Report to the Adaptive Management Work Group,

Glen Canyon Dam Adaptive Management Program

An Independent Review of Ongoing and Proposed Scientific Methods to Assess the Status

& Trends of the Grand Canyon Population of the Humpback Chub (Gila cypha)

Report of a Workshop Conducted During 6-7 November 2003 at the National Center for

Ecological Analysis and Synthesis, Santa Barbara, California

Prepared by:

James F. Kitchell (Chair), Univ. of Wisconsin, Madison WI

Churchill Grimes, National Marine Fisheries Service, Santa Cruz CA

Steven T. Lindley, National Marine Fisheries Service, Santa Cruz CA

David Otis, Iowa State University, Ames, IA

Carl Schwarz, Simon Fraser University, Burnaby, British Columbia, Canada

Report Contents:

Pages 2-4

Pages 5-6

Pages 7-8

Pages 9-18

Pages 19-20

Executive Summary

Appendices

I. Scope of Work

ll. Agenda

1lI. Technical Assessment

Submitted: 5 December 2003
2

Executive Summary

In response to controversy over the methods employed in estimating abundance of

endangered humpback chub (Gila cmha) in the Colorado River, the Adaptive Management

Work Group of the Glen Canyon Dam Adaptive Management Program (GCDAMP) authorized

Grand Canyon Monitoring and Research Center (GCMRC) staff to convene a workshop in

review of the alternative methods currently employed. At present, there .are six populations of

humpback chub in the Colorado River Basin. The Grand Canyon population plus five discrete

populations identified in the Upper Basin as distributed in each of three rivers; one in the Yampa

River, one in the Green River and three in the upper reaches of the Colorado River above Lake

Powell. Mark-recapture methods of population estimation have been employed in the Grand

Canyon since the 1980's. Similar work began more recently in the Upper Basin sites.

The central controversy surrounds assumptions and methods of data analysis. Two

approaches are employed. Closed population approaches, such as those employed in Upper

Basin studies, are based on the assumption that all members of the population are vulnerable to

sampling and that no animals leave or enter the population between sampling occasions.

However, these models do allow relaxation of the assumption that all animals are equally

vulnerable to capture on a given sampling occasion. Open population approaches, such as the

Age-Structured Mark-Recapture (ASMR) model employed by GCMRC studies, assume that the

population size can change over time due to mortality/emigration or recruitment/immigration.

Vulnerability to capture can differ among sampling occasions, and age of fish can also influence

vulnerability. However, open population models assume that all fish of a given age class are

equally vulnerable to capture on a given sampling occasion. These differences in assumptions

are critical. They evoke alternative approaches to data analysis that are central to the basi

questions of population abundance, trend in abundance and recruitment.

A member of the GCDAMP Science Advisory Board, James Kitchell, was asked to organize

this review by developing a Panel of Independent Reviewers to meet with representatives of the

ongoing programs in the Grand Canyon and the Upper Basin. During the period of 6-7

November 2003, this meeting was convened at the National Center for Ecological Analysis and

Synthesis in Santa Barbara, California.

Members of the Independent Panel were chosen because of their experience and expertise in

fish population estimation. The Panel included Churchill Grimes and Steve Lindley of the

National Marine Fisheries Service Laboratory in Santa Cruz CA. Both were selected because of

their extensive experience in working with analogous issues for endangered salmon stocks.

Other members included Carl Schwarz, Simon Fraser University, and David Otis, Iowa State

University. Both are well-known biometricians specializing in the development of models used

in analysis of population data. Prior to the meeting, all members of the Panel were provided with

background material describing current practices by GCMRC and Upper Basin programs.

The Scope of Work (Appendix I) guided our focus. The Agenda (Appendix II) outlines

presentations by representatives of the GCMRC staff and the Upper Basin. Tom Czapla

forwarded a power point presentation as part of his participation by conference call. Discussion

participants and observers included James Rice and William Pine of North Carolina State

University. Both are authors of an extensive review of fish population estimation methods that

appeared in a recent issue of the American Fisheries Society journal, Fisheries (pine et al. 2003).

Also among the observers were Steve Gloss, GCMRC, and Randy Peterson, Bureau of'-
3

Reclamation. Conference calls provided input by Tom Czapla, USFWS, and Chuck McAda,

USFWS. The Panel's review is explicitly detailed in the Technical Assessments (Appendix III).
4

As an overview, the five charges presented in the Scope of Work and the Panel's finding

are paraphrased in the following.

1. Are methods used in the Grand Canyon appropriate for determining status and trends

of the humpback chub population there?

The ASMR model is a variant of well-established and proven approaches. Its purpose

is to reduce the bias in abundance estimates by accounting for changes in both juvenile and adult

vulnerabilities to capture as adults move into or out of the LCR, and to utilize infonnation on

survival from previous tagging in estimation of capture probabilities for each year. The ASMR

method accounts for those dynamics, but can be improved to remove potential biases due to

additional sources of variation in capture probabilities.

2. Are Upper Basin methods appropriate for use in the Grand Canyon?

The ASMR is most appropriate for the Grand Canyon work because it takes advantage

of spawning aggregations in the LCR and efficiently uses the extensive data collected over a

longer period of sampling there. Work in the Upper Basin is limited by the shorter time series,

less extensive sampling, and the consequent constraint on providing estimates of recruitment,

mortality rates, and/or trend in abundance. As more data become available in the Upper Basin

studies, more complex models such as the ASMR can be applied. Upper Basin methods shoUld

not replace those currently employed in the Grand Canyon. There is no compelling scientific

reason to change the basic spring sampling schedule for Grand Canyon/LCR work to a fall

schedule. Doing so might create more problems than solutions.

3. Are there ways to improve methods used ill the Gralld Callyoll work?

The Panel encourages consideration of telemetry approaches to address questions

about migration to and from the LCR, use of simulation studies to evaluate potential biases in

ASMR population estimates, and recommends that results from well-established open population

age-structured methods (Jolly-Seber models) be compared to results from the ASMR models.

Similar analyses of Upper Basin closed model methods will also be infonnative.

4. Do Grand Canyon methods provide rigorous data pertinent to HBC Recovery Goals?

The ASMR method is appropriate for getting estimates of abundance, population

growth rate (i.e., trend), and recruitment, if assumptions about capture probabilities are

reasonable. Upper Basin methods do not provide as much information about these three criteria

because of much lower capture rates. In both cases, the Panel recommends that emphasis be

placed on estimates of population growth rate in determining if a population is to be down-listed

or de-listed.

5. Are the current methods providing scientifically rigorous data to inform decisions of

the Glen Canyon Adaptive Management Program's Adaptive Management Work

Group? Yes. Given the current constraints to work in Grand Canyon, the Panel views the

basic structure of the ASMR model as the appropriate approach. Several potential enhancements

in the approach should be pursued.
5

Conclusions and Recommendations

1. The analytical methods currently employed in the Upper Basin are appropriate pro tem,

but could be improved as more data become available. The Panel encourages development of

open population methods as the database improves and recommends development of simulation

studies as a way to evaluate alternatives. In combination, those could help develop the "robust"

approach advocated by many experts in population biology (Pollock 1982).

2. The Panel finds little merit in changing current sampling practices. Sampling should

occur when the greatest number of fish can be captured with the least hann to the fish - i.e.

spring in the Grand Canyon and fall in the Upper Basin.

3. The ASMR model proposed and applied by Walters and Coggins (2003b) is an

appropriate way to deal with the biases introduced by heterogeneity in catchability related to age.

It is based on the existing and proven methodology of Pollock (1981) and offers "best available

science" as the source of evidence regarding the status and trends of humpback chub in the

Grand Canyon ecosystem. The ASMR method can be improved and the Panel offers

recommendationspecific to future work in the Grand Canyon. Those are:

(a) Further work needs to be done on the extent of potential bias caused by inaccurate aging

at initial capture.

(b) Use the Pollock (1981) Jolly-Seber age model directly to compare the estimates to the

computer program developed by Walters and Coggins as a way to cross-validate that the

method has been implemented correctly.

(c) Use the Pradel (1996) approach to estimating population growth (ignoring age classes) to

cross-validate estimates of population growth/decline.

(d) Age-structured models assume that there is no further heterogeneity in catchability other

than that due to age. Further work (e.g. some simulation experiments) needs to done to

assess the potential degree of bias in parameter estimates that could result from additional

sources of unequal capture probability. Those might be due to behaviors such as skip

spawning, avoidance of sampling gear after first capture, or movement to/from the main

stem.

4. The Panel encourages development of a workshop where Upper Basin and GCMRC

program participants can bring their data sets, work with alternative modeling approaches and

evaluate estimation methods. This would allow sharing of expertise, discussion of differences

among sites, and help build consensus about criteria for de-listing or down-listing.
6

Appendix I: Scope of Work

Scope of Work

An Independent Review of Ongoing and Proposed Scientific Methods to

Assess the Status & Trends of the Grand Canyon Population of the

Humpback Chub (Gila cypha)

BackWund: The federally endangered Humpback Chub, Gila cypha, particularly the Grand

Canyon population, has been a topic of considerable interest in recent months for the Glen

Canyon Dam Adaptive Management Program (GCDAMP). This interest has resulted in part

from the newly developed Recovery Goals for the species (issued in 2002), which contain

criteria for down-listing and de-listing. Determinations of whether these criteria are met

presumably will be based upon status and trend numbers using methods described in a draft Fish

and Wildlife Service guidance document (March, 2002). The Grand Canyon Monitoring and

Research Center (GCMRC), which acts as the research and monitoring arm of the GCDAMP,

has been developing and following procedures somewhat different than those in the guidance

document in studying the status and trends of the Grand Canyon population of HBC. These

stock assessment procedures have documented a substantial decline in recruitment and adult

abundance over the past decade or so.

The decline in numbers and recruitment in this population led the Adaptive Management

Work Group (the FACA committee that makes recommendations to the Secretary of the Interic

as part of the GCDAMP) to form a HBC Ad Hoc Committee in January, 2003 charged win.

developing a comprehensive action plan for improving the status of HBC in Grand Canyon. One

of the projects developed by this group was an experimental implementation of simultaneous

Stock assessment sampling and modeling for the HBC population coupled with a two year

implementation of procedures similar to those suggested by the population estimation guidance

document for the recovery goals. However, implementation of this project in 2004 has been

hampered by controversy over the seasonality, location, and intensity of sampling, as well as

differences of opinion regarding the Stock assessment procedures vs. closed population

estimation procedures. These differences led the HBC Ad Hoc to recommend an evaluation of

the merits of these various approaches by an independrot review panel to be convened by the

Science Advisory Board for the AMWG. This recommendation was concurred with by the

AMWG's Technical Work Group and approved as part of TWG's FY04 budget recommendation

to the AMWG. On August 14th, 2003 the AMWG approved the FY04 budget, which includes

the evaluation of the different methods by the SAB and an independent panel of the gAB's

choosing. This panel and the SAB are to report their findings to the AMWG by their January 1-

8, 2004 meeting to enable the appropriate field sampling aspect of this project, as approved by

the AMWG, to be implemented in the 2004 field season.

GCMRC, in meeting its responsibility to the AMWG, TWG, and HBC Ad Hoc

Committee, is describing herein the scope of work and timetable for the independent review

panel.

Puroose: Through an independent peer review process, determine the relative merits c

population estimation and stock assessment procedures, or some combination thereof, being US(.
7

by the GCDAMP and those being recommended by the Recovery Goal process for estimating the

status and trends of the population ofHBC in Grand Canyon.

Ch~e: Provide substantive written guidance to the GCDAMP AMWG sufficient to infoml a

policy recommendation regarding the implementation of population status and trend estimation

procedures for the HBC population in Grand Canyon based upon the best available and

practicable scientific methods. A report containing this guidance shall be submitted to GCMRC

for transmittal to the AMWG no later than December 5, 2003.

Process.: The SAB (acting through Dr. James Kitchell, the Hasler Professor of Zoology and

Director of the Center for Limnology at the University of Wisconsin) shall convene a panel of

independent scientific experts with background and qualifications in the areas of population

dynamics, statistics, population estimation techniques, and stock assessment procedures as they

pertain to fishery resources. This panel shall gather relevant information through written

documents and in person presentations of information relative to the issue described under

background above and develop a written report to the Adaptive Management Work Group of the

GCDAMP. Based on their acquired knowledge of the HBC populations in the Colorado River

Basin (and particularly Grand Canyon) as well as the field sampling and statistical methods

being used to evaluate the status and trends of those populations, the panel shall produce a report

which addresses:

Recommendations regarding the appropriateness of methods used in the Grand Canyon

to develop status and trend infonnation for the Grand Canyon and Little Colorado River

populations ofHBC.

2. Recommendations regarding the appropriateness of methods being recommended for use

in the Upper Basin HBC populations and their transferability/utility in regards to the

status and trends of the Grand Canyon HBC population.

3. Opportunities for using any combination of the different methods in the Grand

Canyon, including considerations regarding the seasonality, sampling gear, and intensity

of sampling.

4. The appropriateness of the various methOds and approaches in providing scientifically

rigorous data to inform the Recovery Goal process in detennining whether or not downlisting and de-listing criteria have been met.

5. The appropriateness of the various methods and approaches in providing scientifically

rigorous data to infonn decisions of the Glen Canyon Adaptive Management Program's

Adaptive Management Work Group.
8

Appendix II: Agenda

An Independent Review of Ongoing and Proposed Scientific Methods to

Assess the Status & Trends of the Grand Canyon Population of the

Humpback Chub (Gila cypha)

Meeting Agenda

November 6-7, 2003

National Center for Ecological Analysis & Synthesis

Santa BaIbara, CA

Thursday, November 6

8:30am- Welcome and Introductions, Jim Kitchen, University of Wisconsin and Science

Advisory Board, Glen Canyon Adaptive Management Program

8:45am- Review of Agenda and Scope of Work for Independent Review Panel, Kitchell

9:00am- Overview of Humpback Chub Recovery Goals, Criteria for Down-listing & Delisting. Tom Czapla, Upper Colorado Endangered Fish Recovery Program, FWS (by

conference call)

9:45am- Ecology, Distribution, and Sampling Methods for Grand Canyon Population of

Humpback Chub, Lew Coggins, Grand Canyon Monitoring and Research Center, USGS

lO:30am- Ecology, Distribution, and Sampling Methods for Upper Basin Humpback

Chub Populations, Tom Chart, Bureau of Reclamation, Salt Lake City; Chuck McAda.

Grand Junction, CO, FWS, (by conference call), and Doug Osmundson, Grand Junction,

CO, FWS

11:00am Statistical and Modeling Methods to Detelmine Status and Trends of Humpback

Chub in Grand Canyon. Carl Walters, University of British Columbia.

11 :45am Statistical and Modeling Methods to Detennine Status md Trends of Humpback

Chub in the Upper Basin. Kevin Bestgen, Colorado State University.

12:3Opm LUNCH

2:00pm Open discussion, questions and answers from panel members

3:45pm Final Q & A from panel. requests for infonnation.

5:00pm Adjourn
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Friday, November 7 (Closed meeting of review panel)

8:30am-Preliminary discussions & reflections

1 0:30am-Draft Report Outline

12:00pm LUNCH

1 :3Opm- Writing of draft material

5 :OOpm adjourn

Panel Members:

James Kitchell (Chair), Center for Limnology, Univ. of Wisconsin

Churchill Grimes, Southwest Fisheries Science Center, NMFS, Santa Cruz, CA

Steve Lindley, Southwest Fisheries Science Center, NMFS, Santa Cruz, CA

David Otis, Cooperative Fish & Wildlife Research Unit, Iowa State University

Carl Schwarz, Dept. of Statistics & Actuarial Science, Simon Fraser University

Observers and Discussion Participants (day one)

Steve Gloss, USGS SBSC

Randall Peterson, Bureau of Reclamation

Bill Pine, Dept. of Zoology, North Carolina State Univ.

Jim Rice, Dept. of Zoology, North Carolina State Univ.
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Appendix III: Technical Assessment

I. Mark-recapture models

A. Closed models used in the Upper Basin

The closed population model analysis used in the Upper Basin is an appropriate approach

for producing independent population estimates in a given time and year. This method attempts

to correct for potential biases in traditional population estimators that occurs when capture

probabilities vary among individuals (heterogeneity) or vary due to a behavioral response to first

capture, e.g., capture avoidance. However, these methods are not especially powerful in

detecting variation in capture probability when the number of trapping occasions (passes) is

small «5), and average capture probabilities are low «0.10). Unfortunately, both of these

criteria pertain to the current Upper Basin situation. Thus, it is not surprising that population

estimates produced to date by the computer program CAPTURE have poor precision and vary

considerably among models.

Although we expect considerable stochasticity in capture probabilities due to unplanned

environmental and logistical events, computer simulation of the performance of the methods

under a variety of capture probability and population size scenarios is a valuable tool for

assessment of expected outcomes of a proposed sampling protocol. In particular, we suggesthat

it would be a valuable exercise to simulate the bias and precision of the closed population models

under each of a set of hypothetical range of values of the number of sampling occasions,

expected population size, and capture probability structures. The results could be evaluate<

within the context of the population abundance recovery goal. For example, if we constructed a

hypothetical population of N = 2,100 individuals, with reasonable values of expected capture

probabilities based on past data, and simulated the results of a capture-recapture experiment

based on three capture occasions within a short time frame, what would the resulting distribution

of estimates look like with respect to bias and precision? Said another way, what are the chances

that we would conclude that the population was significantly larger or smaller than N = 2,1 OO?

Such an exercise would explicitly inform stakeholders about the sensitivity and uncertainty in the

proposed protocol, and allow an evaluation of alternative protocols.

We also suggesthat the practice of treating data from each year of sampling as indepen~ent

for previous or subsequent years is not the most efficient use of all of the available data (see next

subsection). With respect to sampling of individual populations in the Upper Basin, we agree with the

suggestion to combine the Black Rocks and Westwater populations into a single population, but

recommend that population abundance estimates be generated from stratified models (e.g.

Schwarz and Taylor, 1998) that acknowledge the possibility of movement between the two areas.

The Yampa, Desolation, and Cataract Canyon populations are more problematic in that

abundance and recapture rates are apparently too low to produce credible estimates from capturerecapture sampling. As alternatives to continuance of the current sampling protocol for these

areas, we suggesthat it would be more efficient to either: I) make a single pass through the area

each year and simply generate an index of abundance that could be used to estimate trends in

abundance, or 2) sample these areas more intensively but periodically, e.g., every 3 years.
11

B. Open models-the age-structured mark-recapture (ASMR) model as developed for

the Grand Canyon.

There is a wide range in the type of mark-recapture designs and analyses used to estimate

the important population parameters of abundance, survival, recruitment, and population growth

when fish receive unique tags (see review by Pine et al. 2003). The very simplest design

assumes a closed population (no death, no emigration, no recruitment, and no immigration) and

takes a series of samples of the population. At each sampling occasion, the tag number of

recovered fish is recorded and untagged fish are tagged and released. This is the basic protocol

used for the Upper Basin populations. Because the population size is assumed as fixed, this is

the only parameter that is of interest. A key assumption of these closed population models is that

all fish have the same probability of capture at each sampling occasion (but this probability is

allowed to change among sampling occasions). If this assumption of homogeneous capture

probability is violated (e.g. some fish are more likely to be captured than other fish due to size,

sex or behavior), then estimates of population size can be biased (i.e. tending to be too high or

too low). The direction of bias depends on how the heterogeneity among fish changes over time.

For example, fish that have a higher probability of capture at one occasion also have a higher

probability of capture at another occasion (a "trap happy" behavioral response). In this case, the

estimates of abundance have a negative bias (i.e. produce evidence of a smaller population than

is the actual case). Alternatively, a fish may have a traumatic experience after being captured at

one occasion and is less likely to be captured in subsequent occasions ("trap shy"). In these

cases, estimates of abundance have a positive bias (i.e., overestimate the actual population

abundance.

Several closed-population estimators have been developed for designs with three or more

sampling occasions. Among those are the models Mo, Mt, Mh, and Mb, as summarized by Otis

et al (1978), and implemented in the computer program CAPTURE. These models test for the

presence of capture heterogeneity due to factors such as fish size, behavior or time effects and

compute estimates of abundance that account for these effects.

Once multi-year studies are considered, the assumption of population closure is no longer

tenable - some fish die and some fish recruit to the population. More complex capture-recapture

models have b-een developed for these multi-year studies. They are generally known as JollySeber models (Jolly 1965; Seber 1965). In these models, a capture history for each individually

tagged fish is kept (the sequence of O's and l's indicating if a fish was not seen/seen in a

particular year). From these capture histories, estimates of population abundance, year-to-year

survival rates, and recruitment to the population can be developed. However, even for these

multi-year models, a key assumption is homogeneous capture-probability among fish alive in a

particular year, i.e. all the fish alive in a year should have the same probability of capture,

although this probability can vary over years. In much the same way as in closed population

models, simple heterogeneity (e.g. "trap happy" fish) leads to negative biases in abundance

estimates while changing heterogeneity (e.g. "trap shy" fish) usually leads to positive biases in

abundances.

Walters and Coggins (2003a) examined catchability of pit-tagged fish in relationship to time

of year and age of the fish. They found that older fish have a lower capture probability than

younger fish for many months of the year. The deCline in catchability is most apparent when
12

compared to sub-adult fish, but still could vary by about a factor of 2 between fish of age 5 and

15 years (their Figure 3). Similarly, there was some evidence that during the spring, older fish

are more catchable than younger fish (their Figure 4). In both cases, these are examples of

simple heterogeneity likely related to the age of the fish. Mark-recapture models that simply

"pooled" over all age groups would be expected to produce estimates with a negative bias. This

is probably the reason for the apparent bias in estimates from the SuperTag model that produces

abundance estimates substantially lower than those derived from the ASMR.

Because of the complexity of these multi-year designs, models to adjust for heterogeneity

are not as well developed as for the closed population cases (but see Pledger and Effort, 1998).

However, if the sole source of heterogeneity is related to age, then Pollock (1981) developed a

model (the Jolly-Seber age model) where the population is divided into several age classes.

Capture (and survival) rates are allowed to vary among the age classes and over years, but are

again assumed to be equal for all animals within a particular age class and a particular year.

Because aging is a deterministic process (i.e. animals age by exactly one year each year), the age

class (and hence the capture-probability class) is known for all occasions even when the animal

is not seen. Estimates can be obtained of abundance, survival, and recruitment for each class. If

age class data are the only source of heterogeneity, then estimates of abundance are now

unbiased which is unlike the pooled analysis based on collapsing data over all years.

Walters and Coggins (2003b) present the development of an age-structured model that is

based on the same principles as the Jolly-Seber age model. The population is divided into

individual year age classes and movement of fish among the age classes is deterDlinistic. Each

age class has an individual capture and survival probability. Age specific estimates of

abundance are then obtained and summed to obtain estimates of the total abundance.

A large number of age classes requires a large number of parameter estimates for surviva'

and catchability.. Walters and Coggins (2003b) also developed a model where age-specifil

survival is a function of length (the Lorenzen curve of their Figure 1). This improves the

precision of abundance estimators because the number of parameters to be estimated is reduced

from one for every age class to a total of only two-those describing the shape of the curve for

all age classes.

Accurate estimation of the age class at first capture is a key data requirement for this model.

Unfortunately, age detennination is impossible without harming the fish, so initial age is

assigned based on a fish length at initial capture. Walters and Coggins (2003b) investigated the

potential biases that could be introduced by inaccurate age determination at initial capture. They

found that estimates of recruitment (and abundance) could be negatively biased. This is not

unexpected as errors in age assignment now introduce simple heterogeneity into the probability

of capture at each apparent age class, which leads to negative biases. They report on a suggested

alternative to assigning age based purely on length that appears to reduce biases in estimates of

abundance.

Walters and Coggins (20038, 2003b) indicate that an earlier model (SuperTag) produced

very low estimates of abundance because of differential catchability of fish by age (simple

heterogeneity) and because of movement between the spawning grounds and the main stem

and/or "skip spawning" (i.e., mature adults do not spawn every year),. If skip spawning is

prevalent, then estimates of abundance only refer to the spawning population in that year - not to

the entire population of adults. If movement to/from the main stem is occurring, then this could

lead to positive biases in abundance. As developed in the following, one of our
13

recommendations encourages methods for estimating the non-spawning population in the main

stem.

B. Use of complex models

The Panel found quite a dichotomy between the amount of data available, sampling designs

and models used in the Upper Basin and in the Grand Canyon studies. ~e Upper Basin studies

are characterized by only a few years of data with small number of recaptures. The lower basin

study has many years of data with many recaptures. Consequently, the modeling that can be done

differs considerably between the two locations. In the Upper Basin, estimation is limited by the

data - there are only a few years of data and very few recaptures. Simple models that are robust

to violations of assump.tionshould be used. However, the choice of model should not be a

straightjacket -as more years of data become available, more complex models should be built

for the Upper Basin studies based on experience gained from the GCMRC studies.

Complex multi-year sampling designs allow complex models that can account for nonclosure (e.g. estimating survival and recruitment rates) and for heterogeneity in capture

probabilities (e.g. age classes). This does not mean that the simpler models used in the Upper

Basin studies should not be used as part of GCMRC analyses. Rather, differences between

estimates from the closed population models used in the Upper Basin could be compared with

those derived from similar analyses of GCMRC data. Thus, estimates from the more complex

models applied to GCMRC data could provide some information on the potential size of biases

in the Upper Basin estimates.

Modeling and estimation techniques currently exist that can integrate multi-year data into a

common framework. This allows improvement of population abundance estimates in all years as

data accumulates and permits estimation of additional vital rates such as annual survival rates.

An especially valuable set of models in this regard is that associated with the "robust" design

developed by Pollock (1982). This design assumes multi-year trapping periods, and within each

year there is a set of closely spaced sampling occasions. The idea is to use closed population

models in Program CAPTURE to estimate abundance within years, and open population models

(pollock et al. 1990) to estimate additional parameters such as recruitment, survival and

population growth rate. Such a sampling protocol and associated analysis might be well suited to

the Upper Basin as more intensive sampling is conducted in the immediate future.~

II. HDC sampling issues

A. Simultaneous sampling in main stem and LCR

It has been suggested that simultaneous sampling be undertaken in the main stem concurrent

with the sampling on the LCR. The primary reason for this proposal is to try and estimate the

size of the "hidden population" - i.e. the skip spawners or those that have spawned and moved

out of the spawning grounds to the main stem before or after the sampling effort.

While, in theory, this would seem to provide much useful information, the Panel

understands that there are severe logistical difficulties in sampling the main stem caused by

flows and the types of capture gear that can be used. Evidence presented in the review also

supports the view that LCR sites should continue as the primary focus of sampling effort. As

suggested below, there are alternative methods for _estimating the dynamics of irnmigration-
[4

emigration from the LCR. Further, the Panel questions the sole emphasis on estimates of total

abundance. In fact, estimates of the spawning population may be just as suitable because effort

to estimate the total population are plagued by logistic constraints and may introduce unknown

bias. If estimates of population growth rates (i.e., trend in abundance) are sufficient to advise

management decisions Ie. de-listing and down-listiing, then it may not be necessary to mount a

program of substantial cost in order to get a questionable estimate of total abundance. The

Panel's views on this issue are developed in greater detail in the following.

B. Spring vs. Fall sampling

It was suggested to the Panel that sampling times be similar for all HBC populations, and

that fall is a more appropriate time to sample these fish because of concerns about capture stress,

handling mortality, etc. However, the life history of the Upper Basin and Grand Canyon

populations appear to differ because Grand Canyon fish exhibit annual, site-specific spawning

migrations into the LCR. The Panel was not presented with any evidence of site-specific

spawning migrations in the Upper Basin populations and asswnes that these fish spawn within

the reaches generally designated as habitat for each population. Choice of fall sampling in the

Upper Basin sites appears to derive from a combination of constraints--bigh spring flows, high

summer temperatures, and bycatch of other endangered species (e.g., Colorado pikeminnow). In

combination, those make fall sampling the most appropriate choice.

Because of the long lifetime of theSe fish and the general restriction to abundance estimation

for adults, there is no rationale for standardizing timing of the surveys to make abundance

estimates comparable - i.e., the population size in the spring is likely very similar to the

population size in the fall - well within the precision of any abundance estimate at either tim

point.

Ironically, even though the majority of the population in the Grand Canyon is in the main

stem in the fall, the much lower capture rates in the main stem will lead to fewer fish being

captured and to estimates with lower precision. Thus, requiring a fall sampling schedule for

Grand Canyon work may produce more problems than solutions.

Consequently, the Panel recommends that sampling occur when the greatest number of

f"lSh can be captured with the least harm to the fish - i.e. spring in the Grand Canyon and fall

in the Upper Basin.

III. Additional statistical is!;il£s

A. Model selection and model averaging

A common problem in statistical science revolves around choosing the most appropriate

model for parameter estimation from among a set of proposed models. There is always

uncertainty in this exercise, as the 'true' model can never be known. We can only hope to find a

model that provides a good statistical fit to the observed data and one that has biological

relevance to the problem at hand. Burnham and Anderson (1998) present a contemporary

paradigm for model selection in the ecological sciences. This paradigm emphasizes achieving a

parsimonious tradeofTbetween bias and precision of estimated parameters, i.e., models should be

complicated enough to sufficiently explain the important sources of variation in the data, but bf"'

no more complicated than is necessary. The procedU{e involves a priori development of a set (
15

biologically plausible models. The data are then used to assign an infomlation theoretic

quantitative score to each model, and this score can subsequently be used to rank the relative

support for each of the models. For example, models that assume constant survival and/or

capture rates can be objectively compared to alternative models that allow these rates to vary by

age or time. It often happens that several models may be nearly equally supported by the data.

In such situations it is possible to combine estimates from each of these models in a statistically

optimum way. This produces model-averaged estimates that are statistically robust, allows for

adjustment of violation of model distributional assumptions, and explicitly acknowledges

statistical uncertainty in the model selection process. The ASMR methodology as currently

applied does not involve a fomlal evaluation of the relative strength of support for alternative

models. We suggest such an exercise be conducted with the Grand Canyon data as a way to

compare results and evaluate robustness of model estimates. We note that model-averaging

procedures can also be used on a limited basis with closed population models, although the

statistical advantages are more limited.

B. Estimating population abundance vs. population growth

One of the criteria of the recovery plan relates to the absolute abundance of the

population. Unfortunately, focusing upon absolute abundance as a measure of success/failure

creates three important problems.

The first problem has to do with closure - to what geographical region does the estimate

apply? Not all geographic areas can be sampled because of cost or logistical constraints, i.e.

some stretches simply cannot be sampled. The Panel was presented with evidence of small

number of chub outside the sampled areas in both the Upper Basin and Grand Canyon sites.

Unless there is complete mixing of fish from the entire population with the fish in the sampled

sites, any estimates of abundance can be negatively or positively biased. For example, if all

marked fish moved to inaccessible sites and fish from inaccessible sites move to sampling sites,

then no marked fish would be recaptured and abundance estimates will be strongly, positively

biased. If fish in accessible and inaccessible sites never mixed, then the estimates will be very

negatively biased. While the actual problems in field sampling are probably not this severe, the

degree of mixing is neither well known nor accounted for in the analyses.

Second, mark-recapture estimates of abundance can be seriously biased by heterogeneity

(see Pollock et al 1990; Link in press). While more sophisticated models can be developed to

deal with certain types of heterogeneity (e.g. age related as in the ASMR), these are "data

hungry" and require a long time series with high capture rates. Pradel (1996), Schwarz, (2001),

Nichols and Hines (2002), Hines and Nichols (2002) demonstrate that population growth can be

directly measured from mark-recapture studies. Estimates of population growth are much more

robust to heterogeneity (Schwarz 2001; Hines and Nichols, 2002) under the much less restrictive

assumption that the heterogeneity of the population doesn't dramatically change over time, i.e.

older fish always tend to have higher capture rates. Estimates of population growth do not

depend upon geographic closure as long as the growth/decline rates of the sampled population

matches the population as a whole. Accordingly, the Panel strongly recommends that

population growth rates be given a higher priority than absolute abundance estimates when

evaluating the evidence for down-listing or de-listing.

Lastly, the recovery goals do not appear to incorporate uncertainty in the population

estimate as part of the decision process. For example, if the recovery goal is 2000 fish, then an
16

estimate of 2500 (se 400) fish provides a much different basis for decision-making than an

estimate of 2200 (se 50) fish. The Panel recommends that, if absolute abundance is to be use<

uncertainty in estimates be formally recognized in the review process, e.g., the lower bound 01

the 95% confidence interval for abundance be greater than some target value.

C. Analysis of power to detect population trend

The HBC recovery goals require estimation of population trend during specified time

intervals to evaluate the objective of a stable adult population size. In statistical terms, the Panel

assumes this means that the estimated population growth rate is not different from a value of 1.

We encourage some rigorous assessment of the statistical power of proposed sampling designs

and protocols to detect meaningful departures from a stable growth rate. Such an assessment

could be accomplished by computer simulation studies that rely on informed assumptions and

parameter estimates from existing data.

D. Technical expertise in model fitting

It is clear to the Panel that the Upper Basin and Grand Canyon programs are at different

stages of development in terms of data collection and data analysis. Accordingly, we

recommend that a workshop be convened where Upper Basin and GCMRC scientists can

bring their data sets, work with alternative modeling approaches, and compare various estimation

methods. This would allow sharing of expertise and discussion of differences among sites. This

practice has been put to substantial benefit elsewhere such as among regions attempting to deal

with Northern Spotted Owl issues.
17

IV. Responses to the Scope of Work

Brief responses to the Scope of Work charge are paraphrased and presented in the Executive

Summary. In this section, the Panel responds in detail and specifically to each of the elements:

1. Recommendations regarding the appropriateness of methods used in the Grand Canyon to

develop status and trend information for the Grand Canyon and Little Colorado River

populations of HBC.

The proposed Age Structured Mark Recapture (ASMR) method is a variant of the

established Jolly-Seber-Age model (pollock 1981), and the Panel recommends that existing data

be run with these standard mark-recapture models to obtain some cross validation on the results.

If specific assumptions about the structure of capture probabilities are met, the method should

produce unbiased and efficient estimates of annual survival, trend, recruitment, and absolute

abundance. The method reduces bias of abundance estimates obtained from mark-recapture

models caused by heterogeneity in catchability due to age. This flexibility is important for HBC

population estimates, because there is evidence that older fish have different catchabilities than

younger fish. However, the AMSR method may produce biased estimates of abundance if there

is significant additional variation in capture probabilities within a year due to: 1) inherent

differential catchability among individuals within age classes due to inaccurate aging or unequal

exposure to capture, or 2) a behavioral response due to first capture, e.g., a change in movement

or space use patterns that would reduce probability of subsequent recapture.

2. Recommendations regarding the appropriateness of methods being recommended for we in

the Upper Basin HBC populations and their transferability/utility in regards to the status and

trends of the Grand Canyon HBC population.

The method used in the Upper Basin population is limited to estimation of absolute

abundance during a short time frame within a single year. For this purpose the method is

accepted standard practice1n closed population mark-recapture studies and otTers the flexibility

to handle problems with heterogeneity and behavioral response in capture probabilities (Otis et

al. 1978). However, use of the method to date has resulted in estimates with relatively poor

precision and uncertainty regarding the appropriate assumptions about the structure of the

capture probabilities. We sunnise that these results are due to the small number of sampling

occasions within a year, the low capture probabilities that have been achieved, and the small

number of recaptures obtained. The current number of sampling passes within a year is therefore

likely too small in the Upper Basin and program to ensure reduction of potential biases caused by

heterogeneity and other failures of assumptions.

The current Upper Basin method of using only the data from a given year to estimate

abundance for that year is statistically inefficient for estimation of population trend and does not

produce estimates of additional population vital rates such as survival, because it does not take

advantage of available recapture information among years. Some improvement in trend
i8

estimation is possible using the three or more years of available data rather than concentrating on

simply using the data from a single year. As additional years of data become available, mor

complex models should be fit that will efficiently use all of the data. The GCMRC program has a

long time series of capture-recapture information that naturally lends itself to more complex

models such as Jolly-Seber and ASMR methods for estimating survival rates and population

trend, and these data should be fully utilized in analyses that may not be possible or as promising

with existing data from the Upper Basin. In short, the Upper Basin methods are appropriate for

the present, but could be improved by more expansive use of the existing data and as the data

sets grow to allow analyses such as those employed by GCMRC.

3. Opportunities for using any combination of the different methods in the Grand Canyon,

including considerations regarding the seasonality, sampling gear, and intensity of sampling.

There are no compelling scientific reasons to switch to a fall sampling schedule. The life

history of the species is different in the Grand Canyon because there is substantial movement

associated with spawning migration. Sampling is more difficult and capture probabilities are

lower in the main stem, and therefore fall sampling may result in estimates with less precision

than those from spring sampling because a greater proportion of the population will be less

catchable in the fall. The Panel was unable to comment on sampling gear other to note that some

radiotelemetry (or related methods) may provide valuable information on movements between

the LCR and the main stem, as well as auxiliary information about capture probabilities. Use of

this technology could answer some of questions about why some fish are not catchable because

of skip spawning or early movement from the spawning grounds. The sampling intensit

(number of passes/sampling occasions per year) is inadequate for highly reliable closed modt.

adjustment of within year abundance estimates due to heterogeneity in capture probabilities, but

intensity is probably sufficient for estimation of survival, recruitment and trend.

4. The appropriateness of the various methods and approaches in providing scientifically

rigorous data to inform the Recovery Goal process in determining whether or not down-listing

and de-listing criteria have been met.

Capture-recapture techniques are the most appropriate sampling method for producing

estimates of population size, survival, trend, and recruitment that can be used in the Recovery

Goal process. Goals based primarily on absolute population abundance renders the sampling and

estimation problem much more difficult, because unbiased estimates of this parameter are the

most difficult to produce from capture-recapture data. Increased intensity of sampling within

years will be important for both programs if more reliable annual abundance estimates are

required. An alternative plan is to conduct only a year or two of increased sampling in some

areas to estimate the necessary capture probability structure and then use these estimates to

calibrate future estimates from less intensive sampling. For estimates of trend and recruitment,

multi-year models such as ASMR/Jolly-Seber are most efficient in using all available data, and

should be utilized in both programs. The Panel cautions against thinking in terms of having to

make a choice between one or the other of closed versus open population models. Instead, thr

monitoring program in both basins would benefit from utilizing well-developed robust mod.
19

methods that integrate the best features of both closed and open capture-recapture models

(pollock 1982). In addition, we would strongly suggesthe use of computer simulation exercises

to investigate the potential biases in population estimates that might be expected from using

cunent protocols. This approach would allow assessment of the statistical power of the current

methods to detect change in population trend during specified time frames. That is, decision

makers should be explicitly aware of the sensitivity of current methods to detect meaningful

changes in the Recovery Goal parameters.

5. The appropriateness of the various methods and approaches in providing scientifically

rigorous data to inform decisions of the Glen Canyon Adaptive Management Program's

Adaptive Management Work Group.

As summarized throughout, the Panel feels that the current approach (ASMR) is clearly

most appropriate within the logistical constraints of work in Grand Canyon and, therefore, the

best currently available source of infonnation for decision making. However, there is both need

and potential for improving this basic approach. The Panel's review of the ASMR and

alternative methods are presented above and include recommendations for improvement of

methods employed in both the Upper Basin and Grand Canyon programs.
20

References Cited

Burnham, K. P. and Anderson, D. R. 1998 . Model selection and inference: a practical

infonnation-theoretic approach. New York: Springer Verlag.

Hines, J. E. and Nichols, J. D. 2002. Investigation of potential bias in the estimation of A using

Pradel's (1996) model for capture-recapture data. Journal of Applied Statistics, 29, 573-

588.

Jolly, G. M. 1965. Explicit estimates from capture-recapture data with both death and

immigration - Stochastic model. Biometrika 52, 225-247.

Link, W. A. (in press). Nonidentifiability of population size from capture-recapture data with

heterogeneous detection probabilities. Biometrics, In press.

Nichols, J. D. and Hines, J. E. 2002. Approaches for the direct estimation of A. and demographic

contributions to A., using capture-recapture data. Journal of Applied Statistics, 29, 539-568.

Otis, D.L., Burnham, K. P., White, G.C., and Anderson, D. R. 1978. Statistical inference from

capture data on closed animal populations,- Wildlife Monographs, 62, pp.I-135.

Pine, W. E., Pollock, K. H., Hightower, J. E., Kwak, T. J., and Rice, J. A. 2003. A review of

tagging methods for estimating fish population size and components of mortality. Fisherie

28: 10-23.

Pollock, K. H. 1981. Capture-recapture models allowing for age-dependent survival and capture

rates. Biometrics 37,521-529.

Pol1oc~ K. H. 1982. A capture-recapture design robust to unequal probabilities of capture.

Journal of Wildlife Management 46, 757-760.

Pollock, K. H., Nichols, J. D., Brownie, C., and Hines, J. E. 1990. Statistical inference for

capture-recapture experiments. Wildlife Monographs 107. -

Pledger, S. and Efford, M. 1998. Correction of bias due to heterogeneous capture probability in

capture-recapture studies of open populations. Biometrics 54, 888-898.

Pradel, R. 1996. Utilization of capture-mark-recapture for the study of recruitment and

population growth rates. Biometrics 52,371-377.

Schwarz, C. J. 2001. The Jolly-Seber model: more than just abundance. Journal of Agricultural.

Biological, and Environmental Statistics. 6. 195-205.

Schwarz, C. J. and Taylor, C. G. 1998. The use of the stratified-Petersen estimator in fisheries

management with an illustration of estimating the number of pink salmon (Oncorhynchu
21

gorbuscha) that return to spawn in the Fraser River. Canadian Journal of Fisheries and

Aquatic Sciences 55, 281-296.

Seber, G. A. F. 1965. A note on the multiple recapture census. Biometrika 52, 249-259

Heterogeneity in recapture-probability of pit-tagged

Report to the Grand Canyon Monitoring and Research

Walters, C. and Coggins, L. 2003a.

humpback chub in Grand Canyon.

Center.

Walters, C. and Coggins. L. 2003b. Age-structured mark-recapture analysis (ASMR) for Grand

Canyon native fishes. Report to the Grand Canyon Monitoring and Research Center.

Additional Documents Reviewed by the Panel

McAda, C. W. 2002. Population Size Structure of Humpback Chub in Black Rocks, 1998-

2000. Recovery Program Project Number 22a3. Final Report. US Fish and Wildlife

Service, Grand Junction, Colorado. 26p.

Protocols for Colorado Pikeminnow and Humpback Chub Population Estimates. Draft Report,

Program Director's Office, Upper Colorado Endangered Fish Recovery Program,

Lakewood, Colorado. 77p.

Grand Canyon Monitoring and Research Center. 2003. An Overview of Status and Trend

Information for the Grand Canyon Population of the Humpback Chub, Gila cypha. Report

to the Glen Canyon Dam Adaptive Management Work Group, Ad Hoc Committee on

Humpback Chub. 23p.