Individual Growth

Lake Tjeukemeer Perch

Compare a von Bertalanffy growth function among sexes of Lake Tjeukemeer European Perch.
von Bertalanffy

Derek H. Ogle


Mar 8, 2019


Feb 13, 2023

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.


    1. Plot FL versus age with different symbols for each sex.
      1. Do you foresee any model fitting problems with these data?
      2. Do you observe any possible differences in growth between the sexes?
    2. Fit the typical VBGF with additive errors separately to both sexes.
      1. Describe any problems that you encountered in the model fitting.
      2. Compute point and bootstrapped 95% confidence interval estimates for each parameter in the separate models.
      3. Do you see any issues with the confidence intervals? If so, describe.
    3. Fit the typical VBGF with additive errors where all parameters differ by sex.
      1. Describe any problems that you encountered.
      2. Assess the assumptions from this model fit.
      3. Compute point estimates for each parameter in this model.
      4. How do the point estimates from this model compare to the point estimates from the separate models fit in #2 above?
    4. Find the most parsimonious model that is a subset of the model fit above.
      1. Use the extra sums-of-squares test.
      2. Using the likelihood ratio test.
      3. Using the \(AICc\) criterion.
      4. Summarize (in words) the results of the most parsimonious model identified with the extra sums-of-squares test.
    5. Construct a summary graphic that shows the growth trajectories superimposed on the observed data for both sexes.2
  • 2 See this post.


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    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.