9723

• UCREFRP Catalog Number: 9723
• Author: Coggins, L.G., W.E. Pine, C.J. Walters and S.J.D. Martell.
• Title: Age-structured mark-recapture analysis
• USFW Year: 2006.
• USFW - Doc Type: a virtual-population-analysis-based model for analyzing age-structured capture-recapture data.
• Copyright Material: YES

204

.,,'

25,000

COGGINS ET AL.

,.--..,
'"
,.--..,"0
0..0
] ~ 20,000

"0 '"
.- '-'
"0 '"
~ * 15,000
i:: S
o .-
S ~
'S "2 10,000
b 1;j
0_
..... ;:j
o S
~'r;; 5,000
-0
t::
~

. . . -
. II; -
. x x . If -
x
~ 0 1iI t 8 0 I
0 ~ . . ... . , i
I!I .. ;: , + 11.
+ '!: +
~

x

o
~~~~~~~~~@~~W~*~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~
Year

FIGURE I.-Estimated recruinnent over time for simulated data sets assuming stable recruinnent before 1989 and error in age
assignment due to variation in the simulated growth patterns. Individual growth variation was simulated by setting length at age
for each simulated fish i to l.(a) = (l + d.)(l- e-kli + 0.42)), with the deviations in asymptotic length d. normally distributed with
mean zero and standard d~viation ~30. Each symbol type represents results for a different simula;ed data set incorporating
stochastic error in age assignment.

2006), although the two approaches use distinct
methods to derive the parameter estimates. The ASMR
model predicts the number of both unmarked and
marked fish available for capture using marking data
and survival estimates. This reconstructed annual
abundance at age is then used along with age- and
time-specific capture probabilities to predict the
number of both marked and unmarked fish captured
during each sampling effort. Finally, predicted captures
are compared with the observed capture data to
estimate model parameters (i.e., survival and capture
probabilities or terminal abundance). This approach
differs from Jolly-Seber models, which primarily rely
on recaptures of previously tagged individuals for
survival and population size estimation. While Jolly-
Seber models can be parameterized to include both
age- and time-dependent factors (Le., "Jolly-age"
models; Pollock 1981), we have found that capture-
recapture data sets of long-lived species with many
age-classes (30 in this example with humpback chubs)
and low capture probabilities across ages and years
(generally <0.2) often contain many years with few or
no individuals in several year-classes. In general, we
have found that age-structured Jolly-Seber models do
not perform well in these situations without parameter
constraints because of obviously sparse data. Because
of the large amount of additional age-structure in-

formation and assumptions built into the ASMR model
related to both the tagged and untagged animals,
ASMR models may fit sparse data situations better than
unconstrained Jolly-Seber models if ASMR model
assumptions are met. However, as with traditional VPA
models, ASMR abundance estimates can become
unstable with low overall capture probabilities.
A primary purpose of ASMR is to evaluate the
recruitment responses of individual year-classes in
response to adaptive management experiments related
to water manipulation and exotic species removal.
ASMR differs from Jolly-Seber methods in estimating
recruitment by reconstructing year-classes based on
age-specific survival rates and initial abundances. In
Jolly-Seber methods, "recruitment" into an age-class is
a combination of immigrants and survivors from the
previous time period; thus recruitment can occur with
each year-class. With ASMR, recruitment is only
allowed into the first year-class by design.
ASMR assumes that the relationship between age
and survival is governed by the size of the animals, as
described by Lorenzen (2000). We examined this
assumption within ASMR by individually estimating
each age-specific survival rate and found good
agreement with the Lorenzen function in the overall
shape and magnitude of the survival rates. However,
incorporating the Lorenzen function provides a sub-