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<br />MANAGEMENT BRIEF
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<br />205
<br />
<br />stantial benefit by shrinking the size of the parameter
<br />set. Though it is theoretically possible to introduce this
<br />functional form into a traditional Jolly-Seber model,
<br />we find the ASMR method more flexible in accom-
<br />modating these types of fisheries-specific model
<br />structure for evaluating hypotheses related to various
<br />functional forms. Additionally, the incorporation of
<br />a biologically reasonable assumption related to the
<br />effect of size on natural survival rate probably allows
<br />ASMR models to interpret periods of sparse data more
<br />efficiently than traditional Jolly-Seber models.
<br />Two other important methodological differences
<br />exist between ASMR and Jolly-Seber-type methods.
<br />First, ASMR uses "summary" -type statistics of
<br />captures and recaptures as opposed to the individual-
<br />capture-history approach used in applications such as
<br />MARK. We acknowledge that the individual-capture-
<br />history approach may provide some additional in-
<br />formation on survival and capture probability (Nichols
<br />and Pollock 1983) and facilitate the use of individual
<br />covariates such as length. Future formulations of
<br />ASMR models will examine the use of individual
<br />capture histories.
<br />A second key difference between the two methods is
<br />the use of a Poisson distribution to estimate the number
<br />of captures and recaptures in the ASMR method in
<br />contrast to the multinomial approach used in Jolly-
<br />Seber methods. Binomial distributions can be modeled
<br />as a series of independent Poisson diStributions, both
<br />leading to the same maximum likelihood estimates
<br />(Sandland and Cormack 1984). The use of a Poisson
<br />distribution may lead to estimates of population size
<br />that have a slightly lower variance, but the difference is
<br />probably very small (c. Schwarz, Simon Fraser
<br />University, personal communication). The use of
<br />independent Poisson distributions to model recaptures
<br />is slightly different, as the same fish could be
<br />recaptured multiple times (i.e., the Poisson distribu-
<br />tions are not independent). However, the likelihoods
<br />used for the recaptures do approximate generalized
<br />estimating equations, where Poisson distributions are
<br />commonly used when modeling counts. A drawback to
<br />the ASMR approach is that this routine does not easily
<br />lend itself to routine statistical model selection
<br />procedures (e.g., the likelihood ratio test or Akaike
<br />information criterion, as used in MARK). This is
<br />because the fitting routines employed are a combination
<br />of Poisson likelihood functions and relatively simple
<br />estimating equations. The model selection criteria
<br />assume that the estimating functions are pure like-
<br />lihoods and not a combination approach as used here
<br />(c. Schwarz, Simon Fraser University, personal
<br />communication). Future work with ASMR models
<br />
<br />should include exploring appropriate model selection
<br />procedures.
<br />
<br />Acknowledgments
<br />
<br />We acknowledge the comments of C. Schwarz
<br />regarding the differences between Poisson and multi-
<br />nomial distributions in capture-recapture analysis.
<br />
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