Mooij et al. (1999) examined length-at-age data of European Perch (*Perca fluviatilis*) from Lake Tjeukemeer (The Netherlands) to identify possible sexual dimorphism in growth trajectories. Their data consisted of fork length (FL; cm), ages (yrs) from otoliths, and sex from 69 fish and are recorded in EuroPerchTJ.^{1}

^{1} See “CSV file” link in “Source” section of linked page.

- Plot FL versus age with different symbols for each sex.
- Do you foresee any model fitting problems with these data?
- Do you observe any possible differences in growth between the sexes?

- Fit the typical VBGF with additive errors separately to both sexes.
- Describe any problems that you encountered in the model fitting.
- Compute point and bootstrapped 95% confidence interval estimates for each parameter in the separate models.
- Do you see any issues with the confidence intervals? If so, describe.

- Fit the typical VBGF with additive errors where all parameters differ by sex.
- Describe any problems that you encountered.
- Assess the assumptions from this model fit.
- Compute point estimates for each parameter in this model.
- How do the point estimates from this model compare to the point estimates from the separate models fit in #2 above?

- Find the most parsimonious model that is a subset of the model fit above.
- Use the extra sums-of-squares test.
- Using the likelihood ratio test.
- Using the \(AICc\) criterion.
- Summarize (in words) the results of the most parsimonious model identified with the extra sums-of-squares test.

- Construct a summary graphic that shows the growth trajectories superimposed on the observed data for both sexes.
^{2}

^{2} See this post.

Solution Code:

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## References

Mooij, W., J. van Rooij, and S. Wijnhoven. 1999. Analysis and comparison of fish growth from small samples of length-at-age data: Detection of sexual dimorphism in Eurasian Perch as an example. Transactions of the American Fisheries Society 128:483–490.