁄4 19 in lowangle and 47 in high-angle habitats) were conducted

over four sampling trips between July and November

(Tables 2, 3). Experiments were conducted at either the

daily minimum (n 1⁄4 42) or maximum (n 1⁄4 24) flow.

Each depletion experiment consisted of repeatedly

removing fish from a single site over three (n 1⁄4 62) or

four (n 1⁄4 4) passes and holding them until the

experiment was complete. We allowed a 1–2-h period

between passes and ensured that fishing effort (seconds

shocked per meter of shoreline) was approximately

constant among passes (615%). Site lengths varied

and depended on the number of fish captured on the

first pass. At a minimum, sites were 30 and 50 m long

in low-angle and high-angle shorelines, respectively,

TABLE 1.—Average monthly discharge and average daily

minimum and maximum flows (m3/s) in the Lee’s Ferry reach

during the study months in 2006 and 2007. The daily range is

the difference between the daily minimum and the daily

maximum.

Year Month Average

Daily

minimum

Daily

maximum

Daily

range

2006 Jun 381 253 476 223

Jul 381 269 491 223

Aug 381 269 493 224

Sep 253 173 312 138

Nov 285 197 368 171

2007 Jun 381 253 475 222

Jul 370 255 475 220

Aug 370 255 478 223

Sep 287 182 351 169

Nov 288 202 368 167

TABLE 2.—Summary statistics for data collected from depletion experiments. The daily flow column denotes whether

sampling was conducted at the daily minimum or maximum flow; total catch is total number of fish caught over three passes

across sites; and average FL 1⁄4 the average fork length of fish caught on the first pass.

Habitat

type Daily flow

Sampling

month

Sites

sampled

Meters

sampled

Total

catch

Average

FL (mm)

Low angle Minimum Jul 5 150 217 41

Aug 6 204 188 45

Maximum Aug 5 221 113 51

Sep 3 120 55 63

High angle Minimum Jul 8 400 384 54

Aug 8 400 463 59

Sep 7 377 214 67

Nov 8 589 272 79

Maximum Aug 8 486 195 59

Sep 6 323 132 71

Nov 2 125 29 78

60 KORMAN ET AL.
but were extended up to approximately twice these

distances if time permitted or if catches were low. In

the rare cases in which 10 fish were not captured over

the maximum distance, the site was abandoned and

another random site was selected. Average site lengths

in low- and high-angle habitats were 37 (range1⁄430–61

m) and 57 m (range 1⁄4 50–116 m), respectively.

In 2007, we conducted 42 mark–recapture experiments over five sampling trips between June and

November (n 1⁄4 7 and 35 in low- and high-angle

habitats, respectively; Table 3). On the first pass

(marking pass), fish were captured by electrofishing

and measured to the nearest millimeter. Live fish were

put in an aerated bucket containing neutral red

biological stain (2 g/15 L; Sigma-Aldrich, Ltd.) for

20 min and then transferred to aerated buckets of clear

water to recover (Gaines and Martin 2004). The fork

lengths of dead fish and those that were not actively

swimming after processing were recorded so they

could be excluded from the count of marked fish

released into the site. The remaining marked fish were

released one or two at a time near the shore throughout

most of the length of the sample site. No fish were

released within 5 m of the upstream or downstream

borders of the sites. Sites were resampled by

electrofishing either 1 (n 1⁄4 11) or 24 h (n 1⁄4 31) after

fish were released. All sites were resampled at the same

flow at which they were initially sampled, and sites

resampled after 24 h experienced a complete diel flow

cycle. Effort (seconds electrofished per meter of

shoreline) during the second pass (recapture pass)

was consistent with effort during the initial marking

pass and during depletion experiments in 2006. The

number and fork length of marked and unmarked fish

that were captured on the second pass were recorded.

Average site lengths in low- and high-angle habitat

were 112 (range 1⁄4 95–273 m) and 88 m (range 1⁄4 50–

247 m), respectively. Twenty-five-meter-long shoreline

sections located immediately upstream and downstream of each of the mark–recapture sites were

sampled at the end of the recapture pass. The number

of marked fish captured in these areas was expanded by

the estimated site-specific capture probabilities to

determine the total number of marked fish that had

emigrated between marking and recapture events.

To determine whether electrofishing, handling, and

staining resulted in postrelease mortality of marked

fish, we conducted two holding experiments in

September 2007. A large sample of fish were captured

by backpack and boat electrofishing, and measured to

the nearest millimeter. One-half of all fish with fork

lengths greater than 60 mm had a small portion of the

upper lobe of their caudal fin removed and were held

for 20 min in clear water. The other half of fish larger

than 60 mm and all fish 60 mm or smaller were placed

in neutral red stain for 20 min. This design allowed us

to determine whether use of the neutral red stain

resulted in additional mortality relative to the more

traditional method of marking juvenile fish using fin

clips. Fish were then put in mesh baskets (1 3 0.5 3 0.4

m) that were placed on the stream bottom in calm

water. We returned to the baskets after 24 h, and

counted and measured the number of stained and

clipped live and dead fish.

Model structure and estimation.—Capture probability (p) and population size were estimated from

depletion and mark–recapture experiments following

the generalized mark–recapture and depletion models

of Otis et al. (1978). Capture probability may change

across passes owing to changes in effort, or because of

the effects of past fishing effort on physical habitat

(i.e., increasing turbidity) or fish behavior (Mesa and

Schreck 1989; Peterson et al. 2004). We therefore

evaluated two alternative depletion models: (1) a

simpler model in which the capture probability was

constant across passes (model D1

, where D refers to a

TABLE 3.—Summary statistics for data collected from mark–recapture experiments. Abbreviations are as follows: M 1⁄4the total

number of fish marked; r 1⁄4 the total number of marked fish recaptured; average FL 1⁄4 average fork length of fish caught on the

first pass.

Habitat

type

Recovery

period

Sampling

month

Sites

sampled

Meters

sampled M rr/M

Average

FL (mm)

Low angle 1 h Aug 2 280 424 239 0.56 43

24 h Jul 3 218 271 31 0.11 36

Aug 2 283 365 97 0.27 44

High angle 1 h Jul 4 272 203 46 0.23 55

Aug 4 247 264 94 0.36 57

Sep 1 57 46 13 0.28 61

24 h Jun 5 279 58 16 0.28 90

Jul 4 271 196 46 0.23 60

Aug 4 265 214 63 0.29 62

Sep 4 360 192 38 0.20 62

Nov 9 1,324 723 227 0.31 84

CAPTURE PROBABILITIES IN A LARGE RIVER 61
depletion experiment and the subscript 1 refers to the

number of capture probabilities that are estimated) and

(2) a more complex model in which the capture

probability varies from pass to pass (D2

). We evaluated

simple and complex mark–recapture models in which

capture probability was assumed either to be constant

across passes (MR1

) or to vary (MR2). Parameters for

depletion and mark–recapture models were estimated

by maximizing the log of the multinomial probability

that depends on differences between the observed and

predicted number of fish with different capture

histories. This approach exactly follows Otis et al.

(1978). Computations were done with AD Model

Builder (ADMB) software (Otter Research 2004).

Population density per 100 m of shoreline (N) was

calculated by dividing the most likely estimate (MLE)

of population size by the site length and multiplying by

100. The approximate asymptotic estimate of SE for

the MLE of capture probability was computed from the

inverse of the Hessian matrix returned by the ADMB

software. The coefficient of variation (CV) for capture

probability estimates, computed as the ratio of SE of

the MLE to the MLE, was used to provide a

standardized measure of uncertainty.

The influence of fish size on capture probability was

modeled using mark–recapture data, where the size

distribution of marked fish present at the start of the

recapture event is known. Data from each mark–

recapture experiment were aggregated into 10-mm fork

length-classes. The capture probability for each lengthclass was predicted by means of the following model:

pLj 1⁄4 b

1 þ exp ðL ̄jlÞ

r

h i ; ð1Þ

where pL,j is the predicted capture probability for the

10-mm size-class j (e.g., j1⁄44 for size-class 30–40 mm)

and a midpoint fork length L ̄

j (mm), b is the base

capture probability (the capture probability for which

size is not limiting, i.e., when the denominator 1⁄4 1),

and l and r are the mean and SD of the logistic fork

length–vulnerability function that determine the length

at which capture probability is 50% of the maximum

and the inverse of the slope of the relationship,

respectively. We fit equation (1) to data stratified by

habitat type as well as aggregated across habitats.

Parameters were estimated by maximizing the sum of

the log likelihood of the binomial probability of the

number of recaptures across all length-classes, that is,

ri; j ; binomialðMi; j  pLjÞ;

where pLj is the size-specific capture probability

estimate from equation (1) and ri, j and Mi, j are the

number of recaptures on pass 2 and marks applied on

pass 1 in size-class j at site i, respectively. Note that

this is equivalent to using the multinomial likelihood

from Otis et al. (1978), but without estimation of N or

consideration of the unmarked component of the

population. We refer to the size-based capture

probability model as L3 (L indicates length, 3 the

number of parameters that determine the capture

probability for each size-class). This model collapses

to a null model (L1

) in which capture probability is

assumed to be constant across size-classes by removing

the denominator in equation (1) and only estimating b.

We attempted to fit the size-based capture probability model (equation 1) to depletion data by aggregating

catches across sites within 10-mm size-classes as for

the mark–recapture data. However, parameter estimates

for this model were very uncertain because, in the case

of depletion data, it is necessary to jointly estimate the

size of the aggregate population for each size-class as

well as capture probability parameters. To avoid this

problem yet still evaluate effects of size on capture

probability, we first independently estimated capture

probability and abundance for each size-class using the

standard depletion model of Otis et al. (1978). We then

fitted linear capture probability–fork length models to

the estimates of capture probability and tested whether

the slopes of these models were significantly different

from zero. It was not necessary to transform capture

probability estimates using logit or arcsine transformations prior to conducting regression analyses. Quantile–

quantile plots showed that capture probability estimates

were normally distributed, and only 5 of 108 estimates

were less than 0.2 or greater than 0.8, for which the

effects of transformation would be substantive (Gelman

et al. 2004).

Evaluating effects of flow, habitat, and recovery

period on capture probability.—We defined a series of

candidate models that encompassed our hypotheses

about the effects of sampling, habitat type, flow, and

fish size on capture probability and then compared

these models using an information-theoretic approach.

We used the Akaike information criteria corrected for

small sample size (AICc

) for the comparisons. The

AICc statistic is used to measure the amount of

information lost among competing models by formally

recognizing the tradeoff between bias and variance

(Burnham and Anderson 2002). A more complex

model with more parameters will almost always fit the

data better than a simpler model with few parameters;

however, the parameter estimates from the more

complex model will be more uncertain. When

comparing a range of candidate models, the model

with the lowest AICc value is considered to have the

best out-of-sample predictive power. Models with

similar AICc values relative to the best model are

62 KORMAN ET AL.
considered to have strong support (DAICc 1⁄4 0–2),

while those with larger AICc values are considered to

have moderate (DAICc1⁄4 4–7) or essentially no support

(DAICc . 10).

To evaluate the evidence for changes in capture

probability across passes, we compared model D1 with

D2 for depletion data and model MR1 with MR2 for

mark–recapture data. As we compute the parameters

for each experiment individually, we refer to these

models as D1i

, D2i, MR1i, and MR2i, respectively (the i

subscript denotes individual estimates for each experiment). For each experiment, AICc was computed and

compared across models, and the sum of experimentspecific AICc values was also compared. Note that AIC

support criteria apply to all model comparisons,

whether comparing two models for a single experiment

or two models applied to a group of experiments. The

AICc for the size-based capture probability model (L3

)

was compared with the AICc from the model in which

capture probability was assumed to be constant across

size-classes (L1

). The effects of the combination of

habitat and gear type on capture probability was

evaluated by comparing models having common

capture probabilities across all experiments and habitat

types (D1c or MR2c

, where c denotes a common habitat

type) with more complex models that allowed capture

probabilities to vary by habitat type (D1h or MR2h

,

where h denotes habitat-specific stratification). We

refer to habitat-gear effects as habitat effects throughout the remainder of this paper and provide a rationale

for this nomenclature in the discussion. Note that these

models estimate common capture probabilities across

groups of experiments, but experiment-specific population sizes. In the case of mark–recapture experiments,

it was also possible to evaluate effects of habitat on

size-dependent capture probability by comparing the

sum of AICc values from habitat-specific relationships

(model L3h

) with the AICc from a model that was

common to both habitat types (model L3c

). As the

asymptotic capture probability (b from equation 1) was

similar across habitat types, we also compared L3c and

Lch with a size-dependent model with habitat-specific

means (l) and SDs (r) but a common asymptote

(model L2þ,c

).

The effect of flow on capture probability was

evaluated by comparing models in which capture

probability could vary across habitat types and across

low- (September and November) and high-flow (June–

August) months (D1h(mf) or MR2h(mf), where mf refers

to stratification by monthly flow level) with simpler

models in which capture probability could only vary by

habitat type (D1h or MR2h

). In the case of the depletion

data, we were also able to compare models in which

capture probability could vary across experiments

conducted during the daily minimum and maximum

discharges (D1h(df), where df refers to stratification by

the daily flow level) with models in which capture

probability was constant across these strata (D1h

).

Finally, for mark–recapture data, we evaluated the

effect of the period between marking and recovery by

comparing models in which capture probabilities could

vary between 1- and 24-h experiments (MR2h(rp),

where rp refers to stratification by recovery period)

with the simpler model in which capture probability

was constant across these recovery periods (MR2h

).

Evaluating the effects of density on capture

probability.—We examined the relationship between

estimates of capture probability (p) and population

density (N) to determine whether capture probability

was density dependent. These parameter estimates can

be negatively correlated owing to sampling error alone

because larger estimates of N require smaller estimates

of p (Schnute 1983). We therefore used a bootstrap

procedure to test for density dependence in p following

some of the methods of Speas et al. (2004). We

simulated both three-pass depletion and two-pass

mark–recapture data assuming binomial sampling

error. The population sizes and capture probabilities

used in the simulations were randomly selected from

ranges that bounded the estimates from our data

(simulated p 1⁄4 0.2–0.8, N 1⁄4 10–200 fish/100 m, site

length 1⁄4 50 m for depletion data from 2006; simulated

p 1⁄4 0.05–0.8, N 1⁄4 50–1,500 fish/100 m, site length 1⁄4

100 m for mark–recapture data from 2007). The most

likely estimates of p and N for each set of simulated

data were computed via a nonlinear iterative search

procedure to minimize the log-multinomial likelihood

as described above. The number of estimation failures

was also determined. For depletion data, a failure was

designated whenever the slope of the relationship

between catch on each pass and the cumulative catch

from previous passes was positive, or when the total

catch across three passes was less than or equal to one.

For mark–recapture simulations, a failure was designated whenever the number of fish caught on the first

pass, or the number of marked fish recaptured on the

second pass, was zero. The simulation–estimation

procedure was repeated, and linear ploge

(N) models

(p 1⁄4 a þ b loge

[N]) were fit to the pN estimates for

each level of simulated capture probability. Bias in

capture probability estimates was computed by comparing the estimated values with the true simulated

values (% bias 1⁄4 100 3 [estimated p simulated p]/

simulated p).

Comparisons of simulated and observed ploge

(N)

slopes were made via graphical and probabilistic

approaches. For the graphical comparison, the observed

ploge

(N) slopes were compared with slopes based on

CAPTURE PROBABILITIES IN A LARGE RIVER 63
simulated data, in which the latter slopes were

computed from a fixed range of simulated capture

probabilities (0.2, 0.4, 0.6, and 0.8) and random

population densities within the ranges specified above.

Two hundred and fifty trials were completed for each

simulated capture probability. For the probabilistic

comparison, cumulative frequency distributions (CFDs)

of ploge

(N) slopes were generated based on 100 trials

of either 19 or 47 sets of simulated depletion data, and 7

or 35 sets of simulated mark–recapture data. These

sample sizes reflect those available to estimate the

ploge

(N) slopes from our depletion or mark–recapture

data in low- and high-angle habitats, respectively.

Capture probability and density values used in the

simulations were random draws from the ranges

specified above. The value of the observed ploge

(N)

slope for each habitat type was then overlaid on the

corresponding simulation-based CFD to determine the

probability that the observed slope, or a steeper slope,

could have arisen owing to chance alone. This

probability is equivalent to a type I error rate (i.e., the

probability of incorrectly rejecting the null hypothesis

of no density dependence in capture probability).

Results

Population Closure and Capture Probability Estimates

There were very few captures of marked fish in 25-m

shorelines bordering the downstream and upstream

boundaries of mark–recapture sites. Capture of one or

more marked fish in these areas occurred in two of

seven experiments in low-angle habitat, and in 10 of 35

experiments in high-angle habitat. Incidences of

marked fish being captured outside of the original

sites were limited to the 24-h recovery experiments. Of

1,060 and 1,906 marked fish released in low- and highangle habitats, respectively, only 0.47% (n 1⁄4 5) and

0.68% (n 1⁄4 13) were recaptured in adjacent areas. The

total emigration rates in low- and high-angle habitats,

estimated by expanding the number of marked fish

captured in adjacent areas for each experiment by the

estimated capture probabilities on the second pass

(Figure 1), were 2.61% and 2.24%, respectively.

Averaged across all mark–recapture experiments, there

was an initial mortality due to electrofishing and

capture of 8% (CV 1⁄4 0.37) and 20% (CV 1⁄4 0.57) in

low- (backpack) and high-angle (boat electrofishing)

habitats, respectively. Based on 24-h holding experiments, survival was 100% for all 194 fish captured by

backpack electrofishing (96 stained fish and 98 clipped

fish, fork lengths ranging from 30 to 74 mm), and for

all 157 fish caught by boat electrofishing (85 stained

fish and 72 clipped fish, fork lengths ranging from 40

to 110 mm).

There was essentially no support for the more

complex depletion model that estimated different

capture probabilities for the first and subsequent passes

(D2

). Out of 66 experiments, there were only three cases

in which the AICc from D2i was lower than values from

D1i by more than two units. Summed across all

experiments within habitat types, there was essentially

no support for D2i relative to D1i in both low- and highangle habitats (Table 4). In contrast, the AICc for MR2i

was lower than the AICc for MR1i by more than two

units in 21 out of 42 experiments, and there was strong

support for MR2i relative to MR1i when the AICc values

were summed across experiments (Table 5). The mean

difference between capture probability estimates on the

first pass and second passes across the 42 experiments

was 0.03. This suggests that while there was strong

evidence for variation in capture probabilities between

the marking and recapture passes for individual

experiments, there was no general tendency for either

higher or lower capture probabilities on the second pass.

Based on these results, we used models D1 and MR2 for

subsequent analyses of depletion and mark–recapture

data, respectively.

The average capture probability across 66 depletion

experiments based on model D1i was 0.54 with 80% of

the estimates falling between 0.27 and 0.75 (Figure 1).

The average capture probability on the first and second

passes across 42 mark–recapture experiments based on

model MR2i was 0.31 and 0.28 with 80% of the

estimates falling between 0.17 and 0.48 and between

0.16 and 0.43, respectively (Figure 1). The sampling

error of the capture probability, indexed by the average

of CVs from individual estimates, was 0.26 for both

depletion and mark–recapture experiments.

Effects of Fish Size on Capture Probability

Size-dependent capture probability models based on

mark–recapture data in low- and high-angle habitats

(models L3h

) had strong support relative to models in

which capture probability was assumed to be independent of size (models L1h

; Table 6). The logistic sizedependent capture probability models (equation 1) fit

the length-stratified mark–recapture data well, explaining 90% of the variability in the MLEs of lengthstratified recapture rates (Figure 2a). Fork length also

explained 94% and 71% of the variation in capture

probabilities from depletion experiments independently

estimated for each size-class in low- and high-angle

habitat, respectively (Figure 2b). The slopes of the

relationships were significantly different than zero (P 1⁄4

0.006 and 0.002, respectively).

Effects of Habitat on Capture Probability

The effect of habitat type on capture probability

depended on data type and whether or not the effects of

64 KORMAN ET AL.
fish size were accounted for. Based on depletion data,

there was strong support for both habitat-dependent

(sum of AICc values for D1h models across habitat

types: 281.7 þ 730.9 1⁄4 1,012.6) and independent

models (D1c 1⁄4 1,010.5), and the most likely estimates

of the capture probabilities across habitat types were

very similar (Table 4; Figure 3a). In contrast, there was

strong support for habitat-specific capture probability

models (MR2h

) relative to the habitat-aggregated model

(MR2c) based on mark–recapture data (Table 5). In this

case, capture probability in low-angle habitat tended to

be greater than that in high-angle habitat (Figure 3b),

especially on the first pass (Table 5). A similar result

was obtained from the size-stratified analysis (Table 6).

There was strong support for the habitat-dependent

models (L3h

) relative to the habitat-aggregated one

(L3c

). The major difference between models in this case

was the higher capture probability of small fish (lower

l) in the low-angle habitat type. Asymptotic capture

probabilities (b) were similar among habitat types. As a

result, the model which assumed that the b was

constant across habitat types (L2þ,c

) had slightly better

predictive power than the model that allowed all three

parameters to vary (Table 6).

Effects of Flow on Capture Probability

There was little evidence to suggest that flow

influenced capture probability based on differences

across flows within a day, but flow effects were

somewhat confounded with the effects of fish size in

the case of the across-month flow comparisons. The

most likely estimates of capture probabilities based on

depletion experiments at the daily minimum and

maximum flows, and in high- and low-flow months

FIGURE 1.—Most likely estimates of capture probabilities from (a) depletion and (b) mark–recapture experiments (by

experiment number) based on models D1i and MR2i

, respectively (see text). Error bars denote the SEs of the estimates. The

dashed lines represent the average capture probabilities in low- and high-angle habitats. Experiments are presented in

chronological order within habitat types.

CAPTURE PROBABILITIES IN A LARGE RIVER 65
based on both depletion and mark–recapture data,

differed by no more than 0.08 (Tables 4, 5; Figure 3a).

Depletion models applied to data from low-angle

habitat, which accounted for daily (D1h(df)) or monthly

(D1h(mf)) effects of flow changes, had very similar AICc

values to those from models that did not (D1h; Table 4;

Figure 3a). The addition of a flow effect resulted in a

negligible improvement in fit as evidenced by almost

equivalent log-likelihood values. In this case, the more

complex flow-dependent models are not supported by

the data even though the AICc values are close (see

Burnham and Anderson 2002:131). Small differences

in the magnitude of the flow effect reinforce this result

(Figure 3a). A similar result was obtained for the daily

flow change model in high-angle habitat (D1h(df)). In

contrast, there was moderate support for the monthly

flow effect model in high-angle habitat (D1h(mf)).

However, in this case, fork length increased substantially between high- (July–August) and low- (September and November) flow months (Tables 2, 3), making

it difficult to separate the effects of fork length and

flow on capture probability. A similar result occurred

for the monthly flow comparison in high-angle habitat

from mark–recapture data (Table 5; MR2h(mf) versus

TABLE 4.—Summary of AIC results comparing alternate models applied to depletion data. The column headings p, k, LL, and

AICc denote the most likely capture probability estimates, the number of parameters, the log likelihoods, and Akaike information

criterion values adjusted for small sample size. Subscripts for model names denote the number of capture probabilities (1 1⁄4

common across passes, 21⁄4different probabilities between the first and subsequent passes) and stratification (i1⁄4by experiment, h

1⁄4 by habitat type, df1⁄4 by daily flow, mf1⁄4by monthly flow, and c1⁄4 combined across habitat types). For brevity, the most-likely

estimates for p for the experiment-stratified models are not shown, but the values for D1i and MR2i are shown in Figure 1; N

denotes population size. See text for more details about the models.

Habitat Model Stratum p k LL AICc

Model type (N and p estimated for each experiment)

Low angle D1i 38 106.4 294.3

D2i 57 96.9 320.7

High angle D1i 94 253.1 705.4

D2i 141 234.4 776.8

Flow and habitat effects (N estimated for each experiment but p common)

Low angle D1h 0.50 20 120.1 281.7

D1h(df) Daily minimum 0.48 21 119.6 282.8 Daily maximum 0.54

D1h(mf) High flow 0.50 21 119.9 283.4 Low flow 0.55

High angle D1h 0.51 48 316.0 730.9 D1h(df) Daily minimum 0.50 49 314.1 729.1 Daily maximum 0.57

D1h(mf) High flow 0.48 49 311.5 724.0 Low flow 0.57

Combined D1c 0.51 67 436.2 1,010.5

TABLE 5.—Summary of AIC results comparing alternative models applied to mark–recapture data. The abbreviation rp stands

for recovery period; other abbreviations and subscripts are defined in Table 4.

Habitat Model Stratum p1 p2 k LL AICc

Model type (N and ps estimated for each experiment)

Low angle MR1i 14 129.3 286.8

MR2i 21 93.3 229.1

High angle MR1i 70 372.4 887.2

MR2i 105 257.2 730.1

Flow and habitat effects (N estimated for each experiment but ps common)

Low angle MR2h 0.43 0.35 9 195.5 409.1

High angle MR2h 0.29 0.29 37 419.3 913.2

MR2h(mf) High flow 0.26 0.29 39 401.3 881.4 Low flow 0.34 0.29

Combined MR2c 0.34 0.31 44 644.4 1,377.5

Recovery period (N estimated for each experiment but ps common)

Low angle MR2h(rp) 1 h 0.55 0.47 11 131.7 285.6 24 h 0.27 0.20

High angle MR2h(rp) 1 h 0.28 0.30 39 417.5 913.7 24 h 0.30 0.29

66 KORMAN ET AL.
MR2h

), mainly owing to higher capture probabilities

during low-flow months on the first pass. The fish

size–monthly flow effect confounding was also seen in

the size-stratified analysis for high-angle habitat (Table

6), in which the increase in the number of parameters in

the flow-stratified model (L3h(mf)) relative to the model

that did not account for flow (L3h

) was almost identical

to the increase in the log likelihood across models. As a

result, the AICc values for both models were the same.

Effects of Recovery Period on Capture Probability

Capture probabilities based on 1-h recovery experiments tended to be higher than those from 24-h

experiments, but the magnitude of differences depended on habitat type. The most likely estimate of capture

probability on the second pass of mark–recapture

experiments with a 1-h recovery period in low-angle

habitat was over twice the value based on experiments

with a 24-h recovery period (Table 5; Figure 3b). The

model that accounted for recovery time was strongly

supported relative to the model that did not. The

capture probabilities for the 1- and 24-h recovery

period experiments in high-angle habitat were very

similar, and the difference in AICc values between the

models was negligible. However, in high-angle habitat,

the distribution of 1-h recovery experiments was

concentrated in early months when fish were smaller

relative to the 24-h experiments (Table 3). Thus, the

effect of recovery period was confounded with the

effect of fish size. When the effect of size was

accounted for by repeating the analysis using the sizedependent model, there was moderate support for the

model that accounted for recovery period (L3h(rp))

relative to the model that did not (L3h

; Table 6). There

was strong support for the size-stratified recovery

period model in low-angle habitat.

Density Dependence and Bias in Capture Probability

The effect of density on capture probability

estimates depended on both habitat type and the

method used to estimate capture probability. Based

on depletion data, there was little evidence for density

dependence in capture probability estimates in lowangle habitat, but strong evidence in high-angle habitat.

Capture probability estimates were negatively correlated with estimates of loge population density (Figure 4a,

b; Table 7) and the slopes were significantly different

than zero in both low- (n 1⁄4 19; slope 1⁄4 0.136; P ,

0.001) and high-angle habitats (n1⁄447; slope1⁄40.175;

P , 0.001). However, simulations revealed that the

expected slope of the ploge

(N) relationships due to

sampling error increased as capture probability was

reduced (Figure 4a, b [dashed lines]). Based on the

bootstrap analysis of expected ploge

(N) slopes, the

probability that the observed slope of the ploge

(N)

relationship could be due to chance alone was 23% in

low-angle habitat, but only 1% in high-angle habitats

(Figure 5a). The difference in probabilities of densitydependent effects among habitat types was due both to

the lower observed ploge

(N) slope in low-angle

habitat as well as the greater variance in the distribution

of expected slopes because of smaller sample size.

For the mark–recapture experiments, there was

strong evidence for density dependence in capture

probability estimates in low-angle habitat but little

evidence for this dynamic in high-angle habitat. The

strength of the negative correlation between capture

probability and loge density varied by habitat type

(Figure 4c, d; Table 7). In low-angle habitat, the slope

TABLE 6.—Summary of AIC results comparing alternate models applied to mark–recapture data stratified by 10-mm fork

length-classes. Column headings b, l, and r denote the maximum, mean, and SD of the size–capture probability function

(equation 1). See Tables 4–5 for additional details.

Habitat Model Stratum blr k LL AICc

Habitat and flow effects

Low angle L1h 0.31 1 139.9 281.9

L3h 0.34 26.61 2.60 3 128.4 262.8

High angle L1h 0.29 1 364.8 731.7

L3h 0.31 39.89 4.57 3 348.5 703.0

Combined L3c 0.31 27.21 3.49 3 492.5 990.9

L2þ,c Low angle 0.32 25.25 0.46 5 477.4 964.8 High angle 0.32 40.23 4.85

High angle L3h(mf) High flow 0.33 39.95 4.57 6 345.5 703.0 Low flow 0.30 45.00 0.00

Recovery period effect

Low angle L3h(rp) 1 h 0.52 25.02 0.40 6 82.4 176.9 24 h 0.24 29.52 4.39

High angle L3h(rp) 1 h 0.33 35.42 4.33 6 341.5 695.0 24 h 0.31 45.00 0.01

CAPTURE PROBABILITIES IN A LARGE RIVER 67
was steep and significant (n 1⁄4 7; slope 1⁄4 0.249; P 1⁄4

0.011), while in high-angle habitat it was not (n 1⁄4 35;

slope 1⁄4 0.020; P 1⁄4 0.42). Simulations showed that

when a large number of mark–recapture experiments

are conducted (n 1⁄4 250), there is little correlation

between p and N (Figure 4c, d). This occurs because,

unlike the case for depletion experiments, estimates of

capture probability on the second pass are not

dependent on population size because they are based

on the recovery rate of a known number of marked fish.

This difference also results in lower variance of the

distributions of expected ploge

(N) slopes based on

mark–recapture relative to depletion experiments

(Figure 5). The observed slope in low-angle habitat

was relatively steep, and comparison with the CDF

suggests there was a less than 1% probability that it

could have arisen owing to chance alone. In contrast,

the probability that the observed slope in high-angle

habitat could be due to sampling error was 32%.

The correlation between density and fork length

confounded the evaluation of the effects of density on

capture probability. The loge of density was signifiFIGURE 2.—Relationships between capture probability and fork length in low- (solid black lines) and high-angle (gray dashed

lines) habitat types based on (a) mark–recapture and (b) depletion data. Panel (a) shows the best-fit logistic relationships

(equation 1) with habitat-specific data as well as data combined across habitat types (black dashed line). The data points in

represent the ratios of recaptured fish across experiments to the total number of marked fish, by 10-mm size-class and habitat

type (i.e., independent Peterson estimates). The numbers at the top of panel (a) are the total marked fish and recaptures in each

length class, along with the totals across length-classes (in parentheses). Note that the data point for the 85-mm length-class in

low-angle habitat is not shown (capture probability 1⁄4 1), as it exceeds the maximum value on the y-axis scale. In panel (b), the

data points are the best-fit capture probabilities independently estimated for each size-class; the lines show the best-fit linear

relationships.

68 KORMAN ET AL.
cantly negatively correlated with fork length based on

data from both depletion and mark–recapture experiments in both habitat types (Table 7). This occurred

because fish densities declined and fish grew over the

sample period from early summer through late fall and

because within sampling periods, populations at sites

with higher fish densities tended to be comprised of

smaller fish (Figure 4). The bootstrap analysis implied

strong support for density dependence in capture

probabilities based on depletion data in high-angle

habitat and on mark–recapture data in low-angle

habitat (Figures 4, 5). However, these were also the

only cases in which the relationships between capture

probability and fork length were both positive and

significant (Table 7), and in which the confounding

between size, density, and capture probability was

apparent in the size-stratified capture probability–

density relationships (Figure 4b, c).

Simulations demonstrated that capture probability is

substantially overestimated from depletion data when

the true capture probability is low and population size

at discrete sites is small. Depletion estimation failure

rates were 25%, and capture probability was overestimated by 54% at a simulated capture probability of

FIGURE 3.—Most likely estimates of capture probability from (a) depletion and (b) mark–recapture experiments in low- and

high-angle habitat based on different models (see Tables 4–5). The error bars denote the 95% confidence intervals. The capture

probabilities in panel (a) are based on the depletion model assuming the same capture probability across passes. The capture

probabilities in panel (b) are based on the mark–recapture model assuming that capture probabilities differ across passes; values

for the second pass are shown.

CAPTURE PROBABILITIES IN A LARGE RIVER 69
0.2 across the range of densities we simulated. The

percent bias in capture probability (100 3 [estimated

value simulated value]/simulated value) increased

with decreasing population size when capture probability was 0.4 or less (Figure 4a, b [dashed lines]). At a

simulated capture probability of 0.3 (which is close to

the observed mean from mark–recapture experiments),

capture probability was overestimated by 23%, and the

estimation failure rate was 15% across the range of

densities we simulated. Failure rate and bias in

depletion estimates were minor or negligible at capture

probabilities of 0.6 or more, regardless of density. In

contrast, there was virtually no estimation failures or

bias (,0.4%) at any of the simulated capture

probabilities for mark–recapture experiments.

Discussion

This study has demonstrated that it is feasible to

estimate capture probabilities for juvenile fish in a

range of large river habitat types using a combination

of backpack and boat electrofishing. Capture probabilities based on both depletion and mark–recapture

experiments were reasonably precise (CV 1⁄4 0.26).

While the estimates from the depletion experiments

FIGURE 4.—Relationships between estimated capture probability and population density in (a) low- and (b) high-angle habitats

from depletion experiments and (c) low- and (d) high-angle habitats from mark–recapture experiments. The symbols (see panel

[b]) denote the average fork lengths on the first pass in 10-mm increments. The best-fit log-linear relationships to the estimates

are shown as solid lines. The expected relationships due to sampling error under a range of simulated capture probabilities (0.2–

0.8) and random densities are shown as the dashed lines. The open diamond in panel (c) denotes a point that is off the graph, the

true coordinate being given in parentheses.

TABLE 7.—Pearson correlation coefficients for the relationships between loge population density (loge[N]), capture probability

(p), and fork length on the first pass (FL) based on depletion and mark–recapture data in low- and high-angle habitats; 0.01 , P

 0.05*; 0.001 , P  0.01**; P  0.001***.

Method Habitat Sample size loge(N)p loge(N)FL pFL

Depletion Low angle 19 0.59** 0.48* 0.20

High angle 47 0.70*** 0.35* 0.29a

Mark–recapture Low angle 7 0.87* 0.87* 0.77*

High angle 35 0.14 0.48** 0.10

a P 1⁄4 0.052 for this correlation.

70 KORMAN ET AL.
(mean p1⁄40.54) were higher than those from the mark–

recapture experiments (mean p 1⁄4 0.31 and 0.28 on the

first and second passes, respectively), both were

sufficiently large to allow reasonably precise estimation of population sizes at discrete sites. Capture

probability increased with fish size in both mark–

recapture and depletion experiments, and field data

supported the assumption that populations within

discrete sites can be treated as effectively closed.

Given that capture probability has been shown to

decline with increasing stream size (Peterson et al.

2004; Rosenberger and Dunham 2005), one might

expect capture probability to be low in larger river

systems like the Colorado River. Our data suggest that

this is not the case, as capture probability estimates

were within ranges reported for smaller streams. Eighty

percent of depletion-based estimates were between

0.28 and 0.75, similar to ranges reported for juvenile

brown trout (0.4–0.6; Wyatt 2002), bull trout Salvelinus confluentus and cutthroat trout O. clarkii (0.2–0.6;

Peterson et al. 2004), and rainbow trout (0.5–0.65;

Rosenberger and Dunham 2005). Eighty percent of

mark–recapture-based estimates of capture probability

fell between 0.17 and 0.45, a range similar to those

reported for bull trout and cutthroat trout (0.1–0.3;

Peterson et al. 2004) and rainbow trout (0.3–0.5;

Rosenberger and Dunham 2005). The range in our

capture probability estimates was larger than the ranges

reported in other studies, perhaps because we sampled

age-0 trout over the growing season, in which fish size,

and therefore vulnerability to capture, changed substantially.

Data from holding and mark–recapture experiments

supported the fundamental assumption that populations

at discrete sites are effectively closed. Holding

experiments showed that there is very likely negligible

mortality of marked fish after release for at least 24 h.

In large rivers, it is not logistically feasible to enclose

mark–recapture or depletion sites with stop nets as is

commonly done in small streams. However, capture of

marked fish in 25-m sections adjacent to mark–

recapture sites was extremely rare, indicating that

populations within sites can be treated as effectively

closed for the 24-h period between release and

recapture. This conclusion is supported by studies that

show limited effects of electrofishing (Dunham et al.

2002) and electrofishing-based capture and marking

(Mitro and Zale 2002; Young and Schmetterling 2004)

on salmonid movement, as well as those showing that

salmonids tend to have very restricted movements over

short and sometimes extended time periods (e.g.,

Edmundson et al. 1968; Roni and Fayram 2000;

Rodriquez 2002). It is certainly possible that some

marked fish moved beyond the 25-m lengths of

shoreline that was sampled upstream and downstream

of mark–recapture sites, and that we therefore underestimated the extent of emigration and capture

probability. However, the proportion of a population

that is displaced over increasing large distances is well

described by a steep negative slope (see the metaanalysis of Rodriquez 2002). Considering that there

were few individuals found within the 25-m shoreline

areas bordering the mark–recapture sites, the number of

fish that migrated further than this distance must be

very small and would therefore have a minor effect on

capture probability estimates. In addition, had emigration out of depletion and mark–recapture sites been a

significant problem in our study, capture probability

estimates should have been lower than those reported

for smaller streams in which sites were enclosed with

stop nets, which was not the case.

There was strong evidence from mark–recapture and

depletion experiments that capture probability increased with fish size. A positive relationship between

fish length and electrofishing capture probability, such

as the ones estimated in this study from mark–recapture

data, is consistent with many other investigations

(Borgstrom and Skaala 1993; Anderson 1995; Bayley

FIGURE 5.—Cumulative frequency distributions of the

expected slopes of the capture probability–log population

density relationship (p 1⁄4 a þ b loge

[N]) generated from

simulated data (solid lines) compared with those of the slopes

fit to the data (vertical dashed lines [slopes of the solid lines in

Figure 4]) based on (a) depletion and (b) mark–recapture data.

The distributions were computed by estimating slopes from

100 sets of simulated data based on the actual sample sizes of

19 (low angle; black lines) and 47 (high angle; gray lines) to

represent depletion experiments and seven (low angle) and 35

(high angle) to represent mark–recapture experiments.

CAPTURE PROBABILITIES IN A LARGE RIVER 71
and Austen 2002; Peterson et al. 2004) and is not

surprising considering larger fish have a greater headto-tail voltage potential in an electric field, are easier to

see and net, and make less use of interstitial spaces

relative to smaller fish and are therefore easier to

capture. However, the relationship between size and

capture probability should be estimated for each

specific study, as the functional form can be variable,

ranging from linear (e.g., Borgstrom and Skaala 1993),

to logistic (Peterson et al. 2004; this study), to dome

shaped (Bayley and Austen 2002). The form and

parameters will probably depend on the range of fish

sizes available for capture, gear type, habitat, environmental variables, and fish behavior.

We found significant differences in capture probability across habitat types from mark–recapture experiments. Capture probability tended to be higher in lowangle habitat sampled by backpack electrofishing. The

mean of the size–capture probability function in highangle habitat sampled by boat electrofishing (l 1⁄4 39.9

mm) was greater than in low-angle (l 1⁄4 26.6 mm)

habitat sampled by backpack electrofishing, which

implies lower vulnerability of smaller fish in highangle habitat, a result consistent with depletion data.

This was probably caused by the larger interstitial

spaces between talus blocks in high-angle shorelines,

making it more difficult to see and retrieve very small

fish that were stunned, and because the very immediate

shoreline areas utilized by smaller fish could be more

effectively sampled with a backpack electrofisher than

a boat electrofisher. Our evaluation of ‘‘habitat’’ effects

on capture probability could perhaps be more accurately described as a comparison of ‘‘habitat and gear

type’’ effects. We argue that such a distinction is

irrelevant; what matters is that capture probability be

quantified by habitat type, regardless of whether

different gears, or ways of using the same gear, are

employed. Or stated more broadly, it is not necessary

to use the same gear to quantify relative habitat use as

long as the differences in capture probability between

specific combinations of habitat and gear are accounted

for.

We found that flow did not affect electrofishing

capture probability. Physical conditions within immediate nearshore habitats in the Lee’s Ferry reach are not

very sensitive to flow, at least over the range

experienced in this study. Measurements of nearshore

(1.5 m from shore) average water column velocities

across 24 sites in 2004, taken at discharges of 260

(daily minimum flow) and 500 (daily maximum flow)

m3

/s (very close to the range in this study; Table 1),

differed by no more than 3–6 cm/s (see Table 1 from

Korman and Campana 2009). In large rivers, the

velocities in the immediate nearshore environment that

can be sampled by electrofishing are less influenced by

discharge than those in smaller rivers because the ratio

of nearshore sample width to the total wetted width is

much lower. We suspect this is why our capture

probability estimates were relatively insensitive to the

effects of flow, and perhaps why capture probability

has been shown to be sensitive to indices of flow (such

as cross-sectional area) in smaller systems (e.g.,

Rosenberger and Dunham 2005).

The effects of fish density on capture probability

were challenging to discern, variable among habitat

types and estimation methodologies, and confounded

with the effect of fish size. Using bootstrap simulation,

we concluded there was a significant relationship in

high-angle habitat based on depletion data, and in lowangle habitat based on mark–recapture data. However,

these were also the cases in which a negative

correlation between fish size and density was most

apparent. Density-dependent growth in stream-dwelling populations of age-0 salmon and trout has been

well documented (e.g., Armstrong 1997; Jenkins et al.

1999; Imre et al. 2005), and will result in a negative

correlation between density and fish size among sites

sampled within a short time interval, and among sites

sampled through time. Cumulative growth and mortality over the growing season will also result in a

negative correlation between density and fish size

based on samples collected through time, even in the

absence of density-dependent growth (e.g., Elliott

1994). Effects of density and fish size on capture

probability are separable by manipulations of size and

density in artificial ponds or streams (e.g., Bayley and

Austen 2002). In field studies of juvenile fish such as

the one presented here, it will probably be very difficult

to empirically separate the effects of fish density and

size on capture probability. However, this difficulty is

not necessarily a problem in assessments of juvenile

abundance if the size–density relationship is stationary,

and the relationship between size and capture probability is accounted for in the estimation of capture

probabilities.

The capture probabilities determined from depletion

experiments were on average 80% higher than those

based on mark–recapture. Results from the simulation

study and previous investigations strongly suggest that

the latter estimates are more realistic. Positive bias in

capture probabilities estimated from the depletion

method occurs because of both model misspecification

and the nature of the likelihood function. There was not

enough information in the depletion data to select a

removal model that allowed capture probability to

decline with successive passes, or even between the

first pass and later ones. However, it is well recognized

that the power of such tests is generally very low (Otis

72 KORMAN ET AL.
et al. 1978; Rosenberger and Dunham 2005). Failure to

account for declining capture probability across

successive passes of electrofishing has been shown to

result in overestimates in capture probability of 39%

for bull trout and cutthroat trout (Peterson et al. 2004),

and 30–50% for rainbow trout (Rosenberger and

Dunham 2005), with the extent of bias being greater

for smaller fish that generally have lower capture

probability. Our simulations showed that even if

capture probability is constant over passes, it can still

be substantially overestimated if population size and

capture probability are low. For example, at a true

capture probability of 0.3, capture probability will be

overestimated by 25% at densities of 100 fish/100 m

(or 50 fish in a typical 50-m site). This bias occurs

because the multinomial likelihood function used in

Otis et al. (1978) is derived from probabilities

associated with finite samples, and these probabilities

depend on sample size (Schnute 1983). For example,

the probability of obtaining five heads of a perfectly

balanced coin flipped 10 times will be higher than the

probability of obtaining 50 heads if it is flipped 100

times. Thus, when jointly estimating capture probability and population size in the depletion method by

maximizing the likelihood function, slightly higher

probabilities occur at lower population sizes, resulting

in the tendency to overestimate capture probability.

The combined bias associated with model misspecification reported from previous studies, and from the

likelihood function estimated in this study, implies our

depletion-based estimates of capture probability are

approximately 50–75% too high. The 80th percentile

range of capture probability estimates from depletion

experiments (0.28–0.75), adjusted for biases of 50%

and 75%, were 0.19–0.50 and 0.16–0.43, respectively.

These ranges are much closer to the range from our

mark–recapture experiments of 0.18–0.37.

We recommend that mark–recapture experiments,

rather than depletion experiments, be used to estimate

capture probabilities for juvenile fish in large rivers.

Our recommendation is similar to those from recent

studies conducted in smaller systems (Peterson et al.

2004; Rosenberger and Dunham 2005; Sweka et al.

2006). Over the range of capture probabilities and

population densities experienced in this study, simulation results showed that values determined from

depletion experiments were probably substantially

overestimated owing to the likelihood function.

Differences between mark–recapture and depletion

estimates suggest there was additional bias due to

changing capture probability over passes, a dynamic

that could not be detected from the depletion data

alone. Direct estimation of size-dependent capture

probabilities should be a fundamental component in

the evaluation of juvenile populations if fish size has

the potential to vary substantially over the study period

or among study sites. Mark–recapture experiments

have a distinct advantage over depletion methods in

this respect because they do not require the estimation

of abundance by size-class, reducing the number of

parameters that need to be estimated. Finally, mark–

recapture experiments allow for field-based validation

of key closure assumptions. These assumptions must

be evaluated when electrofishing at discrete sites owing

to the potential for latent mortality and emigration after

release. In this study, we did not test whether marked

fish had the same capture probability as unmarked fish.

We are currently evaluating this assumption by using

different gear types for capture (dipnetting via

snorkeling) and recapture (e.g., electrofishing) passes,

an approach that cannot be used in depletion studies

unless capture probability is allowed to vary among

passes. Although our study was based only on juvenile

rainbow trout, it is likely that the general approach and

recommendations are applicable to a wide range of fish

species.

The dynamics of capture probability for juvenile fish

are complex because they depend in large part on

patterns of behavior and habitat use that occur over a

wide range of temporal and spatial scales. For example,

in this study we showed that daily changes in flow do

not influence capture probability within immediate

nearshore zones that were sampled. However, in a

companion paper (Korman and Campana 2009) we

show that most age-0 trout in the Lee’s Ferry reach do

not migrate with the waters edge as it rises and falls

over a 24-h period with changing discharge. At the

daily maximum flow, most fish remain further offshore

closer to or within the portion of the channel that is

continuously wetted over 24 h. As a result, fish

densities within the immediate nearshore zones that are

sampled at the daily maximum flow were 50–80%

lower than when sampled at the daily minimum. Thus,

if we define capture probability as the proportion of

fish that are caught over a cross section of the river or

on a reachwide basis, rather than within the immediate

shoreline zone of sampling areas (as in this study), flow

can have an effect on capture probability because of its

influence on fine-scale patterns of habitat use. In a

long-term study of recruitment dynamics in the Lee’s

Ferry reach (Korman 2009), we have controlled for this

effect by sampling only at the daily minimum flow,

which is why most of the depletion and mark–recapture

experiments in this study were conducted at the

minimum flow. The long-term study has also clearly

documented an ontogenetic habitat shift from low- to

high-angle shorelines that occurs over a period of a few

months. Had we only used backpack electrofishing to

CAPTURE PROBABILITIES IN A LARGE RIVER 73
sample age-0 trout, a tactic common to many juvenile

fish assessments in rivers, our sampling universe would

have been restricted to low-angle shorelines. Estimates

of capture probability in this habitat type over the

growing season, which would increase with fish size,

would not detect the reachwide decline in capture

probability that results from an increasing proportion of

the population moving to habitats outside of the

sampling universe. Thus, to make valid reach- or

systemwide assessments of juvenile fish populations, it

is not sufficient to simply estimate capture probability

at discrete sites that are logistically or financially

efficient to sample. Rather, sampling and capture

probability estimation should be conducted over the

full range of habitats that are used over the period of

interest, which, in many cases, will probably require

use of more than one gear type and considerably more

effort than is commonly applied.

Acknowledgments

This project was supported through a cooperative

agreement between the U.S. Geological Survey and

Ecometric Research, Inc. Scott Decker, Mike Bradford,

Eric Parkinson, and Brent Mossop provided helpful

comments on an earlier draft. Thanks to Dave Foster,

Steve Jones, Stuart Reeder, and Matt Kaplinski for

assisting with electrofishing, and to Ted Melis, Barbara

Ralston, Carol Fritzinger, and Matthew Andersen of

the Grand Canyon Monitoring and Research Center for

logistical and administrative support. Two anonymous

reviewers and an associate editor from the Transactions of the American Fisheries Society provided

suggestions that greatly improved the quality of this

manuscript.

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