9724

• UCREFRP Catalog Number: 9724
• Author: Coggins, L.G., W.E. Pine, C.J. Walters, D.R. VanHaverbeke, D. Ward and H.C. Johnstone.
• Title: Abundance trends and status of the Little Colorado River population of humpback chub.
• USFW Year: 2006.
• USFW - Doc Type: North American Journal of Fisheries Management
• Copyright Material: YES

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COGGINS ET AL.

TABLE 2.-Jolly-Seber and Pradel population trend models fit to humpback chub data, 1989-2002. The best-fitting model is
the one with the lowest corrected Akaike information criterion (AlC) value.

AlC Model Number of
Model AICc AAICc weights likelihood parameters
Jolly-Seber models
Age-dependent survival; time-dependent capture probability 41,303.2 0.0 1.0 1.0 27
Time-dependent survival and capture probability 42,478.1 1,174.9 0.0 0.0 26
Fixed survival; time-dependent capture probability 42,718.8 1,415.6 0.0 0.0 14
Age-dependent survival and capture probability 45,072.5 3,769.3 28
Fixed survival and capture probability 47,188.8 5,885.6 2
Pradel models
Time-dependent survival, capture probability, and rate of population change 99,755.7 0.0 LO LO 38
Fixed survival; time-dependent capture probability and rate of population change 99,916.8 161.1 0.0 0.0 27
Time-dependent survival and capture probability; fixed rate of population change 100,014.6 258.9 0.0 0.0 28
Fixed survival; time-dependent capture probability; fixed rate of population change lOO.441.1 685.3 0.0 0.0 16

length-stratified, Lincoln-Petersen abundance estima-
tor (Seber 1982). Sampling for each abundance
estimate consisted of a marking event (i.e., the first
trip during each spring) and a recapture event (Le., the
second trip). We compare these recent estimates with
earlier estimates presented by Douglas and Marsh
(1996) and other closed-population estimates of
humpback chub abundance (TL > 200 rnrn) in the
LCR inflow reach (Valdez and Ryel 1995; Trammell
and Valdez 2003).
Open-population models.-We used MARK (White
and Burnham 1999) to estimate the mortality and
capture probability for humpback chub (TL > 150
mm) from both age-structured (i.e., Jolly-age models;
Pollock 1981) and non-age-structured models (i.e.,
traditional Jolly-Seber models; Seber 1982). Models
were developed based on humpback chub life history
(i.e., that they are long-lived fish with type ill survival)
and variability in sampling effort over time. We used
the corrected Akaike information criterion (AIC;
Burnham and Anderson 1998) as a guide in evaluatm"g
the fit of models built in MARK (Table 2). Each model
was further evaluated to be the most biologically
reasonable, parsimonious model. We compared age-
independent models with the age-structured models
(Table 2) to evaluate differences in the mortality
estimates and capture probability trends resulting from
the two model types. We estimated the population size
of adult humpback chub as defined by the ESA
recovery goals (i.e., TL > 200 rnrn, age-4 and older;
USFWS 2(02) using an age-structured Jolly-Seber
model within MARK. Variance estimates were calcu-
lated using the Delta method, and confidence intervals
were constructed following methods from Chao (1989)
outlined in Williams et al. (2002). Because humpback
chub are long lived and capture-recapture data were
sparse for individuals greater than age 15, capture
probabilities and mortality for fish older than age 15
were assumed to be equal to those of 15-year-old fish.

We estimated population change (~) across all ages
(i.e., independent of age) in MARK using temporal
symmetry models (TSMs) described by Pradel (1996;
Table 2). Estimates of population growth are more
robust to heterogeneity in capture probability than
traditional Jolly-Seber models (Schwarz 2001; Hines
and Nichols 2002). However, these models do assume
that capture probability does not change radically over
time. This approach to estimating 1. is also dependent
on the sampled area's remaining constant (e.g., if the
sampling area expands during the study, biased
population growth rate estimates are likely). To meet
this assumption, the TSMs were fit with a subset of the
data, namely, collections made only within the LCR.
The population change estimates do not depend on the
geographic closure of the sample area but do assume
that the trends in the sampled population are indicative
of the population as a whole. Previous investigations
suggest extensive annual movement of fish between the
LCR inflow reach and the LCR (see Introduction), so
that trends generated from data collected in the LCR
should be representative of the overall LCR humpback
chub population.
We chose candidate TSMs to estimate population
change based on the life history characteristics of
humpback chub and sampling methodologies used
throughout the study. The models had three parameters
(survival, <1>; capture probability, p; and rate of
population change, 1.), and each parameter was either
time dependent or time independent. A value of A in
excess of one indicates a population increase, a value
less than one indicates a population decrease, and
a value equal to one indicates that the population is
stable. When constraints (such as fixed time effects) are
placed on either <1> or p, part of the variation around
each of these parameters is shifted to the model
parameters without constraints. We followed the
guidelines in Franklin (2001) to only place constraints