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RESEARCH ARTICLE
Contents Vol 58(10)

Simulation of the estimation of ageing bias inside an integrated assessment of canary rockfish using age estimates from a bomb radiocarbon study

Ian J. Stewart A C and Kevin R. Piner B
+ Author Affiliations
- Author Affiliations

A NOAA Fisheries, NWFSC 2725 Montlake Blvd East, Seattle, WA 98112, USA.

B NOAA Fisheries, SWFSC 8604 La Jolla Shores Drive, La Jolla, CA 92037, USA.

C Corresponding author. Email: Ian.Stewart@noaa.gov

Marine and Freshwater Research 58(10) 905-913 https://doi.org/10.1071/MF07010
Submitted: 18 January 2007  Accepted: 11 September 2007   Published: 30 October 2007

Abstract

The stock of canary rockfish off the west coast of the continental US is currently assessed using an integrated statistical catch-at-age model. The functional form of an ageing bias detected in production ageing (large numbers of ages read for use in stock assessment) from a bomb radiocarbon study with small sample size (n = 16) was estimated externally and used to adjust the age data in the most recent stock assessment. Using simulation methods, the present study evaluated whether integrating the estimation of the ageing bias inside the assessment model would (1) influence the uncertainty in assessment results and (2) improve our ability to differentiate between competing functional forms (linear, linear with intercept and jointed) for specifying the ageing bias. Internal estimation of the ageing bias relationship increased the approximate 95% confidence interval width about the spawning biomass estimate by 1–10% depending on the functional form assumed. The assessment model was not able to reliably distinguish between all competing functional forms of the ageing bias tested, even with increased radiocarbon sample sizes. However, significant under-ageing at the youngest ages was found to be inconsistent with other sources of data in the assessment model. The question of ageing bias form remains important because it had moderate effects on estimates of spawning biomass and assessment model uncertainty.

Additional keywords: ageing bias, bomb radiocarbon, simulation, stock assessment.


Acknowledgements

The authors would like to thank Richard Methot and Mark Maunder for insightful discussions about stock assessment modelling and the use of age data. John Wallace, Nancy Gove, Jim Hastie and three anonymous reviewers provided helpful comments on the manuscript.


References

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Appendix 1: Simulation of new radiocarbon data from known observed-age samples

After the functional form between observed age (Ao) and radiocarbon age (Ar) has been estimated, then both the expectation for observed age at radiocarbon age (Âo) and the variance on the y-dimension (σ2y) are known. Therefore, what is required is to generate a sample of Ar|Ao = c, from one of two observed ages (c = 10 or 30).

To do this it is necessary to find that P(Ar = a|Ao = c) = P(Ar = a) · P(Ao = c|Ar = a), where a = a radiocarbon age P(Ao = c|Ar = a ~ N(Âo|Ar = a, σ2y and assuming a distribution for P(Ar = a). The simplest assumption to make is that the sample of true ages from which to draw, P(Ar = a), is uniformly distributed. This would be the case if observed age c fish were drawn at random from a large number of samples. It is possible that actual samples could be quite non-uniform (single-year collections of ages are frequently dominated by one or more strong cohorts present in the population); however the assumption represents a condition that should be reasonably informative regarding ageing bias. The further assumption of constant variance (σ2y) is also important, but probably less so over a reasonable range of c (e.g. 10 to 30) than at very young or very old ages.

Letting θa = P(Ar = a|Ao = c) to complete the simulation of new data a sample from the multinomial distribution (n θa=1–∞) is used to populate each simulation with n new data points.