Abundance Trends and Sta

Little Colorado River Pop

Humpback Chub

An Update Considering data 

Presentation to the Glen Canyon Dam Tec

Presentation to the Glen Canyon Dam Tec

By

Lew Coggins Lew Coggins

USGS, Grand Canyon Monitoring and R

USGS, Grand Canyon Monitoring and R
Report Objective

Report Objective

 Update 2002 HBC stock asses

Update 2002 HBC stock asses

(Coggins et al. 2006) with most 

(Coggins et al. 2006) with most 

information information

 Catch

-rate Indices (LCR Inflow a

rate Indices (LCR Inflow a

 Summarize Spring LCR Closed P

Summarize Spring LCR Closed P

Estimates Estimates

 Update Age Update Age

-Structured Mark Structured Mark

-Rec

Rec

model with data through 2006 model with data through 2006

 Utilize various model selection tool

Utilize various model selection tool

among ASMR 1 among ASMR 1

-

3

 Estimate age Estimate age

-length relationship fro

length relationship fro

 Incorporate uncertainty in assignme

Incorporate uncertainty in assignm
HBC Catch HBC Catch

-Rate Ind

Rate Ind
HBC Hoop HBC Hoop

-net Catch net Catch

-rate in lower 1,20

rate in lower 1,20

Year

Hoop-Net Catch-Rate

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

0.00 0.05 0.10 0.15 0.20 0.25 0.30 

 Spring Sampling Spring Sampling 30+ days 30+ days Hoop

-nets in nets in 

standardized standardized locations locations

 Error Bars are Error Bars are 

95% CI
HBC Trammel HBC Trammel-net Catch net Catch-rate in LCR 

rate in LCR 

 Monthly Catch Monthly Catch-rate (fish/hour/100m) (fish/hour/100m) Solid dots are Solid dots are 

representative representative sampling sampling

 Open dots are Open dots are limited sampling limited sampling Year

Trammel-Net Catch-Rate

1991

1992

1993

1994

1995

1996

1997

1998

1999

0.0 0.2 0.4 0.6 0.8 1.0
Spring LCR HBC Spring LCR HBC 

Abundance Estima

Abundance Estima
Spring LCR HBC Abundance 

Spring LCR HBC Abundance 



2

-Event Lincoln Event Lincoln

-

Petersen closed Petersen closed population mark population mark

-

recapture recapture experiments experiments

 Abundance of Abundance of 

HBC >= 150 mm HBC >= 150 mm Total Length Total Length

 Error Bars are Error Bars are 

95% CI

Year

Abundance (x1,000)

1992

1993

1994

1995

1996

1997

1998

1999

012345678
ASMR Open Population E

ASMR Open Population E
Background Background – ASMR Mode

ASMR Mode

 Coggins, L.G., Jr., W.E. Pine, III, C.J. Walters, S.J.D

Coggins, L.G., Jr., W.E. Pine, III, C.J. Walters, S.J.D

Age-structured mark structured mark-recapture analysis: a virtual recapture analysis: a virtual-po

po

based model for analyzing age based model for analyzing age-structured capture structured capture-re

re

North American Journal of Fisheries Management. 2

North American Journal of Fisheries Management. 2

 ASSUMPTIONS ASSUMPTIONS

 ASMR assumes a length/age d

ASMR assumes a length/age d

mortality schedule. mortality schedule.
Background Background – ASMR Mode

ASMR Mode

 Lorenzen (2000) type Mortality Sche

Lorenzen (2000) type Mortality Sche

 Mortality rate proportional to 1/length usi

Mortality rate proportional to 1/length usi

Bertalanffy growth parameter k Bertalanffy growth parameter k

 Estimate Mortality of oldest fish Estimate Mortality of oldest fish Von Bertalanffy k and Madult used to ca

Von Bertalanffy k and Madult used to ca

rate of younger fish rate of younger fish

Age Dependent Annual Survival Rate

0

0.10.20.30.40.50.60.70.8

123456789

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

Age

Annual Survival Rate
Background Background – ASMR Mode

ASMR Mode

 ASSUMPTIONS ASSUMPTIONS

 Assumes size (age) dependent 

Assumes size (age) dependent 

rate

 Three different formulations of 

Three different formulations of 

 ASMR 1 and ASMR 2 assume tha

ASMR 1 and ASMR 2 assume th

to capture is asymptotic with age. to capture is asymptotic with age

 ASMR 3 uses conditional maximu

ASMR 3 uses conditional maximu

estimators to estimate each time 

estimators to estimate each time 

specific capture probability specific capture probability
Results Results-Simple Data Ins

Simple Data Ins
Results Results- Adult Abundan

Adult Abundan

456789

1011

ASMR 1

456789

1011

Adult Abundance (x1000) ASMR 2

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

456789

1011

ASMR 3

Year
Results Results- Recruit Abun

Recruit Abun

012345

ASMR 1

012345

Recruit Abundance (x1000) ASMR 2

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

012345

ASMR 3

Brood Year
Results Results- Adult Mort

Adult Mort

Adult Mortality Rate

ASMR 1 ASMR 2 ASMR 

0

0.020.040.060.08

0.1

0.120.140.16
Results Results- Which one is Which one is “

• Who Cares... they all say the same 

adult abundance!

• Maybe we should care... slightly dif

hypotheses about recruitment.

• How to Arbitrate among models?

• Pearson Residual Patterns

• How well does the model fit (predict

• AIC scores

• Kullback-Leibler distance
Results Results- Which one is Which one is “

• Pearson Residuals

t

tata

tata

ta

n

pp

po

r

)1(, ,

,,

,

−

−

=

t

tata

tata

ta

n

pp

po

r

)1(, ,

,,

,

−

−

=

t

tata

tata

ta

n

pp

po

r

)1(, ,

,,

,

−

−

=
Results Results- Which one is Which one is “

ASMR-1

Black=More fish observed than predictedGrey=Fewer fish observed than predicted
Results Results- Which one is Which one is “

ASMR-2

Black=More fish observed than predictedGrey=Fewer fish observed than predicted
Results Results- Which one is Which one is “

ASMR-3

Black=More fish observed than predictedGrey=Fewer fish observed than predicted
Results Results- Which one is Which one is “

Model AIC # Parameters Rank ASMR1 -196278 18 3 ASMR2 -197183 30 2 ASMR3 -198856 895 1 
Results Results- Why is ASMR3 Why is ASMR3 
Is there anything wrong 

Is there anything wrong 

assessment? assessment?

• Estimates are extremely precise... ma• HBC review panel (Kitchell et al. 2003

evaluating the effect of ageing error on 
How do you Age ch

How do you Age ch

 THE OLD WAY THE OLD WAY

USFW

1990 1995 

5

1015202530

Age

451 709 3744 2360 2832 885 342 

Numbe

1990 1995 

5

1015202530

Age

0 19 218 1544 1737 1604 902 1

Number 
The Problems The Problems

 Better describe humpback chu

Better describe humpback chu

Why?

 Based on very limited dataset Based on very limited dataset May not accurately portray grow

May not accurately portray grow

 Particularly growth changes assoc

Particularly growth changes assoc

ontogenetic habitat shifts ontogenetic habitat shifts

 Incorporate uncertainty in age Incorporate uncertainty in age 

assignments into parameter es

assignments into parameter es

from ASMR. Why? from ASMR. Why?

 Current assessments may overs

Current assessments may overs

confidence in monitoring results 

confidence in monitoring results 

honestly incorporating uncertain

honestly incorporating uncertain

ageing process. ageing process.
Problem 1 Problem 1 – Better Grow

Better Grow

 Use Mark Use Mark-Recapture Methods to E

Recapture Methods to E

Growth Curves (Fabens 1965, Wan

Growth Curves (Fabens 1965, Wan

2002)

 General Idea: General Idea: Fit a standard von Fit a standard von 

Bertalanffy Bertalanffy growth model to growth model to predict growth predict growth rate as a function rate as a function of length. of length. -50

0

50

100150200250300

0 50 100 150 200 2

Length a

dL/dt
Problem 1 Problem 1 – Better Grow

Better Grow

 Problem 1.a What if growth is not well represented 

Problem 1.a What if growth is not well represented 

Bertalanffy growth curve? Bertalanffy growth curve?

 Use a differ Use a different growth curve. ent growth curve.

 Can either Can either 

fit growth fit growth rates of rates of small fish small fish well or well or growth rates growth rates of large fish of large fish well.

-50

0

50

100150200250300

0 50 100 150 200 250 

Length at Rele

dL/dt
Problem 1 Problem 1 – Better Grow

Better Grow

 Generalized Von Generalized Von 

Bertalanffy Model Bertalanffy Model

 Essington et al. 2001 Essington et al. 2001

d n kWHW

dt

dW

−=

 Anabolic Anabolic 

= a

W

Processes Processes

 Catabolic Catabolic 

Processes Processes

 Specify a

Specify a

relationsh

relations

α 

dt

dL

=

 Analogo

Analogo

length

 Tempera

Tempera

growth m

growth m

 Rate of Weight Change Rate of Weight Change
Problem 1 Problem 1 – Better Growth 

Better Growth 

 Generalized Von Bertalanffy with Temperatu

Generalized Von Bertalanffy with Temperatu

 Walters and Essington ( Walters and Essington (In Prep. In Prep.)

() () TfLTfL dt dL c m δ η = α −κ

( ) 10

− )10(

=

T

c QTf c

( ) 10

− )10(

=

T

m QTf m
Problem 1 Problem 1 – Better Growth 

Better Growth 

 How do you get the Temperature? How do you get the Temperature? The temperature that a fish experience

The temperature that a fish experienc

whether or not it is in the LCR or the M

whether or not it is in the LCR or the M

what the temperatures are in each of t

what the temperatures are in each of t

( )

20 1

8.0 1 LL t

e

PLCR

−

−

+

−=

0

0.20.40.60.8

1

0 100 200 

To

Probability of LCR Residence

1.2
Problem 1 Problem 1 – Better Growth 

Better Growth 

 The temperature that a fish experience

The temperature that a fish experienc

whether or not it is in the LCR or the M

whether or not it is in the LCR or the M

what the temperatures are in each of t

what the temperatures are in each of t

( ) 

TPLCRtT 

= L

)( 
Growth Curves Fi

Growth Curves Fi

 Temperature Temperature 

independent independent growth curve is growth curve is a compromise a compromise between the between the winter and winter and summer temperature temperature dependent dependent curves 
Growth Curves Fi

Growth Curves Fi

 Growth rate Growth rate 

appears to be appears to be oscillating up oscillating up and down with and down with temperature temperature
Age-Length Relations

Length Relations
Which one is Which one is “Right

 AIC score clearly indicates that the tem

AIC score clearly indicates that the tem

dependent growth model is superior. dependent growth model is superior. 

Model H d m n L∞ σ2L Q Lt Log Likelihood AI

TIGM 163 0.52 .0007 1.15 391 961 -- -- -66,823 13

c

TDGM 21.0 .61 0.46 .89 434 2000 4.59 236 -47,574 95
Problem 2 Problem 2-Incorporate 

Incorporate 

Error

0

50

100150200250300350400450

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 3

Age

Length
Problem 2 Problem 2-Incorporate Age

Incorporate Age

 Generally Generally 

following following ideas by ideas by Taylor et al. Taylor et al. 2005

155

175

195

215

235

255

275

295

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

p(age|length)

Total 

P(a|L) adjusted for mort

0.95-1.000.90-0.950.85-0.900.80-0.850.75-0.800.70-0.750.65-0.700.60-0.650.55-0.600.50-0.550.45-0.500.40-0.450.35-0.400.30-0.350.25-0.300.20-0.250.15-0.200.10-0.150.05-0.100.00-0.05
Problem 2 Problem 2-Incorporate Age

Incorporate Age

 Generate Generate 

seasonal seasonal age|length age|lengthprobability probability surfaces to surfaces to assign age assign age based on month based on month of year fish was of year fish was captured. captured.
Problem 2 Problem 2-Incorporate Age

Incorporate Age

1990 1995 2000 2005

5

1015202530

Year

Age

451 709 3744 2360 2832 885 342 60 61 213 217 696 1131 1103 1001 827 1387 1245

Number of Fish Marked

1990 1995 2000 2005

5

1015202530

Year

Age

0 19 218 1544 1737 1604 902 108 133 102 115 132 469 647 561 500 490 556

Number of Fish Recaptured

 Flow chart of Monte Carlo simulation Flow chart of Monte Carlo simulation...10

10

 Length of each Length of each 

marked and marked and unmarked fish unmarked fish

AGE-Structured 

Mark-Recapture 

Data
Results Results- Adult Abundance without/with 

Adult Abundance without/with 

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

456789

1011

Year

Without Ageing Error

Adult Abundance (x1000)

1989

1990

1991

1992

1993

1994

1995

456789

1011

Adult Abundance (x1000)
Results Results- Recruit Abundance without/wit

Recruit Abundance without/wit

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

0123456

Brood Year

Recruit Abundance (x1000)

Without Ageing Error

1988

1989

1990

1991

1992

0123456

Recruit Abundance (x1000)
Results Results- Retrospective Analy

Retrospective Analy
Conclusions Conclusions

 Model selection tools clearly indicate A

Model selection tools clearly indicate A

consistent with the data. consistent with the data.

 Why big changes in age Why big changes in age

-specific vulnerab

specific vulnerab

 Less trammel Less trammel

-netting in the mainstem? netting in the mainstem?

 More reliance on small hoop More reliance on small hoop

-nets in the LCR? nets in the LCR?

 Limited temporal coverage? Limited temporal coverage?

 ASMR3 adult (4+) abundance estimat

ASMR3 adult (4+) abundance estimat

ageing error: ageing error:

 2006 

- 6,017 (95% CI 5,369 6,017 (95% CI 5,369

–6,747) 

 1989 

- 9,322 (95% CI 8,867 9,322 (95% CI 8,867–9,799)

 ~ 20

-25% increase in point estimates sinc

25% increase in point estimates sinc

 Most likely associated with increased recr

Most likely associated with increased rec

no later than 1999 and possibly as early a

no later than 1999 and possibly as early a
Conclusions Conclusions

 ASMR Results do not track well w

ASMR Results do not track well w

indices or Spring LCR mark indices or Spring LCR mark

-recap

recap

 For catch For catch

-rate data, not too surprisi

rate data, not too surprisi

reliability of catch reliability of catch

-rate metrics. rate metrics.

 A bit disconcerting for Spring LCR a

A bit disconcerting for Spring LCR a

estimates, but not too surprising co

estimates, but not too surprising co

imprecision to detect a 25% increas

imprecision to detect a 25% increas

 Preliminary Spring 2007 LCR abund

Preliminary Spring 2007 LCR abund

looks to be much larger than 2006 ~

looks to be much larger than 2006 ~

Haverbeke, pers. comm.) Haverbeke, pers. comm.)

 Provides support for ASMR, but questi

Provides support for ASMR, but quest

closed population estimates in the LCR

closed population estimates in the LCR
Conclusions Conclusions

 Considering ageing error doesn Considering ageing error doesn’t 

t 

excessive bias, but does decreas

excessive bias, but does decreas

 Need to have big changes in recruit

Need to have big changes in recruit

with ASMR. with ASMR.

 Argues for experimental treatments 

Argues for experimental treatments 

probability to impart large changes 

probability to impart large changes 

 Big changes (decreases in effort) 

Big changes (decreases in effort) 

program are not advised as it is p

program are not advised as it is p

data interpretation. data interpretation.

 Witness long lasting effects of decre

Witness long lasting effects of decre

sampling effort ~1996 sampling effort ~1996

-1999.