To facilitate development Otter Research is seeking partners who would like to have length frequency data sets from exploited fisheries analyzed. While the cost of such analyses will vary widely depending on the circumstances we anticipates that typical costs will be between US$10,000.00 and US$50,000.

While computationally straight-forward, VPA requires certain assumptions that are difficult to test and/or justify in many situations. Catch-at-age data are required and are usually assumed to be correct (unless aging errors are incorporated using Monte-Carlo simulations). The natural mortality rate and the fishing mortality rate for one age class of each cohort must be assumed. Tuning the analysis with catch per unit effort (CPUE) data or other abundance index time series is often employed to avoid the need to specify terminal fishing mortality rates for each cohort, but this invariably involves arbitrary assumptions about catchability. Additionally, VPA involves the computation of one fishing mortality rate for each non-terminal catch-at-age observation and the initial abundance for each cohort. The model is thus fully saturated (no degrees of freedom) and, apart from the statistical errors associated with the tuning procedure, there is no notion of statistical uncertainty in the results.

Statistical catch-at-age models (e.g. Doubleday 1976; Paloheimo 1980; Fournier and Archibald 1982; Pope and Shepherd 1982; Dupont 1983; Deriso et al. 1985) can potentially avoid some of these assumptions. While catch-at-age data are still required, age- or time-related constraints on fishing mortality enable a statistical estimation of initial cohort sizes, fishing mortality rates or related parameters and, in theory, natural mortality rate, by minimizing an objective function based on a statistical criterion such as least squares. Variance estimates, and therefore confidence intervals, for the estimated parameters conditional on the catch-at-age data and the model can also be obtained.

Both VPA and statistical catch-at-age models rely on catch-at-age data typically derived from the analysis of annuli on various body parts of individual fish. These methods are often inappropriate or too expensive for routine application, particularly to large-scale tuna fisheries. For many fisheries, catch-at-length data may provide a convenient and less expensive alternative for analysis by age-structured models.

Most catch-at-age and catch-at-length models consider a spatially-aggregated population and fisheries. However, for many fish stocks, population parameters may not be spatially homogeneous. In such cases, assuming that fisheries which operate in different portions of the stock range exploit a common population may lead to biased results. To avoid such problems, spatial structure can be incorporated into the model.

MULTIFAN-CL is a length-based, age-structured, likelihood model that circumvents many of the difficulties associated with sequential analyses such as VPA. The model incorporates the following features:

- Growth and age structure of the catch are estimated simultaneously with population parameters such as recruitment, selectivity, catchability and natural mortality. Approximate confidence intervals are therefore conditional not on catch-at-age, but on catch-at-length data.
- Spatial structure cvan be included in the model if desired.
- Missing data and data of different temporal resolutions are allowable and are internally managed by the model.
- Auxiliary data (such as tagging data) can be incorporated into the model, as appropriate. Various structural hypotheses, such as density-dependent growth, time-series trends in catchability and seasonal catchability, can be incorporated into the model and tested.

A report of the application of the model to south pacific albacore (*Thunnus alalunga*) is available as a
zipped postscript file, ALBACORE.ZIP.

Doubleday, W.G. 1976. A least squares approach to analyzing catch at age data. Int. Comm. Northw. Atl. Fish. Res. Bull. 12:69-81.

Dupont, W.D. 1983. A stochastic catch-effort method for estimating animal abundance. Biometrics 39:1021-1033.

Fournier, D., and C.P. Archibald. 1982. A general theory for analyzing catch at age data. Can. J. Fish. Aquat. Sci. 39:1195-1207.

Fournier, D.A., J.R. Sibert, J. Majkowski and J. Hampton. 1990. MULTIFAN: a likelihood-based
method for estimating growth parameters and age composition from multiple length frequency
data sets illustrated using data for southern bluefin tuna (*Thunnus maccoyii*). Can. J. Fish.
Aquat. Sci. 47:301-317.

Fournier, D.A., J.R. Sibert, and M. Terceiro. 1991. Analysis of length frequency samples with
relative abundance data for the Gulf of Maine northern shrimp (*Pandalus borealis*) by the
MULTIFAN method. Can J. Fish. Aquat. Sci. 48:591-598.

Gudmundsson, G. 1994. Time-series analysis of catch-at-age observations. Appl. Statist. 43:117- 126.

Hilborn, R. and C.J. Walters. 1992. Quantitative fisheries stock assessment: choice, dynamics and uncertainty. Chapman and Hall, N.Y. 570 p.

Megrey, B.A. 1989. Review and comparison of age-structured stock assessment models from theoretical and applied points of view. American Fisheries Society Symposium 6:8-48.

Schnute, J., and D.A. Fournier. 1980. A new approach to length frequency analysis: growth structure. J. Fish. Res. Board Can. 37:1337-1351.