9711

• UCREFRP Catalog Number: 9711
• Author: Coggins, L.G.
• Title: Abundance trends and status of the Little Colorado River population of humpback chub
• USFW Year: 2008.
• USFW - Doc Type: an update considering 1989-2006 data.
• Copyright Material: NO

4 Abundance Trends and the Status of the little Colorado River Population of Humpback Chub 1989-2006

and Ryel, 1995). Details about these sampling programs are
provided by Coggins and others (2006a).

Tagging-Based Metrics

The heart oftagging-based assessment is the large num-
ber of uniquely tagged sub-adult [l50-199-rnm total length
(TL)] and adult G::200-mm TL) fish that have been captured,
measured. ,md implanted with pa5sive integrated transponder
(PIT) tags. Since 1989, more than 19,000 HBC have been
captured, tagged, and relea5ed with unique identitiers. These
data are maintained in a central database housed at the USGS
Grand Canyon Monitoring and Research Center.
Mark-recapture methods to assess population abundance
and vital rates have been widely used in fisheries and wildlife
studies for more than 50 years, and numerous reviews have
been conducted highlighting the general approaches (e.g.,
Seber, 1982; Williams and others, 2001). Traditional methods
(e.g., Jolly-Seber-type methods) generally rely on recaptures
of tagged individuals to estimate abundance, recruitment, and
survival. Basically, the approach is to create a known popula-
tion of marked, or tagged, fish that are repeatedly sampled to
obtain time series estimates of mark rate (i.e., the proportion
of the overall population that is marked) and the number of
marked fish alive in the population. These metrics are sub-
sequently used to estimate capture probability, abund,mce,
recruitment, and survival.
The ASMR model ditfers from the traditional approach,
because, in general, it contains more structural assumptions
through the specification of a population accounting structure
that governs transition of both marked and unmarked animals
through ages and time. Age-structured stock assessment theory
(Edwards and Megrey, 1989) is used to annually predict the
numbers of marked and unmarked fish available for capture
in a standard fisheries virtual population analysis framework
(Quinn and Deriso, 1999). The total number of marked fish
depends on the number of fi sh recently marked as well as the
number of previously marked fish decremented by mortality
rate. The number of unmarked fish depends on the recmitment
over time, the number of fish marked from a given brood-year
cohort, and the mortality rate. These annual predictions of the
abundance of marked and unmarked fish are further segregated
by age sucb that age-specific survival and capture probability
may be modeled. Parameters are estimated by comparing pre-
dicted and observed age- and time-specific captures of marked
and unmarked fish in a Poisson likelihood framework.
The ASMR model has three different parameteriza-
tions (ASMR 1-3) that vary in how the temlinal abundance is
estimated and how age- and time-specific capture probability
is modeled. Both ASMR 1 and ASMR 2 assume that age- and
time-specific captute probability can be modeled as th~prod-
uet of an annual overall capture probability multiplied by age-
specific vulnerability. This is similar to the common param-
eterization of fishing mortality in assessment models under the
"separability assumption" (Megrey, 1989) and diminishes the
size of the parameter set since it is not necessary to separately

estimate each age- and time-specific capture probability.
These models further assume that vulnerability is asymptotic
with age. As such, vulnerability is assumed to be unity for
fish age-6 and older and estimated only for the younger fish.
Finally, annual age-specific vulnerabilities are assumed to
be equal among each sampling period. as described above.
Implicit in this assumption is that within a sampling period,
annual age-specitic capture probabilities differ only as a scalar
value related to the annual overall capture probability.
The primary difference between ASMR 1 and ASMR
2 is how tbe tcrminal abundances are calculated. ASMR I
estimates an overall terminal-year capture probability and
calculates age-specific tcrminal abundances (both marked
and unmarked) as the ratio of age-specific catch (both marked
and unmarked fish) and age-specific capture probability (i.e.,
product of the terminal-year capture probability and sam-
pling period 4 age-specific vulnerability), In contrast, ASMR
2 treats age-specific terminal abundances up to age-13 as
individual parameters. Terminal abundances for subsequent
ages are estimated by applying age-specific survivorship to the
age-13 abundance. This difference in formulations decreases
the parameter count for ASMR 1 relative to ASMR 2 at the
expense of a5suming that the vulnerability schedule in the
terminal year is identical to the rest of period 4.
ASMR 3 is the most general model; it makes no assump-
tion as to the age- or time-specific pattern in capture prob-
ability. The conditional maximum likelihood estimates of
age- and time-specific capture probability are used to predict
the age- and time-specific catch of marked and unmarked fisb.
Full detai Is of each of the models are provided by Coggins and
others (2006b).
In addition to the ASMR assessments, the time series of
the annual spring abundance estimates in the LCR are updated.
Abundance ofHBC in the LCR greater than or equal to 150
mm TL was estimated during the early ] 990s and 2001-06,
using closed population models. These models included
the CAPTURE suite of models (Otis and others, 1978) ,md
Chapman-modified, Lincoln-Petersen. length-stratified models
(Seber, 1982). The recent estimators use data collected annu-
ally during two sampling occasions in the spring. Full details
of the sampling ,md estimation methods are provided by
Douglas ,md Marsh (1996) and Coggins and others (2006a).
Coggins and others (2006b) recommended exploring the
use of individual capture histories within the ASMR frame-
work to reduce confounding between capture probability and
mortality. Though the updated ASMR models presented in
this report do not yet incorporate individual capture histories,
they clo model recaptured fish by annual-tagging cohort with
the intent of reducing parameter confounding by increasing
the number of observations available for parameter estimation.
In the non-tag cohort, or pooled, version of ASMR described
above and by Coggins and others (2006b), age- and time-spe-
cific predictions of recaptured fish are not separated by year of
tagging. As an example, assume that ASMR 3 predicts that 50
marked age-6 HBC should be captured in 2002. These 50 fish
could be comprised offish tagged as age-5 in 2001, age-4 in