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<br />North American Journal of Fisheries ManagemenJ 26:201-205, 2006
<br />@ Copyright by the American Fisheries Society 2006
<br />DOl: 1O.1577/M05-I33.1
<br />
<br />17;2..3
<br />
<br />[Management Brief]
<br />
<br />Age-Structured Mark-Recapture Analysis:
<br />A Virtual-Population-Analysis-Based Model for
<br />Analyzing Age-Structured Capture-Recapture Data
<br />
<br />LEWIS G. COGGINS, JR.*
<br />
<br />u.s. Geological Survey, Southwest Biological Science Center, Grand Canyon Monitoring and Research
<br />Center, 2255 North Gemini Drive, Flagstaff, Arizona 86001, USA
<br />
<br />WILLIAM E. PINE ill
<br />
<br />Department of Fisheries and AqUfltic Sciences, University of Florida, 7922 Northwest 71st Street,
<br />Gainesville, Florida 32653, USA
<br />
<br />CARL J. WALTERS AND SlEVEN J. D. MARlELL
<br />
<br />Fisheries Centre, University of British Columbia, 2259 Lower Mall,
<br />Vancouver, British Columbia V6T 1M. Canada
<br />
<br />Abstract.-We present a new model to estimate capture
<br />probabilities, survival, abundance, and recruitment using
<br />traditional Jolly-Seber capture-recapture methods within
<br />a standard fisheries virtual population analysis framework.
<br />This approach compares the numbers of marked and un-
<br />marked fish at age captured in each year of sampling with
<br />predictions based on estimated vulnerabilities and abundance
<br />in a likelihood function. Recruitment to the earliest age at
<br />which fish can be tagged is estimated by using a virtual
<br />population analysis method to back-calculate the expected
<br />numbers of unmarked fish at risk of capture. By using
<br />information from both marked and unmarked animals in
<br />a standard fisheries age structure framework, this approach is
<br />well suited to the sparse data situations common in long-term
<br />capture-recapture programs with variable sampling effort.
<br />
<br />Estimating population size is a key component in
<br />developing management plans for a wide variety of
<br />fisheries. Estimates of population size are often used to
<br />evaluate the population status of threatened or endan-
<br />gered species and are a key aspect of most commercial or
<br />recreational fisheries stock assessments. The techniques
<br />used to estimate population size generally fall into two
<br />broad areas, the traditional open- and closed-population
<br />capture-recapture models (e.g., Lincoln-Petersen,
<br />CAPTURE, Jolly-Seber, etc.; see review by Pine et al.
<br />2003) and age- or size-structured virtual population
<br />analysis (VPA)-type methods (Hilborn and Walters
<br />1992). Here we present a new model, called age-
<br />structured mark-recapture analysis (ASMR), that com-
<br />bines attributes of both the traditional Jolly-Seber
<br />models (Jolly 1965; Seber 1965; Williams et al. 2002)
<br />and VPA-type methods widely used in fisheries stock
<br />
<br />* Corresponding author: lcogginS@usgs.gov
<br />
<br />Received May 6, 2005; accepted August 15, 2005
<br />Published online February 3, 2006
<br />
<br />assessments. We develop this model using data from
<br />a long-term tagging program (1989-2002) for hump-
<br />back chub Gila cypha in the Grand Canyon reach of the
<br />Colorado River. Explicit details of this tagging program
<br />are found in the companion paper to this manuscript
<br />(Coggins et al. 2006, this issue).
<br />
<br />Overall Model Structure
<br />
<br />The ASMR estimation method proposed here is
<br />developed in two stages. First, we develop a model for
<br />predicting the numbers of marked and unmarked fish at
<br />risk of capture over time and age, conditional on survival
<br />rate and the marking data. Then we use these predicted
<br />numbers at risk to capture along with capture probability
<br />parameters to predict the numbers of captures and
<br />recaptures that will be observed. After that, we develop
<br />a likelihood function for these observations to be
<br />maximized by varying the unknown survival, vulnera-
<br />bility, and capture probability or tenninal abundance
<br />parameters. By using a virtual population analysis
<br />method to back-calculate the expected number of
<br />unmarked fish at risk of capture, the method avoids
<br />treating unmarked fish by age that were alive at the start
<br />of sampling and new recruits entering the unmarked
<br />population each year as unknown parameters.
<br />The expected numbers of unmarked (Oa) and
<br />marked (M ) fish by age (a = 2, . . ., A) and year
<br />a,1
<br />(t = 1, . . ., T) at risk of capture and recapture are
<br />assumed to have varied as follows:
<br />
<br />Ua+I,HI = Sa(Ua,t - ma,t)
<br />
<br />(1)
<br />
<br />Ma+I,HI = Sa(Ma,t + ma,t), (2)
<br />
<br />where S is the average annual survival rate of an age-
<br />a fish ~d m is the number of age-a fish marked in
<br />a,1
<br />year t. Note that equations (I) and (2) assume that
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