G. Examples with age structured stock assessments

More complicated questions can be asked using the age- and length-structured assessment within GeMS, for example:

• What is the value (in terms of yield, for now) of moving to an age-structured assessment from a production model?
• How well can age structured models estimate natural mortality if it is known to vary over time?
• How will a changing climate influence the reference points, sustainable yield, and optimal selectivity from a population with growth that is positively associated with sea surface temperature?

We first demonstrate an example in which the assumptions of the assessment method match the underlying structure of the operating model to show the types of outputs and expects dynamics. One of the first outputs to be checked after running GeMS is the fits of the model to the data. Depending on the selected data sources, this could include a range of figures. For example, all models will output a figure in which the fits to CPUE, survey, catch and estimated spawning biomass will be output.

The model is able to fit the data sources (survey, CPUE, and catch) well when the underlying assumptions are correct. This results in accurate estimates of spawning biomass and enables the harvest control rule to return the spawning biomass to the target biomass. Checking the fits of the data to the length proportion data for both the catch and survey (if available) is also important to ensure the assessment performed correctly. Fits to the catch proportion at length are shown below, dots are the observations and lines are the model fits.

In this case, both the fits to the catch and survey length proportions are good (as expected, given the matching dynamics of the assessment and operating model). Cases in which the assessment model assumes dynamics other than the dynamics of the operating model present opportunities to assess the robustness of a given configuration of the assessment model. For example, applying an assessment model that assumes time-invariant natural mortality to data collected from an operating model in which natural mortality varies can uncover biases in estimated population processes and calculated reference points and management quantities.

This figure is standard output that shows that natural mortality shifts from 0.2 to 0.25 in year 35 of the simulated period.

Assessment methods that assume a constant natural mortality (grey--black is median) provide difference estimates of key population processes when compared to assessment methods that estimate a time-varying natural mortality (pink-red is median). Positive biases appear in estimated recruitment and fishing mortality from the assessment with time-invariant natural mortality, but the assessment in which natural mortality varies is able to estimate these processes (and natural mortality) approximately without bias on average. Biased estimates of population processes result in biased estimates of reference points used in management.

Estimated spawning biomass, the target biomass and fishing mortality from the assessment in which natural mortality is time-invariant are all positively biased, which ultimately results in a positively biased total allowable catch (denoted 'OFL' here). However, estimates and calculated reference points from the assessment with time-varying natural mortality displayed a smaller bias on average. Spawning biomass and the total catch can also be compared over time.

Given the scale of the data, fits to spawning biomass are a little difficult to see. However, the first column (in which the assessment assumptions match the operating model), the fits are very close and would pass the 'runs test'. The second column (in which the assessment assumes time-invariant natural mortality, but natural mortality varies over time in the operating model), the fits are not as good and there are periods of time that would fail the runs test. Fits in the final column (in which the assessment estimated time-varying natural mortality, and natural mortality varies over time in the operating model) are improved, but noisier as a result of estimating time-varying natural mortality. Estimated total allowable catches mirror the truth in the first column, are biased in the second column, and less biased, but more variable in the third column.